This document summarizes research determining the velocity vector of the Andromeda Galaxy (M31) relative to the Milky Way using Hubble Space Telescope measurements of M31's proper motion. N-body models of M31 are used to correct for internal stellar motions within M31. The results imply M31 is on a radial orbit towards the Milky Way. The velocity vector is then used to estimate the mass of the Local Group, obtaining a value of (3.17 ± 0.57) × 1012 M☉. It is also implied M33 is likely bound to M31.
The document describes measurements of the proper motion of the Andromeda Galaxy (M31) using Hubble Space Telescope imaging data from multiple fields observed at two epochs separated by 5-7 years. Background galaxies in the images are used as stationary reference objects to measure the displacement of thousands of M31 stars between epochs. This allows determining M31's absolute proper motion with an accuracy of 12 microarcseconds per year, providing crucial information about M31 and the Local Group's dynamics and future evolution.
Solar system expansion and strong equivalence principle as seen by the NASA M...Sérgio Sacani
The NASA MESSENGER mission explored the innermost planet of the solar system and obtained a rich data set of range measurements for the determination of Mercury’s ephemeris. Here we use these precise data collected over 7 years to estimate parameters related to general relativity and the evolution of the Sun. These results confirm the validity of the strong equivalence principle with a significantly refined uncertainty of the Nordtvedt parameter η=(−6.6±7.2)×10−5. By assuming a metric theory of gravitation, we retrieved the post-Newtonian parameter β=1+(−1.6±1.8)×10−5 and the Sun’s gravitational oblateness, J2 =(2.246±0.022)×10−7. Finally, we obtain an estimate of the time variation of the Sun gravitational parameter, _ GM=GM =(−6.13±1.47)×10−14, which is consistent with the expected solar mass loss due to the solar wind and interior processes. This measurement allows us to constrain _
Discovery of rotational modulations in the planetary mass companion 2m1207b i...Sérgio Sacani
Rotational modulations of brown dwarfs have recently provided powerful constraints on the properties
of ultra-cool atmospheres, including longitudinal and vertical cloud structures and cloud evolution.
Furthermore, periodic light curves directly probe the rotational periods of ultra-cool objects. We
present here, for the first time, time-resolved high-precision photometric measurements of a planetarymass
companion, 2M1207b. We observed the binary system with HST/WFC3 in two bands and with
two spacecraft roll angles. Using point spread function-based photometry, we reach a nearly photonnoise
limited accuracy for both the primary and the secondary. While the primary is consistent with
a flat light curve, the secondary shows modulations that are clearly detected in the combined light
curve as well as in di↵erent subsets of the data. The amplitudes are 1.36% in the F125W and 0.78%
in the F160W filters, respectively. By fitting sine waves to the light curves, we find a consistent period
of 10.7+1.2
−0.6 hours and similar phases in both bands. The J- and H-band amplitude ratio of 2M1207b
is very similar to a field brown dwarf that has identical spectral type but di↵erent J-H color. Importantly,
our study also measures, for the first time, the rotation period for a directly imaged extra-solar
planetary-mass companion.
This document summarizes a journal article that presents programs to compute the magnetization to density ratio (MDR) and magnetization inclination (MI) from 3D gravity and magnetic anomalies. The programs use vector formulations based on the Poisson theorem to estimate MDR and MI values for 3D geological sources from gridded gravity and magnetic data. Tests on simple geophysical models show the programs can successfully recover magnetization polarity even when bodies cannot be clearly distinguished from anomaly data alone. The results may help map magnetization polarity from marine gravity and magnetic surveys.
The Equation Based on the Rotational and Orbital Motion of the PlanetsIJERA Editor
Equations of dependence of rotational and orbital motions of planets are given, their rotation angles are calculated. Wave principles of direct and reverse rotation of planets are established. The established dependencies are demonstrated at different scale levels of structural interactions, in biosystems as well. The accuracy of calculations corresponds to the accuracy of experimental data
Confirmation of the_planetary_microlensing_signal_and_star_and_planet_mass_de...Sérgio Sacani
This document summarizes follow-up Hubble Space Telescope observations of the planetary microlensing event OGLE-2005-BLG-169. The HST observations confirm the relative proper motion between the source and lens stars predicted by the planetary signal in the original light curve. This provides the first confirmation of a planetary microlensing signal. The HST observations also measure the brightness of the planetary host star, allowing a precise determination of the planet and host star masses as well as their projected separation. Combined with measurements from Keck adaptive optics, the HST observations confirm the identification of the lens star and characterization of the planetary system.
There are relativistic effects in the solar group (proves)Gerges francis
The Main Hypothesis
"There Are Relativistic Effects In The Solar Group"
We can't observe the higher velocity which produces these relativistic effects but we can observe the relativistic effects which are produced by it.
As proves for the relativistic effects, I may refer to the following:
1. The Earth Moon Motion …
2. Mercury Day Period…
The previous 2 phenomena should be discussed in this paper with many other as proves for the relativistic effects are found in the solar group geometry.
This Papers provides 2 Points
1st Point : The Relativistic Effects Proves
2nd Point : The Relativistic effects Geometrical Meaning and Description.
We present long-baseline Atacama Large Millimeter/submillimeter Array (ALMA) observations of
the 870 m continuum emission from the nearest gas-rich protoplanetary disk, around TW Hya, that
trace millimeter-sized particles down to spatial scales as small as 1 AU (20 mas). These data reveal
a series of concentric ring-shaped substructures in the form of bright zones and narrow dark annuli
(1{6AU) with modest contrasts (5{30%). We associate these features with concentrations of solids
that have had their inward radial drift slowed or stopped, presumably at local gas pressure maxima.
No signicant non-axisymmetric structures are detected. Some of the observed features occur near
temperatures that may be associated with the condensation fronts of major volatile species, but the
relatively small brightness contrasts may also be a consequence of magnetized disk evolution (the
so-called zonal
ows). Other features, particularly a narrow dark annulus located only 1 AU from the
star, could indicate interactions between the disk and young planets. These data signal that ordered
substructures on AU scales can be common, fundamental factors in disk evolution, and that high
resolution microwave imaging can help characterize them during the epoch of planet formation.
Keywords: protoplanetary disks | planet-disk interactions | stars: individual (TW Hydrae)
The document describes measurements of the proper motion of the Andromeda Galaxy (M31) using Hubble Space Telescope imaging data from multiple fields observed at two epochs separated by 5-7 years. Background galaxies in the images are used as stationary reference objects to measure the displacement of thousands of M31 stars between epochs. This allows determining M31's absolute proper motion with an accuracy of 12 microarcseconds per year, providing crucial information about M31 and the Local Group's dynamics and future evolution.
Solar system expansion and strong equivalence principle as seen by the NASA M...Sérgio Sacani
The NASA MESSENGER mission explored the innermost planet of the solar system and obtained a rich data set of range measurements for the determination of Mercury’s ephemeris. Here we use these precise data collected over 7 years to estimate parameters related to general relativity and the evolution of the Sun. These results confirm the validity of the strong equivalence principle with a significantly refined uncertainty of the Nordtvedt parameter η=(−6.6±7.2)×10−5. By assuming a metric theory of gravitation, we retrieved the post-Newtonian parameter β=1+(−1.6±1.8)×10−5 and the Sun’s gravitational oblateness, J2 =(2.246±0.022)×10−7. Finally, we obtain an estimate of the time variation of the Sun gravitational parameter, _ GM=GM =(−6.13±1.47)×10−14, which is consistent with the expected solar mass loss due to the solar wind and interior processes. This measurement allows us to constrain _
Discovery of rotational modulations in the planetary mass companion 2m1207b i...Sérgio Sacani
Rotational modulations of brown dwarfs have recently provided powerful constraints on the properties
of ultra-cool atmospheres, including longitudinal and vertical cloud structures and cloud evolution.
Furthermore, periodic light curves directly probe the rotational periods of ultra-cool objects. We
present here, for the first time, time-resolved high-precision photometric measurements of a planetarymass
companion, 2M1207b. We observed the binary system with HST/WFC3 in two bands and with
two spacecraft roll angles. Using point spread function-based photometry, we reach a nearly photonnoise
limited accuracy for both the primary and the secondary. While the primary is consistent with
a flat light curve, the secondary shows modulations that are clearly detected in the combined light
curve as well as in di↵erent subsets of the data. The amplitudes are 1.36% in the F125W and 0.78%
in the F160W filters, respectively. By fitting sine waves to the light curves, we find a consistent period
of 10.7+1.2
−0.6 hours and similar phases in both bands. The J- and H-band amplitude ratio of 2M1207b
is very similar to a field brown dwarf that has identical spectral type but di↵erent J-H color. Importantly,
our study also measures, for the first time, the rotation period for a directly imaged extra-solar
planetary-mass companion.
This document summarizes a journal article that presents programs to compute the magnetization to density ratio (MDR) and magnetization inclination (MI) from 3D gravity and magnetic anomalies. The programs use vector formulations based on the Poisson theorem to estimate MDR and MI values for 3D geological sources from gridded gravity and magnetic data. Tests on simple geophysical models show the programs can successfully recover magnetization polarity even when bodies cannot be clearly distinguished from anomaly data alone. The results may help map magnetization polarity from marine gravity and magnetic surveys.
The Equation Based on the Rotational and Orbital Motion of the PlanetsIJERA Editor
Equations of dependence of rotational and orbital motions of planets are given, their rotation angles are calculated. Wave principles of direct and reverse rotation of planets are established. The established dependencies are demonstrated at different scale levels of structural interactions, in biosystems as well. The accuracy of calculations corresponds to the accuracy of experimental data
Confirmation of the_planetary_microlensing_signal_and_star_and_planet_mass_de...Sérgio Sacani
This document summarizes follow-up Hubble Space Telescope observations of the planetary microlensing event OGLE-2005-BLG-169. The HST observations confirm the relative proper motion between the source and lens stars predicted by the planetary signal in the original light curve. This provides the first confirmation of a planetary microlensing signal. The HST observations also measure the brightness of the planetary host star, allowing a precise determination of the planet and host star masses as well as their projected separation. Combined with measurements from Keck adaptive optics, the HST observations confirm the identification of the lens star and characterization of the planetary system.
There are relativistic effects in the solar group (proves)Gerges francis
The Main Hypothesis
"There Are Relativistic Effects In The Solar Group"
We can't observe the higher velocity which produces these relativistic effects but we can observe the relativistic effects which are produced by it.
As proves for the relativistic effects, I may refer to the following:
1. The Earth Moon Motion …
2. Mercury Day Period…
The previous 2 phenomena should be discussed in this paper with many other as proves for the relativistic effects are found in the solar group geometry.
This Papers provides 2 Points
1st Point : The Relativistic Effects Proves
2nd Point : The Relativistic effects Geometrical Meaning and Description.
We present long-baseline Atacama Large Millimeter/submillimeter Array (ALMA) observations of
the 870 m continuum emission from the nearest gas-rich protoplanetary disk, around TW Hya, that
trace millimeter-sized particles down to spatial scales as small as 1 AU (20 mas). These data reveal
a series of concentric ring-shaped substructures in the form of bright zones and narrow dark annuli
(1{6AU) with modest contrasts (5{30%). We associate these features with concentrations of solids
that have had their inward radial drift slowed or stopped, presumably at local gas pressure maxima.
No signicant non-axisymmetric structures are detected. Some of the observed features occur near
temperatures that may be associated with the condensation fronts of major volatile species, but the
relatively small brightness contrasts may also be a consequence of magnetized disk evolution (the
so-called zonal
ows). Other features, particularly a narrow dark annulus located only 1 AU from the
star, could indicate interactions between the disk and young planets. These data signal that ordered
substructures on AU scales can be common, fundamental factors in disk evolution, and that high
resolution microwave imaging can help characterize them during the epoch of planet formation.
Keywords: protoplanetary disks | planet-disk interactions | stars: individual (TW Hydrae)
This study uses asteroseismology to reveal fast core rotation in red giant stars, finding that the cores rotate at least 10 times faster than the surface by analyzing rotational splitting of mixed modes. Mixed modes that probe the core show larger rotational splitting than modes dominated by the outer layers, indicating non-rigid rotation that increases towards the stellar interior. Models are able to reproduce the observations, confirming theoretical predictions of a steep rotational gradient within red giant cores.
Alignment of th_angular_momentum_vectors_of_planetary_nebulae_in_the_galactic...Sérgio Sacani
This document analyzes the orientations of 130 planetary nebulae (PNe) in the Galactic Bulge to investigate whether there is a preferred alignment. It finds that while the full sample shows a uniform distribution, the bipolar PNe exhibit a non-uniform distribution with a mean orientation along the Galactic plane at a 90 degree position angle, significant at the 0.001 level. This indicates that the orbital planes of binary systems in old stars are oriented perpendicular to the Galactic plane, likely due to strong magnetic fields during star formation that influenced the angular momentum vectors.
Limit radius in a binary system: Cosmological and Post-Newtonian effectsPremier Publishers
Frequently, in dynamical astronomy, the quantitative effect of the large-scale cosmological expansion on local systems is studied in the light of Newtonian approach. We, however, analyze the influence of cosmological expansion on binary systems (galaxies or black holes) in the light of Post-Newtonian approximation. Furthermore, we obtain the new radius at which the acceleration due to the cosmological expansion has the same magnitude as the two-body attraction, and the classical limit radius is obtained when the Schwarzschild radius approaches zero (for example, the Solar System).
1) The paper investigates whether quantum variations around geodesics could circumvent caustics that occur in certain space-times.
2) An action is developed that yields both the field equations and geodesic condition. Quantizing this action provides a way to determine the extent of the wave packet around the classical path.
3) It is shown that replacing plane wave solutions with wave packets in the path integral still yields acceptable results. Determining if the distribution matches expectation values and variances is key to establishing geodesic completeness with quantum variations.
1) Photonic nanojets can influence the trapping behavior of multiple microspheres that are axially trapped in a focused laser beam. 2) Simulations show that when two microspheres approach each other axially in the beam, they are initially pushed apart by scattering forces but can become drawn together by a connecting photonic nanojet that forms between them. 3) Three microspheres may also become tethered when specific refractive index conditions are met between each neighboring pair.
This document summarizes results from simulations of galaxy formation and evolution using hydrodynamical simulations. Higher resolution simulations that include feedback produce galaxies with larger disk scale lengths and smaller bulge-to-disk ratios, in better agreement with observations. Feedback and resolution are necessary to form galaxies with flatter rotation curves and properties matching observed galaxies, like the Tully-Fisher relation. One simulated galaxy has a large disk scale length of 9.2 kpc and small bulge-to-disk ratio of 0.64.
A giant galaxy in the young Universe with a massive ringSérgio Sacani
In the local (redshift z ≈ 0) Universe, collisional ring galaxies make up only ~0.01% of galaxies1 and are formed by head-on galactic collisions that trigger radially propagating density waves2–4. These striking systems provide key snapshots for dissecting galactic disks and are studied extensively in the local Universe5–9. However, not much is known about distant (z > 0.1) collisional rings10–14. Here we present a detailed study of a ring galaxy at a look-back time of 10.8 Gyr (z = 2.19). Compared with our Milky Way, this galaxy has a similar stellar mass, but has a stellar half-light radius that is 1.5–2.2 times larger and is forming stars 50 times faster. The extended, dif- fuse stellar light outside the star-forming ring, combined with a radial velocity on the ring and an intruder galaxy nearby, provides evidence for this galaxy hosting a collisional ring. If the ring is secularly evolved15,16, the implied large bar in a giant disk would be inconsistent with the current understand- ing of the earliest formation of barred spirals17–21. Contrary to previous predictions10–12, this work suggests that massive col- lisional rings were as rare 11 Gyr ago as they are today. Our discovery offers a unique pathway for studying density waves in young galaxies, as well as constraining the cosmic evolution of spiral disks and galaxy groups.
The characterization of_the_gamma_ray_signal_from_the_central_milk_way_a_comp...Sérgio Sacani
This document analyzes the gamma-ray signal from the central Milky Way that is consistent with emission from annihilating dark matter particles. The authors re-examine Fermi data using cuts on an event parameter to improve gamma-ray maps and more easily separate components. They find the GeV excess is robust and well-fit by a 36-51 GeV dark matter particle annihilating to bottom quarks with a cross section of 1-3×10−26 cm3/s. The signal extends over 10 degrees from the Galactic Center and is spherically symmetric, disfavoring explanations from millisecond pulsars or gas interactions.
The Total Solar Eclipse Geometrical Analysis Gerges francis
Paper Hypothesis
Jupiter Provides Us The Chance To See The Total Solar Eclipse
Why We See The Sun Disc = The Moon Disc?
Because
(The sun diameter / the moon diameter) = (Earth orbital distance/ Earth Moon distance)
Jupiter causes to make the (sun/moon) diameters rate = their distances rate to the Earth
How? Because
Jupiter effects on the Earth and its moon creation data to be in consistency with the previous equation
Means – Jupiter causes the moon diameter to be created as (1/400 the sun diameter) and also Jupiter causes the Earth orbital distance to be = (1/400) Earth Moon Distance
These results are produced by Jupiter effect on the Earth Moon Creation.
The paper tries to prove this fact
Gerges Francis Tawdrous +201022532292
1) PSR J033711715 is a millisecond pulsar discovered to be in a hierarchical triple system with two white dwarf companions, making it the first known millisecond pulsar triple system.
2) Precise timing observations using multiple radio telescopes determined the masses of the pulsar (1.4378 solar masses), inner white dwarf companion (0.19751 solar masses), and outer white dwarf companion (0.4101 solar masses) to high precision.
3) The unexpectedly coplanar and nearly circular orbits of the system indicate an exotic evolutionary history and provide an opportunity to test theories of general relativity by studying the interactions between the bodies.
The Moon Orbital Triangle (General discussion) (Revised) (II)Gerges francis
Paper Argument
- The Moon motion has 2 Orbits – we see one of them only
- The moon second orbit is declined by 0.8 degrees on the first one.
- The 2 orbits are neighbors and define together the Lunar Eclipse Umbra Length (1.392 mkm)
- The second orbit is found because the moon moves 2 daily displacements each = (88000 km) but we see one of them only
- Venus Axial Tilt is changed from 1.774 to 177.4 degrees because of Uranus Axial Tilt angle (91.1 degrees) with The Moon Axial Tilt (6.7 deg).
- Venus original axial tilt (1.774 deg) is created as a rate between its diameter and Mars diameter – that shows Mars diameter rate effect on the planets motions
- Mars diameter effect explains the reason why Kepler equation (P2/d3 = Constant) uses (25) as a constant while (25.2 deg = Mars Axial Tilt)
- The moon uses Pythagoras rule in its motion to define its real displacement through its orbit which can be less or equal the value 88000 km.
Gerges Francis Tawdrous +201022532292
Another Force Effects On The Earth Moon Motion (III)Gerges francis
Paper Question
-Can the moon orbit regress and the Earth still in its same point in the space If the Earth moon distances after the regression still equal their values before it?
- The paper question tells us that….
- The moon orbit regression is done because of the moon vertical motion and both are done in consistency with a displacement done by Earth vertically for 1 km per solar day…
- I claim that, there are 3 motions done, but only one motion is seen, we have to conclude the 2 rest hidden motions….
o The seen motion is The Moon Orbit Regression
o The 1st hidden motion is the moon vertical motion…that means, the moon in its revolution around The Earth does a vertical motion, and this vertical motion is the reason of the Metonic Cycle (19 sidereal years)
o The 2nd hidden motion is the Earth motion, where the Earth moves daily a vertical displacement = 1 km
- These 3 motions are done in consistency with each other, and depends on each other (this dependency can be seen in a deep analysis for these 3 motions origin)
Paper Objective
- The paper tries to prove the moon vertical motion by using the moon motion data analysis, after this proof , The paper discusses if a vertical displacement of Earth is a necessary requirement for the moon orbit regression, which is done as a result of the moon vertical motion.
Paper 2nd Question
- Why it's necessary to know if the moon has a vertical motion?
- (1st) The moon motion has pauses can't be explained, as we have seen in our tests for (Gerges Equation for the moon orbital motion)… where the moon moves on a solar day a distance = 4000 km (in average) (for example from 384000 km to 388000 km) but we have found that, the moon in perigee & apogee top points stay for many days without change its orbit (for example during 28th, 29th and 30th January 2020, the moon stayed on (404425 km, 405333km, 405111 km)) – how to explain that?
