1) The document describes general relativistic simulations of collapsing supermassive stars with and without rotation using a numerical code called Nada.
2) The simulations include effects of gas pressure, radiation, electron-positron pairs, and thermonuclear energy from hydrogen and helium burning.
3) Objects with a mass of around 5×105 solar masses explode if non-rotating with a metallicity over 0.007, while rotation lowers the threshold to 0.001. More massive objects have a higher critical metallicity for explosion.
The puzzling source_in_ngc6388_a_possible_planetary_tidal_disruption_eventSérgio Sacani
Artigo descreve a descoberta da destruição de um planeta ao passar próximo a uma estrela do tipo anã branca presente dentro do aglomerado globular de estrelas NGC 6388. Para isso os astrônomos utilizaram um arsenal de telescópios.
A luminous X-ray outburst from an intermediatemass black hole in an off-centr...Sérgio Sacani
A unique signature for the presence of massive black holes in
very dense stellar regions is occasional giant-amplitude outbursts
of multi-wavelength radiation from tidal disruption and
subsequent accretion of stars that make a close approach to
the black holes1
. Previous strong tidal disruption event (TDE)
candidates were all associated with the centres of largely
isolated galaxies2–6. Here, we report the discovery of a luminous
X-ray outburst from a massive star cluster at a projected
distance of 12.5 kpc from the centre of a large lenticular galaxy.
The luminosity peaked at ~1043 erg s−1
and decayed systematically
over 10 years, approximately following a trend
that supports the identification of the event as a TDE. The
X-ray spectra were all very soft, with emission confined to be
≲3.0 keV, and could be described with a standard thermal disk.
The disk cooled significantly as the luminosity decreased—a
key thermal-state signature often observed in accreting stellar-mass
black holes. This thermal-state signature, coupled
with very high luminosities, ultrasoft X-ray spectra and the
characteristic power-law evolution of the light curve, provides
strong evidence that the source contains an intermediatemass
black hole with a mass tens of thousand times that of
the solar mass. This event demonstrates that one of the most
effective means of detecting intermediate-mass black holes is
through X-ray flares from TDEs in star clusters.
Our Sun. V. A Bright Young Sun Consistent with Helioseismology and Warm Temp...XequeMateShannon
The relatively warm temperatures required on early Earth and Mars have been difficult to account for via warming from greenhouse gases. We tested whether this problem can be resolved for both Earth and Mars by a young Sun that is brighter than predicted by the standard solar model. We computed high-precision solar evolutionary models with slightly increased initial masses of M_i = 1.01 to 1.07 M_sun; for each mass, we considered three different mass loss scenarios. We then tested whether these models were consistent with the current high-precision helioseismic observations. The relatively modest mass loss rates in these models are consistent with observational limits from young stars and estimates of the past solar wind obtained from lunar rocks, and do not significantly affect the solar lithium depletion. For appropriate initial masses, all three mass loss scenarios are capable of yielding a solar flux 3.8 Gyr ago high enough to be consistent with water on ancient Mars. We find that all of our mass-losing solar models are consistent with the helioseismic observations. The early solar mass loss of a few percent does indeed leave a small fingerprint on the Sun's internal structure. However, for helioseismology to significantly constrain early solar mass loss would require higher accuracy in the observed solar parameters and input physics, namely, by a factor of about 3 for the observed solar surface composition, and a factor of 2 for the solar interior opacities, the pp nuclear reaction rate, and the diffusion constants for gravitational settling.
The puzzling source_in_ngc6388_a_possible_planetary_tidal_disruption_eventSérgio Sacani
Artigo descreve a descoberta da destruição de um planeta ao passar próximo a uma estrela do tipo anã branca presente dentro do aglomerado globular de estrelas NGC 6388. Para isso os astrônomos utilizaram um arsenal de telescópios.
A luminous X-ray outburst from an intermediatemass black hole in an off-centr...Sérgio Sacani
A unique signature for the presence of massive black holes in
very dense stellar regions is occasional giant-amplitude outbursts
of multi-wavelength radiation from tidal disruption and
subsequent accretion of stars that make a close approach to
the black holes1
. Previous strong tidal disruption event (TDE)
candidates were all associated with the centres of largely
isolated galaxies2–6. Here, we report the discovery of a luminous
X-ray outburst from a massive star cluster at a projected
distance of 12.5 kpc from the centre of a large lenticular galaxy.
The luminosity peaked at ~1043 erg s−1
and decayed systematically
over 10 years, approximately following a trend
that supports the identification of the event as a TDE. The
X-ray spectra were all very soft, with emission confined to be
≲3.0 keV, and could be described with a standard thermal disk.
The disk cooled significantly as the luminosity decreased—a
key thermal-state signature often observed in accreting stellar-mass
black holes. This thermal-state signature, coupled
with very high luminosities, ultrasoft X-ray spectra and the
characteristic power-law evolution of the light curve, provides
strong evidence that the source contains an intermediatemass
black hole with a mass tens of thousand times that of
the solar mass. This event demonstrates that one of the most
effective means of detecting intermediate-mass black holes is
through X-ray flares from TDEs in star clusters.
Our Sun. V. A Bright Young Sun Consistent with Helioseismology and Warm Temp...XequeMateShannon
The relatively warm temperatures required on early Earth and Mars have been difficult to account for via warming from greenhouse gases. We tested whether this problem can be resolved for both Earth and Mars by a young Sun that is brighter than predicted by the standard solar model. We computed high-precision solar evolutionary models with slightly increased initial masses of M_i = 1.01 to 1.07 M_sun; for each mass, we considered three different mass loss scenarios. We then tested whether these models were consistent with the current high-precision helioseismic observations. The relatively modest mass loss rates in these models are consistent with observational limits from young stars and estimates of the past solar wind obtained from lunar rocks, and do not significantly affect the solar lithium depletion. For appropriate initial masses, all three mass loss scenarios are capable of yielding a solar flux 3.8 Gyr ago high enough to be consistent with water on ancient Mars. We find that all of our mass-losing solar models are consistent with the helioseismic observations. The early solar mass loss of a few percent does indeed leave a small fingerprint on the Sun's internal structure. However, for helioseismology to significantly constrain early solar mass loss would require higher accuracy in the observed solar parameters and input physics, namely, by a factor of about 3 for the observed solar surface composition, and a factor of 2 for the solar interior opacities, the pp nuclear reaction rate, and the diffusion constants for gravitational settling.
First emergence of cold accretion and supermassive star formation in the earl...Sérgio Sacani
We investigate the first emergence of the so-called cold accretion, the accretion flows deeply penetrating a halo, in the early
universe with cosmological N-body/SPH simulations. We study the structure of the accretion flow and its evolution within
small halos with . 108 M with sufficiently high spatial resolutions down to ∼ 1 pc scale. While previous studies only
follow the evolution for a short period after the primordial cloud collapse, we follow the long-term evolution until the cold
accretion first appears, employing the sink particle method. We show that the cold accretion emerges when the halo mass
exceeds ∼ 2.2×107 M {(1 + 𝑧) /15}
−3/2
, the minimum halo masses above which the accretion flow penetrates halos. We further
continue simulations to study whether the cold accretion provides the dense shock waves, which have been proposed to give
birth to supermassive stars (SMSs). We find that the accretion flow eventually hits a compact disc near the halo centre, creating
dense shocks over a wide area of the disc surface. The resulting post-shock gas becomes dense and hot enough with its mass
comparable to the Jeans mass 𝑀J ∼ 104−5 M, a sufficient amount to induce the gravitational collapse, leading to the SMS
formation.
Multidimensional Radiation Hydrodynamics Simulations of Pulsational Pair-inst...Sérgio Sacani
Stars with masses of 80–130 Me can encounter pulsational pair-instability at the end of their lives, which triggers
consecutive episodes of explosive burning that eject multiple massive shells. Collisions between these shells produce
bright transients known as pulsational pair-instability supernovae (PPI SNe) that may explain some extreme supernovae.
In this paper, we present the first 2D and 3D radiation hydrodynamics simulations of PPI SNe with the CASTRO code.
Radiative cooling causes the collided shells to evolve into thin, dense structures with hot spots that can enhance the peak
luminosity of the SN by factors of 2–3. The light curve peaks at 1.9–2.1×1043 erg s−1 for 50 days and then plateaus at
2–3×1042 erg s−1 for 200 days, depending on the viewing angle. The presence of 12C and 16O and the absence of 28Si
and 56Fe in its spectra can uniquely identify this transient as a PPI SN in follow-up observations. Our models suggest
that multidimensional radiation hydrodynamics is required to model the evolution and light curves of all shell-collision
SNe, such as Type IIne, not just PPI SNe.
