Marzieh_Master_thesis

Astrometric Orbital Monitoring of Low-Mass Stellar
Binary/Multiple Systems
Master of Science Thesis
Author:
Marzieh Jafarian Dehaghani
E-mail: marzieh.jafarian88@gmail.com
Supervisor:
Markus Janson
November 11, 2015
1

Abstract
Orbital monitoring of binary/multiple systems is a common way to display their fundamental
physical properties. In particular, by means of monitoring the young M-type visual binary
stars, which are evolving before the main sequence, we can estimate their age in the context
of isochrone studies. Here, I continued astrometric monitoring for ≈ 60 targets from the
AstraLux Large Multiplicity Survey, and used the previous works, archival data points and
new data which are analysed in this study. The chosen observed targets are young low mass
(0.1M M 0.5M ) M-type star visual binary/multiple systems with the most rapid
orbital motions, for the purpose of determining their total mass. The aim of this work is
to perform the best-fit of the orbits for those targets which have covered enough fractions
of a complete orbit during different epochs, and also to verify that these samples are truly
binary/multiple systems by investigating if they have common proper motion and orbital
motion. For instance J23172807+1936469 binary has been observed since 2001, and its
astrometric data covers more than a full orbit, therefore making it possible to draw a best
orbit which is very close to the true one. In other hand for J23495365+2427493 system,
even though there are five data points spanning over ≈ 6 years, these have just covered ≈
19.7% of the complete estimated orbit, so there are several plausible examples of orbital
fitting, which means that we need to do more observations to monitor the best-fit orbit and
estimate the orbital parameters precisely. I confirmed that almost half of these observed
targets have common proper motion and orbital motion which means they are now known
to be binary/multiple systems while the remaining targets are already known as systems.
The obtained data in this master thesis helps for future studies to determine the ages of
stars and their associated young co-moving stars groups, and moreover they can provide a
set of empirical isochrones which can be compared with the theoretical one for calibration
purposes.
2

"You ask me if an ordinary person, by studying hard, would get to be able to imagine
these things, like I imagine. Of course! I was an ordinary person who had studied hard.
There is no miracle people. It just happens they got interested in these things and they
learned all these stuﬀ. They are just people. There’s no talent, special, miracle ability to
understand quantum mechanics or a miracle ability to imagine electromagnetic ﬁelds that
comes without practice, learning and study. So if you say it takes an ordinary person who’s
willing to devote a great deal of time, study, work, and thinking in mathematics then he has
become a scientist."
Richard Feynman
3

Contents
1 Introduction 5
1.1 Binary/Multiple systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.1 Multiplicity frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.2 Mass ratio distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.3 Orbital period distribution . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.4 High-order multiple systems . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Orbital parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 M-type stars isochrones on the H–R diagram . . . . . . . . . . . . . . . . . . 9
1.4 Project overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Observation 11
2.1 Lucky Imaging technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Observational parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Analysis 12
3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Astrometry calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 Comparison to literature Astrometry . . . . . . . . . . . . . . . . . . . . . . 16
3.5 Orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.5.1 Common Proper Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.5.2 Orbital motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5.3 Examples of orbit ﬁtting . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4 Conclusion 21
5 References 22
6 Appendix 23
6.1 Notes on individual targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.2 Abbreviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.3 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4

1 Introduction
We have been discovering a variety of stellar characteristics through astrophysical knowledge
and observations with technically sophisticated telescopes and cameras. For instance, the
distance of a star can be determined via its parallax, and its radius, effective temperature,
composition and other parameters can be estimated from black body radiation curves, spec-
tral features etc. By observing the gravitational interaction between stars and other objects
orbiting them we can determine the stellar mass precisely.
To achieve this goal we have been observing the position and movement of stars in some
binary/multiple systems during several decades. Based on these observations and other
relevant data, we can determine astrometric orbital elements and monitor the proper orbit
for each system if there are enough available data. Through application of physical laws (e.g.
Kepler’s laws, Newton’s laws, etc.) we can characterize many physical properties with high
precision such as mass, luminosity, age, etc.
Developments in observational techniques for taking high resolution images and im-
provements of analysis methods have enabled us to increasingly resolve M-dwarf stars in
binary/multiple systems. As M-type stars are very faint, telescopes such as the Hipparcos
Satellite (1989-1993) were often unable to monitor them at the visible wavelengths. How-
ever, we are able to observe them and monitor their orbital motion by taking several images
over extended periods of time with the AstraLux camera, using the Lucky Imaging Method
(which I have used for my master project).
I started this master’s thesis by explaining the general properties of binary/multiple
systems in this introduction and in Section 2 I will describe the observational procedure and
the technique which were used for this study. Section 3 presents the procedure of the analysis
and how we derived numbers of angular separation and position angle for each component in
the relevant system. In the final section (Section 6.3) I will compare these data with previous
work’s data to monitor the best fit orbit for some of those systems that have enough data
points during several different epochs (Table 5).
1.1 Binary/Multiple systems
Most of the visible stars in the night sky are part of binary/multiple systems. When two
stars move around each other (or more specifically, orbit around the system center of mass)
we name them a "Binary system". If the system has three components it is called a "Triple
system" and if it has three or more components it is also known as a "Multiple system".
The most massive star in each system is called the primary star and the next most massive
component name is secondary and so on. Actually there is no consistent definition for what
constitutes the primary star, for M-star binaries the more massive star is almost always the
brighter one as well, and therefore it does not make much difference whether the primary is
selected based on brightness or on mass.
In this thesis I am considering low mass visual binary/multiple stellar systems with M-
type spectral characteristics. Those candidates are low-mass systems with a primary stellar
mass in the range of 0.1M M 0.5M which usually is a M spectral type component.
In the next following subsections I look at statistical distributions of low-mass and solar-mass
stellar systems on the main sequence (MS) and compare some differences and similarities of
their physical characteristics.
1.1.1 Multiplicity frequency
There are two particularly commonly used multiplicity statistics: The first is the number
of multiple systems per total number of observed targets – in other words, the frequency of
multiple systems (MF), and the second is the average number of companions per number of
multiple targets (CF).
Main sequence (MS) solar-type star systems have masses of M ≈ 0.7 − 1.3M and their
spectral types range are from F to the mid-K. Low-mass MS stellar systems have masses of
5

Figure 1: The plot shows mass ratios versus period. Binaries and triples are shown by
plus and triangle signs respectively. Unfilled squares illustrate composite mass in multiple
systems. Figure is from "A Survey of Stellar Families: Multiplicity of Solar-Type Stars"
Raghavan et al. [2010].
M ≈ 0.1 − 0.5M with spectral types ranging in M0-M6. These two groups are compared
in this report.
According to the research of Duquennoy & Mayor [1991] and Raghavan et al. [2010],
the CF for solar-type multiplicity is CFMS
0.7−1.3M = 62 ± 3%. Furthermore, Raghavan et
al. [2010] presents MFMS
0.7−1.3M = 44 ± 2%, which means that most solar-mass stars are
single like our Sun, and do not usually have a companion. Interestingly, after analysing their
samples they found that sub-solar and super-solar dwarf stars have MFMS
0.7−1M = 41 ± 3%
and MFMS
1−1.3M = 50±4% respectively, which indicates that the multiplicity rate of sub-solar
systems is a little lower than for super-solar dwarfs. In addition, they present similar results
for the CF of sub- and super-solar stars: CFMS
0.7−1M = 56 ± 4% and CFMS
1−1.3M = 75 ± 5%.
So perhaps the MF of low-mass systems is a lower number still than the solar-type
system MF? Yes, that is correct. Most studies show that low-mass stellar systems have
fewer companions than solar-type and more massive systems. There are several published
measurements of MF for low-mass systems in the range of 26% to 42%, and by collecting
all the target data from these investigations, Delfosse et al. [2004], Dieterich et al. [2012]
and Reid & Gizis [1997] estimate MFMS
0.1−0.5M = 26 ± 3%, and the companion frequency is
CFMS
0.1−0.5M = 33 ± 5%.
1.1.2 Mass ratio distribution
The mass ratio in a stellar system is defined as q= Msecondary / Mprimary and to quantify
the distribution of mass ratios we used a power law distribution f(q) ∝ qγ
.
There are different results for γ in mass ratio distribution functions for solar-type sys-
tems. The reason is that the distribution function varies for short- and long-period systems.
On average for short orbital periods, there is a significant peak around q ≈ 1 where the dis-
6

tribution function f(q) is increasing slightly [Raghavan et al., 2010], while there is a strong
peak at q ≈ 0.3 for the long-period systems [Duquennoy & Mayor, 1991] and with a slowly
decreasing f(q) function towards high-q. The value of γ is estimated for short-period systems
as γMS,logP ≤5.5
0.7−1.3M = 1.16±0.16 and for long-period systems as γMS,logP >5.5
0.7−1.3M = −0.01±0.03 by
Tokovinin [2011]. But one should be aware that a power law is not a very well-fitting model
for the observed distribution of mass ratios.
Since the mass ratio distribution depends on the system separation (short-/long-period)
and the mass ratios, it is more difficult to find the proper distribution function. Similar to the
solar-type stars, the f(q) function is growing to the high-q for short-period of M-type systems
[Reid & Gizis, 1997]. The mass ratio distribution is different depending on the system’s mass
as is shown by Duchêne & Kraus [2013] γMS
0.1−0.3M = 1.9±1.7 and γMS
0.3−0.5M = −0.2±0.3 .
1.1.3 Orbital period distribution
There is logarithmically-flat orbital distribution for broad separation stellar systems known
as "Öpik’s law" (Öpik 1924) that was a first assumption for all solar-type stars. However,
when considering a large sample of solar-type stars, it is clear that a log-normal description is
a proper fit for the observed distribution [Raghavan et al., 2010]. The full data for the orbital
distribution presents a peak at ¯P ≈ 250yr with a dispersion of σlogP ≈ 2.3 for solar-type
systems.
As pointed out above, there is similarity between solar-type and low-mass systems. A log-
normal function is therefore a better description for low mass systems which have separations
below 500 AU. According to the RECONS1
sample of late-M primaries, there is a peak at
¯P ≈ 12.2yr with σlogP ≈ 1.3 , while for very wide separations, an Öpik-like (log-flat) is
acceptable (Dhital et al. [2010]). In comparison with solar-type systems, the distribution for
low-mass systems displays a narrower dispersion around the peak.
1.1.4 High-order multiple systems
It seems that for equal-solar-mass systems (q ≈ 0.9) which have short periods, more than
half of the systems with logP ≤ 2 are part of high-order multiple systems and this amount
increases even more for the shortest-period systems [Allen et al., 2012]. In addition, several
triple systems can be found among wide systems with separation logP ≤ 4.5 (or ≥ 1000AU).
Approximately 25 percent of all solar-mass type multiple systems are triple and higher-
order multiple systems with distribution function N(n) ∝ 2.5−n
, where n is the companion
number [Eggleton & Tokovinin, 2008], and the distribution for binary systems is N(n) ∝
3.7−n
. Interestingly, the ratio of orbital period among each pair in triple solar-mass systems
is Plong/Pshort ≥ 5 and the mass ratio distribution for the short period pairs is flat and
slightly increases to high-q (q ≈ 0.9), while for the long period subsystems there is a peak
at low-q (q ≤ 0.5), similar to the short-long period binary systems (Raghavan et al. [2010],
Tokovinin [2008]).
Roughly 21 percent of all low-mass M-type multiple systems are triple and higher-order
multiple systems, which is similar to the solar-type systems. The distribution function for
higher-order (more than two companions) systems is N(n) ∝ 3.9−n
, similar or just a small
amount lower than the high-order distribution of solar-type systems, because it is easier to
break apart low-mass systems with a smaller external force and separate them into single
stars.
There is a lack of low-mass binaries with short-period orbits; Figure.1 displays that
most of the short-period systems are members of high-order multiples. The number of filled
triangles (which present triple systems) are more than plus signs (which show binaries). As
you can also see, most of the short-period systems have components with similar masses (q ≈
0.95). In the survey by Raghavan et al. [2010], they studied 16 short-period systems (≈ 100
days), of which seven systems are binaries and nine are triple systems. Their observation has
1
http://www.recons.org
7