Gerges Francis Tawdrous +201022532292
This document summarizes a study that uses distance measurements in the nearby universe to test theories of modified gravity. The study compares distance measurements from cepheid variable stars, tip of the red giant branch stars, and water masers in different galaxies. These distance indicators operate in gravitational fields of different strengths, enabling tests of scalar-tensor gravity theories where fifth forces are screened to different extents depending on the local gravitational potential. The study finds no evidence for the enhanced gravitational forces predicted by chameleon and symmetron screening scenarios, constraining the parameter space of these theories.
Young remmants of_type_ia_supernovae_and_their_progenitors_a_study_of_snr_g19_03Sérgio Sacani
Type Ia supernovae, with their remarkably homogeneous light curves and spectra, have been used as
standardizable candles to measure the accelerating expansion of the Universe. Yet, their progenitors
remain elusive. Common explanations invoke a degenerate star (white dwarf) which explodes upon
reaching close to the Chandrasekhar limit, by either steadily accreting mass from a companion star
or violently merging with another degenerate star. We show that circumstellar interaction in young
Galactic supernova remnants can be used to distinguish between these single and double degenerate
progenitor scenarios. Here we propose a new diagnostic, the Surface Brightness Index, which can
be computed from theory and compared with Chandra and VLA observations. We use this method
to demonstrate that a double degenerate progenitor can explain the decades-long
ux rise and size
increase of the youngest known Galactic SNR G1.9+0.3. We disfavor a single degenerate scenario.
We attribute the observed properties to the interaction between a steep ejecta prole and a constant
density environment. We suggest using the upgraded VLA to detect circumstellar interaction in
the remnants of historical Type Ia supernovae in the Local Group of galaxies. This may settle the
long-standing debate over their progenitors.
Subject headings: ISM: supernova remnants | radio continuum: general | X-rays: general | bi-
naries: general | circumstellar matter | supernovae: general | ISM: individual
objects(SNR G1.9+0.3)
Periodic mass extinctions_and_the_planet_x_model_reconsideredSérgio Sacani
The 27 Myr periodicity in the fossil extinction record has been con-
firmed in modern data bases dating back 500 Myr, which is twice the time
interval of the original analysis from thirty years ago. The surprising regularity
of this period has been used to reject the Nemesis model. A second
model based on the sun’s vertical galactic oscillations has been challenged
on the basis of an inconsistency in period and phasing. The third astronomical
model originally proposed to explain the periodicity is the Planet
X model in which the period is associated with the perihelion precession
of the inclined orbit of a trans-Neptunian planet. Recently, and unrelated
to mass extinctions, a trans-Neptunian super-Earth planet has been proposed
to explain the observation that the inner Oort cloud objects Sedna
and 2012VP113 have perihelia that lie near the ecliptic plane. In this
Letter we reconsider the Planet X model in light of the confluence of the
modern palaeontological and outer solar system dynamical evidence.
Key Words: astrobiology - planets and satellites - Kuiper belt:
general - comets: general
Is There another Orbit For The Moon Motion? Gerges francis
Paper Hypothesis No. (1)
-Another Orbit must be found for the moon motion.
Paper Hypothesis No. (2)
-An interaction is found between Jupiter and the Earth moon motions, this interaction shows that another orbit must be found for the moon motion –
Paper Objective
-The paper tries to prove that, there's an interaction between Jupiter and the moon motion.
-And
-Based on this interaction, Jupiter effect on the moon motion suggests that another orbit is required necessary for the moon orbital motion.
Gerges Francis Tawdrous +201022532292
Inverse Compton cooling limits the brightness temperature of the radiating plasma to a maximum of
1011.5 K. Relativistic boosting can increase its observed value, but apparent brightness temperatures
much in excess of 1013 K are inaccessible using ground-based very long baseline interferometry (VLBI)
at any wavelength. We present observations of the quasar 3C 273, made with the space VLBI mission
RadioAstron on baselines up to 171,000 km, which directly reveal the presence of angular structure as
small as 26 µas (2.7 light months) and brightness temperature in excess of 1013 K. These measurements
challenge our understanding of the non-thermal continuum emission in the vicinity of supermassive
black holes and require a much higher Doppler factor than what is determined from jet apparent
kinematics.
Keywords: galaxies: active — galaxies: jets — radio continuum: galaxies — techniques: interferometric
— quasars: individual (3C 273)
This document summarizes a study of the future orbital evolution and merging of the Milky Way, Andromeda Galaxy (M31), and Triangulum Galaxy (M33) systems using N-body simulations and orbit integrations. Key findings include:
1) The M31 velocity vector implies that the Milky Way and M31 will merge in 5.86 billion years, with a 41% chance of a direct collision within 25 kpc.
2) M31 and M33 will have their first pericenter passage in 0.85 billion years at a distance of 80.8 kpc.
3) There is a 9% chance that M33 collides with the Milky Way before M31.
Keck Integral-field Spectroscopy of M87 Reveals an Intrinsically Triaxial Gal...Sérgio Sacani
The three-dimensional intrinsic shape of a galaxy and the mass of the central supermassive black hole provide key
insight into the galaxy’s growth history over cosmic time. Standard assumptions of a spherical or axisymmetric
shape can be simplistic and can bias the black hole mass inferred from the motions of stars within a galaxy. Here,
we present spatially resolved stellar kinematics of M87 over a two-dimensional 250″ × 300″ contiguous field
covering a radial range of 50 pc–12 kpc from integral-field spectroscopic observations at the Keck II Telescope.
From about 5 kpc and outward, we detect a prominent 25 km s−1 rotational pattern, in which the kinematic axis
(connecting the maximal receding and approaching velocities) is 40° misaligned with the photometric major axis of
M87. The rotational amplitude and misalignment angle both decrease in the inner 5 kpc. Such misaligned and
twisted velocity fields are a hallmark of triaxiality, indicating that M87 is not an axisymmetrically shaped galaxy.
Triaxial Schwarzschild orbit modeling with more than 4000 observational constraints enabled us to determine
simultaneously the shape and mass parameters. The models incorporate a radially declining profile for the stellar
mass-to-light ratio suggested by stellar population studies. We find that M87 is strongly triaxial, with ratios of
p = 0.845 for the middle-to-long principal axes and q = 0.722 for the short-to-long principal axes, and determine
the black hole mass to be ( - ´) 5.37 0.22 10 +
0.25
0.37 9M , where the second error indicates the systematic uncertainty
associated with the distance to M87.
The atacama cosmology_telescope_measuring_radio_galaxy_bias_through_cross_cor...Sérgio Sacani
A radiação cósmica de micro-ondas aponta para a matéria escura invisível, marcando o ponto onde jatos de material viajam a velocidades próximas da velocidade da luz, de acordo com uma equipe internacional de astrônomos. O principal autor do estudo, Rupert Allison da Universidade de Oxford apresentou os resultados no dia 6 de Julho de 2015 no National Astronomy Meeting em Venue Cymru, em Llandudno em Wales.
Atualmente, ninguém sabe ao certo do que a matéria escura é feita, mas ela é responsável por cerca de 26% do conteúdo de energia do universo, com galáxias massivas se formando em densas regiões de matéria escura. Embora invisível, a matéria escura se mostra através do efeito gravitacional – uma grande bolha de matéria escura puxa a matéria normal (como elétrons, prótons e nêutrons) através de sua própria gravidade, eventualmente se empacotando conjuntamente para criar as estrelas e galáxias inteiras.
Muitas das maiores dessas são galáxias ativas com buracos negros supermassivos em seus centros. Alguma parte do gás caindo diretamente na direção do buraco negro é ejetada como jatos de partículas e radiação. As observações feitas com rádio telescópios mostram que esses jatos as vezes se espalham por milhões de anos-luz desde a galáxia – mais distante até mesmo do que a extensão da própria galáxia.
Os cientistas esperam que os jatos possam viver em regiões onde existe um excesso de concentração da matéria escura, maior do que o da média. Mas como a matéria escura é invisível, testar essa ideia não é algo tão direto.
Probing the jet_base_of_blazar_pks1830211_from_the_chromatic_variability_of_i...Sérgio Sacani
This document summarizes ALMA observations of the blazar PKS 1830-211 taken over multiple epochs in 2012. The blazar is lensed by a foreground galaxy, producing two resolved images (NE and SW) separated by 1". The observations were taken at frequencies corresponding to 350-1050 GHz in the blazar rest frame. Analysis of the flux ratio between the two images over time and frequency revealed a remarkable frequency-dependent behavior, implying a "chromatic structure" in the blazar jet. This is interpreted as evidence for a "core-shift effect" caused by plasmon ejection very near the base of the jet. The observations provide a unique probe of activity in the region where plasma acceleration occurs in blazar
The colision between_the_milky_way_and_andromedaSérgio Sacani
The document summarizes a simulation of the future collision between the Milky Way and Andromeda galaxies. It finds that given current observational constraints on their distance, velocity, and masses:
1) The Milky Way and Andromeda are likely to collide in a few billion years, within the lifetime of the Sun.
2) During the interaction, there is a chance the Sun could be pulled into an extended tidal tail between the galaxies.
3) Eventually, after the merger is complete, the Sun would most likely be scattered to the outer halo of the merged galaxy at a distance over 30 kpc.
This study uses asteroseismology to reveal fast core rotation in red giant stars, finding that the cores rotate at least 10 times faster than the surface by analyzing rotational splitting of mixed modes. Mixed modes that probe the core show larger rotational splitting than modes dominated by the outer layers, indicating non-rigid rotation that increases towards the stellar interior. Models are able to reproduce the observations, confirming theoretical predictions of a steep rotational gradient within red giant cores.
Alignment of th_angular_momentum_vectors_of_planetary_nebulae_in_the_galactic...Sérgio Sacani
This document analyzes the orientations of 130 planetary nebulae (PNe) in the Galactic Bulge to investigate whether there is a preferred alignment. It finds that while the full sample shows a uniform distribution, the bipolar PNe exhibit a non-uniform distribution with a mean orientation along the Galactic plane at a 90 degree position angle, significant at the 0.001 level. This indicates that the orbital planes of binary systems in old stars are oriented perpendicular to the Galactic plane, likely due to strong magnetic fields during star formation that influenced the angular momentum vectors.
Limit radius in a binary system: Cosmological and Post-Newtonian effectsPremier Publishers
Frequently, in dynamical astronomy, the quantitative effect of the large-scale cosmological expansion on local systems is studied in the light of Newtonian approach. We, however, analyze the influence of cosmological expansion on binary systems (galaxies or black holes) in the light of Post-Newtonian approximation. Furthermore, we obtain the new radius at which the acceleration due to the cosmological expansion has the same magnitude as the two-body attraction, and the classical limit radius is obtained when the Schwarzschild radius approaches zero (for example, the Solar System).
1) The paper investigates whether quantum variations around geodesics could circumvent caustics that occur in certain space-times.
2) An action is developed that yields both the field equations and geodesic condition. Quantizing this action provides a way to determine the extent of the wave packet around the classical path.
3) It is shown that replacing plane wave solutions with wave packets in the path integral still yields acceptable results. Determining if the distribution matches expectation values and variances is key to establishing geodesic completeness with quantum variations.
1) Photonic nanojets can influence the trapping behavior of multiple microspheres that are axially trapped in a focused laser beam. 2) Simulations show that when two microspheres approach each other axially in the beam, they are initially pushed apart by scattering forces but can become drawn together by a connecting photonic nanojet that forms between them. 3) Three microspheres may also become tethered when specific refractive index conditions are met between each neighboring pair.
This document summarizes results from simulations of galaxy formation and evolution using hydrodynamical simulations. Higher resolution simulations that include feedback produce galaxies with larger disk scale lengths and smaller bulge-to-disk ratios, in better agreement with observations. Feedback and resolution are necessary to form galaxies with flatter rotation curves and properties matching observed galaxies, like the Tully-Fisher relation. One simulated galaxy has a large disk scale length of 9.2 kpc and small bulge-to-disk ratio of 0.64.
A giant galaxy in the young Universe with a massive ringSérgio Sacani
In the local (redshift z ≈ 0) Universe, collisional ring galaxies make up only ~0.01% of galaxies1 and are formed by head-on galactic collisions that trigger radially propagating density waves2–4. These striking systems provide key snapshots for dissecting galactic disks and are studied extensively in the local Universe5–9. However, not much is known about distant (z > 0.1) collisional rings10–14. Here we present a detailed study of a ring galaxy at a look-back time of 10.8 Gyr (z = 2.19). Compared with our Milky Way, this galaxy has a similar stellar mass, but has a stellar half-light radius that is 1.5–2.2 times larger and is forming stars 50 times faster. The extended, dif- fuse stellar light outside the star-forming ring, combined with a radial velocity on the ring and an intruder galaxy nearby, provides evidence for this galaxy hosting a collisional ring. If the ring is secularly evolved15,16, the implied large bar in a giant disk would be inconsistent with the current understand- ing of the earliest formation of barred spirals17–21. Contrary to previous predictions10–12, this work suggests that massive col- lisional rings were as rare 11 Gyr ago as they are today. Our discovery offers a unique pathway for studying density waves in young galaxies, as well as constraining the cosmic evolution of spiral disks and galaxy groups.
The characterization of_the_gamma_ray_signal_from_the_central_milk_way_a_comp...Sérgio Sacani
This document analyzes the gamma-ray signal from the central Milky Way that is consistent with emission from annihilating dark matter particles. The authors re-examine Fermi data using cuts on an event parameter to improve gamma-ray maps and more easily separate components. They find the GeV excess is robust and well-fit by a 36-51 GeV dark matter particle annihilating to bottom quarks with a cross section of 1-3×10−26 cm3/s. The signal extends over 10 degrees from the Galactic Center and is spherically symmetric, disfavoring explanations from millisecond pulsars or gas interactions.
The Total Solar Eclipse Geometrical Analysis Gerges francis
Paper Hypothesis
Jupiter Provides Us The Chance To See The Total Solar Eclipse
Why We See The Sun Disc = The Moon Disc?
Because
(The sun diameter / the moon diameter) = (Earth orbital distance/ Earth Moon distance)
Jupiter causes to make the (sun/moon) diameters rate = their distances rate to the Earth
How? Because
Jupiter effects on the Earth and its moon creation data to be in consistency with the previous equation
Means – Jupiter causes the moon diameter to be created as (1/400 the sun diameter) and also Jupiter causes the Earth orbital distance to be = (1/400) Earth Moon Distance
These results are produced by Jupiter effect on the Earth Moon Creation.
The paper tries to prove this fact
Gerges Francis Tawdrous +201022532292
1) PSR J033711715 is a millisecond pulsar discovered to be in a hierarchical triple system with two white dwarf companions, making it the first known millisecond pulsar triple system.
2) Precise timing observations using multiple radio telescopes determined the masses of the pulsar (1.4378 solar masses), inner white dwarf companion (0.19751 solar masses), and outer white dwarf companion (0.4101 solar masses) to high precision.
3) The unexpectedly coplanar and nearly circular orbits of the system indicate an exotic evolutionary history and provide an opportunity to test theories of general relativity by studying the interactions between the bodies.
The Moon Orbital Triangle (General discussion) (Revised) (II)Gerges francis
Paper Argument
- The Moon motion has 2 Orbits – we see one of them only
- The moon second orbit is declined by 0.8 degrees on the first one.
- The 2 orbits are neighbors and define together the Lunar Eclipse Umbra Length (1.392 mkm)
- The second orbit is found because the moon moves 2 daily displacements each = (88000 km) but we see one of them only
- Venus Axial Tilt is changed from 1.774 to 177.4 degrees because of Uranus Axial Tilt angle (91.1 degrees) with The Moon Axial Tilt (6.7 deg).
- Venus original axial tilt (1.774 deg) is created as a rate between its diameter and Mars diameter – that shows Mars diameter rate effect on the planets motions
- Mars diameter effect explains the reason why Kepler equation (P2/d3 = Constant) uses (25) as a constant while (25.2 deg = Mars Axial Tilt)
- The moon uses Pythagoras rule in its motion to define its real displacement through its orbit which can be less or equal the value 88000 km.
Gerges Francis Tawdrous +201022532292
Another Force Effects On The Earth Moon Motion (III)Gerges francis
Paper Question
-Can the moon orbit regress and the Earth still in its same point in the space If the Earth moon distances after the regression still equal their values before it?
- The paper question tells us that….
- The moon orbit regression is done because of the moon vertical motion and both are done in consistency with a displacement done by Earth vertically for 1 km per solar day…
- I claim that, there are 3 motions done, but only one motion is seen, we have to conclude the 2 rest hidden motions….
o The seen motion is The Moon Orbit Regression
o The 1st hidden motion is the moon vertical motion…that means, the moon in its revolution around The Earth does a vertical motion, and this vertical motion is the reason of the Metonic Cycle (19 sidereal years)
o The 2nd hidden motion is the Earth motion, where the Earth moves daily a vertical displacement = 1 km
- These 3 motions are done in consistency with each other, and depends on each other (this dependency can be seen in a deep analysis for these 3 motions origin)
Paper Objective
- The paper tries to prove the moon vertical motion by using the moon motion data analysis, after this proof , The paper discusses if a vertical displacement of Earth is a necessary requirement for the moon orbit regression, which is done as a result of the moon vertical motion.
Paper 2nd Question
- Why it's necessary to know if the moon has a vertical motion?
- (1st) The moon motion has pauses can't be explained, as we have seen in our tests for (Gerges Equation for the moon orbital motion)… where the moon moves on a solar day a distance = 4000 km (in average) (for example from 384000 km to 388000 km) but we have found that, the moon in perigee & apogee top points stay for many days without change its orbit (for example during 28th, 29th and 30th January 2020, the moon stayed on (404425 km, 405333km, 405111 km)) – how to explain that?
Gerges Francis Tawdrous +201022532292
This document summarizes a study that uses distance measurements in the nearby universe to test theories of modified gravity. The study compares distance measurements from cepheid variable stars, tip of the red giant branch stars, and water masers in different galaxies. These distance indicators operate in gravitational fields of different strengths, enabling tests of scalar-tensor gravity theories where fifth forces are screened to different extents depending on the local gravitational potential. The study finds no evidence for the enhanced gravitational forces predicted by chameleon and symmetron screening scenarios, constraining the parameter space of these theories.
Young remmants of_type_ia_supernovae_and_their_progenitors_a_study_of_snr_g19_03Sérgio Sacani
Type Ia supernovae, with their remarkably homogeneous light curves and spectra, have been used as
standardizable candles to measure the accelerating expansion of the Universe. Yet, their progenitors
remain elusive. Common explanations invoke a degenerate star (white dwarf) which explodes upon
reaching close to the Chandrasekhar limit, by either steadily accreting mass from a companion star
or violently merging with another degenerate star. We show that circumstellar interaction in young
Galactic supernova remnants can be used to distinguish between these single and double degenerate
progenitor scenarios. Here we propose a new diagnostic, the Surface Brightness Index, which can
be computed from theory and compared with Chandra and VLA observations. We use this method
to demonstrate that a double degenerate progenitor can explain the decades-long
ux rise and size
increase of the youngest known Galactic SNR G1.9+0.3. We disfavor a single degenerate scenario.
We attribute the observed properties to the interaction between a steep ejecta prole and a constant
density environment. We suggest using the upgraded VLA to detect circumstellar interaction in
the remnants of historical Type Ia supernovae in the Local Group of galaxies. This may settle the
long-standing debate over their progenitors.
Subject headings: ISM: supernova remnants | radio continuum: general | X-rays: general | bi-
naries: general | circumstellar matter | supernovae: general | ISM: individual
objects(SNR G1.9+0.3)
Periodic mass extinctions_and_the_planet_x_model_reconsideredSérgio Sacani
The 27 Myr periodicity in the fossil extinction record has been con-
firmed in modern data bases dating back 500 Myr, which is twice the time
interval of the original analysis from thirty years ago. The surprising regularity
of this period has been used to reject the Nemesis model. A second
model based on the sun’s vertical galactic oscillations has been challenged
on the basis of an inconsistency in period and phasing. The third astronomical
model originally proposed to explain the periodicity is the Planet
X model in which the period is associated with the perihelion precession
of the inclined orbit of a trans-Neptunian planet. Recently, and unrelated
to mass extinctions, a trans-Neptunian super-Earth planet has been proposed
to explain the observation that the inner Oort cloud objects Sedna
and 2012VP113 have perihelia that lie near the ecliptic plane. In this
Letter we reconsider the Planet X model in light of the confluence of the
modern palaeontological and outer solar system dynamical evidence.
Key Words: astrobiology - planets and satellites - Kuiper belt:
general - comets: general
Is There another Orbit For The Moon Motion? Gerges francis
Paper Hypothesis No. (1)
-Another Orbit must be found for the moon motion.