Detection of anisotropic satellite quenching in galaxy clusters up to z ∼ 1Sérgio Sacani
Satellite galaxies in the cluster environment are more likely to be quenched than galaxies in the general field. Recently, it has
been reported that satellite galaxy quenching depends on the orientation relative to their central galaxies: satellites along the
major axis of centrals are more likely to be quenched than those along the minor axis. In this paper, we report a detection
of such anisotropic quenching up to z ∼ 1 based on a large optically selected cluster catalogue constructed from the Hyper
Suprime-Cam Subaru Strategic Program. We calculate the quiescent satellite galaxy fraction as a function of orientation angle
measured from the major axis of central galaxies and find that the quiescent fractions at 0.25 < z < 1 are reasonably fitted
by sinusoidal functions with amplitudes of a few per cent. Anisotropy is clearer in inner regions (<r200m) of clusters and not
significant in cluster outskirts (>r200m). We also confirm that the observed anisotropy cannot be explained by differences in
local galaxy density or stellar mass distribution along the two axes. Quiescent fraction excesses between the two axes suggest
that the quenching efficiency contributing to the anisotropy is almost independent of stellar mass, at least down to our stellar
mass limit of M∗ = 1 × 1010 M. Finally, we argue that the physical origins of the observed anisotropy should have shorter
quenching time-scales than ∼ 1 Gyr, like ram-pressure stripping, because, for anisotropic quenching to be observed, satellites
must be quenched before their initial orientation angles are significantly changed.
The physical conditions_in_a_pre_super_star_cluster_molecular_cloud_in_the_an...Sérgio Sacani
Artigo descreve estudo feitos pelos astrônomos utilizando o ALMA para descobrir um proto-aglomerado globular de estrelas gigantes se formando no interior das galáxias Antenas, o famoso par de galáxias em interação. É a primeira vez que os astrônomos conseguem observar um objeto desse tipo nos seus estágios iniciais de vida e com o ambiente ao redor inalterado.
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.
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.
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.
Continuum emission from within the plunging region of black hole discsSérgio Sacani
The thermal continuum emission observed from accreting black holes across X-ray bands has the potential to be leveraged as a
powerful probe of the mass and spin of the central black hole. The vast majority of existing ‘continuum fitting’ models neglect
emission sourced at and within the innermost stable circular orbit (ISCO) of the black hole. Numerical simulations, however,
find non-zero emission sourced from these regions. In this work, we extend existing techniques by including the emission
sourced from within the plunging region, utilizing new analytical models that reproduce the properties of numerical accretion
simulations. We show that in general the neglected intra-ISCO emission produces a hot-and-small quasi-blackbody component,
but can also produce a weak power-law tail for more extreme parameter regions. A similar hot-and-small blackbody component
has been added in by hand in an ad hoc manner to previous analyses of X-ray binary spectra. We show that the X-ray spectrum
of MAXI J1820+070 in a soft-state outburst is extremely well described by a full Kerr black hole disc, while conventional
models that neglect intra-ISCO emission are unable to reproduce the data. We believe this represents the first robust detection of
intra-ISCO emission in the literature, and allows additional constraints to be placed on the MAXI J1820 + 070 black hole spin
which must be low a• < 0.5 to allow a detectable intra-ISCO region. Emission from within the ISCO is the dominant emission
component in the MAXI J1820 + 070 spectrum between 6 and 10 keV, highlighting the necessity of including this region. Our
continuum fitting model is made publicly available.
WASP-69b’s Escaping Envelope Is Confined to a Tail Extending at Least 7 RpSérgio Sacani
Studying the escaping atmospheres of highly irradiated exoplanets is critical for understanding the physical
mechanisms that shape the demographics of close-in planets. A number of planetary outflows have been observed
as excess H/He absorption during/after transit. Such an outflow has been observed for WASP-69b by multiple
groups that disagree on the geometry and velocity structure of the outflow. Here, we report the detection of this
planet’s outflow using Keck/NIRSPEC for the first time. We observed the outflow 1.28 hr after egress until the
target set, demonstrating the outflow extends at least 5.8 × 105 km or 7.5 Rp This detection is significantly longer
than previous observations, which report an outflow extending ∼2.2 planet radii just 1 yr prior. The outflow is
blueshifted by −23 km s−1 in the planetary rest frame. We estimate a current mass-loss rate of 1 M⊕ Gyr−1
. Our
observations are most consistent with an outflow that is strongly sculpted by ram pressure from the stellar wind.
However, potential variability in the outflow could be due to time-varying interactions with the stellar wind or
differences in instrumental precision.
X-rays from a Central “Exhaust Vent” of the Galactic Center ChimneySérgio Sacani
Using deep archival observations from the Chandra X-ray Observatory, we present an analysis of
linear X-ray-emitting features located within the southern portion of the Galactic center chimney,
and oriented orthogonal to the Galactic plane, centered at coordinates l = 0.08◦
, b = −1.42◦
. The
surface brightness and hardness ratio patterns are suggestive of a cylindrical morphology which may
have been produced by a plasma outflow channel extending from the Galactic center. Our fits of the
feature’s spectra favor a complex two-component model consisting of thermal and recombining plasma
components, possibly a sign of shock compression or heating of the interstellar medium by outflowing
material. Assuming a recombining plasma scenario, we further estimate the cooling timescale of this
plasma to be on the order of a few hundred to thousands of years, leading us to speculate that a
sequence of accretion events onto the Galactic Black Hole may be a plausible quasi-continuous energy
source to sustain the observed morphology
Efficient spin-up of Earth System Models usingsequence accelerationSérgio Sacani
Marine and terrestrial biogeochemical models are key components of the Earth System Models (ESMs) used toproject future environmental changes. However, their slow adjustment time also hinders effective use of ESMsbecause of the enormous computational resources required to integrate them to a pre-industrial equilibrium. Here,a solution to this "spin-up" problem based on "sequence acceleration", is shown to accelerate equilibration of state-of-the-art marine biogeochemical models by over an order of magnitude. The technique can be applied in a "blackbox" fashion to existing models. Even under the challenging spin-up protocols used for Intergovernmental Panelon Climate Change (IPCC) simulations, this algorithm is 5 times faster. Preliminary results suggest that terrestrialmodels can be similarly accelerated, enabling a quantification of major parametric uncertainties in ESMs, improvedestimates of metrics such as climate sensitivity, and higher model resolution than currently feasible.
Generative AI Deep Dive: Advancing from Proof of Concept to ProductionAggregage
Join Maher Hanafi, VP of Engineering at Betterworks, in this new session where he'll share a practical framework to transform Gen AI prototypes into impactful products! He'll delve into the complexities of data collection and management, model selection and optimization, and ensuring security, scalability, and responsible use.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
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Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
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Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
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PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
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LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
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Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
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The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
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Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
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Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdfPaige Cruz
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
Relativistic collapse and explosion of rotating supermassive stars with thermonuclear effects
1. Submitted for publication in the Astrophysical Journal
Preprint typeset using L TEX style emulateapj v. 8/13/10
A
RELATIVISTIC COLLAPSE AND EXPLOSION OF ROTATING SUPERMASSIVE STARS WITH
THERMONUCLEAR EFFECTS
Pedro J. Montero1 , Hans-Thomas Janka1 , and Ewald Muller1
¨
(Dated: August 17, 2011)
Submitted for publication in the Astrophysical Journal
ABSTRACT
arXiv:1108.3090v1 [astro-ph.CO] 15 Aug 2011
We present results of general relativistic simulations of collapsing supermassive stars with and
without rotation using the two-dimensional general relativistic numerical code Nada, which solves
the Einstein equations written in the BSSN formalism and the general relativistic hydrodynamics
equations with high resolution shock capturing schemes. These numerical simulations use an equation
of state which includes effects of gas pressure, and in a tabulated form those associated with radiation
and the electron-positron pairs. We also take into account the effect of thermonuclear energy released
by hydrogen and helium burning. We find that objects with a mass of ≈ 5 × 105 M⊙ and an initial
metallicity greater than ZCN O ≈ 0.007 do explode if non-rotating, while the threshold metallicity for
an explosion is reduced to ZCN O ≈ 0.001 for objects uniformly rotating. The critical initial metallicity
for a thermonuclear explosion increases for stars with mass ≈ 106 M⊙ . For those stars that do not
explode we follow the evolution beyond the phase of black hole formation. We compute the neutrino
energy loss rates due to several processes that may be relevant during the gravitational collapse of
these objects. The peak luminosities of neutrinos and antineutrinos of all flavors for models collapsing
to a BH are Lν ∼ 1055 erg/s. The total radiated energy in neutrinos varies between Eν ∼ 1056 ergs
for models collapsing to a BH, and Eν ∼ 1045 − 1046 ergs for models exploding.