Figure 2: In this drawing there is an intersection between the orbital plane and the
reference plane which makes a line named the ’line of nodes’ which determines the angles
of inclination (i), Longitude of ascending node (Ω) and Argument of periapsis (ω).
the same results as their hydrodynamical simulations and they suggest a reason: Perhaps
many short- period systems formed at wider separations, but due to dynamical interactions,
components get closer to each other to form stable close multiple systems, for instance
because of gas accretion and interaction of a system with its own circumbinary disk [Bate et
al., 2002, Raghavan et al., 2010].
1.2 Orbital parameters
The orbit of a binary is deﬁned by the secondary relative motion around the primary and
for any binary system, we can represent its orbital motion through a set of orbital elements.
Since we have measured orbital motion, we can represent the position and movement from
past till present, and even predict the future positions for each orbiting body in the system.
Furthermore, through an orbital motion and its elements, we are able to determine many
physical properties for those relevant components in the system. There are seven orbital
parameters which are commonly used in orbital mechanics and astronomy. I describe these
parameters in the following paragraph brieﬂy, and show a sketch of them in Figure 2.
• Semi-major axis [a] is half of an orbit’s major axis, which is equal to half amount of
the sum of the periapsis and apoapsis distances2
.
• Eccentricity [e] represents how much an elliptical orbit is elongated. The range of its
value is 0 < e < 1 and it would look circular- and oval-shaped when e is close to zero
and one respectively.
• Period [p] is the periodic time of a full revolution, or in other words, the time passed
during one orbit.
• Inclination [i] is the angle between the orbital plane and a reference plane (if there is
a satellite which orbits around the Earth, the equatorial plane can be the reference
plane).
• Argument of periapsis [ω] is the angle from the ascending node3
to the periapsis point.
This value determines how the orientation of the orbit looks like in the orbital plane.
2
Along the orbit’s major axis, the two points on the ellipse that are the nearest to and farthest from to the
focal point (or equivalently the center of mass of the system) of the orbit are called periapsis (or periastron) and
apoapsis respectively.
3
In the orbital plane, where the object passes upward through the reference plane.
8

• Longitude of ascending node [Ω] is defined as the swivel of the orbit; it is as an angle
measured from the origin of longitude toward the ascending node (for a satellite that
orbits around the Earth, the origin of longitude would be the vernal equinox).
• Time of periapsis [TP ] is the time at which the orbiting object passes through the
periasis point, and is usually defined as a Julian date4
.
1.3 M-type stars isochrones on the H–R diagram
The Hertzsprung–Russell (H-R) diagram shows the distribution of stars and its relation to
stellar evolution. It is common with given measurements of some parameters such as colour,
magnitude, surface temperature, age, etc. of a group of stars, in order to plot these quantities
versus each other and look for some systematic correlation. To understand the age of a co-
moving group of stars (which consists of many different spectral types of stars) we can use
the M-type star isochrones on the H-R diagram. Using the age of young M-type binaries is
one solution of many, to estimate stellar ages in young co-moving groups.
An isochrone (after Greek iso= same, kronos= time) track is a curve in the H-R diagram
that consists of a collection of points that have the same age but different mass and luminosity.
Since M-type stars evolve very slowly on the Hayashi track in the H-R diagram (lower mass
stars evolve slower), it is possible to estimate their age during the stage when they are
following the track, although when they have evolved down to the main sequence where they
live for a very very long time then it is hard to make such an estimation. By then the M-type
stars have basically the same luminosity forever (not exactly forever, but for much longer
than a Hubble time), commonly after 1 Gyr. Therefore it is very difficult to determine the
age of M-stars older than 1 Gyr, and that was one reason we were observing the young
M-type stars. There are other ways to measure the age of old M-type stars, for instance
with asteroseismology which is a study about the frequency spectra to figure out the interior
density structures of stars when they pulsate. Usually the pulsation amplitude for M-type
stars is so small that it is very resource demanding to characterize and demonstrate (Jørgen
Christensen-Dalsgaard [2008]).
I plotted two isochrones graphs (Figures 3 and 4) with different metallicity (Z = 0.002
and Z = 0.014) according to the data points from a simulation to measure some physical
properties for different stars. This is the relevant link5
which estimates the quantities of the
stars’ luminosities from their masses on the proper isochrones track. Thus with given mass
and luminosity, we can figure out the stellar age.
As the figures display, the blue and black lines almost overlap with each other below
0.5M , which means that these stars almost do not evolve at all between 1Gyr and 10Gyr,
as we would expect. In this present project we only have astrometry for a binary pair, so we
can only derive a total mass for each system and different brightness between components.
However, once the total mass is determined, there are several ways to estimate individual
masses .It is also possible to calculate the total brightness for each system, then by knowing
the difference of brightness we can estimate the individual brightness for each orbiting body,
and therefore find its luminosity (because the distances to these systems are already calcu-
lated). At the end, combining the luminosity with the related mass of the star will pinpoint
the right position on the isochrones curve.
1.4 Project overview
Since low-mass binary/multiple systems are so faint and hard to observe, we used the high-
resolution Lucky Imaging technique with the Astrulax camera, in order to monitor the orbital
motion of such systems. The aim of the present project is to estimate the approximate orbital
motion for several young M-type binary/multiple systems and calculate their total masses.
4
The Julian date is the number of day according to the Julian Day Number which is counting days continuously
from the zero day starting at noon of Greenwich Mean Time, on first of January 4713 BC.
5
http://stev.oapd.inaf.it/cgi-bin/cmd_2.7
9

Figure 3: Isochrones for Z = 0.002 Figure 4: Isochrones Z = 0.014
Through use of observational data, we indicate the angular separation, position angle and
difference of the brightness between components in each individual system6
. In fact these
parts were a main part of my thesis project. As a subsequent step, from the collection of all
these data points, we can estimate the ages of M-type stars in each binary/multiple system
which is a member of a large co-moving group of stars, in order to provide age estimates for
the groups as a whole. The age of all co-moving stars are roughly the same, since they were
born from the same cluster. The ages of some M-type stars have already been estimated
through X-ray luminosity and lithium abundance7
, but they have large uncertainties in the
range of around several tens of mega years (Weintraub et al. [2000]). While, in contrast
to typical age estimations of higher-mass co-moving stars, astrometric orbital monitoring of
the young M-type star members prepare uncertainties of about a few million years, which
provides a reference point for comparisons with different methods and their results.
One important part of astronomy is understanding how stars form, either as singles or
in a multiple system, and how they evolve. Multiple systems are good samples to gain more
information about stellar evolution and planetary systems, and in addition can improve
the isochrones curve on the H-R plane. Indeed by monitoring the orbital motion for some
binary/multiple systems and calculate some physical properties that can provide relevant
data points for future projects to estimate the age of co-moving stellar groups.
In this present study, which is a continuation of the AstraLux Large Multiplicity Survey, I
observed around ∼ 60 targets of young M-type binary/multiple stellar systems and analysed
the data to find the separation and position angle between orbiting bodies in each system.
In the final analysis I estimated elliptical orbits of some systems which have enough data
points (Table 5).
Why were these 60 targets selected as targets? There are three main reasons, a) they are
mostly young M-type stars, b) They have fast orbits which means that they have a short
period and that there is a good chance to monitor their orbit just during several years, c)
for some cases, we do not yet have evidence for whether the stars share a common proper
motion or not.
6
The values of the difference between components are available in the archive
7
The Lithium abundance test is a measurement of the equivalent width of the Li doublet line at 6708 Å.
Younger stars typically have a higher equivalent width of Li than older stars. However, the method has large
error bars.
10

2 Observation
I travelled to Calar Alto, Spain in the end of November 2014 to observe some binary/multiple
systems with another astronomer from Queen’s University Belfast, Stephan Durkan. Unfor-
tunately, the first night (2nd December) was a little snowy at the early night hours, then
had 100 % relative humidity (RH) so that the dome had to be closed. The next night was
less humid (RH ≈ 51%) but had high wind speed (≈ 17 m/s). Although we have some
images from the second night before storm, they are not useful due to high seeing (≈ 2.5").
On one hand we did not get acceptable images, but on the other hand we achieved valuable
experience about how to use the AstraLux camera and work with the large 2.2 m telescope.
The technique we used for this survey is the "Lucky Imaging", which allows to take high
resolution photos with the AstraLux camera on the 2.2 meter telescope. Because of that
bad weather, to be able to do this project I used images which were captured on 11th/12th
August 2014 by Stephen Durkan and Rainer Köhler with the same camera and telescope
instead of our dull images. The following subsections explain more about the technique and
instruments.
2.1 Lucky Imaging technique
As we know, there is turbulence in the atmosphere, so we build observatories above the sea
level in places as high as possible toward mountain peaks or space-based telescopes. There
is another solution to escape from turbulence which is called the "Lucky Imaging" observing
technique. In brief, the "Lucky Imaging" method is to freeze the atmosphere turbulence
in a very short exposure time and capture the best resolution of each target using a high
speed charge coupled device (CCD). According to many papers, it seems that Bob Hufnagel8
(1966) was the first guy who found this method while Fried (1978) was the first person who
calculated the probability of Lucky Imaging [Fried, 1966].
To do this we use the high-speed camera "AstraLux" to take more than 10000 pictures
in a row with a very short exposure time (something around 30 ms), hence based on "Luck"
during good seeing (≈ 0.8"). Around 1-10% of the best frames have nearly diffraction-limited
resolution. The best frames are selected base on the quality of the frame which is judged
by relating the peak flux to the total flux of the brightness object in the frame. In sufficient
weather conditions, we will have this high percentage of good resolution images even without
help of Adaptive Optics (AO). After that we collapse all high resolution images to one frame
to gain the best quality and high resolution of each target. Figure 5 shows the center of
globular cluster M13 with different cameras to compare resolution between cameras and
telescopes. The left one is the conventional image with a good seeing 0.65", middle one was
taken by the Hubble 2.4 m and the right image is taken by LuckyCam and AO with the
Palomar 5.1 m telescope. Thus we can get very good resolution images by improving ground
base techniques and instruments, sometimes approaching the quality of space base telescopes
technology.
2.2 Observational parameters
As I mentioned in the previous section, we need a high speed charge coupled devise (CCD)
with roughly zero readout noise to achieve the Lucky Imaging observing technique. The
CCD reads each image in a very short time before it takes the next image. We therefore
used the "AstraLux" Lucky Imaging camera which is attached to the 2.2 meter telescope in
Calar Alto, Spain. The concept was originated by Bob Tubbs, Craig Mackay, et al. at the
Nordic Optical Telescope (LuckyCam) and AstraLux was built by a team including Wolfgang
Brandner, Thomas Henning, et al. For more information about AstraLux camera, you may
look into this link 9
.
8
http://www.ast.cam.ac.uk/sites/default/files/Hufnagel_RH155_251109.pdf
9
http://www2.mpia-hd.mpg.de/ASTRALUX/
11

