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A&A 464, 635--640 (2007)
DOI: 10.1051/0004­6361:20066224
c
# ESO 2007
Astronomy
&
Astrophysics
Accurate masses of low mass stars
GJ765.2AB (0.83 M#+ 0.76 M# ) #,##
Y. Y. Balega 1 , J.­L. Beuzit 2 , X. Delfosse 2 , T. Forveille 2 , C. Perrier 2 , M. Mayor 3 , D. SÈgransan 3 , S. Udry 3 ,
A. A. Tokovinin 4 , D. Schertl 5 , G. Weigelt 5 , I. I. Balega 1 , and E. V. Malogolovets 1
1 Special Astrophysical Observatory, N. Arkhyz, Karachai­Cherkesia 369167, Russia
e­mail: balega@sao.ru
2 Laboratoire d'Astrophysique de Grenoble, BP 53X, 38041 Grenoble Cedex, France
3 Observatoire de GenÕve, 1290 Sauverny, Switzerland
4 Cerro Tololo Inter­American Observatory, Casilla 603, La Serena, Chile
5 Max­Planck­Institut fÝr Radioastronomie, Auf dem HÝgel 69, 53121 Bonn, Germany
Received 10 August 2006 / Accepted 8 November 2006
ABSTRACT
Context. Because of the lack of precise masses, the coverage of the main­sequence empirical mass­luminosity relation for stars in the
mass range from 0.6 M # to 0.9 M # is incomplete. The nearby K­type visual and spectroscopic binary GJ 765.2 =MLR 224 is a good
candidate for new reliable points in this significant part of the relation.
Aims. We have found a combined orbital solution for the pair and derived physical properties of the components using interferometric
and spectroscopic data.
Methods. The di#raction­limited speckle observations were mostly collected at the 6 m BTA telescope, and the velocities of the
components were obtained using the CORAVEL radial velocity scanner on the Swiss 1 m telescope.
Results. In a combined solution, the orbital period is found to be 11.919 yr. The masses of the GJ 765.2 components are M A =
0.831 ±0.020 M # and M B = 0.763 ±0.019 M # . The obtained orbital parallax of the system, # orb = 31.0 ±0.5 mas, is 7 percent lower
than the Hipparcos value. The absolute V magnitudes of the stars, derived from the measured speckle magnitude di#erences, are:
M A
V = 5.99 ±0.04 and M B
V = 6.64 ±0.05. The e#ective temperatures of the components, T A
e# = 5060±130 K and T B
e# = 4690±160 K,
follow from the V - K and J - K color indices. The star metallicity value, estimated from the 6 m telescope spectrum, is [M/H] =
-0.35 ± 0.15 dex.
Conclusions. The presented individual masses have 2.4% and 2.5% relative accuracies. Therefore, the components of GJ 765.2 rank
among a dozen stars with masses accurate to within a few percent in the mass range 0.6-0.9 M # . The existing data on the kinematics
of GJ 765.2 and its chromospheric activity indicate that the binary belongs to the middle age (3-4 â 10 9 yr) thin disk population of
the galaxy.
Key words. stars: binaries: visual -- stars: fundamental parameters -- stars: late­type
1. Introduction
The coverage of the main­sequence (MS) mass­luminosity re­
lation (MLR) is complete for intermediate­mass stars from the
late­B through the middle G­type, corresponding to the mass
range of 0.9-3.0 M # . From about 50 stars with accurately (bet­
ter than 2-3%) known masses, 35 belong to eclipsing binary
components with masses above 1 M # . At the end of the 90 s, a
burst of very accurate masses at the bottom of the MS (masses
below #0.5 M # ) came from the combination of very precise ra­
dial velocities of double­lined binary systems with adaptive op­
tics and speckle interferometry (SÈgransan et al. 2000; Delfosse
et al. 2000). Masses accurate to within 2-10% for very low­mass
stars were also provided by precise astrometric measurements
using the Fine Guidance Sensors on board of the HST (Torres
et al. 1999; Benedict et al. 2000). A series of accurate mass
# Based on observations made with the 6 m BTA telescope, which
is operated by the Special Astrophysical Observatory, Russia, and the
Observatoire de Haute­Provence, operated by the Centre National de la
Recherche Scientifique de France.