Subject headings: Supermassive stars
1. INTRODUCTION massive BHs would form and then grow via merger and
There is large observational evidence of the presence accretion (Haiman & Loeb 2001; Yoo & Miralda-Escud´ e
of supermassive black holes (SMBHs) in the centres of 2004; Alvarez et al. 2009).
most nearby galaxies (Rees 1998). The dynamical evi- Another possible scenario proposes that if sufficient
dence related to the orbital motion of stars in the cluster primordial gas in massive halos, with mass ∼ 108 M⊙ , is
surrounding Sgr A∗ indicates the presence of a SMBH unable to cool below Tvir 104 K, it may lead to the for-
with mass ≈ 4 × 106 M⊙ (Genzel et al. 2000). In addi- mation of a supermassive object (Bromm & Loeb 2003;
tion, the observed correlation between the central black Begelman et al. 2006), which would eventually collapse
hole masses and the stellar velocity dispersion of the to form a SMBH. This route assumes that fragmenta-
bulge of the host galaxies suggests a direct connection tion, which depends on efficient cooling, is suppressed,
between the formation and evolution of galaxies and possibly by the presence of sufficiently strong UV radi-
SMBHs (Kormendy & Gebhardt 2001). ation, that prevents the formation of molecular hydro-
The observation of luminous quasars detected at red- gen in an environment with metallicity smaller than a
shifts higher than 6 in the Sloan Digital Sky Survey given critical value (Santoro & Shull 2006; Omukai et al.
(SDSS) implies that SMBHs with masses ∼ 109 M⊙ , 2008). Furthermore, fragmentation may depend on
which are believed to be the engines of such powerful the turbulence present within the inflow of gas, and
quasars, were formed within the first billion years af- on the mechanism redistributing its angular momen-
ter the Big Bang (e.g. Fan 2006 for a recent review). tum (Begelman & Shlosman 2009). The “bars-within-
However, it is still an open question how SMBH seeds bars” mechanism (Shlosman et al. 1989; Begelman et al.
form and grow to reach such high masses in such a short 2006) is a self-regulating route to redistribute angular
amount of time (Rees 2001). momentum and sustain turbulence such that the inflow
A number of different routes based on stellar dynamical of gas can proceed without fragmenting as it collapses
processes, hydrodynamical processes or a combination of even in a metal-enriched environment.
both have been suggested (e.g. Volonteri 2010 for a re- Depending on the rate and efficiency of the inflow-
cent review). One of the theoretical scenarios for SMBH ing mass, there may be different outcomes. A low
seed formation is the gravitational collapse of the first rate of mass accumulation would favor the formation
generation of stars (Population III stars) with masses of isentropic supermassive stars (SMSs), with mass ≥
M ∼ 100M⊙ that are expected to form in halos with 5 × 104 M⊙ , which then would evolve as equilibrium con-
virial temperature Tvir < 104 K at z ∼ 20 − 50 where figurations dominated by radiation pressure (Iben 1963;
cooling by molecular hydrogen is effective. As a result Hoyle & Fowler 1963; Fowler 1964). A different outcome
of the gravitational collapse of such Pop III stars, very could result if the accumulation of gas is fast enough so
that the outer layers of SMSs are not thermally relaxed
montero@mpa-garching.mpg.de during much of their lifetime, thus having an entropy
1 Max-Planck-Institut f¨ r Astrophysik, Karl-Schwarzschild-
u stratification (Begelman 2009).
Str. 1, D-85748 Garching, Germany; A more exotic mechanism that could eventually lead to
2. 2 Montero, Janka and M¨ller
u
a SMS collapsing into a SMBH is the formation and evo- about 90% of the total mass would end up in the final
lution of supermassive dark matter stars (SDMS) (Spol- SMBH with a spin parameter of J/M 2 ∼ 0.75.
yar et al 2008). Such stars would be composed pri- The gravitational collapse of differentially rotat-
marily of hydrogen and helium with only about 0.1% ing SMSs in three dimensions was investigated by
of their mass in the form of dark matter, however they Saijo & Hawke (2009), who focused on the post-BH evo-
would shine due to dark matter annihilation. It has re- lution, and also on the gravitational wave (GW) signal re-
cently been pointed out that SDMSs could reach masses sulting from the newly formed SMBH and the surround-
∼ 105 M⊙ (Freese et al. 2010). Once SDMSs run out of ing disk. The GW signal is expected to be emitted in
their dark matter supply, they experience a contraction the low frequency LISA band (10−4 − 10−1 Hz).
phase that increases their baryon density and tempera- Despite the progress made, the final fate rotating isen-
ture, leading to an environment where nuclear burning tropic SMSs is still unclear. In particular, it is still
may become important for the subsequent stellar evolu- an open question for which initial metallicities hydrogen
tion. burning by the β-limited hot CNO cycle and its break-
If isentropic SMSs form, their quasi-stationary evolu- out via the 15 O(α, γ)19 Ne reaction (rp-process) can halt
tion of cooling and contraction will drive the stars to the gravitational collapse of rotating SMSs and gener-
the onset of a general relativistic gravitational instabil- ate enough thermal energy to lead to an explosion. To
ity leading to their gravitational collapse (Chandrasekhar address this issue, we perform a series of general relativis-
1964; Fowler 1964), and possibly also to the for- tic hydrodynamic simulations with a microphysical EOS
mation of a SMBH. The first numerical simula- accounting for contributions from radiation, electron-
tions, within the post-Newtonian approximation, of positron pairs, and baryonic matter, and taking into ac-
Appenzeller & Fricke (1972) concluded that for spheri- count the net thermonuclear energy released by the nu-
cal stars with masses greater than 106 M⊙ thermonuclear clear reactions involved in hydrogen burning through the
reactions have no major effect on the collapse, while less pp-chain, cold and hot CNO cycles and their break-out
massive stars exploded due to hydrogen burning. Later by the rp-process, and helium burning through the 3-
Shapiro & Teukolsky (1979) performed the first relativis- α reaction. The numerical simulations were carried out
tic simulations of the collapse of a SMS in spherical sym- with the Nada code (Montero et al. 2008), which solves
metry. They were able to follow the evolution until the the Einstein equations coupled to the general relativistic
formation of a BH, although their investigations did not hydrodynamics equations.
include any microphysics. Fuller et al. (1986) revisited Greek indices run from 0 to 3, Latin indices from 1 to 3,
the work of Appenzeller & Fricke (1972) and performed and we adopt the standard convention for the summation
simulations of non-rotating SMSs in the range of 105 - over repeated indices. Unless otherwise stated we use
106 M⊙ with post-Newtonian corrections and detailed mi- units in which c = G = 1.
crophysics that took into account an equation of state
(EOS) including electron-positron pairs, and a reaction 2. BASIC EQUATIONS
network describing hydrogen burning by the CNO cy- Next we briefly describe how the system of Einstein
cle and its break-out via the rapid proton capture (rp)- and hydrodynamic equations are implemented in the
process. They found that SMSs with zero initial metal- Nada code. We refer to Montero et al. (2008) for a more
licity do not explode, while SMSs with masses larger than detailed description of the main equations and thorough
105 M⊙ and with metallicity ZCN O ≥ 0.005 do explode. testing of the code (namely single BH evolutions, shock
More recently Linke et al. (2001) carried out general tubes, evolutions of both spherical and rotating relativis-
relativistic hydrodynamic simulations of the spherically tic stars, gravitational collapse to a BH of a marginally
symmetric gravitational collapse of SMSs adopting a stable spherical star, and simulations of a system formed
spacetime foliation with outgoing null hypersurfaces to by a BH surrounded by a self-gravitating torus in equi-
solve the system of Einstein and fluid equations. They librium).
performed simulations of spherical SMSs with masses in
the range of 5 × 105 M⊙ − 109 M⊙ using an EOS that 2.1. Formulation of Einstein equations
accounts for contributions from baryonic gases, and in
a tabulated form, radiation and electron-positron pairs. 2.1.1. BSSN formulation
They were able to follow the collapse from the onset We follow the 3+1 formulation in which the spacetime
of the instability until the point of BH formation, and is foliated into a set of non-intersecting spacelike hyper-
showed that an apparent horizon enclosing about 25% of surfaces. In this approach, the line element is written in
the stellar material was formed in all cases when simula- the following form
tions stopped.