Figure 5: Resolution comparison between different instrument and telescopes. Image
reference is http://www.ast.cam.ac.uk/research/lucky/
The field of view of the AstraLux camera is 512 × 512, corresponding to 23" in the full
frame with the original pixel scale of 47 mas, and its final images are close to the diffraction
limited imaging for wavelengths longer than 800 nm. The AstraLux hardware is actually
divided into two main parts, one is the camera computer and electronic cell, another one
is a Windows computer and Linux pipeline machine (which splits the data into a sequence
of steps and makes simultaneous calculations). After taking images, the pipeline which is
developed specially for this kind of survey does the data reduction. The pipeline applies
bias, flat field and dark frame corrections to all the images, and at the end combines all good
seeing images to one science frame. The pipeline uses the drizzle algorithm and the data gets
oversampled by a factor 2 (during the data reduction), so the final pixel scale became ≈ 23
mas. Hormuth et al. [2008] provides more information about how the pipeline and AstraLux
hardware work.
We used the sloan digital sky survey (SDSS) ’z’ band filter during the observation. SDSS
z-band is a broad band in the infrared zone with wavelength around 9100 Angstroms. We
selected this band because the Strehl ratio is larger than the other SDSS bands. Strehl
ratio (S) is a measure to asses the quality of optical image formation of an object, it is
the fraction of the intensity peak of the measured point spread function (PSF) over the
ideal diffraction-limited PSF of the object. Normally, AO is used to correct the received
wavelengths, so following the naming standards in AO we name the height of intensity peak
hc after correction and hp for the perfect PSF, i.e. the PSF as it would look when aberration-
free. The ratio is:
S =
hc
hp
The intensity peak of the PSF for diffraction-limited images is always sharp and higher
than the measured ones even after corrections, hence the Strehl ratio is between 0 and 1 and
in the proper measured situation it becomes close to one [Roberts et al., 2004]. Indeed for
long wavelength bands the Strehl ratio is normally closer to one than at shorter wavelength
bands and this was the main reason we used SDSS z-band filter during the observation.
3 Analysis
I began the analysis by looking at the science frames with DS910
to make an initial estimate
of the components’ positions in each system. First I zoomed on each object to find the
position of its brightness center and also varied the brightness scale to display a different
range of brightness in each frame, until we can see how many components exist in the frame
which are recorded into a list of targets with the components’ positions. In some imaged
10
DS9 is an astronomical visualization application to illustrate images.
12

Figure 6: J0215589-20929121 is a triple
system which can be divided into a C2
pair and a W2 pair.
Figure 7: I00088+2050 is a close binary
system with a ghost image, and thus clas-
sified as C3.
systems, there is a fake stellar image whose position we enter as a ghost component in the
list.
We provided a classification for each binary/multiple system: close and wide binary11
systems are labelled C2 and W2 respectively. For a multiple system we count the number
of binary pairs where the primary forms a pair with each of the two other components. In
order to make the classification scheme more clear, we can consider a few concrete examples:
for instance, W2 represents a wide binary system, C2 is a close binary and C3 shows a close
binary system with a fake ghost image (Figure 7). If there is a triple system where one
component is close to and the other one is far from the primary star, it is separated into two
pairs with the classifications of C2 and W2 respectively (Figure 6). Because we are looking
at the low mass systems which do not have a strong gravitational effect on each other, we can
separate them into individual pairs. This provides a simple and convenient way to analyse
the data.
Some systems are called "false triple", because in fact they are two stars, usually with
same brightness in the system and the third object is called a "ghost". It often happens in
Lucky Imaging and we also get a few false triple targets in this survey as well. Lucky Imaging
shifts the images to add all the primary stars (which we suppose is the brightest one in each
frame) from high resolution frames to make the final science frame. Since these two stars
have equal brightness, in some frames the secondary was selected as a primary, therefore in
the final image the secondary is fainter than its real brightness and the fake and faint image
of the ghost appears with the same separation as the secondary, but on the opposite side of
the primary. Figure 7 displays the target I00088 + 2050 as an example of C3 which is a false
triple.
The goal of analysing the data in this section is to calculate the position angle and angular
separation between the primary and other components in each binary/multiple system. The
unit used for position angle is degrees (deg) and for separation is arcseconds (arcsec).
3.1 Data
There are 56 targets of young low-mass stars systems which were observed on 11th and 12th
of August 2014. We have been following the motion of orbiting bodies of some targets for
a long time (some more than a few decades and some a couple of years). For examples:
J22332264-0936537, J15553178+3512028 have been monitored for more than 16 years and
J01034210+4051158 during 54 years. Other targets have been monitored since a few years
ago, such as J01071194-1935359 and I22035+0340 around four and two years respectively.
11
In this present paper, we named wide binary systems as those having orbiting bodies at least 0.92 arcsec away
from the primary.
13

Some of the fundamental properties of all these targets are compiled in Table 2 which
contains information about each target’s coordinate, spectral type, distance and magnitude
in the J-band.
3.2 Astrometry calibration
In order to transform from sky to detector coordinates, we need to find the angular scale
per each pixel. For this purpose we took an image from a part of the cluster M15 as a
calibration frame. We used the separation and position angle values between some stars
from van der Marel et al. [2002] search which contains a stellar catalogue of around 31,900
stars in this cluster with several properties such as positions, U, V, B magnitude, etc. All
data are available in this link12
.
To calibrate the pixel scale and detector rotation, I selected the five brightest stars which
are marked by green circles in the observed frame and Figure 8 illustrates those. Once
I found the right ascension (RA) and declination (Dec) for those stars then I calculated
separations and position angles between each pair and also I counted the number of pixels
between those stellar pairs in the observed frame. Consequently I estimated the pixel size
in the observed image, by dividing the separation per pixel number and since there is one
answer per each pair, I computed the mean value and its standard deviation for the image
pixel size. Furthermore the difference between the true position angle and observed one for
each pair displays the orientation of the "true North" in the observed frame, therefore there
are several results for the "true North" point as well which provide its error measurement.
After these computations, I obtained 0.0234692 ± 2.24.10−5
arcsec/pixel for the pixel
scale and 1.94418 ± 0.177482 degrees for the "true North" direction. Hence all the observed
images should be corrected by that angle in a clockwise direction, in order for them to point
toward the "true North". Then I modified the results for separation through this subsequent
step:
Sep.Size = Num. of Pixels × 0.0234692
and in order to derive a true position angle in sky coordinates we should add the true North
angle to the position angle measured in the observed frame, by this step:
True Pos.Ang. = Pos.Ang. + 1.94418
Therefore, at this point, we have the separation size in arcseconds and the position angle
relative to the true North direction in degrees (as are shown in Table 3).
3.3 Astrometry
When we achieve precise measurements of separations and position angles between celestial
objects, then we can draw their movements on the relevant orbit, indeed astometry can
provide estimations of some physical properties about celestial bodies. I therefore started
to find the two parameters separations and position angles in each observed system, and
subsequently calculated some physical properties.
To do that, I sorted all the systems into two appropriate groups: the first group includes
wide binaries (W2) and close binaries (C2), second group consists of close/wide binaries with
a ghost star image (W3/C3). In this survey’s candidate list, there are two triple systems
which are divided into separate binary pairs (explained in section 3), each counted as being
part of the first group. I used the codes which were written in Interactive Data Language
(IDL) by Markus Janson to determine the separation and position angle between orbiting
components.
We used two different PSF fitting schemes to characterize the best values for angular
separation and position angle between components, Gussian centroiding was used for W2, and
12
http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=J/AJ/124/3255
14

Figure 8: The M15 cluster with chosen stars to calibrate the angular scale of each pixel
and "true North" orientation.
(a) 2MASS J02155892-0929121 (b) Modulation of PSF fitting
Figure 9: 2MASS J02155892-0929121 is the triple system and the image shows the PSF
of the wide pair (W2).
a PSF reference fitting scheme was used for C2 and the same for C3, but for three components
instead of two. For the group W2, Gaussian centroiding is used to find the proper fit for
the primary and secondary PSFs because they are far enough from each other to resolve the
best fit. Figure 9 displays the PSFs of the wide stars pair in the 2MASS J02155892-0929121
triple system as an example for the W2 group, and the right side image shows residuals of the
fitting. Indeed the program tried to move the Gaussian centering up/down and right/left,
to find the least-value of fitting with observed PSFs and then computes the separation and
position angle between these stars. There is one result for separations and position angles
between components for each system with a measure of error bars.
For the second group W3/C3 which have a ghost star image in the frame, I used PSFs
references of three different single stars which have nearly perfect and diffraction-limited
PSFs. After running the codes13
, some data and figures appeared as in Figure 10 which
is chosen as an example of a close binary (or a false triple). The left image of the figure
shows the raw image of the false triple PSF and the middle one displays the PSFs without
wings, because high-pass filtering (or unsharp-masking) is used on the observed PSF and also
on the PSF template, in order to preserve high spatial frequencies and remove low spatial
frequencies. The right image shows residuals between the reference and observed stars. The
13
Were written by ...
15

(a) Raw PSF (b) After using unsharp-mask (c) Modulation of PSF
Figure 10: (a) shows the raw PSF of the 2MASS J17383964+6114160 close binary system
with the ghost PSF, (b) displays PSFs after using the unsharp-masking and (c) is the
residual of fitting between reference and observed stars.
code tries to find the best fit between the PSF reference and observed one, through moving
PSF reference up/down and right/left sequentially. There are hence values of separations
and position angles and their error measures for each reference PSF individually and the
final values and errors are taken as the mean and standard deviation of these three values.
First of all after achieving the separation from each reference, I convert the pixel num-
ber to pixel size (arcsec) and computed the mean value and standard deviation of the all
separations for one specific system. These are the simple relations which is used:
Average Sep. = mean (Sep. sizePSF1, Sep. sizePSF2, Sep. sizePSF3)
StDev. Sep. = StDev. (Sep. sizePSF1, Sep. sizePSF2, Sep. sizePSF3)
In the same way, I corrected all the position angles by imposing the "true North" orienta-
tion for the achieved result of each reference and then obtained the mean value and standard
deviation for all the position angles as follows:
Average Pos.Ang. = mean (Pos.Ang. PSF1 + Pos.Ang. PSF2 + Pos.Ang. PSF3)
StDev. Pos.Ang. = StDev. (Pos.Ang. PSF1 + Pos.Ang. PSF2 + Pos.Ang. PSF3)
In order to represent the values of separation and position angles, I should estimate the
total error measurement. For measuring the total error of separation, there is another error
which arises from the estimation of the pixel scale (section 3.2) that is:
Error [Pixel scale] =
Average Sep. × Error of Pixel scale Calib.
Pixel scale
Thus the final error measurement for separation is computed with this relation:
Total Error Sep. = (StDev. Sep.)2 + (Error [Pixel scale])2
and similarly, to calculate the total error of position angle, I combined the sigma of the
measurement of the mean value with the error of the estimation of the true North direction
through the use of this relation:
Total Error Ang. = (StDev. Pos.Ang.)2 + (Error [true North])2
In Table 3 I summarize all final results of separations and position angles with the indi-
vidual error measurements of those targets which are observed as candidates for this project.
3.4 Comparison to literature Astrometry
So far, many groups and astronomers have been determining separations and position angles
between components in many stellar systems. In this project, which is a continuation of
the AstraLux M-dwarf multiplicity sample survey, there are estimations of orbiting bodies
positions in some candidate of binary/multiple systems. Table 4 provides a collection of data
16