Paper Hypothesis No. (2)
-An interaction is found between Jupiter and the Earth moon motions, this interaction shows that another orbit must be found for the moon motion –
Paper Objective
-The paper tries to prove that, there's an interaction between Jupiter and the moon motion.
-And
-Based on this interaction, Jupiter effect on the moon motion suggests that another orbit is required necessary for the moon orbital motion.
Gerges Francis Tawdrous +201022532292
Inverse Compton cooling limits the brightness temperature of the radiating plasma to a maximum of
1011.5 K. Relativistic boosting can increase its observed value, but apparent brightness temperatures
much in excess of 1013 K are inaccessible using ground-based very long baseline interferometry (VLBI)
at any wavelength. We present observations of the quasar 3C 273, made with the space VLBI mission
RadioAstron on baselines up to 171,000 km, which directly reveal the presence of angular structure as
small as 26 µas (2.7 light months) and brightness temperature in excess of 1013 K. These measurements
challenge our understanding of the non-thermal continuum emission in the vicinity of supermassive
black holes and require a much higher Doppler factor than what is determined from jet apparent
kinematics.
Keywords: galaxies: active — galaxies: jets — radio continuum: galaxies — techniques: interferometric
— quasars: individual (3C 273)
This document summarizes a study of the future orbital evolution and merging of the Milky Way, Andromeda Galaxy (M31), and Triangulum Galaxy (M33) systems using N-body simulations and orbit integrations. Key findings include:
1) The M31 velocity vector implies that the Milky Way and M31 will merge in 5.86 billion years, with a 41% chance of a direct collision within 25 kpc.
2) M31 and M33 will have their first pericenter passage in 0.85 billion years at a distance of 80.8 kpc.
3) There is a 9% chance that M33 collides with the Milky Way before M31.
Keck Integral-field Spectroscopy of M87 Reveals an Intrinsically Triaxial Gal...Sérgio Sacani
The three-dimensional intrinsic shape of a galaxy and the mass of the central supermassive black hole provide key
insight into the galaxy’s growth history over cosmic time. Standard assumptions of a spherical or axisymmetric
shape can be simplistic and can bias the black hole mass inferred from the motions of stars within a galaxy. Here,
we present spatially resolved stellar kinematics of M87 over a two-dimensional 250″ × 300″ contiguous field
covering a radial range of 50 pc–12 kpc from integral-field spectroscopic observations at the Keck II Telescope.
From about 5 kpc and outward, we detect a prominent 25 km s−1 rotational pattern, in which the kinematic axis
(connecting the maximal receding and approaching velocities) is 40° misaligned with the photometric major axis of
M87. The rotational amplitude and misalignment angle both decrease in the inner 5 kpc. Such misaligned and
twisted velocity fields are a hallmark of triaxiality, indicating that M87 is not an axisymmetrically shaped galaxy.
Triaxial Schwarzschild orbit modeling with more than 4000 observational constraints enabled us to determine
simultaneously the shape and mass parameters. The models incorporate a radially declining profile for the stellar
mass-to-light ratio suggested by stellar population studies. We find that M87 is strongly triaxial, with ratios of
p = 0.845 for the middle-to-long principal axes and q = 0.722 for the short-to-long principal axes, and determine
the black hole mass to be ( - ´) 5.37 0.22 10 +
0.25
0.37 9M , where the second error indicates the systematic uncertainty
associated with the distance to M87.
The atacama cosmology_telescope_measuring_radio_galaxy_bias_through_cross_cor...Sérgio Sacani
A radiação cósmica de micro-ondas aponta para a matéria escura invisível, marcando o ponto onde jatos de material viajam a velocidades próximas da velocidade da luz, de acordo com uma equipe internacional de astrônomos. O principal autor do estudo, Rupert Allison da Universidade de Oxford apresentou os resultados no dia 6 de Julho de 2015 no National Astronomy Meeting em Venue Cymru, em Llandudno em Wales.
Atualmente, ninguém sabe ao certo do que a matéria escura é feita, mas ela é responsável por cerca de 26% do conteúdo de energia do universo, com galáxias massivas se formando em densas regiões de matéria escura. Embora invisível, a matéria escura se mostra através do efeito gravitacional – uma grande bolha de matéria escura puxa a matéria normal (como elétrons, prótons e nêutrons) através de sua própria gravidade, eventualmente se empacotando conjuntamente para criar as estrelas e galáxias inteiras.
Muitas das maiores dessas são galáxias ativas com buracos negros supermassivos em seus centros. Alguma parte do gás caindo diretamente na direção do buraco negro é ejetada como jatos de partículas e radiação. As observações feitas com rádio telescópios mostram que esses jatos as vezes se espalham por milhões de anos-luz desde a galáxia – mais distante até mesmo do que a extensão da própria galáxia.
Os cientistas esperam que os jatos possam viver em regiões onde existe um excesso de concentração da matéria escura, maior do que o da média. Mas como a matéria escura é invisível, testar essa ideia não é algo tão direto.
Probing the jet_base_of_blazar_pks1830211_from_the_chromatic_variability_of_i...Sérgio Sacani
This document summarizes ALMA observations of the blazar PKS 1830-211 taken over multiple epochs in 2012. The blazar is lensed by a foreground galaxy, producing two resolved images (NE and SW) separated by 1". The observations were taken at frequencies corresponding to 350-1050 GHz in the blazar rest frame. Analysis of the flux ratio between the two images over time and frequency revealed a remarkable frequency-dependent behavior, implying a "chromatic structure" in the blazar jet. This is interpreted as evidence for a "core-shift effect" caused by plasmon ejection very near the base of the jet. The observations provide a unique probe of activity in the region where plasma acceleration occurs in blazar
The colision between_the_milky_way_and_andromedaSérgio Sacani
The document summarizes a simulation of the future collision between the Milky Way and Andromeda galaxies. It finds that given current observational constraints on their distance, velocity, and masses:
1) The Milky Way and Andromeda are likely to collide in a few billion years, within the lifetime of the Sun.
2) During the interaction, there is a chance the Sun could be pulled into an extended tidal tail between the galaxies.
3) Eventually, after the merger is complete, the Sun would most likely be scattered to the outer halo of the merged galaxy at a distance over 30 kpc.
A vlt flames_survey_for_massive_binaries_in_westerlund_1Sérgio Sacani
1) The authors conducted a radial velocity survey of stars in the young massive cluster Westerlund 1 to search for a potential pre-supernova companion to the magnetar CXO J1647-10.2-455216 located within the cluster.
2) They identified a candidate star, Wd1-5, that has anomalous velocities compared to other stars in the cluster, suggesting it was impacted by the supernova that created the magnetar.
3) Analysis of Wd1-5 found evidence of chemical enrichment that is difficult to explain by single star evolution, but could be explained if Wd1-5 was once part of a close binary system where it accreted material from
A Neutron Star with a Massive Progenitor in Westerlund 1GOASA
1) The authors conducted a radial velocity survey of stars in the young massive cluster Westerlund 1 to search for a potential pre-supernova companion to the magnetar CXO J1647-10.2-455216 located within the cluster.
2) They identified a candidate star, Wd1-5, that has anomalous velocities compared to other stars in the cluster, suggesting it was impacted by the supernova of the magnetar's progenitor star.
3) Analysis of Wd1-5 found evidence of chemical enrichment that is difficult to explain by single star evolution, suggesting it was part of a binary system where it accreted material from the magnetar's progenitor prior to its
This document summarizes cosmological parameters measured from galaxy surveys. It discusses:
1) Direct measurements of the Hubble constant from the Hubble Space Telescope and Planck, finding values of 72-74 km/s/Mpc and 67.3 km/s/Mpc respectively.
2) Supernova surveys finding evidence for an accelerating universe with matter density of ~30% and dark energy density of ~70%.
3) Measurements of cosmic microwave background from COBE, WMAP and Planck, determining ages and densities of the universe.
4) Galaxy clustering surveys like SDSS detecting baryon acoustic oscillations to measure dark energy properties.
- The document investigates the implications of a proposed metallicity-dependent initial mass function (IMF), which suggests the IMF varies based on the metallicity of a star formation environment.
- Using observations of globular cluster Palomar 14 and open cluster M42, the author constrains an upper bound for metallicity dependence, resulting in a two-part power law IMF function that depends on metallicity.
- However, the document concludes that current evidence is inadequate to prove a metallicity-dependent IMF, as measurements of cluster IMFs are complicated by issues like dynamics, binaries, and evolution over time.
Observational constraints on mergers creating magnetism in massive starsSérgio Sacani
Massive stars (those ≥8 solar masses at birth) have radiative envelopes that cannot sustain the dynamos that produce magnetic fields in lower mass stars. Despite this, ∼7% of massive stars have observed magnetic fields. We use multi-epoch interferometric and spectroscopic observations to characterise a magnetic binary system formed of two massive stars. We find that only one star of the binary is magnetic. Using the non-magnetic star as an independent reference clock to estimate the age of the system, we show that the magnetic star appears younger than its companion. The system properties, and a surrounding bipolar nebula, can be reproduced by a model in which this system was originally a triple within which two of the stars merged, producing the magnetic massive star. Thus, our results provide observational evidence that magnetic fields form in at least some massive stars through stellar mergers.
Third epoch magellanic_clouud_proper_motionsSérgio Sacani
The document analyzes proper motion data from the Hubble Space Telescope to study the three-dimensional rotation field of the Large Magellanic Cloud (LMC) galaxy. It finds that:
1) The proper motion data implies a stellar dynamical center that coincides with the HI dynamical center from previous studies.
2) Combining the proper motion and line-of-sight velocity data provides insights into the LMC's rotation curve, disk viewing angles, and circular rotation speed of 91.7 km/s outside the central region.
3) The data paint a consistent picture of LMC rotation and yield improved constraints on the galaxy's distance, mass profile, and orbital history around the Milky Way.
Detection of solar_like_oscillations_in_relies_of_the_milk_way_asteroseismolo...Sérgio Sacani
Asteroseismic constraints on K giants make it possible to infer radii, masses and ages of tens
of thousands of field stars. Tests against independent estimates of these properties are however
scarce, especially in the metal-poor regime. Here, we report the detection of solar-like
oscillations in 8 stars belonging to the red-giant branch and red-horizontal branch of the globular
cluster M4. The detections were made in photometric observations from the K2 Mission
during its Campaign 2. Making use of independent constraints on the distance, we estimate
masses of the 8 stars by utilising different combinations of seismic and non-seismic inputs.
When introducing a correction to the Δν scaling relation as suggested by stellar models, for
RGB stars we find excellent agreement with the expected masses from isochrone fitting, and
with a distance modulus derived using independent methods. The offset with respect to independent
masses is lower, or comparable with, the uncertainties on the average RGB mass
(4 − 10%, depending on the combination of constraints used). Our results lend confidence to
asteroseismic masses in the metal poor regime. We note that a larger sample will be needed
to allow more stringent tests to be made of systematic uncertainties in all the observables
(both seismic and non-seismic), and to explore the properties of RHB stars, and of different
populations in the cluster.
MUSE sneaks a peek at extreme ram-pressure stripping events. I. A kinematic s...Sérgio Sacani
- MUSE observations of the galaxy ESO137-001 reveal an extended gaseous tail over 30 kpc long traced by H-alpha emission, providing evidence of an extreme ram pressure stripping event as the galaxy falls into the massive Norma galaxy cluster.
- Analysis of the H-alpha kinematics and stellar velocity field show that ram pressure has removed the interstellar medium from the outer disk while the primary tail is still fed by gas from the galaxy center, with gravitational interactions not appearing to be the main mechanism of gas removal.
- The stripped gas retains evidence of the disk's rotational velocity out to around 20 kpc downstream, indicating the galaxy is moving radially along the plane of the sky, while
This document describes observations of the galaxy ESO137-001 using the MUSE instrument on the VLT. The key points are:
1) MUSE observations reveal an extended gas tail stretching over 30 kpc from the galaxy, tracing ongoing ram pressure stripping as it falls into the Norma galaxy cluster.
2) Analysis of the gas kinematics and stellar velocity field show that ram pressure has removed the interstellar medium from the outer disk while the primary tail is still fed by gas from the galaxy center.
3) The stripped gas retains evidence of the disk's rotational velocity out to 20 kpc downstream, indicating the galaxy is moving radially through the cluster. Beyond this the gas shows greater turbulence,
Studies of ngc_6720_with_calibrated_hst_wfc3_emission_line_filter_imagesSérgio Sacani
This study uses calibrated Hubble Space Telescope images of the Ring Nebula (NGC 6720) taken 12.925 years apart to measure tangential motions within the nebula. Individual features were measured in nitrogen emission line images as well as dark knots seen against oxygen emission. The results indicate that the nebula is expanding homologously, but at a faster rate along its major axis. Dark knots were found to expand more slowly than the nebular gas. The tangential motion measurements allow estimates of the nebula's distance and dynamic age to be about 720 pc and 4000 years, respectively.
This document summarizes the results of a deep near-infrared survey of the Carina Nebula complex using the HAWK-I instrument on the VLT. The survey imaged an area of 0.36 square degrees down to magnitudes of J=23, H=22, and Ks=21, detecting over 600,000 infrared sources. Color-magnitude diagrams of the sources were analyzed to determine properties of the low-mass stellar population such as ages and masses. The survey found that about 3200 sources have masses above 1 solar mass, consistent with expectations from the initial mass function. It also found that about half of the young stars in Carina are in a widely distributed, non-clustered configuration. Six
The build up_of_the_c_d_halo_of_m87_evidence_for_accretion_in_the_last_gyrSérgio Sacani
Observações recentes obtidas com o Very Large Telescope do ESO mostraram que Messier 87, a galáxia elíptica gigante mais próximo de nós, engoliu uma galáxia inteira de tamanho médio no último bilhão de anos. Uma equipe de astrônomos conseguiu pela primeira vez seguir o movimento de 300 nebulosas planetárias brilhantes, encontrando evidências claras deste evento e encontrando também excesso de radiação emitida pelos restos da vítima completamente desfeita.
Mapping spiral structure on the far side of the Milky WaySérgio Sacani
Little is known about the portion of the Milky Way lying beyond the Galactic center at distances
of more than 9 kiloparsec from the Sun. These regions are opaque at optical wavelengths
because of absorption by interstellar dust, and distances are very large and hard to measure.
We report a direct trigonometric parallax distance of 20:4þ2:8
2:2 kiloparsec obtained with the Very
Long Baseline Array to a water maser source in a region of active star formation. These
measurements allow us to shed light on Galactic spiral structure by locating the ScutumCentaurus
spiral arm as it passes through the far side of the Milky Way and to validate a
kinematic method for determining distances in this region on the basis of transverse motions.
This document summarizes an article that proposes an alternative explanation for dark energy and dark matter based on a modified theory of gravity. It begins by providing background on dark matter and dark energy in standard cosmology and the evidence that supports their existence. It then outlines the proposed alternative theory, which modifies Einstein's field equations by adding a function of the Ricci scalar. This introduces new curvature terms that could potentially drive accelerated expansion, providing an alternative to dark energy. The theory aims to match observations without requiring dark matter or energy, but reduces to general relativity in the solar system scale where it has been tightly tested.
Water vapour absorption in the clear atmosphere of a Neptune-sized exoplanetGOASA
1) The transmission spectrum of the exoplanet HAT-P-11b was observed using Hubble and Spitzer space telescopes.
2) Water vapor absorption was detected at 1.4 micrometers in the atmosphere, indicating a clear atmosphere down to 1 mbar pressure.
3) The detection of water vapor and relatively large atmospheric scale height places an upper limit on the abundance of heavy elements in the atmosphere of around 700 times the solar value, consistent with core accretion planet formation theories.
Anti-Universe And Emergent Gravity and the Dark UniverseSérgio Sacani
Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional ‘dark’ gravitational force describing the ‘elastic’ response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton’s constant and the Hubble acceleration scale a0 = cH0, and provide evidence for the fact that this additional ‘dark gravity force’ explains the observed phenomena in galaxies and clusters currently attributed to dark matter.
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Gliese 12 b: A Temperate Earth-sized Planet at 12 pc Ideal for Atmospheric Tr...Sérgio Sacani
Recent discoveries of Earth-sized planets transiting nearby M dwarfs have made it possible to characterize the
atmospheres of terrestrial planets via follow-up spectroscopic observations. However, the number of such planets
receiving low insolation is still small, limiting our ability to understand the diversity of the atmospheric
composition and climates of temperate terrestrial planets. We report the discovery of an Earth-sized planet
transiting the nearby (12 pc) inactive M3.0 dwarf Gliese 12 (TOI-6251) with an orbital period (Porb) of 12.76 days.
The planet, Gliese 12 b, was initially identified as a candidate with an ambiguous Porb from TESS data. We
confirmed the transit signal and Porb using ground-based photometry with MuSCAT2 and MuSCAT3, and
validated the planetary nature of the signal using high-resolution images from Gemini/NIRI and Keck/NIRC2 as
well as radial velocity (RV) measurements from the InfraRed Doppler instrument on the Subaru 8.2 m telescope
and from CARMENES on the CAHA 3.5 m telescope. X-ray observations with XMM-Newton showed the host
star is inactive, with an X-ray-to-bolometric luminosity ratio of log 5.7 L L X bol » - . Joint analysis of the light
curves and RV measurements revealed that Gliese 12 b has a radius of 0.96 ± 0.05 R⊕,a3σ mass upper limit of
3.9 M⊕, and an equilibrium temperature of 315 ± 6 K assuming zero albedo. The transmission spectroscopy metric
(TSM) value of Gliese 12 b is close to the TSM values of the TRAPPIST-1 planets, adding Gliese 12 b to the small
list of potentially terrestrial, temperate planets amenable to atmospheric characterization with JWST.
Gliese 12 b, a temperate Earth-sized planet at 12 parsecs discovered with TES...Sérgio Sacani
We report on the discovery of Gliese 12 b, the nearest transiting temperate, Earth-sized planet found to date. Gliese 12 is a
bright (V = 12.6 mag, K = 7.8 mag) metal-poor M4V star only 12.162 ± 0.005 pc away from the Solar system with one of the
lowest stellar activity levels known for M-dwarfs. A planet candidate was detected by TESS based on only 3 transits in sectors
42, 43, and 57, with an ambiguity in the orbital period due to observational gaps. We performed follow-up transit observations
with CHEOPS and ground-based photometry with MINERVA-Australis, SPECULOOS, and Purple Mountain Observatory,
as well as further TESS observations in sector 70. We statistically validate Gliese 12 b as a planet with an orbital period of
12.76144 ± 0.00006 d and a radius of 1.0 ± 0.1 R⊕, resulting in an equilibrium temperature of ∼315 K. Gliese 12 b has excellent
future prospects for precise mass measurement, which may inform how planetary internal structure is affected by the stellar
compositional environment. Gliese 12 b also represents one of the best targets to study whether Earth-like planets orbiting cool
stars can retain their atmospheres, a crucial step to advance our understanding of habitability on Earth and across the galaxy.
The importance of continents, oceans and plate tectonics for the evolution of...Sérgio Sacani
Within the uncertainties of involved astronomical and biological parameters, the Drake Equation
typically predicts that there should be many exoplanets in our galaxy hosting active, communicative
civilizations (ACCs). These optimistic calculations are however not supported by evidence, which is
often referred to as the Fermi Paradox. Here, we elaborate on this long-standing enigma by showing
the importance of planetary tectonic style for biological evolution. We summarize growing evidence
that a prolonged transition from Mesoproterozoic active single lid tectonics (1.6 to 1.0 Ga) to modern
plate tectonics occurred in the Neoproterozoic Era (1.0 to 0.541 Ga), which dramatically accelerated
emergence and evolution of complex species. We further suggest that both continents and oceans
are required for ACCs because early evolution of simple life must happen in water but late evolution
of advanced life capable of creating technology must happen on land. We resolve the Fermi Paradox
(1) by adding two additional terms to the Drake Equation: foc
(the fraction of habitable exoplanets
with significant continents and oceans) and fpt
(the fraction of habitable exoplanets with significant
continents and oceans that have had plate tectonics operating for at least 0.5 Ga); and (2) by
demonstrating that the product of foc
and fpt
is very small (< 0.00003–0.002). We propose that the lack
of evidence for ACCs reflects the scarcity of long-lived plate tectonics and/or continents and oceans on
exoplanets with primitive life.