## Tables 1 and 2 are only available in electronic form at
http://www.aanda.org
determinations allowed the improvement of the empirical MLR
in its lower part. However, for the mass range of 0.6-0.9 M # ,
corresponding to late­G to late­K dwarfs, the need for precise
masses remains important. This is a large region of the MS with
very few known eclipsing systems. Andersen's (1991) critical
compilation includes only one binary in this mass range; namely,
HS Aur with masses of 0.900 and 0.879 M # . The reason for
this deficiency is selection e#ects: eclipses of these small stars
are rare, they have low luminosities, and short­period pairs have
high rotation velocities and, therefore, blended spectral lines.
A second reason for a more thorough study of this mass
range is the discrepancy between the measured properties of
components of binary systems with masses 0.7-1.0 M # and
stellar evolution models (Lastennet et al. 2003). By fixing the
accurately determined masses and luminosities for the pairs of
this type, it is easier to operate with other model parameters
(metallicity, age and mixing length parameter) to be able to fit
the basic properties of the models. A larger sample of binaries
covering just that region of masses would therefore be required.
Fifteen years after Andersen's compilation list, the de­
velopment of correlation techniques for radial velocity mea­
surements, accurate photometry and precise astrometry, now

636 Y. Y. Balega et al.: Parameters of GJ 765.2
achievable using interferometric techniques, have led to new
suitable late­G to late­K systems with accurate masses. These
include an old and somewhat evolved secondary component in
the eclipsing double­lined spectroscopic binary (eSB2) RS Cvn
type system UV Psc (Popper 1997), the secondary in the interfer­
ometric SB2 binary Iota Peg (Boden et al. 1999), the secondary
early­K dwarf star in the Hyades eSB2 system vB22 (Torres &
Ribas 2002), the secondary in the old metal­poor interferomet­
ric SB2 system HD 195987 (Torres et al. 2002), both compo­
nents of the isolated eSB2 system GU Boo (Lopez­Morales &
Ribas 2005), the secondary component in the old interferomet­
ric SB2 HD 9939 (Boden et al. 2006), and a few others.
The high proper­motion star GJ 765.2 = HD 186922 =
HIP 96656 [# = 19 h 39 m 06.4 s , # = +76 # 25 # 19 ## (2000), K1V,
m V = 8.08] has attracted attention over the past two decades
as an additional good candidate for a comparison with de­
tailed evolutionary calculations in the discussed mass range.
The star is listed in the Third Version of the Nearby Star
Catalogue (Gliese & Jahreiss 1991) with a trigonometric paral­
lax # trg = 43.9 ± 11.2 mas taken from the preliminary version of
the General Catalog of Trigonometric Stellar Parallaxes, Fourth
Edition (Van Altena et al. 1995). The trigonometric parallax cat­
alogues, compiled at the Yale University Observatory, included
GJ 765.2 with parallax values in the range of 19-52 mas. It
is obvious that such inconsistency cannot be explained simply
by the errors of astrometry. In 1971, the star was first recog­
nized as a visual binary by Muller (1973), who used an eyepiece
micrometer at the Nice Observatory 20­inch refractor. The bi­
nary, designated as MLR 224, has been observed regularly by
the discoverer (see Table 1), often giving discrepant relative po­
sitions and remaining unresolved in many cases. Twenty years
after Muller's first visual observations, the system was included
in the list of Hipparcos targets. The astrometric satellite gave
the first reliable relative positions and magnitude di#erences for
the binary: PA = 116.0 # , sep = 159 mas (epoch 1991.25), and
#Hp = 0.68 ± 0.28 (ESA 1997). In addition, it provided the
precise parallax value, # hip = 33.28 ± 0.69 mas, which placed
the star significantly farther from the sun than derived from the
ground­based astrometry.