Figure 11: Orbital motion of 2MASS J23172807+1936469
in several epochs, which provides an opportunity to compare the new results with previous
ones and see how orbiting stars change their relative positions in each system during multiple
epochs and even predict what their next positions will be.
In Table 4, the data is recorded from different references and epochs. Some multiple
systems were confirmed as a binary/multiple system according to common proper motion
(CPM) in the sky. This table contains the achieved data from our analysis and also includes
information about the CPM to confirm whether they belong to one system. In addition I
looked at the orbital motion, similarly to previous researches, to say whether the orbiting
bodies are either moving around each other or not (section 3.5).
3.5 Orbit
Eventually, when enough data points of stellar positions in several epochs (at least more than
three epochs) have been collected for one system, its orbital motion can be constrained. We
calculated those orbits using a code which was written by Rainer Köhler and Markus Janson
(2002-2003). We presented what the orbital motion of each targets looks like (Figure 11)
and also computed some of the orbital parameters14
values with their error measurements.
Those obtained parameters are ’pericenter’ (time of preapsis when the secondary star passed
that point), ’period’, ’axis’ (semi-major axis), ’Excent’ (eccentricity), ’periast’ (argument of
periastron), ’ascnode’ (longitude of the ascending node), ’inclin’ (inclination angle) and the
total mass of components in the system. In addition, when running this codes, it calculates
the expected, values for separation and position angle of the components in a system accord-
ing to the best orbital fit with all data, compares with the observed values, and relates the
deviation to the calculated error bars.
In this section of the survey we try to find the best fit for the orbital motion for each
system based on the component position as a function of time. Figure 11 displays one
example of the orbital fitting, the white dashed ellipse shows the best orbital motion fitting
for all observed astrometric data points of 2MASS J23172807+1936469 binary system. This
illustrates how the secondary star has been orbiting around the primary since 2001 and it
14
I wrote the same abbreviation name as I obtained results, after running the code
17

Figure 12: The proper motion of a primary star and its components, with a comparison
to distant objects.
can be measured that the period of this system is around 11.5 years.
How did I use the code to plot the best fit of elliptical orbit for each system? Judging
by how much the orbiting stars have changed their position angles during time, I assessed
what values would be most probable for the pericenter, period and eccentricity for each
system. Then I entered ranges around those amounts as free input values and run the code.
In fact I made a range of assumptions for each of these three parameters which starts with
minimum values and ends with maximum and also I defined the step size for the intermediate
intervals. The code thus uses my approximation for these three parameters, starts from the
minimum value with the next step until it reaches the maximum value and for each specific
amount of the parameters calculated the four remaining orbital parameters by means of a
mathematical transformation (for more information about this transformation you may look
at the Wöllert et al. [2014] study). But if the true values are outside of the approximated
range, the program gives the same answer as the assumptions which means I should expand
the range and again run the code until I achieve reasonable results and error bars (look for
error bars to be less than 3σ). After that I can narrow the appropriate range to minimize
error bars for each parameter as much as possible and therefore through iteration I obtained
the relevant results for each system. In section 3.5.3, there are several reasonably reliable
examples of the best orbital fitting and relevant physical properties are provided for those
systems with enough astrometric data points.
3.5.1 Common Proper Motion
Stellar motion is split into two components, one is toward or away from the Earth and is
known as radial velocity, and another one is transverse velocity which can be measured via
proper motion. Proper motion is the observed movement of an object on the celestial sphere
and it is a vector measure which has a size and direction, is separated into two components
shown in Figure 12: one along the right ascension axis µα and the other along declination
axis µδ of proper motion. We can see the large proper motions of nearby objects over the
course of a year, while farther objects are observable over the course of a century; typically
their proper motions are represented in a few mas per year, in other words farther objects
have smaller movements. Due to very small movement, they often measure in arcsecond per
year (arcsec/yr) or mas per year. Therefore, the most distance objects seem firmly stable in
the sky field which are known as background objects.
In a binary/multiple system, all components must have the same proper motion known as
common proper motion (CPM), because they are physically bound to each other and when
the primary moves in the celestial field, the secondary and other components should follow
that movement with the same magnitude and direction, as well. If we fix the center of the
18

Figure 13: The movement of 2MASS J23570417−0337559 during around seven years.
coordinate system on a moving nearby star (e.g. the primary in a binary system), we will
observe that when the star moves, it seems that the background stars move in the inverse
direction or just having a very small change. Indeed, this is one way to distinguish a true
secondary star which is a real component of the system from background ones which happen
to appear close to the primary star through projection. Therefore we can require that the
secondary has to have a common proper motion with the primary as the critical argument
for demonstrating the system is a real binary/multiple system. Table 4 shows the candidates
with CPM by letter ’Y’ (which means ’Yes’, the system has CPM), in addition some of those
were confirmed as a binary/multiple system (due to CPM) in this paper which had not been
demonstrated already.
How did I calculate whether the secondary star has the same proper motion as the pri-
mary? If we assume there are values of separation and position angle for a system in two
separate epochs, then we can obtain the R.A. and Dec. of the secondary relative to the
primary for each epoch and then estimate how much the secondary position have changed
during that time (Figure 13). Then we can determine the movement value into two com-
ponents as R.A and Dec. per year with their relevant error bar. Through the catalogue
PPMXL in the VizieR link 15
, I could find the relevant proper motion and its error bar of
the primary in each system that should be the same for the secondary as well. Finally I
computed the sigma where the secondary was assumed to be a background star instead and
if the deviation is larger than 3σ then the secondary has low probability to be a background
object. Thus, if the deviation is more than 3σ then it is considered that the secondary has
a common proper motion with the primary. Just to be clear I write down the procedure of
CPM confirmation for the candidate 2MASS J23570417−0337559.
The expected motion of a background star is shown in Table 1. When calculating the
secondary motion it should be remembered that I found the movement of secondary in the
X-Y coordinate, while the proper motion of the primary determined in the N-E coordinate,
hence I should be aware to calculate the sigma in the right coordinate system. These are the
15
http://vizier.u-strasbg.fr/viz-bin/VizieR
19

Table 1: Considering for proper motion of the target 2MASS J23570417−0337559
Epoch Sep. P.A. µR.A = x µDec. = y ∆µR.A. ∆µDec.
arcsec degree mas mas mas/yr mas/yr
2007.85 0.184 ± 0.014 281.9 ± 0.3 180.05 ± 7.54 37.9 ± 7.54
7.34 ± 1.6 -16.33± 1.6
2014.61 0.241 ± 0.011 252.5 ± 1.2 229.85 ± 7.66 -72.47 ± 7.66
The Primary P.M.=⇒ µR.A. : 74.4 ± 3.9 mas/yr µDec. : -57.7 ± 3.9 mas/yr
The background motion=⇒ µb.g.
R.A. : -74.4 ± 3.9 mas/yr µb.g.
Dec. : -57.7 ± 3.9 mas/yr
relations to get the final sigma:
σR.A. =
| µb.g.
R.A. − ∆µR.A. |
Error µb.g.
2 + Error µR.A.
2
σDec. =
| µb.g.
Dec − ∆µDec. |
Error µb.g.
2 + Error µDec.
2
σT otal CP M = σR.A.
2 + σDec.
2
In those cases, where the total σ is more than 3σ the secondary star is confirmed as a
component for the binary system. That means that the secondary star has a low probability
to be a background star.
3.5.2 Orbital motion
Motion is a measure of movement relative to the surroundings and here orbital motion means
changing position of the components in relation to the primary. To determine whether the
secondary has orbital motion in the system, we used a simple way which is looking at how
much this object has been moving relative to the primary. If we just divide the secondary
movement between the first observed position and the new position in the last epoch (2014.61)
over the error bars of measuring these values, then we can recognize how much probability
the secondary has to be stable relative to the primary. This value which represents the sigma
of being stationary were calculated in this way:
σ∆X =
| Xfirst epoch − X2014.61 |
Error2
first epoch + Erro2
2014.61
σ∆Y =
| Yfirst epoch − Y2014.61 |
Error2
first epoch + Erro2
2014.61
σT otal OM = σ2
∆X + σ2
∆Y
When the σT otal OM > 3σ, the secondary is proved to have an orbital motion relative to
the primary, so then I added the letter ’Y’ for those targets which have not been recognized
before. For instance, I show orbital motion of the target above to determine it has either
orbital motion or not. According to the recorded data in Table 1, we can get the values of
∆X and ∆Y and their error bars during ≈ 6.76 years, hence:
σ∆X =
| 229.85 − 180.05 |
√
7.572 + 7.662
≈ 4.6
σ∆Y =
| −72.47 − 37.94 |
√
7.572 + 7.662
≈ 10.27
20

σT otal OM = 4.62 + 10.272 ≈ 11.25
As seen it is larger than 3σ and the secondary has not been stationary and it has been
moving around the primary, so we confirmed that this system has orbital motion.
3.5.3 Examples of orbit fitting
A sequence of observations in several different epochs, covering a large fraction of one com-
plete orbit, makes it possible to match the best orbital fitting corresponding to the observed
positions, and thus finally helps to reveal all orbital elements with lower error bars. While
for the astrometric data of those targets which cover a small fraction of a full orbit, there
are several plausible orbits in the fitting and it is hard to characterize the best one. In those
cases we need more data points from more observations over a long time scale.
There are some stellar systems in our target list which have a best fit with low sigma
(most of them have σ < 3σ16
) and they are recorded in Table 5. The table shows some
of the observed candidates for which an orbit fitting allowed to identify one probable orbit
and also displays some orbital parameters. For those targets that cover a small part of the
orbital path, there are several possible orbits in the fitting and in the left column of Table 5
I just show one possibility (like 2MASS J23495365+2427493).
4 Conclusion
By taking all available astrometric data points into account for several young M-type bi-
nary/multiple systems, I have monitored the probable orbit for each one and estimated their
orbital parameters and total mass for those targets with enough data points. To achieve
that, I started to look at the 56 observed images which were taken by AstraLux camera
(2.2m telescope at Calar Alto observatory, Spain) and used the "Lucky Imaging" method to
display the targets with high resolution. From those images I could analyse 49 targets to
estimate separations and position angles of the target’s components.
Out of the 49 targets, 23 systems are already classified as real binary/multiple stellar
systems from previous observations and since they are already classified, I did not do CPM
and OM analysis on these systems but I have new observations which could be useful to
include in the future work. The remaining 24 targets were analysed and out of these, 8 targets
for which CPM could previously only be inferred now have confirmed CPM. 7 systems with
previously confirmed CPM but unconfirmed OM, now have confirmed OM. The remaining
systems were completely unknown and have now been confirmed in this thesis. Only two
systems out of 49 are still unknown and we are waiting for more observations to make a
conclusion. There are more details for each individual target in appendix 6.1.
Analysing the results of astrometry is necessary to perform the best orbit fitting for
systems which makes it possible to calculate the total mass of the system. In this thesis I
performed the best orbit fitting and calculated their total mass for 11 targets (5). These
results are useful for estimation of young M-type stellar ages and improves comparisons
between empirical and theoretical isochrones. All of the obtained results after analysis are
available in Table 4 with relevant archive data from previous works. In addition I confirmed
those targets which are truly binary/multiple systems by means of verifying common proper
motion and orbital motion, as mentioned in the table as well.
16
The sigma in this section represents the error measurement of values in the observed data, and the total
residual of fitting considers the total distance from the observed position to the expected value in the orbit fitting
for all of epochs
21