A Giant Impact Origin for the First Subduction on EarthSérgio Sacani
Hadean zircons provide a potential record of Earth's earliest subduction 4.3 billion years ago. Itremains enigmatic how subduction could be initiated so soon after the presumably Moon‐forming giant impact(MGI). Earlier studies found an increase in Earth's core‐mantle boundary (CMB) temperature due to theaccumulation of the impactor's core, and our recent work shows Earth's lower mantle remains largely solid, withsome of the impactor's mantle potentially surviving as the large low‐shear velocity provinces (LLSVPs). Here,we show that a hot post‐impact CMB drives the initiation of strong mantle plumes that can induce subductioninitiation ∼200 Myr after the MGI. 2D and 3D thermomechanical computations show that a high CMBtemperature is the primary factor triggering early subduction, with enrichment of heat‐producing elements inLLSVPs as another potential factor. The models link the earliest subduction to the MGI with implications forunderstanding the diverse tectonic regimes of rocky planets.
Climate extremes likely to drive land mammal extinction during next supercont...Sérgio Sacani
Mammals have dominated Earth for approximately 55 Myr thanks to their
adaptations and resilience to warming and cooling during the Cenozoic. All
life will eventually perish in a runaway greenhouse once absorbed solar
radiation exceeds the emission of thermal radiation in several billions of
years. However, conditions rendering the Earth naturally inhospitable to
mammals may develop sooner because of long-term processes linked to
plate tectonics (short-term perturbations are not considered here). In
~250 Myr, all continents will converge to form Earth’s next supercontinent,
Pangea Ultima. A natural consequence of the creation and decay of Pangea
Ultima will be extremes in pCO2 due to changes in volcanic rifting and
outgassing. Here we show that increased pCO2, solar energy (F⨀;
approximately +2.5% W m−2 greater than today) and continentality (larger
range in temperatures away from the ocean) lead to increasing warming
hostile to mammalian life. We assess their impact on mammalian
physiological limits (dry bulb, wet bulb and Humidex heat stress indicators)
as well as a planetary habitability index. Given mammals’ continued survival,
predicted background pCO2 levels of 410–816 ppm combined with increased
F⨀ will probably lead to a climate tipping point and their mass extinction.
The results also highlight how global landmass configuration, pCO2 and F⨀
play a critical role in planetary habitability.
Constraints on Neutrino Natal Kicks from Black-Hole Binary VFTS 243Sérgio Sacani
The recently reported observation of VFTS 243 is the first example of a massive black-hole binary
system with negligible binary interaction following black-hole formation. The black-hole mass (≈10M⊙)
and near-circular orbit (e ≈ 0.02) of VFTS 243 suggest that the progenitor star experienced complete
collapse, with energy-momentum being lost predominantly through neutrinos. VFTS 243 enables us to
constrain the natal kick and neutrino-emission asymmetry during black-hole formation. At 68% confidence
level, the natal kick velocity (mass decrement) is ≲10 km=s (≲1.0M⊙), with a full probability distribution
that peaks when ≈0.3M⊙ were ejected, presumably in neutrinos, and the black hole experienced a natal
kick of 4 km=s. The neutrino-emission asymmetry is ≲4%, with best fit values of ∼0–0.2%. Such a small
neutrino natal kick accompanying black-hole formation is in agreement with theoretical predictions.
Detectability of Solar Panels as a TechnosignatureSérgio Sacani
In this work, we assess the potential detectability of solar panels made of silicon on an Earth-like
exoplanet as a potential technosignature. Silicon-based photovoltaic cells have high reflectance in the
UV-VIS and in the near-IR, within the wavelength range of a space-based flagship mission concept
like the Habitable Worlds Observatory (HWO). Assuming that only solar energy is used to provide
the 2022 human energy needs with a land cover of ∼ 2.4%, and projecting the future energy demand
assuming various growth-rate scenarios, we assess the detectability with an 8 m HWO-like telescope.
Assuming the most favorable viewing orientation, and focusing on the strong absorption edge in the
ultraviolet-to-visible (0.34 − 0.52 µm), we find that several 100s of hours of observation time is needed
to reach a SNR of 5 for an Earth-like planet around a Sun-like star at 10pc, even with a solar panel
coverage of ∼ 23% land coverage of a future Earth. We discuss the necessity of concepts like Kardeshev
Type I/II civilizations and Dyson spheres, which would aim to harness vast amounts of energy. Even
with much larger populations than today, the total energy use of human civilization would be orders of
magnitude below the threshold for causing direct thermal heating or reaching the scale of a Kardashev
Type I civilization. Any extraterrrestrial civilization that likewise achieves sustainable population
levels may also find a limit on its need to expand, which suggests that a galaxy-spanning civilization
as imagined in the Fermi paradox may not exist.
Jet reorientation in central galaxies of clusters and groups: insights from V...Sérgio Sacani
Recent observations of galaxy clusters and groups with misalignments between their central AGN jets
and X-ray cavities, or with multiple misaligned cavities, have raised concerns about the jet – bubble
connection in cooling cores, and the processes responsible for jet realignment. To investigate the
frequency and causes of such misalignments, we construct a sample of 16 cool core galaxy clusters and
groups. Using VLBA radio data we measure the parsec-scale position angle of the jets, and compare
it with the position angle of the X-ray cavities detected in Chandra data. Using the overall sample
and selected subsets, we consistently find that there is a 30% – 38% chance to find a misalignment
larger than ∆Ψ = 45◦ when observing a cluster/group with a detected jet and at least one cavity. We
determine that projection may account for an apparently large ∆Ψ only in a fraction of objects (∼35%),
and given that gas dynamical disturbances (as sloshing) are found in both aligned and misaligned
systems, we exclude environmental perturbation as the main driver of cavity – jet misalignment.
Moreover, we find that large misalignments (up to ∼ 90◦
) are favored over smaller ones (45◦ ≤ ∆Ψ ≤
70◦
), and that the change in jet direction can occur on timescales between one and a few tens of Myr.
We conclude that misalignments are more likely related to actual reorientation of the jet axis, and we
discuss several engine-based mechanisms that may cause these dramatic changes.
The solar dynamo begins near the surfaceSérgio Sacani
The magnetic dynamo cycle of the Sun features a distinct pattern: a propagating
region of sunspot emergence appears around 30° latitude and vanishes near the
equator every 11 years (ref. 1). Moreover, longitudinal flows called torsional oscillations
closely shadow sunspot migration, undoubtedly sharing a common cause2. Contrary
to theories suggesting deep origins of these phenomena, helioseismology pinpoints
low-latitude torsional oscillations to the outer 5–10% of the Sun, the near-surface
shear layer3,4. Within this zone, inwardly increasing differential rotation coupled with
a poloidal magnetic field strongly implicates the magneto-rotational instability5,6,
prominent in accretion-disk theory and observed in laboratory experiments7.
Together, these two facts prompt the general question: whether the solar dynamo is
possibly a near-surface instability. Here we report strong affirmative evidence in stark
contrast to traditional models8 focusing on the deeper tachocline. Simple analytic
estimates show that the near-surface magneto-rotational instability better explains
the spatiotemporal scales of the torsional oscillations and inferred subsurface
magnetic field amplitudes9. State-of-the-art numerical simulations corroborate these
estimates and reproduce hemispherical magnetic current helicity laws10. The dynamo
resulting from a well-understood near-surface phenomenon improves prospects
for accurate predictions of full magnetic cycles and space weather, affecting the
electromagnetic infrastructure of Earth.
Extensive Pollution of Uranus and Neptune’s Atmospheres by Upsweep of Icy Mat...Sérgio Sacani
In the Nice model of solar system formation, Uranus and Neptune undergo an orbital upheaval,
sweeping through a planetesimal disk. The region of the disk from which material is accreted by
the ice giants during this phase of their evolution has not previously been identified. We perform
direct N-body orbital simulations of the four giant planets to determine the amount and origin of solid
accretion during this orbital upheaval. We find that the ice giants undergo an extreme bombardment
event, with collision rates as much as ∼3 per hour assuming km-sized planetesimals, increasing the
total planet mass by up to ∼0.35%. In all cases, the initially outermost ice giant experiences the
largest total enhancement. We determine that for some plausible planetesimal properties, the resulting
atmospheric enrichment could potentially produce sufficient latent heat to alter the planetary cooling
timescale according to existing models. Our findings suggest that substantial accretion during this
phase of planetary evolution may have been sufficient to impact the atmospheric composition and
thermal evolution of the ice giants, motivating future work on the fate of deposited solid material.
Exomoons & Exorings with the Habitable Worlds Observatory I: On the Detection...Sérgio Sacani
The highest priority recommendation of the Astro2020 Decadal Survey for space-based astronomy
was the construction of an observatory capable of characterizing habitable worlds. In this paper series
we explore the detectability of and interference from exomoons and exorings serendipitously observed
with the proposed Habitable Worlds Observatory (HWO) as it seeks to characterize exoplanets, starting
in this manuscript with Earth-Moon analog mutual events. Unlike transits, which only occur in systems
viewed near edge-on, shadow (i.e., solar eclipse) and lunar eclipse mutual events occur in almost every
star-planet-moon system. The cadence of these events can vary widely from ∼yearly to multiple events
per day, as was the case in our younger Earth-Moon system. Leveraging previous space-based (EPOXI)
lightcurves of a Moon transit and performance predictions from the LUVOIR-B concept, we derive
the detectability of Moon analogs with HWO. We determine that Earth-Moon analogs are detectable
with observation of ∼2-20 mutual events for systems within 10 pc, and larger moons should remain
detectable out to 20 pc. We explore the extent to which exomoon mutual events can mimic planet
features and weather. We find that HWO wavelength coverage in the near-IR, specifically in the 1.4 µm
water band where large moons can outshine their host planet, will aid in differentiating exomoon signals
from exoplanet variability. Finally, we predict that exomoons formed through collision processes akin
to our Moon are more likely to be detected in younger systems, where shorter orbital periods and
favorable geometry enhance the probability and frequency of mutual events.
Emergent ribozyme behaviors in oxychlorine brines indicate a unique niche for...Sérgio Sacani
Mars is a particularly attractive candidate among known astronomical objects
to potentially host life. Results from space exploration missions have provided
insights into Martian geochemistry that indicate oxychlorine species, particularly perchlorate, are ubiquitous features of the Martian geochemical landscape. Perchlorate presents potential obstacles for known forms of life due to
its toxicity. However, it can also provide potential benefits, such as producing
brines by deliquescence, like those thought to exist on present-day Mars. Here
we show perchlorate brines support folding and catalysis of functional RNAs,
while inactivating representative protein enzymes. Additionally, we show
perchlorate and other oxychlorine species enable ribozyme functions,
including homeostasis-like regulatory behavior and ribozyme-catalyzed
chlorination of organic molecules. We suggest nucleic acids are uniquely wellsuited to hypersaline Martian environments. Furthermore, Martian near- or
subsurface oxychlorine brines, and brines found in potential lifeforms, could
provide a unique niche for biomolecular evolution.
Generating privacy-protected synthetic data using Secludy and MilvusZilliz
During this demo, the founders of Secludy will demonstrate how their system utilizes Milvus to store and manipulate embeddings for generating privacy-protected synthetic data. Their approach not only maintains the confidentiality of the original data but also enhances the utility and scalability of LLMs under privacy constraints. Attendees, including machine learning engineers, data scientists, and data managers, will witness first-hand how Secludy's integration with Milvus empowers organizations to harness the power of LLMs securely and efficiently.
How to Get CNIC Information System with Paksim Ga.pptxdanishmna97
Pakdata Cf is a groundbreaking system designed to streamline and facilitate access to CNIC information. This innovative platform leverages advanced technology to provide users with efficient and secure access to their CNIC details.
Salesforce Integration for Bonterra Impact Management (fka Social Solutions A...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on integration of Salesforce with Bonterra Impact Management.
Interested in deploying an integration with Salesforce for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slackshyamraj55
Discover the seamless integration of RPA (Robotic Process Automation), COMPOSER, and APM with AWS IDP enhanced with Slack notifications. Explore how these technologies converge to streamline workflows, optimize performance, and ensure secure access, all while leveraging the power of AWS IDP and real-time communication via Slack notifications.
How to Interpret Trends in the Kalyan Rajdhani Mix Chart.pdfChart Kalyan
A Mix Chart displays historical data of numbers in a graphical or tabular form. The Kalyan Rajdhani Mix Chart specifically shows the results of a sequence of numbers over different periods.
Building Production Ready Search Pipelines with Spark and MilvusZilliz
Spark is the widely used ETL tool for processing, indexing and ingesting data to serving stack for search. Milvus is the production-ready open-source vector database. In this talk we will show how to use Spark to process unstructured data to extract vector representations, and push the vectors to Milvus vector database for search serving.
Project Management Semester Long Project - Acuityjpupo2018
Acuity is an innovative learning app designed to transform the way you engage with knowledge. Powered by AI technology, Acuity takes complex topics and distills them into concise, interactive summaries that are easy to read & understand. Whether you're exploring the depths of quantum mechanics or seeking insight into historical events, Acuity provides the key information you need without the burden of lengthy texts.
Programming Foundation Models with DSPy - Meetup SlidesZilliz
Prompting language models is hard, while programming language models is easy. In this talk, I will discuss the state-of-the-art framework DSPy for programming foundation models with its powerful optimizers and runtime constraint system.
5th LF Energy Power Grid Model Meet-up SlidesDanBrown980551
5th Power Grid Model Meet-up
It is with great pleasure that we extend to you an invitation to the 5th Power Grid Model Meet-up, scheduled for 6th June 2024. This event will adopt a hybrid format, allowing participants to join us either through an online Mircosoft Teams session or in person at TU/e located at Den Dolech 2, Eindhoven, Netherlands. The meet-up will be hosted by Eindhoven University of Technology (TU/e), a research university specializing in engineering science & technology.
Power Grid Model
The global energy transition is placing new and unprecedented demands on Distribution System Operators (DSOs). Alongside upgrades to grid capacity, processes such as digitization, capacity optimization, and congestion management are becoming vital for delivering reliable services.
Power Grid Model is an open source project from Linux Foundation Energy and provides a calculation engine that is increasingly essential for DSOs. It offers a standards-based foundation enabling real-time power systems analysis, simulations of electrical power grids, and sophisticated what-if analysis. In addition, it enables in-depth studies and analysis of the electrical power grid’s behavior and performance. This comprehensive model incorporates essential factors such as power generation capacity, electrical losses, voltage levels, power flows, and system stability.
Power Grid Model is currently being applied in a wide variety of use cases, including grid planning, expansion, reliability, and congestion studies. It can also help in analyzing the impact of renewable energy integration, assessing the effects of disturbances or faults, and developing strategies for grid control and optimization.
What to expect
For the upcoming meetup we are organizing, we have an exciting lineup of activities planned:
-Insightful presentations covering two practical applications of the Power Grid Model.
-An update on the latest advancements in Power Grid -Model technology during the first and second quarters of 2024.
-An interactive brainstorming session to discuss and propose new feature requests.
-An opportunity to connect with fellow Power Grid Model enthusiasts and users.
Introduction of Cybersecurity with OSS at Code Europe 2024Hiroshi SHIBATA
I develop the Ruby programming language, RubyGems, and Bundler, which are package managers for Ruby. Today, I will introduce how to enhance the security of your application using open-source software (OSS) examples from Ruby and RubyGems.
The first topic is CVE (Common Vulnerabilities and Exposures). I have published CVEs many times. But what exactly is a CVE? I'll provide a basic understanding of CVEs and explain how to detect and handle vulnerabilities in OSS.
Next, let's discuss package managers. Package managers play a critical role in the OSS ecosystem. I'll explain how to manage library dependencies in your application.
I'll share insights into how the Ruby and RubyGems core team works to keep our ecosystem safe. By the end of this talk, you'll have a better understanding of how to safeguard your code.
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdfMalak Abu Hammad
Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
* What is Vector Search?
* Importance and benefits of vector search
* Practical use cases across various industries
* Step-by-step implementation guide
* Live demos with code snippets
* Enhancing LLM capabilities with vector search
* Best practices and optimization strategies
Perfect for developers, AI enthusiasts, and tech leaders. Learn how to leverage MongoDB Atlas to deliver highly relevant, context-aware search results, transforming your data retrieval process. Stay ahead in tech innovation and maximize the potential of your applications.
#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
Driving Business Innovation: Latest Generative AI Advancements & Success StorySafe Software
Are you ready to revolutionize how you handle data? Join us for a webinar where we’ll bring you up to speed with the latest advancements in Generative AI technology and discover how leveraging FME with tools from giants like Google Gemini, Amazon, and Microsoft OpenAI can supercharge your workflow efficiency.
During the hour, we’ll take you through:
Guest Speaker Segment with Hannah Barrington: Dive into the world of dynamic real estate marketing with Hannah, the Marketing Manager at Workspace Group. Hear firsthand how their team generates engaging descriptions for thousands of office units by integrating diverse data sources—from PDF floorplans to web pages—using FME transformers, like OpenAIVisionConnector and AnthropicVisionConnector. This use case will show you how GenAI can streamline content creation for marketing across the board.
Ollama Use Case: Learn how Scenario Specialist Dmitri Bagh has utilized Ollama within FME to input data, create custom models, and enhance security protocols. This segment will include demos to illustrate the full capabilities of FME in AI-driven processes.
Custom AI Models: Discover how to leverage FME to build personalized AI models using your data. Whether it’s populating a model with local data for added security or integrating public AI tools, find out how FME facilitates a versatile and secure approach to AI.
We’ll wrap up with a live Q&A session where you can engage with our experts on your specific use cases, and learn more about optimizing your data workflows with AI.
This webinar is ideal for professionals seeking to harness the power of AI within their data management systems while ensuring high levels of customization and security. Whether you're a novice or an expert, gain actionable insights and strategies to elevate your data processes. Join us to see how FME and AI can revolutionize how you work with data!
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?Speck&Tech
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
1. The M31 Velocity Vector.
II. Radial Orbit Towards the Milky Way
and Implied Local Group Mass
arXiv:1205.6864v1 [astro-ph.GA] 31 May 2012
Roeland P. van der Marel
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218
Mark Fardal
Department of Astronomy, University of Massachusetts, Amherst, MA 01003
Gurtina Besla
Department of Astronomy, Columbia University, New York, NY 10027
Rachael L. Beaton
Department of Astronomy, University of Virginia, PO Box 3818, Charlottesville, VA
22903, USA
Sangmo Tony Sohn, Jay Anderson, Tom Brown
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218
Puragra Guhathakurta
UCO/Lick Observatory, Department of Astronomy and Astrophysics, University of
California at Santa Cruz, 1156 High Street, Santa Cruz, CA 95064
ABSTRACT
We determine the velocity vector of M31 with respect to the Milky Way
and use this to constrain the mass of the Local Group, based on Hubble Space
Telescope proper-motion measurements of three fields presented in Paper I. We
construct N-body models for M31 to correct the measurements for the contri-
butions from stellar motions internal to M31. This yields an unbiased estimate
for the M31 center-of-mass motion. We also estimate the center-of-mass mo-
tion independently, using the kinematics of satellite galaxies of M31 and the
Local Group, following previous work but with an expanded satellite sample.
All estimates are mutually consistent, and imply a weighted average M31 helio-
centric transverse velocity of (vW , vN ) = (−125.2 ± 30.8, −73.8 ± 28.4) km s−1 .
2. –2–
We correct for the reflex motion of the Sun using the most recent insights into
the solar motion within the Milky Way, which imply a larger azimuthal veloc-
ity than previously believed. This implies a radial velocity of M31 with respect
to the Milky Way of Vrad,M31 = −109.3 ± 4.4 km s−1 , and a tangential velocity
Vtan,M31 = 17.0 km s−1 , with 1σ confidence region Vtan,M31 ≤ 34.3 km s−1 . Hence,
the velocity vector of M31 is statistically consistent with a radial (head-on col-
lision) orbit towards the Milky Way. We revise prior estimates for the Local
Group timing mass, including corrections for cosmic bias and scatter, and obtain
MLG ≡ MMW,vir + MM31,vir = (4.93 ± 1.63) × 1012 M⊙ . Summing known esti-
mates for the individual masses of M31 and the Milky Way obtained from other
dynamical methods yields smaller uncertainties. Bayesian combination of the
different estimates demonstrates that the timing argument has too much (cos-
mic) scatter to help much in reducing uncertainties on the Local Group mass,
but its inclusion does tend to increase other estimates by ∼ 10%. We derive a
final estimate for the Local Group mass from literature and new considerations
of MLG = (3.17 ± 0.57) × 1012 M⊙ . The velocity and mass results imply at 95%
confidence that M33 is bound to M31, consistent with expectation from observed
tidal deformations.