Shibata & Shapiro (2002) carried out general relativis- ds2 = −(α2 − βi β i )dt2 + 2βi dxi dt + γij dxi dxj , (1)
tic numerical simulations in axisymmetry of the collapse
of uniformly rotating SMSs to BHs. They did not take where α, β i and γij are the lapse function, the shift three-
into account thermonuclear burning, and adopted a Γ- vector, and the three-metric, respectively. The latter is
law EOS, P = (Γ − 1)ρǫ with adiabatic index Γ = 4/3, defined by
where P is the pressure, ρ the rest-mass density, and γµν = gµν + nµ nν , (2)
ǫ the specific internal energy. Although their simula-
tions stopped before the final equilibrium was reached, where nµ is a timelike unit-normal vector orthogonal to
the BH growth was followed until about 60% of the mass a spacelike hypersurface.
had been swallowed by the SMBH. They estimated that We make use of the BSSN formulation (Nakamura
1987; Shibata & Nakamura 1995; Baumgarte & Shapiro
3. Collapse of supermassive stars 3
1999) to solve the Einstein equations. Initially, a confor- are rewritten in Cartesian coordinates for y = 0. The fol-
mal factor φ is introduced, and the conformally related lowing definitions for the hydrodynamical variables are
metric is written as used
ρ∗ ≡ ρW e6φ , (10)
γij = e−4φ γij
˜ (3)
such that the determinant of the conformal metric, γij ,
˜ ui uj
ˆ
vi ≡ t
= −β i + αγ ij , (11)
is unity and φ = ln(γ)/12, where γ = det(γij ). We u hW
also define the conformally related traceless part of the ui ≡ hui ,
ˆ (12)
extrinsic curvature Kij ,
e6φ P
˜ 1 ˆ≡
e Tµν nµ nν = hW − , (13)
Aij = e−4φ Aij = e−4φ Kij − γij K , (4) ρ∗ ρW
3
W ≡ αut , (14)
where K is the trace of the extrinsic curvature. We
evolve the conformal factor defined as χ ≡ e−4φ where W and h are the Lorentz factor and the specific
˜
(Campanelli et al. 2006), and the auxiliary variables Γi , fluid enthalpy respectively, and P is the pressure. The
known as the conformal connection functions, defined as conserved variables are ρ∗ , Ji = ρ∗ ui , E∗ = ρ∗ˆ. We
ˆ e
refer to Shibata (2003) for further details.
˜ ˜ ˜
Γi ≡ γ jk Γi jk = −∂j γ ij ,
˜ (5)
3. SUPERMASSIVE STARS AND MICROPHYSICS
˜
where Γi jk are the connection coefficients associated 3.1. Properties of SMSs
with γij .
˜
During the evolution we also enforce the constraints Isentropic SMSs are self-gravitating equilibrium con-
˜ figurations of masses in the range of 104 − 108 M⊙ , which
Tr(Aij ) = 0 and det(˜ij ) = 1 at every time step.
γ
are mainly supported by radiation pressure, while the
We use the Cartoon method (Alcubierre et al. 2001) to
pressure of electron-positron pairs and of the baryon gas
impose axisymmetry while using Cartesian coordinates.
are only minor contributions to the EOS. Such configu-
2.1.2. Gauge choices
rations are well described by Newtonian polytropes with
polytropic index n = 3 (adiabatic index Γ = 4/3). The
In addition to the BSSN spacetime variables ratio of gas pressure to the total pressure (β) for spherical
γ ˜ ˜
(˜ij , Aij , K, χ, Γi ), there are two more quantities left un- SMSs can be written as (Fowler & Hoyle 1966)
determined, the lapse, α and the shift vector β i . We used 1/2
the so-called “non-advective 1+log” slicing (Bona et al. Pg 4.3 M⊙
1997), by dropping the advective term in the “1+log” β= ≈ , (15)
Ptot µ M
slicing condition. In this case, the slicing condition takes
the form where µ is the mean molecular weight. Thus β ≈ 10−2
∂t α = −2αK. (6) for M ≈ 106 M⊙ .
Since nuclear burning timescales are too long for
For the shift vector, we choose the “Gamma-freezing con- M 104 M⊙ , evolution of SMSs proceeds on the Kelvin-
dition” (Alcubierre et al. 2003) written as Helmholtz timescale and is driven by the loss of energy
3 i and entropy by radiation as well as loss of angular mo-
∂t β i = B, (7) mentum via mass shedding in the case of rotating con-
4 figurations.
˜
∂t B i = ∂t Γi − ηB i , (8) Although corrections due to the nonrelativistic gas of
baryons and electrons and general relativistic effects are
where η is a constant that acts as a damping term, orig- small, they cannot be neglected for the evolution. Firstly,
inally introduced both to prevent long term drift of the gas corrections raise the adiabatic index slightly above
metric functions and to prevent oscillations of the shift 4/3
vector.
4 β
Γ≈ + + 0(β 2 ). (16)
2.2. Formulation of the hydrodynamics equations 3 6
The general relativistic hydrodynamics equations, ex- Secondly, general relativistic corrections lead to the
pressed through the conservation equations for the stress- existence of a maximum for the equilibrium mass as a
energy tensor T µν and the continuity equation are function of the central density. For spherical SMSs this
means that for a given mass the star evolves to a critical
∇µ T µν = 0 , ∇µ (ρuµ ) = 0, (9) density beyond which it is dynamically unstable against
radial perturbations (Chandrasekhar 1964):
where ρ is the rest-mass density, uµ is the fluid four-
velocity and ∇ is the covariant derivative with respect to
3 7/2
the spacetime metric. Following Shibata (2003), the gen- 0.5 M⊙
eral relativistic hydrodynamics equations are written in ρcrit = 1.994 × 1018 gcm−3 . (17)
µ M
a conservative form in cylindrical coordinates. Since the
Einstein equations are solved only in the y = 0 plane with The onset of the instability also corresponds to a criti-
Cartesian coordinates (2D), the hydrodynamic equations cal value of the adiabatic index Γcrit , i.e. configurations
4. 4 Montero, Janka and M¨ller
u
become unstable when the adiabatic index drops below possible to compute the temperature T by a Newton-
the critical value Raphson algorithm that solves the equation ǫ∗ (ρ, T ) = ǫ
for T ,
4 2GM
Γcrit = + 1.12 . (18)
3 Rc2 ∂ǫ∗ (ρ, T )
−1
This happens when the stabilizing gas contribution to Tn+1 = Tn − (ǫ∗ (ρ, Tn ) − ǫ) , (22)
∂T Tn
the EOS does not raise the adiabatic index above 4/3 to
compensate for the destabilizing effect of general relativ- where n is the iteration counter.
ity expressed by the second term on the righ-hand-side
of Eq. (18). 3.3. Nuclear burning
Rotation can stabilize configurations against the ra- In order to avoid the small time steps, and CPU-time
dial instability. The stability of rotating SMSs with demands connected with the solution of a nuclear reac-
uniform rotation was analyzed by Baumgarte & Shapiro tion network coupled to the hydrodynamic evolution, we
(1999a,b). They found that stars at the onset of the apply an approximate method to take into account the
instability have an equatorial radius R ≈ 640GM/c2, a basic effects of nuclear burning on the dynamics of the
spin parameter q ≡ cJ/GM 2 ≈ 0.97, and a ratio of rota- collapsing SMSs. We compute the nuclear energy re-
tional kinetic energy to the gravitational binding energy lease rates by hydrogen burning (through the pp-chain,
of T /W ≈ 0.009. cold and hot CNO cycles, and their break-out by the rp-
process) and helium burning (through the 3-α reaction)
3.2. Equation of State as a function of rest-mass density, temperature and mass
To close the system of hydrodynamic equations (Eq. 9) fractions of hydrogen X, helium Y and CNO metallicity
we need to define the EOS. We follow a treatment which ZCN O . These nuclear energy generation rates are added
includes separately the baryon contribution on the one as a source term on the right-hand-side of the evolution
hand, and photons and electron-positron pairs contri- equation for the conserved quantity E∗ .
butions, in a tabulated form, on the other hand. The The change rates of the energy density due to nuclear
baryon contribution is given by the analytic expressions reactions, in the fluid frame, expressed in units of [erg
for the pressure and specific internal energy cm−3 s−1 ] are given by:
RρT • pp-chain (Clayton 1983):
Pb = , (19)
µb
2 RρT ∂e
ǫb = , (20) = ρ(2.38 × 106 ρg11 X 2 T6
−0.6666
3 µb ∂t pp
0.3333
where R the universal gas constant, T the temperature, e−33.80/T6 ), (23)
ǫb the baryon specific internal energy, and µb is the mean
molecular weight due to ions, which can be expressed as where T6 = T /106K, and g11 is given by
a function of the mass fractions of hydrogen (X), helium 0.3333
g11 = 1 + 0.0123T6 0.66666
+ 0.0109T6 +
(Y ) and heavier elements (metals) (ZCN O ) as
0.0009T6. (24)
1 Y ZCN O
≈X+ + , (21)
µb 4 A • 3-α (Wiescher et al. 1999):
where A is the average atomic mass of the heavy el- ∂e
ements. We assume that the composition of SMSs (ap- = ρ(5.1 × 108 ρ2 Y 3 T9 e−4.4/T9 ),
−3
(25)
∂t 3α
proximately that of primordial gas) has a mass fraction of
hydrogen X = 0.75 − ZCN O and helium Y = 0.25, where where T9 = T /109K.