5 References
Allen, P. R., Burgasser, A. J., Faherty, J. K., & Kirkpatrick, J. D. 2012, AJ, 144, 62
Bate, M. R., Bonnell, I. A., & Bromm, V. 2002, MNRAS, 336, 705
Bergfors, C., Brandner, W., Janson, M., et al. 2010, A & A, 520, A54
Beuzit, J.-L., Ségransan, D., Forveille, T., et al. 2004, A & A, 425, 997
Daemgen, S., Siegler, N., Reid, I. N., & Close, L. M. 2007, ApJ, 654, 558
Delfosse, X., Beuzit, J.-L., Marchal, L., et al. 2004, Spectroscopically and Spatially Re-
solving the Components of the Close Binary Stars, 318, 166
Dhital, S., West, A. A., Stassun, K. G., & Bochanski, J. J. 2010, Aj, 139, 2566
Dieterich, S. B., Henry, T. J., Golimowski, D. A., Krist, J. E., & Tanner, A. M. 2012,
AJ, 144, 64
Duchêne, G., & Kraus, A. 2013, ARAA, 51, 269
Dupuy, T. J., Liu, M. C., Bowler, B. P., et al. 2010, ApJ, 721, 1725
Duquennoy, A., & Mayor, M. 1991, AAp, 248, 485
Eggleton, P. P., & Tokovinin, A. A. 2008, MNRAS, 389, 869
Fried, D. L. 1966, Journal of the Optical Society of America (1917-1983), 56, 1380
Horch, E. P., Bahi, L. A. P., Gaulin, J. R., et al. 2012, AJ, 143, 10
Hormuth, F., Hippler, S., Brandner, W., Wagner, K., & Henning, T. 2008, Proc.SPIE,
7014, 701448
Janson, M., Hormuth, F., Bergfors, C., et al. 2012, ApJ, 754, 44
Janson, M., Bergfors, C., Brandner, W., et al. 2014, ApJ, 789, 102
Janson, M., Bergfors, C., Brandner, W., et al. 2014, ApJs, 214, 17
Jódar, E., Pérez-Garrido, A., Díaz-Sánchez, A., et al. 2013, MNRAS, 429, 859
Köhler, R., Ratzka, T., Petr-Gotzens, M. G., & Correia, S. 2013, AAP, 558, A80
Law, N. M., Hodgkin, S. T., & Mackay, C. D. 2008, MNRAS, 384, 150
Lowrance, P. J., Becklin, E. E., Schneider, G., et al. 2005, AJ, 130, 1845
Mason, B. D., Wycoff, G. L., Hartkopf, W. I., Douglass, G. G., & Worley, C. E. 2001,
AJ, 122, 3466
McCarthy, C., Zuckerman, B., & Becklin, E. E. 2001, AJ, 121, 3259
Montagnier, G., Ségransan, D., Beuzit, J.-L., et al. 2006, A & A, 460, L19
Öpik, E. 1924, Publications of the Tartu Astrofizica Observatory, 25, 1
Perryman, M. A. C., Lindegren, L., Kovalevsky, J., et al. 1997, A & A, 323, L49
Pravdo, S. H., Shaklan, S. B., Wiktorowicz, S. J., et al. 2006, ApJ, 649, 389
Wöllert, M., Brandner, W., Reffert, S., et al. 2014, APP, 564, A10
Raghavan, D., McAlister, H. A., Henry, T. J., et al. 2010, ApJS , 190, 1
Reid, I. N., & Gizis, J. E. 1997, AJ, 113, 2246
Roberts, L. C., Jr., Perrin, M. D., Marchis, F., et al. 2004, Proc.SPIE, 5490, 504
Jørgen Christensen-Dalsgaard, Lecture Notes on Stellar Structure and Evolution, Sixth
Edition, 2008
Strigachev, A., & Lampens, P. 2004, A & A, 422, 1023
Tokovinin, A. 2008, MNRAS, 389, 925
Tokovinin, A. 2011, AJ, 141, 52
Van der Marel, R. P., Gerssen, J., Guhathakurta, P., Peterson, R. C., & Gebhardt, K.
2002, AJ, 124, 3255
Weintraub, D. A., Saumon, D., Kastner, J. H., & Forveille, T. 2000, ApJ, 530, 867
22

6 Appendix
6.1 Notes on individual targets
In this section, I list comments on some targets separately. It can be useful for the future to
analyse some of them in more detail.
I00077 +6022 : In this binary system, the secondary star moves very slowly and we do
not have enough data points to monitor the proper orbit. The orbital fit of this system, as
Table 5 displays, is very elliptical in shape and the value of total mass is too large (maximum
mass value is ≈ 1.0M ). We definitely need more observations of this system, possibly over
a long time.
I00088 +2050 : The system has two components, both with almost the same brightness,
so there is a ghost image in the science frame. This binary has a rapid orbital motion, and
during thirteen years has been passing through roughly the whole of the orbit. We are not
able to monitor this short orbit because there is few available data points which are not
enough.
2MASS J00325313 −0434068 : The system is a triple one, the component AC is very
close (54 mas) and the other one AB is far (615 mas). As you can see the orbital motion of
the AB pair of this system has high value of residual of the fitting, so we should do more
observation to plot the orbit more precisely. There is no data point in 2008, maybe it was
invisible because it was behind the primary and now according to the new position compared
with the previous one. It seems that it has a quite rapid orbital motion. So hopefully we
can estimate the AC orbital parameters in a short timescale. In addition, a sharp airy disk
can be seen in the original science frame which was observed.
I00395 +1454N : According to Janson et al. [2014] study, this system is a triple one,
although I just saw one close component, and certainly the wide component was outside of
the field of view in the previous epoch and in the last epoch (2014.61) because its angular
separation is at 17" according to Janson et al. [2014]. In the science frame, there is a very
faint distance object at ≈ 4.14 arcsec from the primary toward East-South (≈ clock 20:00)
which is probably one of the background stars.
2MASS J00503319 +2449009 : This binary system has a quite slow orbit and just
has ≈ 9 deg difference between the first observation and the last one (during 54 years). The
reason for this slow movement might be, that the orbiting star is passing the apoapsis or near
to it. Table 5 illustrates the orbital fit which is very elliptical and implies that the secondary
is close to the apoapsis area, but as you see the total mass is too large for a M-type system
and there is a large residual after finding the best fit for the orbit. Interestingly, there is
another close object which is very faint to the primary and it is hard to tell what the object
is. The object is clarified by a green circle in Figure 14.
I01032 +7113 : This is actually a rapid orbit, moving ≈ 80 deg during two years. The
secondary was so close to the primary that probably in the next close observation it would
be invisible.
2MASS J01034210 + 4051158 : If we ignore the first data point from 1960, then it
seems this wide system is relatively slow orbit, moves ≈0.6 deg/yr. It seems we should not
trust the data point from 1960.
2MASS J01071194 −1935359 : There is a ghost image in the science frame, which
means both stars have rather the same brightness.
2MASS J01112542 +1526214 : This binary system have been observing spanning 14
years and covering the large part of its orbit and it is moving ≈7.8 deg/yr. By observing a
few more decades, the orbits will get reasonable fits and hope to figure out the proper total
mass as well.
2MASS J01154885 +4702259 : According to the obtained data, the secondary star
moves ≈ 7 deg/yr which can be used to estimate that the period might be around 50 years.
Thus it is not a very rapid system.
2MASS J01212520 +2926143 :Orbital motion of the secondary star spans 73 degrees
over 6 years, and the system’s period could be approximately 30 years. Because of a lack
23

Figure 14: The science frame of 2MASS J00503319 +2449009 with the third close faint
object to the primary.
of sufficient data points, we could not monitor its orbit but soon the secondary can cover
a substantial fraction of the orbit during a few decades, then we will obtain enough data
positions and we will therefore be able to accomplish a reasonable fit for the orbit.
I02019 +7332 : Table 5 represents the orbital motion of this binary system and the
values of total mass and residual after the fitting is acceptable. The speed of orbital motion
has increased rapidly for the two last epochs, as a consequence of coming close to the periapsis
point, as you can see on the figure in the left column of Table 5. The difference of position
angles between the two last epochs is a lot larger than the first epochs.
2MASS J02155892 −0929121 : This triple system has one very close component and
another one is far. The close AB pair has been moving very slowly, and the AC pair moves
a little bit faster than the close component. We could not monitor this slow orbital motion,
even though there are many data points, since they only covered a small fraction of the
orbit.
2MASS J15553178 +3512028 : The movement of secondary has covered ≈ 9 degrees
during almost 16 years. It is one of the slow binary system.
I17076 +0722 : This system has two components with roughly the same brightness, so
as usual there is a ghost image on the frame. It was hard to distinguish brightness between
the real star and ghost image, and because of that we obtained a position which did not
follow the previous positions. It did not make sense at all, but when we add 180◦
to the
given position angle value, then it seems correct. The value of its position angle that is
shown on Table 3 is adjusted.
2MASS J17383964 +6114160 : In the literature, there are many astrometric points
available which have been collected by other instruments. By combining the data from
AstraLux with others, an orbital solution has been determined for this binary system.
2MASS J19213210 +4230520 : It seems to not have orbital motion even though it
has a common proper motion. Since the system was only observed two times during six
years, there are three cases that may have occurred that made the orbital motion hard to
recognize. First case: if this target is one of the more rapid systems, then in the second
observed time it may have passed through the whole of its orbit and came back close to the
first observed position. Second case: The secondary may be farther from the primary than
it appears, due to projection along the line of sight. I drew a sketch in Figure 15. That
measured angular separation is not the real separation for this system. The real separation
is much larger and just seems small from our point of view. The second star therefore orbits
slowly around the primary since the semi-major axis is large. Third case: It may be that
the orbiting bodies are at the apoastron point in a very elliptical orbit and so it moves very
24