Subject headings: galaxies: kinematics and dynamics — Local Group — M31.
1. Introduction
The Milky Way (MW) is a member of a small group of galaxies called the Local Group
(LG). The LG is dominated by its two largest galaxies, the MW and the Andromeda galaxy
(M31). The mass and dynamics of this group have been the topic of many previous studies
(e.g., van den Bergh 2000; van der Marel & Guhathakurta 2008, hereafter vdMG08; Li &
White 2008; Cox & Loeb 2008; and references therein). Analysis of these topics is important
for interpretation of structures inside the LG, such as dark halos, satellite galaxies, and tidal
streams. It is also important for understanding the LG in a proper cosmological context,
since it provides the nearest example of both Large Scale Structure and hierarchical galaxy
formation. While much progress has been made in understanding the LG mass and dynamics,
this has not been based on actual knowledge of the three-dimensional velocity vector of M31.
This is because until now, the proper motion (PM) of M31 has been too small to measure
with available techniques.
In Paper I (Sohn, Anderson & van der Marel 2012) we reported the very first absolute
PMs of M31 stars in three different fields observed with the Hubble Space Telescope (HST):
3. –3–
a field along the minor axis sampling primarily the M31 spheroid (the “spheroid field”), a
field along the major axis sampling primarily the M31 outer disk (the “disk field”), and a
field along M31’s Giant Southern Stream (GSS) sampling primarily the stars that constitute
this stream (the “stream field”). For each field we measured the average PM of the M31 stars
with respect to the stationary reference frame of background galaxies. The results are listed
in Table 1. PMs in mas/yr were converted to velocities (vW , vN ) in km/s in the directions
of West and North using the known distance D of M31. Throughout this paper we adopt
D = 770 ± 40 kpc (see references in vdMG08). The velocity uncertainties are dominated by
the PM uncertainties, with distance uncertainties making only a minimal contribution.
In the present paper we use the observed PMs to determine both the direction and
size of the M31 velocity vector with respect to the MW, and we use this knowledge with
the Local Group timing argument (Kahn & Woltjer 1959; vdMG08; and Li & White 2008)
to estimate the LG mass. We then compare the velocity and mass results to independent
estimates of the same quantities. For example, vdMG08 estimated the transverse motion of
M31 based on the kinematics of satellite galaxies of M31 and the Local Group. Furthermore,
the mass of the Local Group has been estimated independently by adding up the individual
masses of the MW and M31, as estimated from various dynamical tracers (e.g. Klypin et
al. 2002; Watkins et al. 2010). By statistically combining all the results we are able to build
an improved and comprehensive understanding of the dynamics and mass of the LG.
The outline of this paper is as follows. In Section 2 we use N-body models of M31 and its
prominent tidal substructures to calculate predictions for the internal kinematics of M31 stars
in the three fields observed with HST. We use the results to correct the transverse velocities
measured with HST, to estimate the transverse velocity of the M31 center-of-mass (COM).
In Section 3 we revisit the methods of vdMG08 to estimate the M31 transverse motion from
the kinematics of satellites, but with an expanded satellite sample. We combine the results
with the HST measurements to obtain a final estimate for the M31 transverse motion. In
Section 4 we derive the corresponding space motion in the Galactocentric rest frame, taking
into account the latest insights about the solar motion in the MW. The results are consistent
with a radial orbit for M31 towards the MW. In Section 5 we use the M31 motion to estimate
the LG mass using the timing argument. We find that the estimate is quite uncertain due
to cosmic scatter, and we show how a more accurate estimate can be obtained by combining
it with estimates of the individual MW and M31 masses. In Section 6 we consider the
galaxy M33, the third most massive galaxy of the Local Group (van den Bergh 2000), and
we derive its relative velocity with respect to M31. We also derive an estimate for the mass
of M33, and show that M33 is most likely bound to M31, as is usually assumed. We use
this knowledge to further refine our estimate for the Local Group mass. In Section 7 we
discuss and summarize the main results of the paper. An Appendix presents a discussion of
4. –4–
various parameterizations used in the literature (and the paper text) to quantify the dark
halo density profiles and masses of galaxies. Where necessary to compare the properties
of Local Group galaxies with predictions from cosmological simulations, we use a Hubble
constant H0 = 70 km s−1 Mpc−1 and a matter density Ωm = 0.27 (Jarosik et al. 2011).
This is the second paper in a series of three. Paper III (van der Marel et al. 2012, in
prep.) will present a study of the future orbital evolution and merging of M31, M33, and
the MW, using the velocities and masses derived in the present paper as starting conditions.
2. Correction for Internal Kinematics
The PMs measured with HST in M31 fields contain contributions from both the M31
COM motion, and from the internal kinematics of M31. In each field, different fractions
of the stars are contributed by different structural components. Specifically, the galaxy has
different equilibrium components, including both a disk and spheroids (bulge/halo). We will
refer to these jointly as the “base galaxy”. The galaxy also contains material that is in the
process of being accreted. This includes in particular the material responsible for the creation
of the GSS (which in fact is spread out over a large fraction of the projected area of the
galaxy, and not just the actual position of the Stream). To estimate the M31 COM motion,
we need to know for each field observed with HST both the fraction of the stars in each
component, and the transverse motion kinematics of those stars. The fractional contributions
can in principle be estimated purely observationally from line-of-sight (LOS) velocity studies.
However, estimates of the transverse motion kinematics requires a full dynamical model, since
these motions are not directly constrained observationally. We therefore resort to N-body
models for M31 like those previously constructed by some of us (e.g., Geehan et al. 2006;
Fardal et al. 2006, 2007, 2008) to understand various observed features of M31.
2.1. N-body models of M31 Structure
The M31 model we use here is constructed from two separate but related parts. The
base galaxy is an N-body realization of a model of the mass and light in M31 itself. The
GSS component is a snapshot from a dynamical N-body simulation of the formation of the
GSS, performed using the same mass model of M31. Taken together, these two components
reproduce reasonably well the features in M31 that are expected to contribute to our HST
fields.
The base galaxy, which is a slightly altered version of the model from Geehan et
5. –5–
al. (2006), contains bulge, disk, and halo components. The bulge and disk are assumed
to be mostly baryonic and therefore trace the light. To the dark halo present in Geehan
et al. (2006) we add a stellar halo, which is necessary to reproduce the extended power-law
component that has been discovered in the halo regions (Guhathakurta et al. 2005; Irwin
et al. 2005; Kalirai et al. 2006b; Chapman et al. 2006; Ibata et al. 2007). We assume this
stellar halo follows the mass distribution of the dark halo, although it contains only a tiny
fraction of that mass. When added together, these components satisfy the surface-brightness
profiles of M31’s bulge, disk, and halo regions reasonably well. Most importantly for this
study, they also satisfy a series of kinematic constraints, including the disk rotation curve,
the bulge velocity dispersion, and constraints on the halo mass from statistical tracers such
as globular clusters, planetary nebulae, satellite galaxies, and red giant stars. We created
the particle realization of this model using the ZENO library (Barnes 2011).
The GSS component is created by simulating the disruption of a satellite galaxy, in a
fixed potential corresponding to the mass model just discussed. The model is an updated
version of that found in Fardal et al. (2007), to which we refer the reader for a physical
discussion. This model uses a spherical progenitor, although it is possible that the progenitor
may in fact have been a disk galaxy (Fardal et al. 2008). After starting at large radius with
carefully chosen initial conditions, the satellite disrupts at its first pericentric passage. The
model is evolved using the PKDGRAV tree N-body code (Stadel 2001) for nearly 1 Gyr,
until it forms orbital wraps closely resembling features in M31 including the GSS itself, and
the NE and W shelves. We refer to all the particles generated by this component as the GSS
component, regardless of where they are on the sky.
All the parameters of the base model, N-body simulations, and data-model comparisons
are presented in Fardal et al. (2012, in prep.). However, many properties and details are
similar to preceding papers (Geehan et al. 2006; Fardal et al. 2006, 2007, 2008). Besides the
morphological evidence, the GSS model satisfies a set of observational constraints, includ-
ing the detailed kinematic pattern in the W Shelf, the precise sky position of the GSS, the
distance to various fields along the GSS (McConnachie et al. 2003), and their peak LOS ve-
locities (Ibata et al. 2004; Guhathakurta et al. 2006; Kalirai et al. 2006a; Gilbert et al. 2009).
We do not use the observed color-magnitude diagrams (CMDs) of the HST PM fields to con-
strain the models, since those are not easily decomposed into distinct structural components.
In fact, the CMDs of the HST spheroid field and the HST stream field are strikingly similar,
given that they are believed to be dominated by different structural components (Brown et
al. 2006).
Figure 1 shows a smoothed projected view of the N-body model. The GSS is visible
South-East of the galaxy center, and the North-East and Western shelf are emphasized with
6. –6–
dashed outlines. This image can be compared to star-count maps of giant stars in M31,
which show the same features (e.g., Ibata et al. 2005; Gilbert et al. 2009; or Paper I, which
also shows the location of our PM fields). Figure 2 shows a smoothed view of the N-body
model in LOS velocity vs. projected distance space, for particles South-East of the galaxy
center. There is good agreement between the outline of the GSS in this representation (dark
band in the figure), and the observed peak LOS velocity of the GSS as a function of radius
(blue points), including that measured in the HST stream PM field of Paper I (circle).
2.2. Proper-Motion Corrections for HST Fields
The predictions of the N-body model for M31 are summarized in Table 1 for each of
the three HST fields. The quantity fbase is the fraction of the stars that belongs to the base
galaxy, and fGSS is the fraction of the stars that belongs to the GSS. The average velocities
in the LOS, W, and N directions are listed for both the base and the GSS components, and
also for their properly weighted average (“all”). The quantities were extracted over fields
that are somewhat larger than the HST fields (up to 10 arcmin from the field center), to
decrease the N-body shot noise. All velocities are expressed in a reference frame in which
M31 is at rest.
The average internal transverse velocity kinematics of the M31 stars in the HST fields
(vW , vN )(all) are generally small, always below 125 km/s in absolute value. There are several
reasons for this. In the HST spheroid field we are sampling primarily the spheroidal compo-
nents of M31. At large radii these have limited mean rotation (Dorman et al. 2012). In the
HST disk field we are primarily sampling the M31 disk, which has a sizeable circular velocity
(∼ 250 km/s). However, M31 has a large inclination. So along the major axis, most of the
rotation is seen along the LOS, and not in the transverse direction. In the HST stream field
we are primarily sampling the GSS, which has a significant mean three-dimensional velocity
(254 km/s). However, the inclination of the stream is such that most of the velocity is seen
along the LOS. Moreover, some 20% of the stars in the stream field do not belong to the
GSS, but mostly to the spheroid component.
For all three fields, the contribution to the observed transverse motion from the internal
kinematics of M31 is similar to or smaller than the random errors in the HST measurements.
Even significant fractional changes in the model predictions therefore do not strongly affect
our final results. It therefore did not seem worthwhile in the context of the present study
to further refine the model. Nonetheless, it is worth pointing out that the model is far
from perfect, and that there are some salient features of M31 that it fails to reproduce.
For example, the model with a spherical progenitor overestimates the contribution of GSS
7. –7–
particles on their first orbital wrap to fields along the minor axis (especially those more
distant than our spheroid field). Also, LOS velocity studies of the GSS have revealed a
secondary cold component (in addition to the GSS and base galaxy; e.g., Kalirai et al. 2006a;
Gilbert et al. 2007, 2009) which is not reproduced by our model. This could be, e.g., from
a severely warped disk component, or from wrapped-around material of a GSS loop not
included in our model. And finally, some authors have proposed models for the structure
of M31’s outer and accreted components that differ from those in our models (e.g., Ibata et
al. 2005; Gilbert et al. 2007).
To estimate the transverse M31 COM motion from the data for each HST field, we
first subtract the contribution from internal M31 kinematics (v(all)) from the measurement
(v(HST )). We then correct for the effect of viewing perspective as described in van der
Marel et al. (2002) and vdM08. This corrects for the fact that at the position of each field,
the M31 COM systemic LOS and transverse velocity, respectively, are not exactly aligned
along the local LOS and transverse directions. The corrections are small (below 10 km/s
in absolute value), because all fields are located within 2 degrees of the M31 center. The
final estimates are listed in Table 1 as (vW , vN )(COM), and are summarized also at the top
of Table 3. In propagating the uncertainties, we assigned an uncertainty of 20 km/s per
coordinate to the model of the M31 internal kinematics. This number need not be known
accurately, since the final uncertainties are always dominated by measurement errors in the
PMs.
The results for the three different fields are mutually consistent with each other at the
1σ level (see also Paper I1 ). This justifies the use of a straightforward weighted average to
combine the results, which gives (vW , vN )(COM) = (−162.8 ± 47.0, −117.2 ± 45.0) km/s.
For comparison, the direct weighted average of the HST observations, with no corrections for
internal M31 kinematics, is (vW , vN )(HST ) = (−154.1 ± 44.9, −112.9 ± 42.9) km/s. Clearly,
the corrections for internal kinematics make only a small difference for the final transverse
velocity estimate. The fact that the differences are below 10 km/s is due to our combination
of results for well-chosen fields, since the per-field corrections are much larger than this.
3. Transverse Velocity from Satellite Kinematics
In vdMG08 we presented several methods for estimating the space motion of M31 from
the kinematics of satellites, which assume that the satellites of M31 and the LG on average
1
Paper I defines a χ2 quantity, χ3 , that assesses the extent to which measurements for different fields
2
2
agree. Table 3 implies χ3 = 3.5, for NDF = 4 degrees of freedom.
8. –8–
follow their motion through space. The M31 transverse velocity derived in that paper has
random error bars of 34 to 41 km/s. This is somewhat smaller than what we have obtained
here from the HST PM measurements, although the systematic error bars on the vdMG08
values may be larger (because the underlying methodology makes more assumptions). Either
way, these results remain of considerable interest as an independent constraint on the M31
space motion. We therefore update here the results from vdMG08 using additional satellite
data that has become available more recently.
3.1. Constraints from Line-of-Sight Velocities of M31 Satellites
The first method of vdM08 is based on the fact that any transverse motion of M31
induces an apparent solid body rotation in the line-of-sight velocity field of its satellites,
superposed on their otherwise primarily random motions. The amplitude and major axis
of the rotation field are determined by the size and direction of M31’s transverse motion.
In vdM08 we constrained the M31 transverse motion by fitting the velocities of 17 M31
satellites with known line-of-sight velocities.
For the present study we added the satellites listed in Table 2. These are objects that
previously either did not have LOS velocity measurements available, or which had not yet
been discovered. This includes six dSph galaxies: And XI, XIII, XV, XVI, XXI, and XXII.
Three other recently discovered dSph galaxies, And XVII, XIX, XX, have not yet had their
LOS velocities measured. As in vdMG08, we leave out And XII and XIV, because their
large negative LOS velocities with respect to M31 indicate that they may be falling into
M31 for the first time (Chapman et al. 2007; Majewski et al. 2007). We also leave out the
more recently discovered And XVIII, which may be too distant from M31 to be directly
associated with it (McConnachie et al. 2008). We do include And XXII, even though it
may be a satellite of M33 rather than M31 (Martin et al. 2009; Tollerud et al. 2012). We
note that And IV is not included in our combined sample because it is a background galaxy
(Ferguson et al. 2000), while And VIII is not a galaxy at all (Merrett et al. 2006). For all
dSphs, including those from Paper I and not listed in Table 2, we used the newly measured
LOS velocities from Tollerud et al. (2012), where available. Otherwise, the values listed in
Paper I or the sources listed in Table 2 were used. Our new sample in Table 2 also includes
the 8 globular clusters of M31 that lie at projected distances > 40 kpc and have known LOS
velocities.
We repeated the vdMG08 analysis, using the combined sample of the 17 satellites in
Table 1 of vdMG08 and the 14 satellites in Table 2. The implied space motion of M31 is
listed in Table 3 in the row labeled “M31 satellites”. The result for (vW , vN ) differs from that
9. –9–
derived in vdMG08 by (−40.1, 13.4) km/s. This is considerably smaller than the error bars
in the result of (144.1, 85.4) km/s. The addition of the 14 new satellites has not decreased
the error bars on the result. This is in part because most satellites are observed relatively
close to M31, so that any solid-body rotation signal would be small. As before, the new
result is roughly consistent at the 1σ level with zero transverse motion. So no solid-body
rotation component is confidently detected, which in turn implies that M31 cannot have a
very large transverse motion. The fits imply a one-dimensional velocity dispersion for the
satellite sample of σsat = 84.8 ± 10.6 km/s. This is 8.5 km s−1 larger than the value derived
in vdMG08, which again is within the uncertainties.
3.2. Constraints from Proper Motions of M31 Satellites
The second method of vdM08 is based on the M31 satellites M33 and IC 10. These
galaxies have accurately known PMs from water-maser observations (Brunthaler et al. 2005,
2007). The three-dimensional velocity vectors of these galaxies give an estimate of the M31
space motion to within an accuracy of σsat per coordinate. Transplanting the M33 and IC
10 velocity vectors to the position of M31, followed by projection onto the local LOS, W,
and N directions, yields the results listed in Table 3 in the rows labeled “M33 PM” and
“IC 10 PM”. These are identical to what was derived in vdMG08, but with slightly larger
uncertainties (due to the increased estimate of σsat ).
3.3. Constraints from Line-of-Sight Velocities of Outer Local Group Galaxies
The third method of vdMG08 is based on the line-of-sight velocities of Local Group
satellites that are not individually bound to the MW or M31. In vdMG08 the method
was applied to 5 satellites (see their Table 2). The Cetus dSph (RA= 6.54597◦, DEC=
−11.04432◦) was excluded because of lack of knowledge of its LOS velocity at the time. For
the present study we have rerun the analysis including Cetus, using vLOS = −87 ± 2 km/s
from Lewis et al. (2007). Its distance D = 755 ± 23 kpc (McConnachie et al. 2005) places
Cetus at Dbary ≈ 600 kpc from the Local group barycenter. With addition of the Cetus dSph
to the vdMG08 analysis, the implied space motion of M31 is listed in Table 3 in the row
labeled “Outer LG Galaxies”. The result for (vW , vN ) differs from that derived in vdMG08
by (−14.9, −13.5) km/s. This is considerably smaller than the error bars in the result of
(58.0, 52.5) km/s.
10. – 10 –
3.4. Comparison and Combination of Constraints
In general, modeling of satellite galaxy dynamics can be complicated for a variety of
reasons, especially when the goal is to estimate galaxy masses: the satellite system may not
be virialized, with continueing orbital evolution (Mateo et al. 2008) or infall (e.g., Chapman
et al. 2007; Majewski et al. 2007); the distribution of satellite orbits may not be isotropic
(e.g., Watkins et al. 2010); satellites on large-period orbits are not expected to be randomly
distributed in orbital phase (e.g., Zaritsky & White 1994); satellites may have correlated
kinematics (e.g., van den Bergh 1998); and the three-dimensional distribution of satellites
may not be spherical (Koch & Grebel 2006) or symmetric (McConnachie & Irwin 2006).
However, many of these potential issues do not affect the analysis that we have presented here
and in vdMG08 to estimate the M31 transverse velocity. Sections 3.1 and 3.2 only assume
that the M31 satellites are drawn from a distribution that has the same mean velocity as
M31, and which has no mean rotation. Section 3.3 only assumes that the LG satellites are
drawn from a distribution that has the same mean velocity as the LG barycenter. Virialized
equilibrium, isotropy, random phases, or symmetry are not required. Nonetheless, there
is always the possibility that residual systematics may have affected the results. To get a
handle on this, we have compared in detail the results for the M31 transverse velocity from
the different techniques.
The (vW , vN ) for M31 inferred from the different methods in Sections 3.1–3.3 are in
mutual agreement to within the uncertainties. The same was true also in the original analysis
of vdMG08. Since the methods and the underlying data are quite different for the various
estimates, this in itself is a direct indication that any residual systematics cannot be large.
Since the results from the different methods are in agreement, it is reasonable to take their
weighted average, as listed in Table 3. The result for (vW , vN ) differs from that derived in
vdMG08 by (−19.0, −7.1) km/s. This is considerably smaller than the error bars in the
result of (40.7, 36.6) km/s, so the new analysis presented here has not significantly altered
the results previously derived by vdMG08.
An even stronger check on any residual systematics is provided by Figure 3. It compares
the weighted average of the HST PM measurements (with corrections for internal kinematics)
from Section 2 (as listed in Table 3) with the weighted average from the updated vdMG08
analysis. The difference between these results is (∆vW , ∆vN ) = (−65.8 ± 62.2, −72.1 ± 58.0).