the metallity ZCN O = 1 − X − Y is an initial parameter,
typically of the order of ZCN O ∼ 10−3 (see Table 1 de- • Cold-CNO cycle (Shen & Bildsten 2007):
tails). Thus, for the initial compositions that we consider
the mean molecular weight of baryons is µb ≈ 1.23 (i.e.
corresponding to a molecular weight for both ions and ∂e
= 4.4 × 1025 ρ2 XZCN O
electrons of µ ≈ 0.59). ∂t CCN O
Effects associated with photons and the creation of 1/3
−2/3 −15.231/T9
electron-positron pairs are taken into account employ- (T9 e +
ing a tabulated EOS. At temperatures above 109 K, not + 8.3 × 10 −5 −3/2 −3.0057/T9
T9 e ). (26)
all the energy is used to increase the temperature and
pressure, but part of the photon energy is used to create
the rest-mass of the electron-positron pairs. As a result • Hot-CNO cycle (Wiescher et al. 1999):
of pair creation, the adiabatic index of the star decreases,
which means that the stability of the star is reduced. ∂e
Given the specific internal energy, ǫ and rest-mass den- = 4.6 × 1015 ρZCN O . (27)
sity, ρ, as evolved by the hydrodynamic equations, it is ∂t HCN O
5. Collapse of supermassive stars 5
• rp-process (Wiescher et al. 1999): SMSs. The rates are computed using the fitting
formula given by Haft et al. (1994).
∂e
= ρ(1.77 × 1016 ρY ZCN O 4. COMPUTATIONAL SETUP
∂t rp
−3/2 −5.85/T9 The evolution equations are integrated by the method
29.96T9 e ). (28) of lines, for which we use an optimal strongly stability-
preserving (SSP) Runge-Kutta algorithm of fourth-order
Since we follow a single fluid approach, in which we with 5 stages (Spiteri & Ruuth 2002). We use a second-
solve only the hydrodynamics equations Eq. (9) (i.e. we order slope limiter reconstruction scheme (MC limiter) to
do not solve additional advection equations for the abun- obtain the left and right states of the primitive variables
dances of hydrogen, helium and metals), the elemental at each cell interface, and a HLLE approximate Riemann
abundances during the time evolution are fixed. Nev- solver (Harten et al. 1983; Einfeldt 1988) to compute the
ertheless, this assumption most possibly does not af- numerical fluxes in the x and z directions.
fect significantly the estimate of the threshold metallicity Derivative terms in the spacetime evolution equa-
needed to produce a thermal bounce in collapsing SMSs. tions are represented by a fourth-order centered finite-
The average energy release through the 3-α reaction is difference approximation on a uniform Cartesian grid ex-
about 7.275 MeV for each 12 C nucleus formed. Since the cept for the advection terms (terms formally like β i ∂i u),
total energy due to helium burning for exploding mod- for which an upwind scheme is used.
els is ∼ 1045 ergs (e.g. 9.0 × 1044 ergs for model S1.c); The computational domain is defined as 0 ≤ x ≤ L and
and even considering that this energy is released mostly 0 ≤ z ≤ L, where L refers to the location of the outer
in a central region of the SMS containing 104 M⊙ of its boundaries. We used a cell-centered Cartesian grid to
rest-mass (Fuller et al. 1986), it is easy to show that the avoid that the location of the BH singularity coincides
change in the metallicity is of the order of 10−11 . There- with a grid point.
fore, the increase of the metallicity in models experienc-
ing a thermal bounce is much smaller than the critical 4.1. Regridding
metallicities needed to trigger the explosions. Similarly,
the average change in the mass fraction of hydrogen due Since it is not possible to follow the gravitational
to the cold and hot CNO cycles is expected to be ∼ 10% collapse of a SMS from the early stages to the phase
for exploding models. of black hole formation with a uniform Cartesian
grid (the necessary fine zoning would be computation-
3.4. Recovery of the primitive variables ally too demanding), we adopt a regridding procedure
(Shibata & Shapiro 2002). During the initial phase of
After each time iteration the conserved variables the collapse we rezone the computational domain by
(i.e. ρ∗ , Jx , Jy , Jz , E∗ ) are updated and the primitive hy- moving the outer boundary inward, decreasing the grid
drodynamical variables (i.e. ρ, v x , v y , v z , ǫ) have to be re- spacing while keeping the initial number of grid points
covered. The recovery is done in such a way that it allows fixed. Initially we use N ×N = 400×400 grid points, and
for the use of a general EOS of the form P = P (ρ, ǫ). place the outer boundary at L ≈ 1.5re where re is the
We calculate a function f (P ∗ ) = P (ρ∗ , ǫ∗ ) − P ∗ , where equatorial radius of the star. Rezoning onto the new grid
ρ∗ and ǫ∗ depend only on the conserved quantities and is done using a polynomial interpolation. We repeat this
the pressure guess P ∗ . The new pressure is computed procedure 3-4 times until the collapse timescale in the
then iteratively by a Newton-Raphson method until the central region is much shorter than in the outer parts.
desired convergence is achieved. At this point, we both decrease the grid spacing and also
increase the number of grid points N in dependence of
3.5. Energy loss by neutrino emission the lapse function typically as follows: N ×N = 800×800
The EOS allows us to compute the neutrino losses due if 0.8 > α > 0.6, N × N = 1200 × 1200 if 0.6 > α > 0.4,
to the following processes, which become most relevant and N × N = 1800 × 1800 if α < 0.4. This procedure en-
just before BH formation: sures the error in the conservation of the total rest-mass
to be less than 2% on the finest computational domain.
• Pair annihilation (e+ + e− → ν + ν): most impor-
¯
tant process above 109 K. Due to the large mean 4.2. Hydro-Excision
free path of neutrinos in the stellar medium at the To deal with the spacetime singularity from the newly
densities of SMSs the energy loss by neutrinos can formed BH we use the method of excising the matter
be significant. For a 106 M⊙ SMS most of the en- content in a region within the horizon as proposed by
ergy release in the form of neutrinos originates from Hawke et al. (2005) once an apparent horizon (AH) is
this process. The rates are computed using the fit- found. This excision is done only for the hydrodynamical
ting formula given by Itoh et al. (1996). variables, and the coordinate radius of the excised region
• Photo-neutrino emission (γ + e± → e± + ν + ν):
¯ is allowed to increase in time. On the other hand, we do
neither use excision nor artificial dissipation terms for
dominates at low temperatures T 4 × 108 K and the spacetime evolution, and solely rely on the gauge
densities ρ 105 gcm−3 (Itoh et al. 1996). conditions.
• Plasmon decay (γ → ν + ν): This is the least rele-
¯
vant process for the conditions encountered by the 4.3. Definitions
models we have considered because its importance Here we define some of the quantities listed in Table 1.
increases at higher densities than those present in We compute the total rest-mass M∗ and the ADM mass
6. 6 Montero, Janka and M¨ller
u
TABLE 1
Main properties of the initial models studied. From left to right the columns show: model, gravitational mass, initial
central rest-mass density, Tk /|W |, angular velocity, initial central temperature, metallicity, the fate of the star, radial
kinetic energy after thermal bounce, and total neutrino energy output.
Model M ρc Tk /|W | Ω Tc Initial metallicity Fate ERK Eν
[105 M⊙ ] [10−2 g/cm3 ] [10−5 rad/s] [107 K] [10−3 ] [1056 erg] [erg]
S1.a 5 2.4 0 0 5.8 5 BH ... 3.4 × 1056
S1.b 5 2.4 0 0 5.8 6 BH .. ...
S1.c 5 2.4 0 0 5.8 7 Explosion 5.5 9.4 × 1045
R1.a 5 40 0.0088 2.49 13 0.5 BH ... 5.4 × 1056
R1.b 5 40 0.0088 2.49 13 0.8 BH ... ...
R1.c 5 40 0.0088 2.49 13 1 Explosion 1.0 ...
R1.d 5 40 0.0088 2.49 13 2 Explosion 1.9 8.9 × 1045
S2.a 10 0.23 0 0 2.6 30 BH ... 6.8 × 1056
S2.b 10 0.23 0 0 2.6 50 Explosion 35 8.0 × 1046
R2.a 10 12 0.0087 1.47 9.7 0.5 BH ... 3.1 × 1056
R2.b 10 12 0.0087 1.47 9.7 0.8 BH ... ...
R2.c 10 12 0.0087 1.47 9.7 1.0 BH ... ...