Figure 15: Sketch of probable cases for orbital motion 2MASS J19213210+4230520
slowly in that region.
I19500 +3235 : As the data points display in the first two epochs (during 4 years), the
secondary passed around 66 degrees, while in the two last observed epochs (two years) it
covered 74 degree of orbit. The reason is the secondary passed the area close to apoapsis and
so moves faster, therefore it passes a larger fraction of the orbit. In Table 5 the proper orbital
fitting for those data points is shown with reasonable amount of total mass and residual after
finding the best fit for the orbit.
2MASS J20163382 −0711456 : The second object in this system seems to not have
CPM. When I analysed with the proper motion coordinate of the primary from PPMXL
catalogue and the object has a high probability (1.3σ) to be a background star, but the
values of the proper motion coordinate from NOMAD catalogue, show the system has CPM
between orbiting bodies. On the other hand, a statistical argument can also be made that
it should be uncommon for a background star to be so close to the primary (187 mas). In
my view the common proper motion for this system is unknown and should be studied more
carefully.
I20593 +5303 : This binary system has now been confirmed to have CPM and also
OM which was unsure in the previous study. It is also one of the slow systems, only passing
about 2 degrees during the two years. Hence we are awaiting further observations.
I21000 +4004E : Even though this binary system is one of the relatively rapid systems
(moves ≈ 7 deg/yr), it has only covered around 24 degrees of the whole of its orbit which is
very small fraction and of course not enough to find the best fit of the orbit. Table 5 displays
one sample of a best-fit orbit but the value of total mass is not acceptable at all. Indeed we
need more observations to better figure out future positions of the secondary.
2MASS J22240821 +1728466 : There are four available data points which cover a
small fraction of the orbit. In Table 5 there is one possible example best-fit for this target.
We need more data points which can cover larger fraction of the orbit to reveal the best-fit
of its orbit. Even though the values of total mass and residual seem reasonable, there are
many different possible good fits with quite the same results for mass and residual.
2MASS J22332264 −0936537 : It is one of the slow orbits, we have been keeping
track of it for 17 years, and only cover 8 degrees. Because it covers a very small fraction of
the orbit, we could not find any good orbital fits for this binary system.
2MASS J23172807 +1936469 : GJ 4326 is a binary system which orbiting body have
passed a whole period and more, so consequently the orbit fit matches very well with the
observed data points. The values of total mass and residual also are acceptable for a M-type
young system (Table 5), as you see the residual value is a little too large, because there are
25

seven positions. Estimating the mass for each component in this system, it is probable with
sufficient precisions.
2MASS J23261182 +1700082 : The system is quite nearby, so the orbital motion
could be very rapid. The orbital motion for this system seems clockwise and relatively fast.
The P.A. goes from 51.8 deg to -25.5 deg, so around ≈77.3 degrees in 6 years.
2MASS J23261707 +2752034 : This binary system is a short-period system, the
secondary has passed a large fraction of the orbit during about 6 years. Although still there
are not enough data points to find a sufficient best fit for the true orbit.
2MASS J23450477 +1458573AC : The wide AC pair is visible on the observed frame
but not the AB one. The AC pair has a very slow movement, only having moved around 1
deg/yr.
2MASS J23495365 +2427493 : One of the probable example fits for this close binary
system was illustrated in Table 5 and the achieved values of total mass and residual are
acceptable for a M-kind system. The secondary has orbited around 72 degrees of the whole
orbit in 6 years.
6.2 Abbreviation
• Adaptive Optic : AO
• Angle : Ang.
• Calibration : Calib.
• Charge Coupled Device : CCD
• Common Proper Motion : CPM
• Companion Frequency : CF
• Declination : Dec
• Hertzsprung–Russell diagram : H-R
• Interactive Data Language : IDL
• Main sequence : MS
• Mean value of position angle : Average Pos.Ang.
• Mean value of separation : Average Sep.
• Multiple Frequency : MF
• Number : Num.
• Orbital motion : OM
• Position Angle : Pos.Ang.
• Relative Humidity : RH
• Right Ascension : RA
• Point Spread Function : PSF
• Separation : Sep.
• Sloan Digital Sky Survey : SDSS
• Standard deviation of position angle : StDev. Pos.Ang.
• Standard deviation of separation : StDev. Sep.
26

6.3 Tables
Table 2: Properties of all targets in this survey
Target IDa
Other name R.A. Dec. SpTb
Dist.c
J
(hh mm ss) (dd mm ss) (pc) (mag)
J00063925-0705354 - 00 06 39.25 -07 05 35.4 M3.5 14 9.86
I00077+6022 G 217-32 00 07 42.620 +60 22 54.34 M3.8 14.6 8.91
I00088+2050 GJ 3010 00 08 53.922 +20 50 25.45 M4.5 14.8 8.87
J00325313-0434068 - 00 32 53.13 -04 34 06.8 M3.5 (12) 9.27
I00395+1454N G 32-37 B 00 39 33.799 +14 54 34.92 M5.0 28.3 9.83
J00503319+2449009 GJ 3060A 00 50 33.19 +24 49 00.9 M3.5 12(P97) 7.92
I01032+7113 LHS 1182 01 03 14.452 +71 13 12.72 m5.0 18.3 9.69
J01034210+4051158 G 132-51 01 03 42.10 +40 51 15.8 K7.0 32(G04) 9.37
J01071194-1935359 - 01 07 11.94 -19 35 35.9 M1.0 (37) 8.15
J01112542+1526214 GJ 3076 01 11 25.42 +15 26 21.4 M5.0 (9) 9.08
J01154885+4702259 LP 151-21 01 15 48.85 +47 02 25.9 M4.0 (27) 10.23
J01212520+2926143 - 01 21 25.20 +29 26 14.3 M3.5 (30) 9.38
I01431+2101 - 01 43 11.861 +21 01 10.64 m5.0 12 9.25
I02019+7332 GJ 3125 02 01 54.060 +73 32 31.91 M4.5 11.4 9.25
J02155892-0929121 - 02 15 58.92 -09 29 12.1 M2.5 (27) 8.43
J02255447+1746467 LP 410-22 02 25 54.47 +17 46 46.7 M4.0 (39) 10.22
J15553178+3512028 GJ 3928 15 55 31.78 +35 12 02.8 M4.0 (11) 9.00
I16280+1533 G 138-33 16 28 02.047 +15 33 57.10 M2.5 24.4 9.38
I17076+0722 GJ 1210 17 07 40.847 +07 22 06.73 M5.0 12.8 9.28
J17383964+6114160 HD 160934 17 38 39.64 +61 14 16.0 M2-M3 36.5 7.59
I18427+1354 GJ 4071 18 42 44.993 +13 54 17.05 M4.0 10.7 8.36
J19213210+4230520 - 19 21 32.10 +42 30 52.0 M2.0 (27) 8.65
I19500+3235 LHS 3489 19 50 02.454 +32 35 00.48 M2.5 17 8.65
I20021+1300 - 20 02 10.554 +13 00 31.53 m5.0 14.6 9.73
J20100002-2801410 - 20 10 00.02 -28 01 41.0 M3.0 (32) 8.65
J20163382-0711456 - 20 16 33.82 -07 11 45.6 M0.0 (50) 8.59
I20298+0941 - 20 29 48.325 +09 41 20.19 M4.5 8.8 8.23
I20300+0023 - 20 30 01.919 +00 23 55.33 m5.0 14.8 9.91
I20314+3833 LHS 3559 20 31 25.642 +38 33 44.34 M4.0 14.9 9.19
I20337+2322 G 186-29 20 33 42.751 +23 22 13.80 M3.0 22.2 9.11
I20488+1943 G 144-39 20 48 52.449 +19 43 04.86 M4.0 33.6 9.24
I20593+5303 - 20 59 20.361 +53 03 04.93 m4.5 51.3 9.91
I21000+4004E GJ 815 21 00 05.405 +40 04 13.36 M3.0 15.3 6.67
I21013+3314 G 187-14 21 01 20.632 +33 14 27.97 M3.5 16.9 8.94
I21014+2043 LHS 3610 21 01 24.836 +20 43 38.10 M3.5 22.7 9.94
I21173+2053N G 145-31 21 17 22.639 +20 53 58.55 M3.0 21.9 8.91
J21372900-0555082 - 21 37 29.00 -05 55 08.2 M3.0 (25) 8.80
I21376+0137 - 21 37 40.188 +01 37 13.76 M5.0 10.5 8.80
I21554+5938 - 21 55 24.360 +59 38 37.15 M4.0 11 9.18
I22035+0340 - 22 03 33.384 +03 40 23.64 m5.0 14.9 9.74
J22240821+1728466 - 22 24 08.21 +17 28 46.6 M4.0 (22) 10.26
I22300+4851 - 22 30 04.182 +48 51 34.66 m5.0 16.1 9.52
J22332264-0936537 GJ 865 22 33 22.64 -09 36 53.7 M2.5 (36) 8.53
J23172807+1936469 GJ 4326 23 17 28.07 +19 36 46.9 M3.0 (21) 8.02
J23261182+1700082 - 23 26 11.82 +17 00 08.2 M4.5 (17) 9.30
J23261707+2752034 - 23 26 17.07 +27 52 03.4 M3.0 (31) 8.46
J23450477+1458573 G 68-39 23 45 04.77 +14 58 57.3 M1.0 (59) 9.41
J23495365+2427493 - 23 49 53.65 +24 27 49.3 M3.5 (51) 9.88
Continued on next page
27

Table 2: continued.
Target IDa
Other name R.A. Dec. SpTb
Dist.c
J
(hh mm ss) (dd mm ss) (pc) (mag)
J23570417-0337559 - 23 57 04.17 -03 37 55.9 M4.0 (71) 10.90
a members of 2MASS start with letter (J) and Lepine IDs begin with (I).
b Spectral type; Small letter plus number imply the SpT of each target inferred from photometric-color and
capital letter plus number show the SpT from spectrum.
c The distance that mentioned in this table divided in two group, those have parenthesis shows the value
are gained by spectroscopy (distance module) and those without parenthesis are calculated with parallax.
Table 3: Properties of all stars observed in this survey
Target Average Sep.a
Total error of Sep. Average Pos.Ang. Total error of Ang.
(arcsec) (arcsec) (deg) (deg)
J00063 0.3 ± 0.005 5.3 ±0.3
I00077 0.777 ± 0.001 99.3 ±0.2
I00088 0.147 ± 0.002 97.5 ± 1.02
J00325AB 0.054 ±0.004 349.9 ± 2.2
J00325AC 0.615 ± 0.001 191.8 ± 0.2
I00395 0.108 ± 0.005 222.3 ±5.4
J00503 0.965 ± 0.001 324.1 ± 0.2
J01032 0.092 ± 0.005 113.2 ±4.3
J01034 2.479 ± 0.002 101.3 ± 0.2
J01071 0.47 ± 0.001 169.6 ± 0.2
J01112 0.34 ± 0.004 256.8 ± 0.2
J01154 0.216 ± 0.004 306.8 ± 0.9
J01212 0.171 ± 0.002 239.4 ± 1.5
I01431 0.383 ± 0.001 340.3 ±0.2
J02019 0.443 ± 0.002 69.6 ± 0.2
J021557 0.553 ± 0.001 291.0 ±0.3
J02255 0.145 ± 0.005 135.0 ± 2.6
J15553 1.625 ± 0.002 257.3 ± 0.2
J16280 0.597 ± 0.002 32.8 ± 0.2
I17076 0.388 ±0.003 231.0 ±0.2
J17383 0.174 ± 0.003 271.8 ± 2.3
I18427 4.565 ± 0.004 181.5 ±0.2
J19213 0.091 ± 0.027 156.1 ± 1.4
I19500 0.175 ± 0.003 59.4 ±0.5
I20021 0.241 ± 0.004 60.3 ± 0.3
J20100 0.702 ± 0.007 285.9 ±0.8
J20163 0.186 ±0.001 303.9 ± 1.8
J20163b 0.187 ± 0.001 303.3 ± 0.9
I20298 0.133 ±0.014 257.6 ± 5.6
I20300 0.395 ± 0.00049 349.1 ±0.2
J20314 0.116 ± 0.011 253.4 ± 5.5
J20337 0.908 ± 0.001 177.8 ±0.2
J20488 0.218 ± 0.002 157.2 ± 0.5
J20593 0.443 ± 0.001 21.2 ± 0.2
J21000 0.793 ± 0.002 54.4 ± 0.2
28