This means that the results are consistent within the uncertainties: the probability of a
residual this large occurring by chance in a two-dimensional Gaussian distribution is 26%.
Since the methods employed are totally different, and have quite different scopes for possible
systematic errors, this is very successful agreement. This suggests not only that there are
no large residual systematics in the results from the satellite kinematics, but also that there
11. – 11 –
are no large residual systematics in the M31 PM analysis. This is a very important cross-
check, since the displacements on which our PM measurements are based are below 0.01
detector pixels (see Paper I for a detailed discussion of the systematic error control in the
PM analysis).
Since the HST PM analysis and the satellite kinematics analysis yield statistically con-
sistent results for the M31 transverse velocity, it is reasonable to take the weighted average
of the results from the two methodologies. This yields
(vW , vN ) = (−125.2 ± 30.8, −73.8 ± 28.4) km s−1 , (1)
as listed in the bottom row of Table 3 and shown in black in Figure 3. This is the final result
that we use for the remainder of our analysis.
4. Space Motion
4.1. Galactocentric Rest Frame and Solar Motion
As in vdMG08, we adopt a Cartesian coordinate system (X, Y, Z), with the origin
at the Galactic Center, the Z-axis pointing towards the Galactic North Pole, the X-axis
pointing in the direction from the Sun to the Galactic Center, and the Y -axis pointing in the
direction of the Sun’s Galactic rotation. We choose the origin of the frame to be at rest (the
Galactocentric rest frame), and we wish to calculate the velocity of galaxies in this frame.
This requires knowledge of the solar velocity in the Milky Way, since the solar reflex motion
contributes to any observed velocities (such as the heliocentric velocities listed in Table 3).
In vdMG08 we adopted the standard IAU values (Kerr & Lynden-Bell 1986) for the
distance of the Sun from the Galactic Center R0 = 8.5 kpc, and the circular velocity of the
Local Standard of Rest (LSR), V0 = 220 km/s. Neither of these quantities has historically
been known particularly accurately though, and their exact values continue to be debated.
Recently, a number of new methodologies have become available. These provide new insights
into R0 and V0 , and we therefore use the results from these studies here.
Some of the best constraints on R0 now come from studies of the orbits of stars around
the Sgr A* supermassive black hole. Gillessen et al. (2009) obtained R0 = 8.33 ± 0.35 kpc
(consistent also with Ghez et al. 2008). Most of the available constraints on the velocity V0
are actually constraints on the ratio V0 /R0 . The best constraint on this ratio now comes
from the observed PM of Sgr A*, since the black hole is believed to be at rest in the
galaxy to within ∼ 1 km/s. Reid & Brunthaler (2004) obtained that (V0 + Vpec )/R0 =
30.2 ±0.2 km s−1 kpc−1 . Here Vpec is the peculiar velocity of the Sun in the rotation direction.
12. – 12 –
In vdMG08 we adopted the solar peculiar velocity from Dehnen & Binney (1998). However,
there is now increasing evidence that Vpec from that study (and other studies) is too small
by ∼ 7 km/s. We adopt here the more recent estimates from Sch¨nrich, Binney, & Dehnen
o
(2010): (Upec , Vpec , Wpec ) = (11.1, 12.24, 7.25), with uncertainties of (1.23, 2.05, 0.62) km s−1
(being the quadrature sum of the random and systematic errors). Combination of these
results implies that V0 = 239.3 ± 10.3 km/s, significantly larger than the canonical IAU
value of 220 km/s. The uncertainty is dominated entirely by the uncertainty in R0 , and the
errors in V0 and R0 are highly correlated.
Observations of masers in high-mass star-formation regions in the MW have been used to
argue independently for a value of V0 in excess of the canonical 220 km s−1 (Reid et al. 2009).
However, McMillan & Binney (2010) showed that these data by themselves do not strongly
constrain the Galactic parameters. On the other hand, McMillan (2011) showed that when
combined with the other constraints described above through detailed models, the maser data
do help to constrain R0 more tightly, and therefore V0 . He obtained: R0 = 8.29 ± 0.16 kpc
and V0 = 239 ± 5 km/s. These are the values we adopt here.
4.2. M31 Space Motion
Based on the adopted M31 distance and solar parameters, the position of M31 in the
Galactocentric rest frame is
rM31 = (−378.9, 612.7, −283.1) kpc. (2)
The velocity of the Sun projects to (vsys , vW , vN )⊙ = (191.9, 142.5, 78.5)km s−1 at the position
of M31. Since one observes the reflex of this, these values must be added to the observed
M31 velocities to obtain its velocity in the Galactocentric rest frame. The velocity vector
corresponding to the observed COM LOS velocity vLOS = −301 ± 1 km s−1 (vdMG08) and
the final weighted average (vW , vN ) given in Table 3, transformed to the Galactocentric rest
frame, is then
vM31 = (66.1 ± 26.7, −76.3 ± 19.0, 45.1 ± 26.5) km s−1 . (3)
The errors (which are correlated between the different components) were obtained by prop-
agation of the errors in the individual position and velocity quantities (including those for
the Sun) using a Monte-Carlo scheme.
If the transverse velocity of M31 in the Galactocentric rest frame, Vtan , equals zero, then
M31 moves straight towards the Milky Way on a purely radial (head-on collision) orbit. This
orbit has (vW , vN )rad = (−141.5 ± 3.0, −78.8 ± 1.7) km s−1 (this is approximately the reflex
of the velocity of the Sun quoted above, because the lines from the Sun to M31 and from the
13. – 13 –
Galactic Center to M31 are almost parallel). The listed uncertainty is due to propagation
of the uncertainties in the solar velocity vector. The radial orbit is indicated as a starred
symbol in Figure 3. The velocity vM31 calculated in the previous paragraph corresponds to
a total velocity
|VM31| = 110.6 ± 7.8 km s−1 . (4)
The radial velocity component is
Vrad,M31 = −109.2 ± 4.4 km s−1 , (5)
and the tangential velocity component is
Vtan,M31 = 17.0 km s−1 (1σ confidence region : Vtan,M31 ≤ 34.3 km s−1 ). (6)
The uncertainties were calculated as in vdMG08, using a flat Bayesian prior probability for
Vtan . These results imply that the velocity of M31 is statistically consistent with a radial
orbit at the 1σ level.2
It has been known for a long time that the transverse velocity of M31 is probably
Vtan,M31 200km s−1 . The large scale structure outside the LG does not provide enough tidal
torque to have induced a much larger transverse motion, subsequent to the radial expansion
started by the Big Bang (Gott & Thuan 1978; Raychaudhury & Lynden-Bell 1989). Li &
White (2008) used the ΛCDM cosmological Millenium simulation to identify some thousand
galaxy pairs that resemble the MW-M31 pair in terms of morphology, isolation, circular
velocities, and radial approach velocity. The median tangential velocity of the pairs was
Vtan = 86km s−1 , with 24% of the pairs having Vtan < 50km s−1 (see their figure 6). Therefore,
the observed M31 tangential velocity is somewhat below average compared to cosmological
expectation, but it is not unusually low. The exact reason why the tangential velocity of the
MW-M31 pair has ended up below-average is not clear, but it may be related to the details
of the growth history and the local environment of the LG.
Peebles et al. (2001) showed that at values Vtan,M31 200 km s−1 , many velocities can be
consistent with the observed positions and velocities of galaxies in the nearby Universe. Our
new observational result that Vtan,M31 ≤ 34.3 km s−1 at 1σ confidence therefore significantly
reduces the parameter space of possible orbits. Peebles et al. (2011) recently proposed
a model for the history and dynamics of the LG in which Vtan,M31 = 100.1 km s−1 and
(vW , vN ) = (−240.5, −63.1) km s−1 . This is inconsistent with our final velocity estimates at
> 3σ confidence.
2
If the IAU value V0 = 220 km/s is used for the LSR circular velocity and the Dehnen & Binney
(1998) values are used for the solar peculiar velocity (as in vdMG08), then a radial orbit has (vW , vN )rad =
(−126.6, −71.4) km s−1 . With these assumptions, the inferred velocity of M31 is still statistically consistent
with a radial orbit at the 1σ level.
14. – 14 –
5. Local Group Mass
The velocity vector of M31 with respect to the Milky Way constrains the mass of the
Local Group through the so-called “timing argument” (Kahn & Woltjer 1959; Lynden-Bell
1981, 1999; Einasto & Lynden-Bell 1982; Sandage 1986; Raychaudhury & Lynden-Bell 1989;
Kroeker & Carlberg 1991; Kochanek 1996). Recent applications of this method were pre-
sented in vdMG08 and Li & White (2008). In Section 5.1 we provide a revised estimate
of the Local Group timing mass using the new insights into the M31 velocity vector from
Section 4.2. In Section 5.2 we combine the result in statistical fashion with results from
other independent methods for constraining the Local Group mass.
Different studies often quote different mass quantities. However, for proper use and
comparison it is important to transform all measurements to a common definition. For each
galaxy, the total mass is dominated by a very extended dark halo. Common characterizations
of dark matter halos are summarized in Appendix A. The density profile is often modeled as
an NFW profile (Navarro et al. 1997; eq. [A2]) or a Hernquist (1990; eq. [A8]) profile. The
former has infinite mass, while the latter has finite mass MH . Common characterizations of
halo masses also include the virial mass Mvir enclosed within radius rvir (eq. [A1]), the mass
M200 enclosed within the radius r200 (eq. [A5]), or the mass M(r) enclosed within some given
physical radius r in kpc (eqs. [A3,A9]).
In our discussion of galaxy masses, we transform all results into Mvir estimates. The
transformation requires knowledge of the density profile, which for this purpose we assume
to be of the NFW form with known concentration cvir (eq. [A3]). For the MW and M31 we
take cvir = 10 ± 2, based on a combination of specific models (Klypin et al. 2002; Besla et
al. 2007), and cosmological simulation results (Neto et al. 2007; Klypin et al. 2011). This
implies M200 /Mvir = 0.839 ± 0.014 (eq. [A7]).
5.1. Timing Argument
Under the assumption of Keplerian motion, the relative orbit of M31 and the MW
is determined by four parameters: the total mass Mtot ; the semi-major axis length a (or
alternatively, the orbital period T ); the orbital eccentricity e; and the current position within
the orbit, determined by the eccentric anomaly η. In turn, four observables are available to
constrain the orbit: the current M31 distance D; the radial and tangential M31 velocities in
the Galactocentric rest frame, Vrad,M31 and Vtan,M31 ; and the time t since the last pericenter
passage, which should be equal to the age of the Universe t = 13.75 ± 0.11 Gyr (Jarosik et
al. 2011; when the matter of both galaxies originated together in the Big Bang). There are
15. – 15 –
as many observables as unknowns, so the orbital parameters and MLG can be determined
uniquely. The implied value of Mtot is called the “timing mass”. Most commonly, the relevant
equations are solved under the assumption of a radial orbit (e = 1 and Vtan,M31 = 0), but
this assumption is not necessary when a measurement of Vtan,M31 is actually available (e.g.,
vdMG08).
For the M31 space motion derived above, the “timing mass” Mtot,timing = (4.27 ±0.53) ×
12
10 M⊙ . When a radial orbit is assumed (which is consistent with the data) then Mtot,timing =
(4.23 ± 0.45) × 1012 M⊙ (this is somewhat smaller, because any transverse motion increases
the timing mass). The listed uncertainties are the RMS scatter of Monte-Carlo simulations
as in vdMG08, which take into account all the observational uncertainties. The black curve
in the top panel of Figure 4 shows the complete probability histogram for the radial orbit
case.
These timing mass results are about 1.0–1.3 × 1012 M⊙ lower than what was obtained
by, e.g., vdMG08 and Li & White (2008). This can be viewed as an improvement, since
previous estimates of Mtot appeared anomalously high compared to independent estimates
of the masses of the individual M31 and MW galaxies (as summarized in vdMG08). Some
of the decrease in timing mass is due to the fact that Vtan,M31 found here is slightly smaller
than in vdMG08. However, most of the decrease in timing mass is not due to the new HST
measurements, but due to the new values for the solar motion used here. The solar velocity
in the Y -direction, vY = V0 + Vpec , is 251.2 km/s in our calculations here. By contrast, it was
26 km/s lower in the calculations of vdMG08. The Y component of the solar motion projects
predominantly along the LOS direction towards M31, and not the W and N directions. The
component of the solar motion in the LOS direction is therefore 20.2 km/s higher than what
it was in vdMG08. As a consequence, in the Galactocentric rest frame, M31 approaches
the MW with a radial velocity that is 20.2 km/s slower than what is was in vdMG08. This
slower approach implies a lower timing mass.
The timing argument equations are based on a simple Keplerian formalism. To assess
how accurate this argument is in a cosmological context one must make comparisons to N-
body simulations (Kroeker & Carlberg 1991). Li & White (2008) did this for the currently
favored ΛCDM cosmology, using results from the Millennium simulation. They identified
simulated galaxy pairs like the MW-M31 system, with known masses, and quantified the
accuracy of the radial orbit timing argument. They found that the timing argument has
very little bias, when viewed as an estimate of the sum Mtot,200 of the galaxy’s M200 values,
but significant scatter. They quantified this “cosmic scatter”, by averaging over pairs with
all possible transverse velocities. However, not surprisingly, their Figure 6 shows that the
scatter increase with Vtan . Since we now know that M31 actually has a low value of Vtan , it
16. – 16 –
is more appropriate to quantify the cosmic scatter by restricting the statistics to pairs in the
simulation with low Vtan . We measured by hand from their Figure 6 all pairs with Vtan ≤ 50
km/s, and extracted the ratio Mtot,200 /Mtot,timing . We folded the probability distribution of
these ratios into our Monte-Carlo scheme for estimating the total mass from the radial orbit
timing argument. This yields the estimate Mtot,200 = (4.14 ± 1.36) × 1012 M⊙ , which has a
three times larger uncertainty than what is implied by observational errors alone. This can
be converted into an estimate for the summed virial masses using to formulae of Appendix A,
which yields
Mtot,vir = (4.93 ± 1.63) × 1012 M⊙ (timing argument). (7)
This is our final estimate from the timing argument, which takes into account observational
uncertainties, cosmic bias, and cosmic scatter. The red curve in the top panel of Figure 4
shows the complete probability histogram for Mtot,vir .
5.2. Combination with Other Milky Way and M31 Mass Constraints
The best alternative method for estimating the mass of the Local Group is to add up
estimates of the masses of the individual M31 and MW galaxies.3 Estimates for the masses
of these galaxies were already summarized in vdMG08, so here we highlight primarily some
more recent results.
Watkins et al. (2010) studied the kinematics of M31 satellites and found that the mass
within 300 kpc is determined fairly robustly, MM31 (300 kpc) = (1.40 ± 0.43) × 1012 M⊙ . The
quoted uncertainty is the quadrature sum of the random error of 0.40 × 1012 M⊙ , and a sys-
tematic uncertainty of 0.15×1012 M⊙ due to the assumed velocity anisotropy of the satellites.
There may be other systematic uncertainties in the analysis, but these are more difficult to
quantify and are neglected here. At this mass and with the relevant halo concentrations,
M(300kpc)/Mvir = 1.018±0.002 (see Appendix A). Hence, MM31,vir = (1.38±0.43)×1012 M⊙ .
We use this to set a Gaussian probability distribution for MM31,vir in our discussion below
(blue curve in top panel of Figure 4). This is consistent with the study of Klypin et al. (2002),
which folded in a wider range of observational constraints, and obtained successful models
with dark halo masses MM31,dark,vir of either 1.43 × 1012 M⊙ or either 1.60 × 1012 M⊙ . This
corresponds to a total mass of MM31,vir = 1.52 × 1012 M⊙ or 1.69 × 1012 M⊙ , respectively,
after adding in also the combined stellar mass of the M31 disk and bulge. The Watkins et
3
The other method of estimating Mtot from the size of the Local Group turn-around radius yields esti-
mates that tend to be biased low. A radial infall model is generally assumed, which is almost certainly an
oversimplification (see vdMG08).
17. – 17 –
al. results are also consistent with the recent results of Tollerud et al. (2012). They applied
a mass estimator calibrated on cosmological simulations to the M31 satellite kinematics and
obtained MM31,vir = 1.2+0.9 × 1012 M⊙ .
−0.7
Watkins et al. (2010) showed that mass estimates for the mass of the MW from satellite
kinematics are much more uncertain. This is due to the unknown velocity anisotropy, com-
bined with the fact that we see most satellites almost radially from near the Galactic Center.
Good mass estimates therefore need to fold in a more diverse set of observational constraints.
Moreover, uncertainties are reduced significantly by assuming that the radial profile of the
dark matter is known, and follows a cosmologically motivated parameterization. McMillan
(2011) used such methods to obtain a dark halo mass MMW,dark,200 = (1.26 ± 0.24) × 1012 M⊙ .
This corresponds to MMW,dark,vir = (1.50 ± 0.29) × 1012 M⊙ . This is consistent with the study
of Klypin et al. (2002), who favored MMW,dark,vir = 1.0×1012 M⊙ , but showed that reasonable
models with MMW,dark,vir = 2.0 × 1012 M⊙ can be constructed as well. Adding the combined
stellar mass of the MW disk and bulge to obtain the total MMW,vir adds ∼ 0.06 × 1012 to
these values. The rapid motion of the Magellanic Clouds and Leo I have been used to argue
for masses at the high end of this range of values (e.g., Zaritsky et al. 1989; Shattow &
Loeb 2008; Li & White 2008; Boylan-Kolchin et al. 2011). However, the underlying assump-
tions in these arguments cause significant uncertainties. Based on the range of results in
the literature, we adopt here, fairly arbitrarily, a flat probability distribution for MMW,vir
between 0.75 and 2.25 × 1012 M⊙ (green curve in top panel of Figure 4). This distribution
has the same mean (1.50 × 1012 M⊙ ) as inferred by McMillan (2011), and the same dispersion
(0.43 × 1012 M⊙ ) as we use for M31, but with a broader, flatter shape.4
We use the listed probability distributions for the individual M31 and MW masses
as priors; this also sets a prior probability distribution for Mtot,vir ≡ MM31,vir + MMW,vir
(magenta curve in top panel of Figure 4). We then fold in the timing argument results
to determine posterior probability distributions, as follows. We draw a random mass from
the probability distribution for Mtot,vir derived from the timing argument (red curve in top
panel of Figure 4). We then draw a random MMW,vir from its prior distribution. We then
calculate the corresponding MM31,vir = Mtot,vir − MMW,vir , and its probability p given the
prior distribution for MM31,vir . This set of values is then accepted or rejected in Monte-Carlo
4
There do exist models in the literature that yield or use higher mass estimates for M31 and the MW
than we use here. This includes estimates based on halo occupation distributions (e.g., Guo et al. 2010) or
the timing argument (e.g., Loeb et al. 2005; Cox & Loeb 2008). It should be kept in mind though that such
estimates are statistical in nature. Cosmic scatter must therefore be taken into account, and this yields large
uncertainties (e.g., Li & White 2008; Guo et al. 2010). It is therefore important that any mass estimate for
an individual galaxy, as opposed to an ensemble of galaxies, also take into account the actually observed
resolved properties, rotation curves, and satellite kinematics.
18. – 18 –
sense, depending on the probability p. We thus build up posterior probability distributions
for MMW,vir , MM31,vir , and Mtot,vir , which are shown as dotted lines with the same colors in
the bottom panel of Figure 4.
The posterior distribution for MM31,vir is still roughly Gaussian, but its average has
increased from (1.38 ± 0.43) × 1012 M⊙ to (1.51 ± 0.42) × 1012 M⊙ . The posterior distribution
for MMW,vir is not flat like its prior, but skewed towards higher masses. Its average has
increased from 1.50 to 1.63 × 1012 M⊙ . The likelihood of MW and M31 masses at the low
end of the prior distributions is significantly reduced in the posterior distributions. This is
relevant, since some previously reported mass estimates do fall on this low-mass end (e.g.,
Evans et al. 2000; Ibata et al. 2004). At the best-estimate virial masses for the MW and
M31, the corresponding virial radii are 308 kpc and 300 kpc, respectively (eq. [A1]). Since
the distance between the galaxies is D = 770 ± 40 kpc, the virial spheres are not currently
overlapping.