R2.d 10 12 0.0087 1.47 9.7 1.5 Explosion 1.5 2.1 × 1046
M as for the onset of the collapse of a configuration with
L L
given mass and entropy. A list of the different SMSs
M∗ = 4π xdx ρ∗ dz, (29) we have considered is provided in Table 1. Models S1
0 0
and S2 represent a spherically symmetric, nonrotating
L L
SMS with gravitational mass of M = 5 × 105 M⊙ and
eφ ˜ M = 1 × 106 M⊙ , respectively, while models R1 and R2
M = −2 xdx dz −2πEe5φ + R
0 0 8 are uniformly rotating initial models again with masses
of M = 5 × 105 M⊙ and M = 1 × 106 M⊙ , respec-
e5φ ˜ ˜ 2 tively. The rigidly and maximally rotating initial models
− Aij Aij − K 2 , (30)
8 3 R1 and R2 are computed with the Lorene code (URL
http://www.lorene.obspm.fr). We also introduce a per-
where E = nµ nν T µν (nµ being the unit normal to the turbation to trigger the gravitational collapse by reduc-
˜
hypersurface) and R is the scalar curvature associated to ing the pressure overall by ≈ 1.5%.
the conformal metric γij .
˜ In order to determine the threshold metallicity re-
The rotational kinetic energy Tk and the gravitational quired to halt the collapse and produce an explosion we
potential energy W are given by carry out several numerical simulations for each initial
L L model with different values of the initial metallicity. The
Tk = 2π x2 dx ρ∗ uy Ωdz,
ˆ (31) initial metallicities along with the fate of the star are
0 0 given in Table 1.
where Ω is the angular velocity.
6. RESULTS
W = M − (M∗ + Tk + Eint ), (32)
6.1. Collapse to BH vs. Thermonuclear explosion
where the internal energy is computed as First we consider a gravitationally unstable spheri-
L L cally symmetric SMS with a gravitational mass of M =
Eint = 4π xdx ρ∗ ǫdz. (33) 5 × 105 M⊙ (S1.a, S1.b and S1.c), which corresponds to
0 0 a model extensively discussed in Fuller et al. (1986),
and therefore allows for a comparison with the results
In axisymmetry the AH equation becomes a nonlinear presented here. Fuller et al. (1986) found that unstable
ordinary differential equation for the AH shape function,
spherical SMSs with M = 5×105 M⊙ and an initial metal-
h = h(θ) (Shibata 1997; Thornburg 2007). We employ
licity ZCN O = 2 × 10−3 collapse to a BH while models
an AH finder that solves this ODE by a shooting method
with an initial metallicity ZCN O = 5 × 10−3 explode due
using ∂θ h(θ = 0) = 0 and ∂θ h(θ = π/2) = 0 as boundary
to the nuclear energy released by the hot CNO burning.
conditions. We define the mass of the AH as
They also found that the central density and tempera-
A ture at thermal bounce (where the collapse is reversed to
MAH = , (34) an explosion) are ρc,b = 3.16 g/cm3 and Tc,b = 2.6 × 108
16π
K, respectively.
where A is the area of the AH. The left panels in Figure 1 show the time evolution of
the central rest-mass density (upper panel) and central
5. INITIAL MODELS temperature (lower panel) for models S1.a, S1.c, R1.a
The initial SMSs are set up as isentropic objects. All and R1.d, i.e., non-rotating and rotating models with a
models are chosen such that they are gravitationally un- mass of M = 5 × 105 M⊙ . In particular, the solid lines
stable, and therefore their central rest-mass density is represent the time evolution of the central density and
slightly larger than the critical central density required temperature for model S1.c (ZCN O = 7×10−3 ) and R1.d
7. Collapse of supermassive stars 7
Fig. 1.— Left upper panel shows the time evolution of the central rest-mass density for models S1 and R1 (i.e., spherical and rotating
stars with mass M = 5 × 105 M⊙ ), and the lower left panel shows the time evolution of the central temperature. Horizontal dotted lines
mark the temperature range in which nuclear energy is primarily released by the hot CNO cycle. Similarly, the time evolution of the
same quantities for model S2 and R2 (i.e., spherical and rotating stars with mass M = 1 × 106 M⊙ ) are shown in the upper and lower
right panels. As the collapse proceeds, the central density and temperature rise rapidly, increasing the nuclear energy generation rate by
hydrogen burning. If the metallicity is sufficiently high, enough energy can be liberated to produce a thermal bounce. This is the case for
models S1.c, R1.d, S2.b and R2.d shown here.
(ZCN O = 5 × 10−4 ). As the collapse proceeds, the cen- at t ≈ 7.31 × 105 s and begins to expand into the low
tral density and temperature rise rapidly, which increases density outer layers of the SMS.
the nuclear energy generation rate by hydrogen burning. The evolutionary tracks for the central density and
Since the metallicity is sufficiently high, enough energy temperature of the rotating models R1.a and R1.d are
can be liberated to increase the pressure and to produce a also shown in Figure 1. A dashed line corresponds to
thermal bounce. This is the case for model S1.c. In Fig- model R1.a, with an initial metallicity ZCN O = 5×10−4 ,
ure 1 we show that a thermal bounce occurs (at approxi- which collapses to a BH. A solid line denotes model R1.d
mately t ∼ 7 × 105 s) entirely due to the hot CNO cycle, with ZCN O = 2×10−3, which explodes due to the energy
which is the main source of thermonuclear energy at tem- released by the hot CNO cycle. We find that Model R1.c
peratures in the range 2 × 108 K ≤ T ≤ 5 × 108 K. The with a lower metallicity of ZCN O = 1×10−3 also explodes
rest-mass density at bounce is ρc,b = 4.8 g/cm3 and the when the central temperature is the range dominated by
temperature Tc,b = 3.05 × 108K. These values, as well as the hot CNO cycle.
the threshold metallicity needed to trigger a thermonu- As a result of the kinetic energy stored in the rotation
clear explosion (ZCN O = 7×10−3 ), are higher than those of models R1.c and R1.d, the critical metallicity needed
found by Fuller et al. (1986) (who found that a spher- to trigger an explosion decreases significantly relative to
ical nonrotating model with the same rest-mass would the non-rotating case. We observe that rotating models
explode, if the initial metallicity was ZCN O = 5 × 10−3 ). with initial metallicities up to ZCN O = 8 × 10−4 do not
On the other hand, dashed lines show the time evo- explode even via the rp-process, which is dominant at
lution of the central density and temperature for model temperatures above T ≈ 5 × 108 K and increases the
S1.a (ZCN O = 5 × 10−3 ). In this case, as well as for hydrogen burning rate by 200 − 300 times relative to
model S1.b, the collapse is not halted by the energy re- the hot CNO cycle. We also note that the evolution
lease and continues until an apparent horizon is found, time scales of the collapse and bounce phases are reduced
indicating the formation of a BH. because rotating models are more compact and have a
We note that the radial velocity profiles change contin- higher initial central density and temperature than the
uously near the time where the collapse is reversed to an spherical ones at the onset of the gravitational instability.
explosion due to the nuclear energy released by the hot The right panels in Figure 1 show the time evolu-
CNO burning, and an expanding shock forms only near tion of the central rest-mass density (upper panel) and
the surface of the star at a radius R ≈ 1.365 × 1013 cm the central temperature (lower panel) for models S2.a,
(i.e. R/M ≈ 180) where the rest-mass density is ≈ S2.b, R2.a and R2.d, i.e., of models with a mass of
3.5 × 10−6gcm−3 . We show in Figure 2 the profiles of the M = 106 M⊙ . We find that the critical metallicity for an
x-component of the three-velocity v x along the x-axis explosion in the spherical case is ZCN O = 5×10−2 (model
(in the equatorial plane) for the nonrotating spherical S2.b), while model S2.a with ZCN O = 3 × 10−2 collapses
stars S1.a (dashed lines) and S1.c (solid lines) at three to a BH. We note that the critical metallicity leading to a
different time slices near the time at which model S1.c thermonuclear explosion is higher than the critical value
experiences a thermal bounce. Velocity profiles of model found by Fuller et al. (1986) (i.e., ZCN O = 1 × 10−2 ) for
S1.c are displayed up to the radius where a shock forms a spherical SMS with the same mass. The initial metal-
licity leading to an explosion in the rotating case (model
8. 8 Montero, Janka and M¨ller
u
Fig. 2.— Profiles of the x-component of the three-velocity vx Fig. 3.— Nuclear energy generation rate in erg/s for the explod-
along the x-axis (in the equatorial plane) for the nonrotating spher- ing models (S1.c, R1.d, R1.c, S2.b and R2.d) as a function of time
ical stars S1.a (dashed lines) and S1.c (solid lines) at three different near the bounce. The contribution to the nuclear energy gener-
time slices near the time at which model S1.c experiences a ther- ation is mainly due to hydrogen burning by the hot CNO cycle.
mal bounce. Velocity profiles of model S1.c are displayed up to the The peak values of the energy generation rate at bounce lie be-
radius where takes place the formation of a shock that expands tween ≈ 1051 [erg/s] for the rotating models (R1.d and R2.d), and
into the low density outer layers of the SMS. ≈ 1052 − 1053 [erg/s] for the spherical models (S1.c and S2.b).