Table 3 – Continued from previous page
Target Average Sep.a
Total error of Sep. Average Pos.Ang. Total error of Ang.
(arcsec) (arcsec) (deg) (deg)
J21013 0.146 ± 0.003 114.2 ± 2.0
J21014 0.394 ± 0.005 38.4 ± 0.8
J21173 4.317 ±0.004 345.1 ±0.2
J21372 0.245 ± 0.0005 318.5 ±0.4
J21376 0.389 ± 0.001 339.8 ± 0.2
J21554 0.274 ± 0.001 77.4 ± 0.2
J22035 0.468 ± 0.001 355.9 ±0.2
J22240 0.134 ±0.007 43.4 ± 2.1
J22300 2.337 ± 0.002 256.3 ± 0.2
J22332 1.43 ± 0.001 280.1 ± 0.2
J23172 0.109 ±0.004 55.8 ± 2.9
J23261 0.253 ±0.003 334.5 ±0.2
J232617 0.128 ± 0.001 130.4 ± 1.1
J23450 1.167 ±0.001 182.4 ±0.2
J23495 0.156 ± 0.00042 28.9 ± 0.2
J23570 0.241 ±0.011 252.5 ±1.2
Table 4: Comparison astrometry of all data of binary/multiple systems
Target ID Sep. Pos. Ang. Epoch Ref.a
CPMb
OMc
(arcsec) (deg)
I00077 + 6022 0.612±0.006 82.5±0.3 2011.85 JI14 Y Y
I00077 + 6022 0.661±0.007 86.9±0.3 2012.65 JI14 Y Y
I00077 + 6022 0.674±0.007 87.9±0.3 2012.89 JI14 Y Y
I00077 + 6022 0.777± 0.001 99.3 ± 0.2 2014.61 TP Y Y
I00088 + 2050 0.111±0.005 169.9± 0.5 2001.6 B04 Y Y
I00088 + 2050 0.133±0.005 271.9±1.7 2012.02 JI14 Y Y
I00088 + 2050 0.147 ± 0.0015 97.5 ± 1.02 2014.61 TP Y Y
J00325313 − 0434068AB 0.422±0.012 180.0±2.2 2008.63 J12 Y Y
J00325313 − 0434068AB 0.422±0.006 179.0±0.9 2008.88 J12 Y Y
J00325313 − 0434068AB 0.508±0.005 183.5±0.3 2012.02 J12 Y Y
J00325313 − 0434068AB 0.615 ±0.001 191.8± 0.2 2014.61 TP Y Y
I00395 + 1454N 0.151±0.002 223.9±1.7 2012.9 JI14 I -
I00395 + 1454N 0.108 ± 0.005 222.3±5.4 2014.61 TP Y Y
J00503319 + 2449009 1.0 315.0 1960.01 M01 Y Y
J00503319 + 2449009 2.080±0.032 316.0±1.0 1991.25 P97 Y Y
J00503319 + 2449009 1.648±0.017 317.1±0.1 2002.64 S04 Y Y
J00503319 + 2449009 1.370±0.014 318.3±0.3 2007.61 J12 Y Y
J00503319 + 2449009 1.353±0.014 318.6±0.3 2008.03 J12 Y Y
J00503319 + 2449009 1.320±0.013 319.0±0.3 2008.59 J12 Y Y
J00503319 + 2449009 1.288±0.013 318.7±0.3 2008.86 B10 Y Y
J00503319 + 2449009 0.965 ± 0.001 324.1 ± 0.2 2014.61 TP Y Y
I01032 + 7113 0.147±0.003 34.2±0.7 2012.01 JI14 I -
I01032 + 7113 0.092 ± 0.005 113.2 ± 4.3 2014.61 TP Y Y
J01034210 + 4051158 1.5 90.0 1960 M01 Y N
29

CPMb
OMc
(arcsec) (deg)
J01034210 + 4051158 2.473±0.025 96.1±0.3 2008.03 J12 Y N
J01034210 + 4051158 2.477±0.025 96.8±0.3 2008.64 J12 Y N
J01034210 + 4051158 2.470±0.025 96.7±0.3 2009.13 J12 Y N
J01034210 + 4051158 2.479 ± 0.002 101.3± 0.2 2014.61 TP Y Y
J01071194 − 1935359 0.412±0.004 169.8±0.3 2008.87 B10 Y Y
J01071194 − 1935359 0.421±0.004 169.5±0.3 2010.08 J12 Y Y
J01071194 − 1935359 0.430±0.004 168.8±0.3 2010.81 J14 Y Y
J01071194 − 1935359 0.439±0.004 167.6±0.3 2012.01 J14 Y Y
J01071194 − 1935359 0.470 ± 0.001 169.6± 0.2 2014.61 TP Y Y
J01112542 + 1526214 0.409 147.2 2000.62 B04 Y Y
J01112542 + 1526214 0.309±0.003 186.1±0.3 2006.86 J12 Y Y
J01112542 + 1526214 0.304±0.003 188.0±0.3 2007.01 J12 Y Y
J01112542 + 1526214 0.297±0.003 197.3±0.4 2008.03 J12 Y Y
J01112542 + 1526214 0.292±0.003 203.1±0.3 2008.64 J12 Y Y
J01112542 + 1526214 0.289±0.003 205.1±0.3 2008.88 J12 Y Y
J01112542 + 1526214 0.303±0.005 231.5±0.5 2011.85 J14 Y Y
J01112542 + 1526214 0.308±0.004 238.4±0.3 2012.65 J14 Y Y
J01112542 + 1526214 0.327±0.015 241.1±0.8 2012.89 J14 Y Y
J01112542 + 1526214 0.340 ± 0.004 256.8 ± 0.2 2014.61 TP Y Y
J01154885 + 4702259 0.271±0.003 265.6±0.4 2008.63 J12 U -
J01154885 + 4702259 0.267±0.003 267.4±0.4 2008.88 J12 U -
J01154885 + 4702259 0.216 ± 0.004 306.8± 0.9 2014.61 TP Y Y
J01212520 + 2926143 0.260±0.003 312.5±0.3 2008.63 J12 Y Y
J01212520 + 2926143 0.257±0.003 309.8±0.3 2008.87 J12 Y Y
J01212520 + 2926143 0.171± 0.002 239.4 ± 1.5 2014.61 TP Y Y
I01431 + 2101 0.355±0.004 325.8±0.3 2012.02 JI14 I -
I01431 + 2101 0.383± 0.001 340.3± 0.2 2014.61 TP Y Y
I02019 + 7332 0.438±0.004 266.3±0.3 2011.86 JI14 Y Y
I02019 + 7332 0.436±0.004 260.2±0.3 2012.65 JI14 Y Y
I02019 + 7332 0.437±0.004 258.8±0.6 2012.89 JI14 Y Y
I02019 + 7332 0.443 ± 0.002 69.6 ± 0.2 2014.61 TP Y Y
J02155892 − 0929121AB 0.623±0.006 292.0±0.3 2008.87 J12 Y Y
J02155892 − 0929121AB 0.611±0.006 291.4±0.3 2010.82 J14 Y Y
J02155892 − 0929121AB 0.583±0.006 289.5±0.3 2012.01 J14 Y Y
J02155892 − 0929121AB 0.554 ± 0.001 291.0±0.3 2014.61 TP Y Y
J02155892 − 0929121AC 3.464±0.035 299.1±0.3 2008.87 J12 Y N
J02155892 − 0929121AC 3.448±0.035 299.5±0.3 2010.82 J14 Y N
J02155892 − 0929121AC 3.412±0.034 298.8±0.3 2012.01 J14 Y N
J02155892 − 0929121AC 3.4 ± 0.003 302.4 ± 0.2 2014.61 TP Y Y
J02255447 + 1746467 0.106±0.001 269.0±2.0 2008.63 J12 Y Y
J02255447 + 1746467 0.098±0.001 278.2±1.9 2008.87 J12 Y Y
J02255447 + 1746467 0.145±0.005 135.0 ± 2.6 2014.61 TP Y Y
J15553178 + 3512028 1.500±0.100 266.0±4.0 1998.3 Mc01 Y N
J15553178 + 3512028 1.571±0.016 261.2±0.1 2005.4 D07 Y N
J15553178 + 3512028 1.585±0.016 257.9±0.3 2007.01 J12 Y N
J15553178 + 3512028 1.594±0.016 257.5±0.3 2008.45 J12 Y N
J15553178 + 3512028 1.625 ± 0.002 257.3 ± 0.2 2014.61 TP Y Y
I16280 + 1533 0.558±0.006 35.1±0.3 2012.43 JI14 I -
I16280 + 1533 0.597 ± 0.002 32.8 ± 0.2 2014.61 TP Y Y
I17076 + 0722 0.183±0.005 266.7±0.5 2008.47 H12 Y Y
30