The prior distribution for Mtot,vir corresponds to (2.88 ± 0.61) × 1012 M⊙ , while its
posterior distribution corresponds to (3.14 ± 0.58) × 1012 M⊙ . Therefore, inclusion of the
timing argument increases the estimate of the LG mass by only ∼ 9%, due to the large
cosmic variance. Since this is considerably smaller than the prior uncertainties on MMW,vir
and MM31,vir , the timing argument does not in fact help much to constrain the total LG
mass, beyond what we already know from the MW and M31 individually. We have found
this to be a robust conclusion, independent of the exact probability distributions adopted
for M31 and the MW, and independent of the exact solar and M31 motion adopted in the
timing argument.
6. Mass Constraints from M33
The galaxy M33 is the most massive companion of M31 (e.g., van den Bergh 2000).
In the past decade, evidence has been found from both HI (Braun & Thilker 2004) and
star-count maps (McConnachie et al. 2009) for tidal features indicative of past interactions
between these galaxies. Models for these features such as those presented by McConnachie et
al. (2009) require that M33 be bound to M31.5 The galaxy M33 is one of the few galaxies in
the Local Group for which an accurate PM measurement is available from VLBA observations
of water masers. Hence, combined with our new M31 results, the relative motion of M33
with respect to M31 is now known with reasonable accuracy (Section 6.1). The mass of M33
5
While the MW also has a massive companion, namely the Large Magellanic Cloud, it is unclear whether
the galaxies in this pair form a bound system (Besla et al. 2007).
19. – 19 –
can also be estimated independently (Section 6.2). With knowledge of the relative velocity
and mass, the assumption that M33 is bound to M31 can be used to further refine our
understanding of the M31 mass, and hence the Local Group mass (Section 6.3).
6.1. M33 Space Motion
To establish the binding energy of the M31-M33 system, we need to know the cur-
rent position rM33 and velocity vM33 of M33 in the Galactocentric rest frame. These were
determined in similar fashion as for M31 (see Section 4.2), but now based on the following
observables: a distance DM33 = 794 ±23 kpc (McConnachie et al. 2004), line-of-sight velocity
vlos,M33 = −180 ± 1 km s−1 (vdMG08), and PM from water masers as measured by Brun-
thaler et al. (2005) and discussed in vdMG08. This yields rM33 = (−476.1, 491.1, −412.9)kpc,
and vM33 = (43.1 ± 21.3, 101.3 ± 23.5, 138.8 ± 28.1) km s−1 . The observational errors in the
Galactocentric velocity of M33 are similar to those for M31 reported in Section 4.2.
The positions of the three galaxies MW, M31 and M33 define a plane in the Galacto-
centric rest frame. For simplicity, we will refer to this plane as the “trigalaxy plane”. It is of
interest for understanding the orbital evolution of the MW-M31-M33 system, to know how
the M33 velocity vector is oriented with respect to this plane. To assess this, we introduce a
new Cartesian coordinate system (X ′ , Y ′ , Z ′ ) based on the following definitions: the frame
has the same origin as the (X, Y, Z) system (i.e., the Galactic Center); the X ′ -axis points
from the origin to M31 at t = 0; the Y ′ -axis is perpendicular to the X ′ -axis, and points from
M31 to M33 as seen in projection from the Galactic Center; and the Z ′ -axis is perpendicular
to the X ′ - and Y ′ -axes in a righthanded sense. With these definitions, the trigalaxy plane is
the (X ′ , Y ′ ) plane. Hence, let us refer to the (X ′ , Y ′ , Z ′ ) system as the “trigalaxy coordinate
system”.
Based on the position vectors rM31 and rM33 from Sections 4.2 and 6.1, the unit vectors
of the (X ′ , Y ′ , Z ′ ) system can be expressed in (X, Y, Z) coordinates as
uX ′ = (−0.48958, 0.79153, −0.36577),
uY ′ = (−0.47945, −0.60013, −0.64029),
uZ ′ = (−0.72632, −0.13810, 0.67331). (8)
If r is a vector expressed in Galactocentric (X, Y, Z) coordinates, then the corresponding
vector r ′ expressed in the trigalaxy coordinate system is
r ′ = (X ′ , Y ′ , Z ′) = (r · uX ′ , r · uY ′ , r · uZ ′ ), (9)
20. – 20 –
where · denotes the vector inner product. We use equations (8,9) as the fixed definition of
the (X ′ , Y ′ , Z ′ ) system throughout this paper, even when we vary the positions of the Sun,
M31, and M33 within their observational uncertainties.
Observational uncertainties of ∼ 20–30km s−1 aside, the velocities of M31 and M33 in tri-
galaxy coordinates are vM31 = (−109.2, −15.5, −7.1)km s−1 and vM33 = (8.3, −170.3, 48.2)km s−1 .
′ ′
These vectors make angles with the (X ′ , Y ′ ) plane of only −3.7◦ and 15.8◦ , respectively. By
definition, the MW galaxy currently has zero velocity in the Galactocentric rest frame. How-
ever, the gravitational attraction from M31 and M33 will set it in motion with a velocity
directed in the (X ′ , Y ′ ) plane. Hence, all three galaxies start out in the (X ′ , Y ′ ) plane,
with velocity vectors that are close to this plane. This implies that the orbital evolution of
the entire MW-M31-M33 system will happen close to the trigalaxy plane, with the “verti-
cal” Z ′ -component playing only a secondary role. Detailed calculations of the future orbital
evolution and merging of the MW-M31-M33 system are the topic of Paper III.
6.2. M33 Mass
The mass of M33 is not negligible with respect to that of M31. It is therefore necessary
to know the mass of M33 to determine whether the M31-M33 system is bound. Corbelli
(2003) modeled the rotation curve and mass content of M33. The rotation curve rises to
∼ 130 km s−1 out to the last data point at 15 kpc. Since the data do not reveal a turnover
in the rotation curve, both the halo concentration and virial mass are poorly constrained
(Fig. 6b of Corbelli 2003). Moreover, the rotation field is complex with significant twisting
(Corbelli & Schneider 1997). This complicates interpretation in terms of circular motion.
To estimate the M33 virial mass it is therefore necessary to use more indirect arguments.
For this, we compare M33 to M31.
Corbelli (2003) used her rotation curve fits to estimate the mass-to-light ratio of the
M33 disk. From this, she inferred a stellar mass 2.8–5.6 ×109 M⊙ at 3σ confidence.6 Higher
values correspond to a maximum-disk fit, while lower values correspond to a sub-maximal
disk. Guo et al. (2010) instead used the observed B − V color of M33 with stellar population
model predictions to estimate the mass-to-light ratio. With an assigned uncertainty of 0.1
dex for this method, one obtains (2.84 ± 0.73) × 109 M⊙ . We combine these methods into a
single rough estimate MM33,∗ = (3.2 ± 0.4) × 109 M⊙ .
6
Corbelli’s mass scale for H0 = 65 km s−1 Mpc−1 was transformed to the Hubble constant used here. The
small mass contribution from the nuclear component of M33 is well within the quoted uncertainties. M33
has no bulge.
21. – 21 –
For M31, Klypin et al. (2002) used rotation-curve fits to estimate both the disk and the
bulge mass. The two models they present cover the ranges MM31,disk = 7.0–9.0 × 1010 M⊙
and MM31,bulge = 1.9–2.4 × 1010 M⊙ . Upon subtraction of the gas mass of ∼ 0.6 × 1010 (van
den Bergh 2000), this yields MM31,∗ = (8.3–10.8) × 1010 M⊙ . The Guo et al. (2010) method
based on the galaxy B − V color yields instead MM31,∗ = (7.0 ± 1.8) × 1010 M⊙ . We combine
these methods into a single rough estimate MM31,∗ = (7.9 ± 0.9) × 1010 M⊙ .
These estimates imply that MM33,∗ /MM31,∗ = 0.041 ± 0.007. This can be compared
to the baryonic mass ratio implied by the Tully Fisher relation, (VM33 /VM31 )4 (McGaugh
2005). With VM33 ≈ 130 km s−1 (Corbelli & Salucci 2000) and VM31 ≈ 250 km s−1 (Corbelli
et al. 2010) this yields 0.073. This is consistent with the estimate of MM33,∗ /MM31,∗ , if one
takes in to account that in M33 the stars make up only ∼ 57% of the baryonic mass, the
rest being mostly in neutral and molecular gas (Corbelli 2003).
Models of the halo occupation distribution of galaxies predict a relation for M∗ /M200
as function of halo mass M200 , when matching observed galaxy properties from the Sloan
Digitial Sky Survey to the properties of dark matter halos seen in simulations (e.g., Wang et
al. 2006; Guo et al. 2010). From Section 5.2 we have MM31,vir = (1.50±0.38)×1012 M⊙ , which
corresponds to MM31,200 = (1.26±0.32)×1012 M⊙ . Combined with knowledge of the observed
MM33,∗ /MM31,∗ , this can be used to estimate M200 for M33, and hence the virial mass.7 This
yields MM33,vir = (0.170 ± 0.059) × 1012 M⊙ based on the Guo et al. relations, and MM33,vir =
(0.127±0.055)×1012 M⊙ based on the Wang et al. relations. The uncertainties were estimated
using a simple Monte-Carlo scheme that includes, in addition to the observational errors, the
Gaussian cosmic scatter of ∼ 0.2 dex in stellar mass at fixed halo mass (Guo et al. 2010).8
The difference in normalization between the predictions from Wang et al. and Guo et al. is
not well understood. So we treat this as an additional model uncertainty, and allow all values
bracketed between the two relations with equal probability. This yields as our final estimate
MM33,vir = (0.148 ± 0.058) × 1012 M⊙ .9
7
In relating M200 to Mvir for M33, we assume that cvir = 10 ± 2, as we did for the MW and M33. While
the lower mass of M33 would in principle lead one to expect a higher concentration, this is not supported
by fits to the rotation curve (Corbelli 2003).
8
This exceeds the observational errors in M∗ for both M33 and M31. As a result, it is not necessary for
the present method to have particularly robust estimates of these observational uncertainties.
9
We could instead have used the mass MM33,∗ directly to estimate MM33,vir , with no reference to M31.
This yields MM33,vir = (0.225 ± 0.055) × 1012 M⊙ based on the Guo et al. relations, and MM33,vir = (0.123 ±
0.034) × 1012 M⊙ based on the Wang et al. relations. Both of these estimates are consistent with what we
use here. However, there is a significant difference in absolute mass normalization between the theoretical
relations. The relations agree better in a relative sense, which is why we prefer the method used here. The
22. – 22 –
Strictly speaking, the mass inferred from halo occupation distributions is the so-called
infall mass. Thus we assume that mass loss to M31 has not yet been significant. On the
other hand, the uncertainty on MM33,vir is significant. Also, our MM33,vir estimate falls below
what is implied by direct application of the Guo et al. relations. Therefore, significant mass
loss would not be inconsistent with the range of masses we explore here.
6.3. Mass Implications of a Bound M31-M33 Pair
To assess the likelihood, given the data, that M31 and M33 are bound, we set up mass
and velocity combinations in Monte-Carlo sense. The initial masses Mvir for both galaxies
were drawn as in Sections 5.2 and 6.2. The initial phase-space coordinates were drawn
as in Sections 4 and 6.1. This scheme propagates all observational distance and velocity
uncertainties and their correlations, including those for the Sun10 . For each set of initial
conditions we calculated the binding energy of the M33-M31 system. The M33-M31 system
was found to be bound in 95.3% of cases. Therefore, our observational knowledge of the
masses, velocities, and distances of these two galaxies indicates that indeed, they most likely
form a bound pair.
The observation of tidal features associated with M33 independently implies that M31
and M33 are likely a bound pair (Braun & Thilker 2004; McConnachie et al. 2009). If
we enforce this as a prior assumption, then this affects our posterior estimates of the M31
and M33 masses. To enforce this assumption, we merely need to remove from our Monte-
Carlo scheme those initial conditions in which M33 and M31 are not bound. Figure 4b
shows as solid histograms the posterior distributions after application of this additional prior.
The main effect is to disallow some of the initial conditions in which MM31 (blue curve) is
on the low end of its probability distribution. The average and RMS mass increase from
MM31,vir = (1.51 ± 0.42) × 1012 M⊙ to (1.54 ± 0.39) × 1012 M⊙ . The mass distribution of M33
is not appreciably affected. The posterior mass distribution for Mtot,vir = MMW,vir + MM31,vir
is shown as the cyan histogram. Its average and RMS are
Mtot,vir = (3.17 ± 0.56) × 1012 M⊙ (final estimate). (10)
This is similar to the result from Section 5.2, which was Mtot,vir = (3.14 ± 0.58) × 1012 M⊙ .
Hence, the assumption that M33 must be bound to M31 does not help much to reduce the
latter uses only relative theoretical predictions, combined with the kinematically determined virial mass for
M31.
10
Uncertainties in the RA and DEC of M31 and M33 are negligible and were ignored.
23. – 23 –
uncertainties in the LG mass, since the fact that they are bound is already implied at high
confidence by the observed velocities.
The probability distributions of M31 and M33 distances and velocities are not appre-
ciably affected by the additional prior that M31 and M33 be bound. The average positions
and velocities in the Galactocentric rest frame remain the same to within 1 kpc and a few
km/s, respectively, after the unbound orbits are removed.
7. Discussion and Conclusions
We have presented the most accurate estimate to date of the transverse motion of M31
with respect to the Sun. This estimate was made possible by the first PM measurements for
M31, made using HST, and presented in Paper I. We have combined these measurements
with other insights to constrain the transverse motion of M31 with respect to the MW. We
have used the resulting motion to improve our understanding of the mass of the Local Group,
and its dominant galaxies M31 and the MW.
The HST PM measurements from Paper I pertain to three fields in M31. The PM for
each field contains contributions from three components: the M31 COM motion, the known
viewing perspective, and the internal kinematics of M31. To correct for the contributions
from internal kinematics, we have constructed detailed N-body models. The models include
both the equilibrium disk, bulge, spheroid, and dark-halo components, as well as the material
from a tidally disrupted satellite galaxy that is responsible for the GSS. Even though the
stars in M31 move at velocities of hundreds of km/s, the internal-kinematics corrections
to the observed PMs averaged over all fields is quite small ( 25 km s−1 , well below the
random uncertainties in the measurements). This is largely due to the known properties of
the carefully chosen field locations, and the galaxy components that they sample.
The resulting M31 transverse motion should be largely free from systematic errors,
based on the many internal consistency checks built into our PM program, as discussed in
Paper I. This includes the fact that the observations for the three different fields, including
observations with different instruments at different times, all yield statistically consistent
estimates for the M31 COM motion. Nonetheless, an entirely independent check on the
results is obtained by comparison to the M31 transverse motion estimates implied by the
methods from vdMG08, which are based exclusively on the kinematics of the satellite galaxies
of M31 and Local Group.
Instead of using the published results from vdMG08 directly, we have redone their anal-
ysis using expanded satellite samples, including new data that has become available in recent
24. – 24 –
years. The end result is similar to what was already published by vdMG08. More impor-
tantly, the result is statistically consistent with that obtained from the HST PM program.
Since the methods employed are totally different, and have very different scopes for possible
systematic errors, this is very successful agreement. This gives added confidence in both re-
sults, and also suggests that a further reduction in the uncertainties can be obtained by taking
the weighted average of both methods. This yields (vW , vN ) = (−125.2 ± 30.8, −73.8 ± 28.4),
which is our final estimate for the heliocentric transverse motion of M31. The uncertainties
in this result are similar to what has been obtained from VLBA observations of water masers
in the M31 satellites M33 and IC10 (Brunthaler et al. 2005, 2007).
To understand the motion of M31 with respect to the MW, it is necessary to correct
for the reflex motion of the Sun. We adopted the most recent insights into the solar motion
within the Milky Way. These imply an azimuthal motion for the Sun (the sum of the LSR
motion and the solar peculiar velocity) of ∼ 250 km/s, which is ∼ 25 km/s higher than
what has typically been used in previous studies. This implies a radial approach velocity
of M31 with respect to the Milky Way of Vrad,M31 = −109.2 ± 4.4 km s−1 , which is ∼ 20
km/s slower than what has typically been used in previous studies. The best estimate
for the tangential velocity component is Vtan,M31 = 17.0 km s−1 , with 1σ confidence region
Vtan,M31 ≤ 34.3 km s−1 . Hence, the velocity of M31 is statistically consistent with a radial
(head-on collision) orbit towards the MW at the 1σ level.
The new insights into the motion of M31 with respect to the MW allowed us to revise
estimates of the Local Group timing mass, as presented most recently by vdMG08 and Li
& White (2008). This yields Mtot,timing = 4.23 × 1012 M⊙ for an assumed radial orbit, with
a random error from observational uncertainties of 0.45 × 1012 M⊙ . This result is ∼ 20%
lower than typically found in previous studies, due to the lower Vrad,M31 used here. We
calibrated the timing mass as in Li & White (2008) based on cosmological simulations.
However, we selected from their galaxy pairs in the Millennium simulation only those with
low Vtan,M31 , for consistency with the observations. This yields Mtot,vir ≡ MMW,vir +MM31,vir =
(4.93 ± 1.63) × 1012 M⊙ , where the uncertainty now includes cosmic scatter (which dominates
over random errors).
We have presented a Bayesian statistical analysis to combine the timing mass estimate
for Mtot,vir with estimates for the individual masses of M31 and the MW obtained from
other dynamical methods. For the individual masses we used relatively broad priors that
encompass most values suggested in the literature. Even then, the cosmic scatter in the
timing mass is too large to help much in constraining the mass of the Local Group. Its main
impact is to increase by ∼ 10% the mass estimates already known for the individual galaxies
(and their sum).
25. – 25 –
In an attempt to further refine the M31 and Local Group mass estimates, we have
studied the galaxy M33. Its known PM allowed us to study the relative motion between
M31 and M33. A range of arguments suggests that the mass of M33 is ∼ 10% of the M31
mass. The masses and relative motions of M31 and M33 indicate that they are a bound
pair at 95% confidence. Observational evidence for tidal deformation between M33 and M31
suggests that the small 5% probability for unbound pairs, as allowed by the observational
uncertainties, may not be physical. This makes low values for the M31 mass unlikely, and
hence increases the expectation value for the Local Group mass, but only by ∼ 1%. Our final
estimate for the Local Group mass from all considerations is Mtot,vir = (3.17±0.57)×1012 M⊙ .
The velocity vectors between M31, M33 and the MW are all closely aligned with the
plane that contains these galaxies. Paper III presents a study of the future orbital evolu-
tion and merging of these galaxies, using the velocities and masses derived here as starting
conditions.
Support for Hubble Space Telescope proposal GO-11684 was provided by NASA through
a grant from STScI, which is operated by AURA, Inc., under NASA contract NAS 5-26555.
The PKDGRAV code used in Section 2.1 was kindly made available by Joachim Stadel and
Tom Quinn, while the ZENO code used in that section was kindly made available by Josh
Barnes. The authors are grateful to T. J. Cox for contributing to the other papers in this
series, and to the anonymous referee for useful comments and suggestions.
A. Dark Halo Profiles, Masses, and Sizes
Spherical infall models show that a virialized mass Mvir has an average overdensity ∆vir
compared to the average matter density of the Universe. The virial radius rvir therefore
3
satisfies ρvir ≡ 3Mvir /4πrvir = ∆vir Ωm ρcrit , or in physical units (Besla et al. 2007)
−1/3 1/3
∆vir Ωm Mvir
rvir = 206h−1 kpc 12 h−1 M
. (A1)
97.2 10 ⊙
For the cosmological parameters used here, h = 0.7 and Ωm = 0.27, one has ∆vir = 360
(Klypin et al. 2011).