R2.d) is more than an order of magnitude smaller than in estimate the photon luminosity produced in association
the spherical case. As for the models with a smaller grav- with the thermonuclear explosion, we make use of the
itational mass, the thermal bounce takes place when the fact that within the diffusion approximation the radia-
physical conditions in the central region of the star allow tion flux is given by
for the release of energy by hydrogen burning through
the hot CNO cycle. Overall, the dynamics of the more c
massive models indicates that the critical initial metal- Fγ = − ∇U, (35)
3κes ρ
licity required to produce an explosion increases with the
rest-mass of the star. where U is the energy density of the radiation, and κes is
Figure 3 shows the total nuclear energy generation rate the opacity due to electron Thompson scattering, which
in erg/s for the exploding models as a function of time is the main source of opacity in SMSs. The photon lumi-
during the late stages of the collapse just before and af- nosity in terms of the temperature gradient and for the
ter bounce. The main contribution to the nuclear energy spherically symmetric case can be written as
generation is due to hydrogen burning by the hot CNO 16πacr2 T 3 ∂T
cycle. The peak values of the energy generation rate Lγ = − , (36)
at bounce lie between several 1051 erg/s for the rotating 3κes ρ ∂r
models (R1.d and R2.d), and ≈ 1052 − 1053 erg/s for the where a is the radiation constant, and c the speed of light.
spherical models (S1.c and S2.b). As expected the max- As can be seen in the last panel of Figure 4 the distribu-
imum nuclear energy generation rate needed to produce tion of matter becomes spherically symmetric during the
an explosion is lower in the rotating models. Moreover, phase of expansion after the thermonuclear explosion. In
as the explosions are due to the energy release by hy- this figure (Fig. 4) we show the isodensity contours for
drogen burning via the hot CNO cycle, the ejecta would the rotating model R1.d. The frames have been taken at
mostly be composed of 4 He. the initial time (left figure), at t = 0.83 × 105 s (central
As a result of the thermal bounce, the kinetic energy figure) just after the thermal bounce (at t = 0.78 × 105 s),
rises until most of the energy of the explosion is in the and at t = 2.0 × 105 s when the radius of the expanding
form of kinetic energy. We list in the second but last matter is roughly 4 times the radius of the star at the
column of Table 1 the radial kinetic energy after thermal onset of the collapse.
bounce, which ranges between ERK = 1.0 × 1055 ergs for The photon luminosity computed using Eq.(36) for
the rotating star R1.c, and ERK = 3.5 × 1057 ergs for the model R1.d is displayed in Figure 5, where we also in-
spherical star S2.b. dicate with a dashed vertical line the time at which the
thermal bounce takes place. The photon luminosity be-
6.2. Photon luminosity fore the thermal bounce is computed at radii inside the
Due to the lack of resolution at the surface of the star, star unaffected by the local dynamics of the low den-
it becomes difficult to compute accurately the photo- sity outer layers which is caused by the initial pressure
sphere and its effective temperature from the criterion perturbation and by the interaction between the surface
that the optical depth is τ = 2/3. Therefore, in order to of the SMS and the artificial atmosphere. Once the ex-
9. Collapse of supermassive stars 9
Fig. 4.— Isodensity contours of the logarithm of the rest-mass density (in g/cm3 ) for the rotating model R1.d. The frames have been
taken at the initial time (left figure), at t = 0.83 × 105 s (central figure) just after a thermal bounce takes place, and at t = 2.0 × 105 s
when the radius of the expanding matter is roughly 4 times the radius of the star at the onset of the collapse.
Fuller et al. 1986 for a nonrotating star).
6.3. Collapse to BH and neutrino emission
The outcome of the evolution of models that do not
generate enough nuclear energy during the contraction
phase to halt the collapse is the formation of a BH.
The evolutionary tracks for the central density and tem-
perature of some of these models are also shown in
Figure 1. The central density typically increases up
to ρc ∼ 107 gcm−3 and the central temperature up to
Tc ∼ 1010 K just before the formation of an apparent
horizon.
Three isodensity contours for the rotating model R1.a
collapsing to a BH are shown in Figure 6, which display
the flattening of the star as the collapse proceeds. The
frames have been taken at the initial time (left panel),
at t = 0.83 × 105 s (central panel) approximately when
model R1.d with higher metallicity experiences a thermal
bounce and, at t = 1.127 × 105s, where a BH has already
formed and its AH has a mass of 50% of the total initial
mass.
Fig. 5.— Logarithm of the photon luminosity of model R1.d At the temperatures reached during the late stages of
in units of erg/s as a function of time. The vertical dashed line the gravitational collapse (in fact at T ≥ 5 × 108 K) the
indicates the time at which the thermal bounce takes place. most efficient process for hydrogen burning is the break-
out from the hot CNO cycle via the 15 O(α, γ)19 Ne re-
panding shock forms near the surface, the photon lumi- action. Nevertheless, we find that models which do not
nosity is computed near the surface of the star. The release enough nuclear energy by the hot CNO cycle to
lightcurve shows that, during the initial phase, the lu- halt their collapse to a BH, are not able to produce a
minosity is roughly equal to the Eddington luminosity thermal explosion due to the energy liberated by the
15
≈ 5 × 1043 erg/s until the thermal bounce. Then, the O(α, γ)19 Ne reaction. We note that above 109 K, not
photon luminosity becomes super-Eddington when the all the liberated energy is used to increase the temper-
expanding shock reaches the outer layers of the star and ature and pressure, but is partially used to create the
reaches a value of Lγ ≈ 1 × 1045 erg/s. This value of rest-mass of the electron-positron pairs. As a result of
the photon luminosity after the bounce is within a few pair creation, the adiabatic index of the star decreases,
percent difference with respect to the photon luminos- which means the stability of the star is reduced. More-
ity Fuller et al. (1986) found for a nonrotating SMS of over, due to the presence of e± pairs, neutrino energy
same rest-mass. The photon luminosity remains super- losses grow dramatically.
Eddington during the phase of rapid expansion that fol- Figure 7 shows (solid lines) the time evolution of the
lows the thermal bounce. We compute the photon lu- redshifted neutrino luminosities of four models collaps-
minosity until the surface of the star reaches the outer ing to a BH (S1.a, R1.a, S2.a, and R2.a), and (dashed
boundary of the computational domain ≈ 1.0 × 105 lines) of four models experiencing a thermal bounce
after the bounce. Beyond that point, the luminosity (S1.c, R1.d, S2.b, and R2.d). The change of the slope
is expected to decrease, and then rise to a plateau of of the neutrino luminosities at ∼ 1043 erg/s denotes the
∼ 1045 erg/s due to the recombination of hydrogen (see transition from photo-neutrino emission to the pair an-
10. 10 Montero, Janka and M¨ller
u
Fig. 6.— Isodensity contours of the logarithm of the rest-mass density (in g/cm3 ) for the rotating model R1.a. The frames have been
taken at the initial time (left panel), at t = 0.83 × 105 s (central panel), at t = 1.127 × 105 s, where a BH has already formed and its
apparent horizon encloses a mass of 50% of the total initial gravitational mass.
nihilation dominated region. The peak luminosities in
all form of neutrino for models collapsing to a BH are
Lν ∼ 1055 erg/s. Neutrino luminosities can be that im-
portant because the densities in the core prior to BH
formation are ρc ∼ 107 gcm−3 , and therefore neutrinos
can escape. The peak neutrino luminosities lie between
the luminosities found by Linke et al. (2001) for the col-
lapse of spherical SMS, and those found by Woosley et al.
(1986) (who only took into account the luminosity in the
form of electron antineutrino). The maximum luminos-
ity decreases slightly as the rest-mass of the initial model
increases, which was already observed by Linke et al.
(2001). In addition, we find that the peak of the red-
shifted neutrino luminosity does not seem to be very sen-
sitive to the initial rotation rate of the star. We also note
that the luminosity of model R1.a reflects the effects of
hydrogen burning at Lν ∼ 1043 erg/s.
The total energy output in the form of neutrinos is
listed in the last column of Table 1 for several models.