CPMb
OMc
(arcsec) (deg)
I17076 + 0722 0.436±0.004 236.3±0.3 2012.43 JI14 Y Y
I17076 + 0722 0.390 ± 0.001 231.0 ± 0.2 2014.61 TP Y Y
J17383964 + 6114160 0.155 ± 0.001 275.5 ± 0.2 1998.5 L05 Y Physically bounded
J17383964 + 6114160 0.215 ± 0.002 270.9 ± 0.3 2006.52 L05 Y -
J17383964 + 6114160 0.174±0.003 271.8 ± 2.3 2014.61 TP Y Y
J17383964 + 6114160b 0.176 ± 0.004 269.4 ± 1.6 2014.61 TP Y Y
I18427 + 1354 3.695±0.037 176.6±0.3 2012.66 JI14 - BG?
I18427 + 1354 4.565±0.004 181.5±0.2 2014.61 TP Y Y
J19213210 + 4230520 0.126±0.004 154.4±0.3 2008.63 J12 - Physically bounded
J19213210 + 4230520 0.091±0.027 156.1 ± 1.4 2014.61 TP Y N
I19500 + 3235 0.378±0.010 274.2±2.0 2008.43 J13 Y Y
I19500 + 3235 0.238±0.002 340.0±0.4 2012.43 JI14 Y Y
I19500 + 3235b 0.235±0.002 340.7±0.3 2012.43 JI14 Y Y
I19500 + 3235 0.222±0.002 345.1±0.7 2012.67 JI14 Y Y
I19500 + 3235 0.175 ± 0.003 59.4 ± 0.5 2014.61 TP Y Y
I20021 + 1300 0.261±0.004 42.9±0.5 2012.43 JI14 - -
I20021 + 1300 0.241 ± 0.004 60.3 ± 0.3 2014.61 TP Y Y
J20100002 − 2801410 0.607±0.006 280.2±0.3 2008.87 B10 Y Y
J20100002 − 2801410 0.648±0.007 281.8±0.3 2010.82 J14 Y Y
J20100002 − 2801410 0.702 ±0.007 285.9 ± 0.8 2014.61 TP Y Y
J20163382 − 0711456 0.107±0.007 352.4±2.1 2008.44 J12 U -
J20163382 − 0711456 0.176±0.002 320.7±0.7 2011.85 J14 U -
J20163382 − 0711456 0.186±0.001 303.9±1.8 2014.61 TP U Y
J20163382 − 0711456 0.187±0.001 303.3± 0.9 2014.61 TP U Y
I20300 + 0023 0.398±0.004 354.3±0.3 2012.66 JI14 - -
I20300 + 0023 0.395 ± 0.00049 349.1 ± 0.2 2014.61 TP Y Y
I20314 + 3833 0.118±0.006 252.4±1.4 2012.66 JI14 I -
I20314 + 3833 0.116 ± 0.11 253.4 ± 5.5 2014.61 TP Y Y
I20337 + 2322 0.906±0.009 176.2±0.3 2012.66 JI14 I -
I20337 + 2322 0.908± 0.001 177.8 ± 0.2 2014.61 TP Y Y
I20488 + 1943 0.219±0.002 133.6±0.8 2012.67 JI14 I -
I20488 + 1943 0.218±0.002 157.2 ± 0.5 2014.61 TP Y Y
I20593 + 5303 0.433±0.004 23.2±0.7 2012.01 JI14 Y N
I20593 + 5303 0.445±0.004 20.9±0.4 2012.67 JI14 Y N
I20593 + 5303 0.444±0.004 21.4±0.4 2012.90 JI14 Y N
I20593 + 5303 0.443± 0.001 21.2 ± 0.2 2014.61 TP Y Y
I21000 + 4004E 0.609±0.006 29.7±0.3 2011.86 JI14 Y Y
I21000 + 4004E 0.668±0.007 37.1±0.3 2012.65 JI14 Y Y
I21000 + 4004E 0.685±0.007 39.0±0.3 2012.90 JI14 Y Y
I21000 + 4004E 0.793± 0.002 54.4 ± 0.2 2014.61 TP Y Y
I21013 + 3314 0.142±0.003 34.0±0.3 2012.01 JI14 I -
I21013 + 3314 0.146±0.003 114.2 ± 2.0 2014.61 TP Y Y
I21014 + 2043 0.392±0.008 41.9±0.6 2012.67 JI14 I -
I21014 + 2043 0.394± 0.005 38.4 ± 0.8 2014.61 TP Y Y
I21173 + 2053N 3.800±0.500 347.0±5.0 1960.5 WDS Y N
I21173 + 2053N 4.281±0.043 341.3±0.3 2012.66 JI14 Y N
I21173 + 2053N 4.317± 0.004 345.1 ± 0.2 2014.61 TP Y Y
J21372900 − 0555082 0.245±0.002 170.2±0.3 2008.63 J12 Y Y
J21372900 − 0555082 0.219±0.002 172.0±0.3 2008.88 J12 Y Y
J21372900 − 0555082 0.245± 0.00050 318.5 ± 0.4 2014.61 TP Y Y
31

CPMb
OMc
(arcsec) (deg)
I21376 + 0137 0.433±0.004 341.1±0.3 2012.67 JI14 - -
I21376 + 0137 0.389 ±0.001 339.8 ± 0.2 2014.61 TP Y Y
I21554 + 5938 0.199±0.002 102.3±0.3 2012.02 JI14 - -
I21554 + 5938 0.274 ± 0.001 77.4 ± 0.2 2014.61 TP Y Y
I22035 + 0340 0.412±0.004 351.9±0.3 2012.66 JI14 - -
I22035 + 0340 0.468±0.001 355.9 ± 0.2 2014.61 TP Y Y
J22240821 + 1728466 0.171±0.003 205.7±0.7 2007.84 J12 Y Y
J22240821 + 1728466 0.160±0.002 205.7±0.1 2008.59 J12 Y Y
J22240821 + 1728466 0.146±0.007 208.8±0.8 2009.42 J12 Y Y
J22240821 + 1728466 0.134 ± 0.007 43.4 ± 2.1 2014.61 TP Y Y
I22300 + 4851 2.300±0.023 252.9±0.3 2012.02 JI14 I -
I22300 + 4851 2.337 ± 0.002 256.3 ± 0.2 2014.61 TP Y Y
J22332264 − 0936537 1.660±0.050 272.3±2.0 1997.6 MC01 Y Y
J22332264 − 0936537 1.571±0.016 279.7±0.1 2005.44 D07 Y Y
J22332264 − 0936537 1.547±0.016 278.5±0.3 2007.85 J12 Y Y
J22332264 − 0936537 1.403±0.028 278.4±0.3 2008.87 B10 Y Y
J22332264 − 0936537 1.497±0.015 277.6±0.3 2010.81 J14 Y Y
J22332264 − 0936537 1.430± 0.001 280.1 ± 0.2 2014.61 TP Y Y
J23172807 + 1936469 0.142 209.0 2001.59 B04 Y Y
J23172807 + 1936469 0.232±0.002 39.3±0.3 2003.94 J14 Y Y
J23172807 + 1936469 0.308±0.003 34.5±0.3 2004.73 J14 Y Y
J23172807 + 1936469 0.293±0.003 19.2±0.3 2008.59 J12 Y Y
J23172807 + 1936469 0.091±0.003 347.2±0.3 2010.79 J14 Y Y
J23172807 + 1936469 0.145±0.002 220.2±3.5 2012.65 J14 Y Y
J23172807 + 1936469 0.109± 0.004 55.8± 2.9 2014.61 TP Y Y
J23261182 + 1700082 0.195±0.002 51.8±0.7 2008.63 J12 Y Y
J23261182 + 1700082 0.273±0.004 1.7±0.3 2011.85 J14 Y Y
J23261182 + 1700082 0.253±0.003 334.5±0.2 2014.61 TP Y Y
J23261707 + 2752034 0.151±0.002 14.1±0.3 2008.59 J12 Y Y
J23261707 + 2752034 0.109±0.002 328.7±0.6 2011.86 J14 Y Y
J23261707 + 2752034 0.128 ± 0.001 130.4 ± 1.1 2014.61 TP Y Y
J23450477 + 1458573AC 1.222±0.012 175.9±0.3 2008.59 J12 Y Y
J23450477 + 1458573AC 1.191±0.012 177.3±0.3 2011.86 J14 Y Y
J23450477 + 1458573AC 1.167 ± 0.001 182.4 ± 0.2 2014.61 TP Y Y
J23495365 + 2427493 0.132±0.005 316.9±0.7 2008.59 J12 Y Y
J23495365 + 2427493 0.135±0.003 317.9±1.0 2008.63 J12 Y Y
J23495365 + 2427493 0.129±0.001 324.4±1.6 2008.88 J12 Y Y
J23495365 + 2427493 0.141±0.002 359.3±1.8 2011.86 J14 Y Y
J23495365 + 2427493 0.156 ± 0.00042 28.9± 0.2 2014.61 TP Y Y
J23570417 − 0337559 0.184±0.014 281.9±0.3 2007.85 J12 Y N
J23570417 − 0337559 0.191±0.003 282.2±1.9 2008.59 J12 Y N
J23570417 − 0337559 0.189±0.002 282.2±0.4 2008.88 J12 Y N
J23570417 − 0337559 0.241 ±0.011 252.5±1.2 2014.61 TP Y Y
32

CPMb
OMc
(arcsec) (deg)
a
Reference of astrometry at the relevant epoch and use these abbreviation for each of them.
TP: This paper. P97: Perryman et al. [1997]
WDS: Washington Double Star Catalogue, Mason et al. [2001]. Mc01: McCarthy et al. [2001]
M01: Mason et al. [2001]
S04: Strigachev & Lampens [2004]. B04: Beuzit et al. [2004]; uniform errors assumed
L05: Lowrance et al. [2005]
M06: Montagnier et al. [2006]. P06: Pravdo et al. [2006]
D07: Daemgen et al. [2007]
L08: Law et al. [2008]
D10: Dupuy et al. [2010]. B10: Bergfors et al. [2010]
H12: Horch et al. [2012]. J12: Janson et al. [2012]
J13: Jódar et al. [2013]
J14: Janson et al. [2014]. JI14: Janson et al. [2014]
b
Common proper motion; estimated between the ﬁrst and last measurement in
observed epochs. Yes (Y), no (N) and inferred (I).
c
Orbital motion; considered the ﬁrst and last data of observed epochs.Yes (Y), no(N),
Unknown (U), or background star (BG).
33

Orbital-motion Parameters : Values
• ID : I00077+6022
• PeriJD(t): 20-Jun-1873 (2405330 JD)
• Period(p): 24090 days ≈ 66 yr
• Axis(a): 96.4915 Au
• Excent(e): 0.99
• Mass : 206.526 M
• Total residual of ﬁtting: 33.7496
• ID : J00325313-0434068AB
• PeriJD(t): 2-Jun-1867 (2403120 JD)
• Period(p): 14610 days ≈ 40.03 yr
• Axis(a): 11.9372 Au
• Excent(e): 0.85
• Mass : 1.06314 M
• ID : J00503319+2449009
• PeriJD(t): 18-Jun-2045 (2468150 JD)
• Period(p): 31650 days ≈ 86.7 yr
• Axis(a): 51.3845 Au
• Excent(e): 0.95
• Mass : 18.0688 M
• ID : J01112542+1526214
• PeriJD(t): 24-Apr-1882 (2408560 JD)
• Period(p): 23680 days ≈ 64.88 yr
• Axis(a): 3.83672 Au
• Excent(e): 0.22
• Mass : 0.0134368 M
34

Orbital-motion Parameters :Values
• ID : I02019+7332
• PeriJD(t): 8-Apr-1866 (2402700 JD)
• Period(p): 57100 days ≈ 156.44 yr
• Axis(a): 20.6902 Au
• Excent(e): 0.85
• Mass : 0.362414 M
• ID : I19500+3235
• PeriJD(t): 18-Jun-2045 (2407100 JD)
• Period(p): 5550 days ≈ 15.2 yr
• Axis(a): 5.08310 Au
• Excent(e): 0.45
• Mass : 0.568826 M
• ID : J20163382-0711456
• PeriJD(t): 1-Feb-1890 (2411400 JD)
• Period(p): 10650 days ≈ 29.18 yr
• Axis(a): 9.42285 Au
• Excent(e): 0.6
• Mass : 0.984074 M
• ID : I21000+4004E
• PeriJD(t): 27-Jun-1864 (2402050 JD)
• Period(p): 26550 days ≈ 73.74 yr
• Axis(a): 75.6316 Au
• Excent(e): 0.98
• Mass : 81.8769 M
35

Orbital-motion Parameters :Values
• ID : J22240821+1728466
• PeriJD(t): 15-Mar-1861 (2400850 JD)
• Period(p): 9750 days ≈ 26.71 yr
• Axis(a): 9.04328 Au
• Excent(e): 0.989998
• Mass : 1.03789 M
• ID : J23172807+1936469
• PeriJD(t): 29-Jan-1864 (2401900 JD)
• Period(p): 4190 days ≈ 11.48 yr
• Axis(a): 5.55554 Au
• Excent(e): 0.45
• Mass : 1.30296 M
• ID : J23495365+2427493
• PeriJD(t): 17-Mar-1874 (2405600 JD)
• Period(p): 16850 days ≈ 46.16 yr
• Axis(a): 9.86604 Au
• Excent(e): 0.2
• Mass : 0.451242 M
Table 5: Examples of orbital ﬁtting
36

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