Dark halo density profiles in cosmological simulations are well described by an NFW
density profile (Navarro et al. 1997),
ρN (r) = ρs x−1 (1 + x)−2 , x ≡ r/rs . (A2)
26. – 26 –
The enclosed mass is
3 x
MN (r) = 4πρs rs f (x) = Mvir f (x)/f (cvir ), f (x) = ln(1 + x) − , (A3)
1+x
where the concentration is defined as cvir = rvir /rs . The average enclosed mass density equals
ρN (r) ≡ 3MN (r)/4πr 3 = 3ρs (rs /r)3 f (x). (A4)
Another characteristic radius that is often used is the radius r200 so that the average
3
enclosed density is 200 times the critical density of the Universe, ρ200 ≡ 3M200 /4πr200 =
200ρcrit , where M200 is the enclosed mass. It follows from the respective definitions that
q ≡ ρ200 /ρvir = (200/∆vir )Ω−1 ,
m (A5)
which yields q = 2.058 for the cosmological parameters used here. This exceeds unity, and
therefore r200 < rvir and M200 < Mvir . For the NFW profile, r200 is the solution of the
equation ρN (r200 ) = qρN (rvir ), which implies
1/3
f (c200 )
c200 /cvir = (A6)
qf (cvir )
where c200 ≡ r200 /rs . This equation can be quickly solved numerically using fixed point
iteration, starting from an initial guess for c200 on the right hand side. The corresponding
mass ratio is
M200 /Mvir = f (c200 )/f (cvir ). (A7)
As discussed in Springel et al. (2005), it is often convenient for numerical reasons to
model dark halos with a Hernquist (1990) profile. This is what we will do in our exploration
of the orbital evolution of the MW-M31-M33 system in Paper III. In this case the density
profile is
MH
ρH (r) = y −1 (1 + y)−3, y ≡ r/a. (A8)
2πa3
Here MH is the total mass of the system, which is finite, unlike for the NFW profile. The
enclosed mass is
MH (r) = MH y 2(1 + y)−2. (A9)
The Hernquist profile has the same density as the NFW profile for r → 0 if
MH = 2πρs a2 rs . (A10)
We can choose the scale radius a so that the enclosed mass of the NFW and Hernquist
profiles is the same for some radius r, MN (˜) = MH (˜). This implies
˜ r r
−1
a/rs = [2f (˜)]−1/2 − (1/˜)
x x , (A11)
27. – 27 –
where x ≡ r /rs . The corresponding total mass of the Hernquist profile satisfies
˜ ˜
MH /Mvir = (a/rs )2 /[2f (cvir )] (A12)
If we choose x = c200 , then the NFW and Hernquist profiles have the same enclosed mass
˜
M200 within r200 .11 . We denote by a200 the corresponding value of a from equation (A11),
and by MH,200 the corresponding value of MH from equation (A12). If instead we choose
x = cvir , then the NFW and Hernquist profiles have the same enclosed mass Mvir within
˜
rvir . In this case we denote by avir the corresponding value of a from equation (A11), and
byMH,vir the corresponding value of MH from equation (A12).
As an example, we consider a halo with cvir = 10. This yields c200 = 7.4, M200 /Mvir =
0.84, a200 /rs = 2.01, MH,200 /Mvir = 1.36, avir /rs = 2.09, and MH,vir /Mvir = 1.46.
REFERENCES
Barnes, J. E., 2011, Astrophysics Source Code Library, record ascl:1102.027
Besla, G., Kallivayalil, N., Hernquist, L., Robertson, B., Cox, T. J., van der Marel, R. P., &
Alcock, C. 2007, ApJ, 668, 949
Boylan-Kolchin, M., Besla, G., & Hernquist, L. 2011, MNRAS, 414, 1560
Braun, R., & Thilker, D. 2004, A&A, 417, 421
Brown, T. M., Smith, E., Guhathakurta, P., Rich, R. M., Ferguson, H. C., Renzini, A.,
Sweigart, A. V., & Kimble, R. A. 2006, ApJL, 636, L89
Brunthaler, A., Reid, M. J., Falcke, H., Greenhill, L. J., & Henkel, C. 2005, Science, 307,
1440
Brunthaler, A., Reid, M. J., Falcke, H., Henkel, C., & Menten, K. M. 2007, A&A, 462, 101
Chapman, S. C., Ibata, R., Lewis, G. F., Ferguson, A. M. N., Irwin, M., McConnachie, A.,
& Tanvir, N. 2006, 653, 255
Chapman, S. C., et al. 2007, ApJ, 662, L79
Collins, M. L. M., et al. 2009, MNRAS, 396, 1619 (C09)
11
This is what Springel et al. (2005) aimed to achieve. However, their equation (2) is only an approximation
to equation (A11), so they do not actually achieve this equality.
28. – 28 –
Corbelli, E., & Salucci, P. 2000, MNRAS, 311, 441
Corbelli, E. & Schneider, S. E. 1997, ApJ, 479, 244
Corbelli, E. 2003, MNRAS, 342, 199
Corbelli, E., Lorenzoni, S., Walterbos, R., Braun, R., & Thilker, D. 2010, A&A, 511, 89
Cox, T. J., & Loeb, A. 2008, MNRAS, 386, 461
Dehnen, W., Binney, J. J. 1998, MNRAS, 298, 387
Dorman, C., et al. 2012, ApJ, submitted
Einasto, J., & Lynden-Bell, D. 1982, MNRAS, 199, 67
Evans, N. W., Wilkinson, M. I., Guhathakurta, P., Grebel, E. K., Vogt, S. S. 2000, ApJ,
540, L9
Fardal, M. A., Babul, A., Geehan, J. J., & Guhathakurta, P. 2006, MNRAS, 366, 1012
Fardal, M. A., Guhathakurta, P., Babul, A., & McConnachie, A. W. 2007, MNRAS, 380, 15
Fardal, M. A., Babul, A., Guhathakurta, P., Gilbert, K., & Dodge, C. 2008, ApJ, 682, L33
Ferguson, A. M. N., Gallagher, J. S., & Wyse, Rosemary F. G, 2000, AJ, 120, 821
Galleti, S., Bellazzini, M., Federici, L., & Fusi Pecci, F. 2005, A&A, 436, 535 (G05)
Galleti, S., Bellazzini, M., Federici, L., Buzzoni, A., & Fusi Pecci, F. 2007, A&A, 471, 127
(G07)
Geehan, J. J., Fardal, M. A., Babul, A., & Guhathakurta, P. 2006, MNRAS, 366, 996
Ghez, A. M., et al. 2008, ApJ, 689, 1044
Gilbert, K. M. 2007, ApJ, 668, 245
Gilbert, K. M., Guhathakurta, P., Kollipara, P., Beaton, R. L., Geha, M. C., Kalirai, J. S.,
Kirby, E. N., Majewski, S. R., Patterson, R. J. 2009, ApJ, 705, 1275
Gillessen, S., Eisenhauer, F., Trippe, S., Alexander, T., Genzel, R., Martins, F., & Ott, T.
2009, ApJ, 692, 1075
Gott, J. R., & Thuan, T. X. 1978, ApJ, 223, 426
29. – 29 –
Guhathakurta, P., Ostheimer, J. C., Gilbert, K. M., Rich, R. M., Majewski, S. R., Kalirai,
J. S., Reitzel, D. B., & Patterson, R. J. 2005, ArXiv e-prints, astro-ph/0502366
Guhathakurta, P., et al. 2006, AJ, 131, 2497
Guo, Qi, White, S. D. M., Li, C., & Boylan-Kolchin, M. 2010, MNRAS, 404, 1111
Ibata, R., Chapman, S., Ferguson, A. M. N., Irwin, M., Lewis, G. F., & McConnachie, A.
W. 2004, MNRAS, 351, 117
Ibata, R., Martin, N. F., Irwin, M., Chapman, S., Ferguson, A. M. N., Lewis, G. F., &
McConnachie, A. W. 2007, ApJ, 671, 1591
Irwin, M. J., Ferguson, A. M. N., Ibata, R. A., Lewis, G. F., & Tanvir, N. R. 2005, ApJL,
628, L105
Jarosik, N. et al. 2011, ApJS, 192, 14
Kahn, F. D., & Woltjer, L. 1959, ApJ, 130, 705
Kalirai, J. S., Guhathakurta, P., Gilbert, K. M., Reitzel, D. B., Majewski, S. R., Rich, R.
M., Cooper, M. C., 2006a, ApJ, 641, 268
Kalirai, J. S., et al. 2006b, ApJ, 648, 389
Kerr, F. J., & Lynden-Bell, D. 1986, MNRAS, 221, 1023
Klypin, A., Zhao., H. S., & Somerville, R. S. 2002, 573, 597
Klypin, A., Trujillo-Gomez, S., Primack, J. 2011, ApJ, in press [arXiv:1002.3660]
Koch, A., & Grebel, E. K. 2006, AJ, 131, 1405
Kochanek, C. S. 1996, ApJ, 457, 228
Kroeker, T. L., & Carlberg, R. G. 1991, ApJ, 376, 1
Lewis, G. F., Ibata, R. A., Chapman, S. C., McConnachie, A., Irwin, M. J., Tolstoy, E., &
Tanvir, N. R. 2007, MNRAS, 375, 1364
Li, Y.-S., & White, S. D. M. 2008, MNRAS, 384, 1459
Loeb, A., Reid, M. J., Brunthaler, A., & Falcke, H. 2005, ApJ, 633, 894
Lynden-Bell, D. 1981, The Observatory, 101, 111
30. – 30 –
Lynden-Bell, D. 1999, in “The stellar content of Local Group galaxies”, Proc. IAU Symp. 192,
Whitelock, P., & Cannon, R., eds., p. 39 (San Francisco: Astronomical Society of the
Pacific)
Majewski, S. R., et al. 2007, ApJL, 670, L9
Martin, N. F., et al. 2009, ApJ, 705, 758
Mateo, M, Olszewski, E. W., & Walker, M. G. 2008, ApJ, 675, 201
McConnachie, A. W., Irwin, M. J., Ibata, R. A., Ferguson, A. M. N., Lewis, G. F., & Tanvir,
N. 2003, MNRAS, 343, 1335
McConnachie, A. W., Irwin, M. J., Ferguson, A. M. N., Ibata, R. A., Lewis, G. F., & Tanvir,
N. 2004, MNRAS, 350, 243
McConnachie, A. W., Irwin, M. J., Ferguson, A. M. N., Ibata, R. A., Lewis, G. F., & Tanvir,
N. 2005, MNRAS, 356, 979
McConnachie, A. W., & Irwin, M. J. 2006, MNRAS, 365, 902
McConnachie, A. W. et al. 2008, ApJ, 688, 1009
McConnachie, A. W. et al. 2009, Nature, 461, 66
McGaugh, S. S. 2005, ApJ, 632, 859
McMillan, P. J., & Binney, J. J. 2010, MNRAS, 402, 934
McMillan, P. J. 2011, MNRAS, 414, 2446
Merrett, H. R., et al. 2006, MNRAS, 369, 120
Navarro, J. F., Frenk, C. S., White, S. D. M. 1997, ApJ, 490, 493
Neto, A. F., et al. 2007, MNRAS, 381, 1450
Peebles, P. J. E., Phelps, S. D., Shaya, E. J., & Tully, R. B. 2001, ApJ, 554, 104
Raychaudhury, S., & Lynden-Bell, D. 1989, MNRAS, 240, 195
Reid, M. J., & Brunthaler, A. 2004, ApJ, 616, 872
Reid, M. J., et al. 2009, ApJ, 700, 137
Sandage, A. 1986, ApJ, 307, 1
31. – 31 –
Sch¨ rich, R., Binney, J., & Dehnen, W. 2010, MNRAS, 403, 1829
n
Shattow, G., & Loeb, A., 2009, MNRAS, 392, L21
Sohn, S. T., Anderson, J., & van der Marel, R. P. 2012, ApJ, submitted (Paper I)
Stadel, J. G. 2001, Ph.D. thesis “Cosmological N-body simulations and their analysis”,
University of Washington
Tollerud, E., et al. 2012, ApJ, submitted [arXiv:1112.1067v1]
van den Bergh, S. 1998, AJ, 116, 1688
van den Bergh, S. 2000, The Galaxies of the Local Group (Cambridge: Cambridge University
Press)
van der Marel, R. P., Alves, D. R., Hardy, E., & Suntzeff, N. B. 2002, AJ, 124, 2639
van der Marel, R. P., & Guhathakurta, P. 2008, ApJ, 678, 187 (vdMG08)
Wang, L., Li, C., Kauffmann, G., & De Lucia, G. 2006, MNRAS, 371, 537
Watkins, L. L., Evans, N. W., & An, J. H. 2010, MNRAS, 406, 264
Zaritsky, D., Olszewski, E., Schommer, R., Peterson, R., Aaronson, M. 1989, ApJ, 345, 759
Zaritsky, D., & White, S. D. M. 1994, ApJ, 435, 599
This preprint was prepared with the AAS L TEX macros v5.2.
A
32. – 32 –
Table 1. M31 Transverse Velocity: Proper Motions and Internal Kinematics
Spheroid Field Disk Field Stream Field
HST PM Measurements
vW (HST) km/s −167.2 ± 60.2 −194.6 ± 89.8 −65.3 ± 101.5
vN (HST) km/s −137.2 ± 56.2 −38.0 ± 89.1 −130.3 ± 99.3
M31 Internal Kinematics Model
f (base) 0.738 0.922 0.195
f (GSS) 0.262 0.078 0.805
vLOS (base) km/s -1.1 219.8 4.8
vLOS (GSS) km/s 71.9 -82.3 -185.0
vLOS (all) km/s 18.0 196.3 -148.0
vW (base) km/s 11.0 -25.9 12.0
vW (GSS) km/s 22.7 -82.6 73.4
vW (all) km/s 14.1 -30.3 61.4
vN (base) km/s -14.3 -49.3 -7.1
vN (GSS) km/s 2.5 41.8 157.5
vN (all) km/s -9.9 -42.2 125.4
M31 COM Motion (HST PMs + Internal Kinematics Model + Viewing Perspective)
vW (COM) km/s −179.1 ± 64.1 −158.0 ± 92.4 −126.3 ± 103.6
vN (COM) km/s −122.6 ± 60.0 −0.5 ± 91.3 −247.5 ± 102.1
Note. — Kinematical quantities for the three HST fields observed in Paper I. The top part of the
table lists the HST PM measurements, transformed to km/s using D = 770 ± 40 kpc. The middle
part gives the predictions of the M31 internal kinematics model described in Section 2. Predictions
are split into two components, the “base” equilibrium galaxy model (disk, bulge, and halo), and
the accreted “GSS” tidal stream component. The fraction f gives the amount contributed by
each component. Predictions for all model stars (independent of component), are also listed (i.e.,
averages suitably weighted by the corresponding fractions f ). Average velocities are given in the
line-of-sight (LOS), West, and North directions. The directions are defined at the center of each
field. The internal kinematics velocities are expressed in a frame in which M31 is at rest. The bot-
tom part of the table gives the estimates for the center-of-mass (COM) motion of M31 that result
from correcting the HST measurements for both internal kinematics and the viewing perspective.
For the COM velocities, the West and North directions are always defined at the COM.
33. – 33 –
Table 2. Addition to vdMG08 M31 Satellite Galaxy Sample
Name Type ρ Φ vlos
deg deg km/s
(1) (2) (3) (4) (5)
B517 GC 3.29 77.48 -272 ± 54 (G07)
Mac-GC1 GC 3.39 -115.38 -219 ± 15 (G07)
B514 GC 4.04 -145.58 -456 ± 23 (G05)
EC4 GC 4.39 135.88 -288 ± 2 (C09)
B516 GC 4.76 28.44 -181 ± 5 (G07)
B518 GC 5.74 -110.08 -200 ± 48 (G07)
And XV dSph 6.84 114.86 -323 ± 1 (T12)
B519 GC 7.35 165.67 -268 ± 47 (G07)
And XI dSph 7.50 174.23 -462 ± 4 (T12)
And XIII dSph 8.46 166.90 -185 ± 2 (T12)
Mar-GC1 GC 8.50 168.61 -312 ± 17 (G07)
And XXI dSph 9.00 -78.35 -361 ± 6 (T12)
And XVI dSph 9.50 158.04 -367 ± 3 (T12)
And XXII dSph 16.06 141.60 -127 ± 3 (T12)
Note. — The sample of additional M31 satellites, which was combined with the sample from
Table 1 of vdMG08 for the modeling of Section 3.1. Column (1) lists the name of the object and
column (2) its type. Objects labeled “GC” are distant globular clusters. Columns (3) and (4)
define the position on the sky: ρ is the angular distance from M31 and Φ is the position angle with
respect to M31 measured from North over East, calculated from the sky positions (RA,DEC) as in
van der Marel et al. (2002). The satellites in the table are sorted by their value of ρ. Column (5)
lists the heliocentric line-of-sight velocity and its error. The source of the measurement is listed
in parentheses — Collins et al. (2009): C09; Tollerud et al. (2012): T12; Galleti et al. (2005):
G05; Galleti et al. (2007): G07. Sky positions were obtained from the listed sources or the NASA
Extragalactic Database.
34. – 34 –
Table 3. M31 Center-of-Mass Heliocentric Velocity Estimates
Method vLOS vW vN
km/s km/s km/s
(1) (2) (3) (4)
HST PMs + Internal Kinematics Model + Viewing Perspective (Section 2)
Spheroid Field ... −179.1 ± 64.1 −122.6 ± 60.0
Disk Field ... −158.0 ± 92.4 −0.5 ± 91.3
Stream Field ... −126.3 ± 103.6 −247.5 ± 102.1
Weighted Av. ... −162.8 ± 47.0 −117.2 ± 45.0
Analysis of Satellite LOS Kinematics (Section 3)
M31 Satellites -279.3 ± 16.4 -176.1 ± 144.1 8.4 ± 85.4
M33 PM -183.1 ± 84.9 -47.7 ± 88.2 70.9 ± 91.5
IC 10 PM -346.1 ± 84.8 -16.2 ± 88.0 -47.3 ± 89.3
Outer LG Galaxies -361.3 ± 83.6 -140.5 ± 58.0 -102.6 ± 52.5
Weighted Av. -281.1 ± 15.6 -97.0 ± 40.7 -45.1 ± 36.6
All methods combined
Weighted Av. ... -125.2 ± 30.8 -73.8 ± 28.4
Note. — Estimates of the heliocentric velocity of the M31 COM from different methods, as
indicated in column (1). The top part of the table gives the results from the HST PM measurements,
corrected for internal kinematics as described in Section 2. The weighted average of the results
from the three different HST fields is listed as well. The middle part of the table gives the results
from the updated vdMG08 analysis, based on the kinematics of M31 and LG satellite galaxies, as
described in Section 3. The weighted average of the four independent estimates is listed as well.
Column (2) lists the estimated M31 systemic line-of-sight velocities (the actual velocity measured
directly from M31 itself is known to be −301 ± 1 km/s; vdMG08). Columns (3) and (4) list the
estimated M31 transverse velocities in the West and North directions, respectively. The bottom
line of the table lists the weighted average of the two weighted averages from the different methods.
This is the final result used in the remainder of our study.
35. – 35 –
Fig. 1.— Smoothed projected view of the N-body model used to calculate the internal M31
PM kinematics for our HST fields from Paper I. A standard sky projection is used, with
North up and East to the left. The GSS is visible South-East of the galaxy center, and the
observed positions of the North-East and Western shelf are shown with dashed outlines. This
image can be compared to star count maps of giant stars in M31, such as that reproduced
in Figure 1 of Paper I, which show very similar features.
36. – 36 –
Fig. 2.— Smoothed view in LOS velocity vs. projected distance space of the N-body model
used to calculate the internal M31 PM kinematics for our HST fields from Paper I. Only
particles with Y < −0.75◦ are shown (located South-East of the galaxy center), where Y is
a cartesian coordinate along the projected galaxy minor axis. The dark band in the figure is
due to the GSS, while the base galaxy contributes most of the remaining particles. The GSS
location matches the observed peak LOS velocity of the GSS as a function of radius (blue
points; Ibata et al. 2004; Guhathakurta et al. 2006; Kalirai et al. 2006a; Gilbert et al. 2009),
including that measured in the HST stream PM field of Paper I (circle).
37. – 37 –
Fig. 3.— Estimates of the M31 heliocentric transverse velocity in the West and North
directions. Data points with error bars are from Table 3. Red: Weighted average of HST
proper-motion measurements, corrected for internal kinematics (Section 2). Blue: Weighted
average of methods based on satellite kinematics (update of vdMG08 result; Section 3).
Black: Overall weighted average of all measurements. The starred symbol indicates the
transverse velocity that corresponds to a radial orbit for M31 with respect to the Milky
Way. The measurements are consistent with a radial orbit.
38. – 38 –
Fig. 4.— Probability distributions for the mass of the Milky Way, M31, and their sum
Mtot . The top panel shows prior probability distributions based on several lines of evidence.
M31 (blue) and MW (green): probability distributions based on studies of these galaxies as
discussed in the text; Sum of M31 and MW (magenta); Timing argument Mtot with inclusion
of observational errors (black), and with additional inclusion of cosmic variance from Li &
White (2008; red). The bottom panel shows with the same color coding posterior probability
distributions, obtained by combining constraints as described in the text. Dotted: knowledge
of the individual galaxies combined with the the timing argument; the timing argument does
not help much to constrain the masses, due to its large cosmic variance. Solid: Requiring
also that M33 and M31 be a bound pair; this reduces the probability of low M31 masses.