The total radiated energies vary between Eν ∼ 1056 ergs
for models collapsing to a BH, and Eν ∼ 1045 − 1046
ergs for exploding models. These results are in reason-
able agreement with previous calculations. For instance, Fig. 7.— Time evolution of the redshifted neutrino luminosities
for models R1.a, S1.a, R2.a, and S2.a all collapsing to a BH; and for
Woosley et al. (1986) obtained that the total energy out- models R1.d, S1.c, R2.d, and S2.b experiencing a thermal bounce.
put in the form of electron antineutrinos for a spherical The time is measured relative to the collapse timescale of each
SMS with a mass 5 × 105 M⊙ and zero initial metallic- model, R1, S1, R2 and S2, with t0 ≈ (1, 7, 0.2, 6) in units of 105 s.
ity was 2.6 × 1056 ergs, although their simulations ne- due to the expansion and disruption of the star after the
glected general relativistic effects which are important bounce.
to compute accurately the relativistic redshifts. On the
other hand, Linke et al. (2001), by means of relativistic 6.4. Implications for gravitational wave emission
one-dimensional simulations, found a total radiated en- The axisymmetric gravitational collapse of rotating
ergy in form of neutrinos of about 3 × 1056 ergs for the SMSs with uniform rotation is expected to emit a burst
same initial model, and about 1 × 1056 ergs when red- of gravitational waves (Saijo et al. 2002; Saijo & Hawke
shifts were taken into account. In order to compare with 2009) with a frequency within the LISA low frequency
the results of Linke et al. (2001), we computed the red- band (10−4 − 10−1 Hz). Although through the simula-
shifted total energy output for Model S1.a, having the tions presented here we could not investigate the devel-
same rest-mass, until approximately the same evolution opment of nonaxisymmetric features in our axisymmet-
stage as Linke et al. (2001) did (i.e. when the differen- ric models that could also lead to the emission of GWs,
tial neutrino luminosity dLν /dr ∼ 4 × 1045 erg/s/cm). Saijo & Hawke (2009) have shown that the three dimen-
We find that the total energy released in neutrinos is sional collapse of rotating stars proceeds in a approxi-
1.1 × 1056 ergs. mately axisymmetric manner.
The neutrino luminosities for models experiencing a In an axisymmetric spacetime, the ×-mode vanishes
thermonuclear explosion (dashed lines in Fig. 7) peak at and the +-mode of gravitational waves with l = 2
much lower values Lν ∼ 1042 − 1043 erg/s, and decrease computed using the quadrupole formula is written as
11. Collapse of supermassive stars 11
(Shibata & Sekiguchi 2003)
¨ ¨
Ixx (tret ) − Izz (tret )
hquad =
+ sin2 θ, (37)
r
¨
where Iij refers to the second time derivative of the
quadrupole moment. The gravitational wave quadrupole
¨ ¨
amplitude is A2 (t) = Ixx (tret ) − Izz (tret ). Following
Shibata & Sekiguchi (2003) we compute the second time
derivative of the quadrupole moment by finite differenc-
ing the numerical results for the first time derivative of
Iij obtained by
˙
Iij = ρ∗ v i xj + xi v j d3 x. (38)
We calculate the characteristic gravitational wave
strain (Flanagan & Hughes 1998) as
2 G 1 dE(f )
hchar (f ) = , (39)
π c3 D2 df
where D is the distance of the source, and dE(f )/df Fig. 8.— Characteristic gravitational wave strain for model R1.a
the spectral energy density of the gravitational radiation assuming that the source is located at a distance of 50 Gpc, to-
gether with the design noise spectrum h(f ) = f Sh (f ) for LISA
given by detector.
dE(f ) c3 (2πf )2 ˜ 2
= A2 (f ) , (40) development of the nonaxisymmetric Papaloizou-Pringle
df G 16π instability during the evolution of such tori would lead to
with the emission of quasiperiodic GWs with peak amplitude
˜ ∼ 10−18 −10−19 and frequency ∼ 10−3 Hz and maintained
A2 (f ) = A2 (t)e2πif t dt. (41)
during the accretion timescale ∼ 105 s.
We have calculated the quadrupole gravitational wave 6.5. Conclusions
emission for the rotating model R1.a collapsing to a BH.
We plot in Figure 8 the characteristic gravitational wave We have presented results of general relativistic simu-
strain (Eq.39) for this model assuming that the source lations of collapsing supermassive stars using the two-
is located at a distance of 50 Gpc (i.e., z ≈ 11) , to- dimensional general relativistic numerical code Nada,
which solves the Einstein equations written in the BSSN
gether with the design noise spectrum h(f ) = f Sh (f )
formalism and the general relativistic hydrodynamic
of the LISA detector (Larson et al. 2000). We find that,
equations with high resolution shock capturing schemes.
in agreement with Saijo et al. (2002), Saijo & Hawke
These numerical simulations have used an EOS that in-
(2009) and Fryer & New (2011), the burst of gravita-
cludes the effects of gas pressure, and tabulated those
tional waves due to the collapse of a rotating SMS could
associated with radiation pressure and electron-positron
be detected at a distance of 50 Gpc and at a frequency
pairs. We have also taken into account the effects of
which approximately takes the form (Saijo et al. 2002)
thermonuclear energy release by hydrogen and helium
burning. In particular, we have investigated the effects
3/2 of hydrogen burning by the β-limited hot CNO cycle and
106 M⊙ 5M
fburst ∼ 3 × 10−3 [Hz], (42) its breakout via the 15 O(α, γ)19 Ne reaction (rp-process)
M R
on the gravitational collapse of nonrotating and rotating
where R/M is a characteristic mean radius during black SMSs with non-zero metallicity.
hole formation (typically set to R/M = 5). We have found that objects with a mass of ≈ 5×105M⊙
Furthermore, Kiuchi et al. (2011) have recently in- and an initial metallicity greater than ZCN O ≈ 0.007
vestigated, by means of three-dimensional general explode if non-rotating, while the threshold metallicity
relativistic numerical simulations of equilibrium tori for an explosion is reduced to ZCN O ≈ 0.001 for ob-
orbiting BHs, the development of the nonaxisym- jects which are uniformly rotating. The critical initial
metric Papaloizou-Pringle instability in such systems metallicity for a thermal explosion increases for stars
(Papaloizou & Pringle 1984), and have found that a non- with a mass of ≈ 106 M⊙ . The most important con-
axisymmetric instability associated with the m = 1 mode tribution to the nuclear energy generation is due to the
grows for a wide range of self-gravitating tori orbiting hot CNO cycle. The peak values of the nuclear energy
BHs, leading to the emission of quasiperiodic GWs. In generation rate at bounce range from ∼ 1051 erg/s for ro-
particular, Kiuchi et al. (2011) have pointed out that tating models (R1.d and R2.d), to ∼ 1052 − 1053 erg/s
the emission of quasiperiodic GWs from the torus result- for spherical models (S1.c and S2.b). After the ther-
ing after the formation of a SMBH via the collapse of a mal bounce, the radial kinetic energy of the explosion
SMS could be well above the noise sensitivity curve of rises until most of the energy is kinetic, with values
LISA for sources located at a distance of 10Gpc. The ranging from EK ∼ 1056 ergs for rotating stars, to up
12. 12 Montero, Janka and M¨ller
u
EK ∼ 1057 ergs for the spherical star S2.b. The neutrino the gravitational collapse of a SMS into an explosion. If
luminosities for models experiencing a thermal bounce so, the final fate of the gravitational collapse of rotating
peak at Lν ∼ 1042 erg/s. SMSs would be the formation of a SMBH and a torus.
The photon luminosity roughly equal to the Edding- In a follow-up paper, we aim to investigate in detail the
ton luminosity during the initial phase of contraction. dynamics of such systems (collapsing of SMS to a BH-
Then, after the thermal bounce, the photon luminosity torus system) in 3D, focusing on the post-BH evolution
becomes super-Eddington with a value of about Lγ ≈ and the development of nonaxisymmetric features that
1×1045erg/s during the phase of rapid expansion that fol- could emit detectable gravitational radiation.
lows the thermal bounce. For those stars that do not ex-
plode we have followed the evolution beyond the phase of
black hole formation and computed the neutrino energy
loss. The peak neutrino luminosities are Lν ∼ 1055 erg/s. We thank B. M¨ller and P. Cerd´-Dur´n for use-
u a a
SMSs with masses less than ≈ 106 M⊙ could have ful discussions. Work supported by the Deutsche
formed in massive halos with Tvir 104 K. Although the Forschungsgesellschaft (DFG) through its Transregional
amount of metals that was present in such environments Centers SFB/TR 7 “Gravitational Wave Astronomy”,
at the time when SMS might have formed is unclear, and SFB/TR 27 “Neutrinos and Beyond”, and the Clus-
it seems possible that the metallicities could have been ter of Excellence EXC153 “Origin and Structure of the
smaller than the critical metallicities required to reverse Universe”.
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