GJ 765.2 was first observed by speckle interferometry at the
6 m BTA telescope in 1993, as a rapidly moving binary with
an angular separation of <
# 0.2 ## . Shortly thereafter, Tokovinin
(1994) calculated a preliminary orbit for the pair with a period
of 11.76 yr and a semi­major axis of 225 mas using his measure­
ments of radial velocities in combination with a few visual and
speckle observations. Since then the pair has been measured re­
peatedly using speckle techniques, and the phase coverage of its
orbit is now satisfactorily uniform. Radial velocities of GJ 765.2
have been monitored since 1983 with the CORAVEL spectro­
velocimeter at the Haute­Provence Observatory, France. Based
on these data, we present a new combined orbital solution and
report the main physical properties of GJ 765.2 in this paper.
2. Observations
A short description of the instrumentation and observing tech­
niques for speckle interferometry (Labeyrie 1970) with the 6 m
BTA telescope at visible wavelengths can be found in Balega I.
et al. (2002). We have accumulated 16 speckle measurements
of GJ 765.2 over a period of 13.1 years, including 7 unpub­
lished points. The binary is usually well­resolved by the di#rac­
tion limit of the 6 m telescope; the separation between the
components always remains larger than #25 mas. The mea­
surements were performed at 12 epochs, uniformly distributed
on the orbit. Three of the speckle observations were obtained
in 1997 and 2001 in the infrared J and K spectral windows using
the PICNIC and HAWAII­I array detectors of the Max­Planck­
Institut fÝr Radioastronomie, Bonn. The bispectrum speckle in­
terferometry reconstruction procedure (Weigelt 1977; Lohmann
et al. 1983) provides true images of an object and thus enables
one to avoid the 180 # ambiguity in the speckle position angles.
Based on our experience in binary star measurements, we can
adopt # # = 0.50 # and # # = 1.5 mas for the uncertainties in
the BTA 1994-2006 observations. Exceptions are the 2002 mea­
surements, which were obtained with four di#erent filters under
poor seeing conditions; therefore, they are given the weight 0.75
in the subsequent analysis. This is also why the magnitude dif­
ferences are not presented for this date. For the two earlier mea­
surements in 1993, the uncertainties are higher: # # = 3.0 # and
# # = 4.0 mas. In that period, the old generation television
photon­counting detector with higher instability and field aber­
rations was used for data recording. Unfortunately, these points
are the most important for determining the shape of the orbit
because of their closeness to the periastron.
The complete collection of interferometric observations is
given in Table 1, together with 13 visual observations per­
formed by Muller, one point from Hipparcos, and one speckle
measurement made by Mason et al. in 2001.499. The visual
data, as well as speckle observations published before 2006,
were extracted from the Washington Double Star Catalog
(http://ad.usno.navy.mil/wds). For completeness, in the
table we provide the 6 epochs when the pair was not resolved by
experienced visual observers. New speckle measurements with
the 6 m BTA telescope in the period 2001.8-2006.4 are incor­
porated into our analysis of the orbital motion. Data in Table 1
include: the epoch of observation expressed as the fractional
Besselian year; the position angle # in degrees; the angular sepa­
ration # in milli­arcseconds; the residuals to the calculated orbit;
magnitude di#erence #m together with the error of the measure­
ment; filter specifications; the code of the observer or original
reference.
A total of 50 radial velocity measurements for GJ 765.2 A
and B were obtained between 1983 and 1998 with the
CORAVEL radial velocity scanner (Baranne et al. 1979) on the
Swiss 1 m telescope at the Observatoire de Haute Provence,
spanning 15.1 years and 1.3 system periods. They are listed in
Table 2, which also gives the heliocentric Julian date, the orbital
phase, and velocity residuals. For an 8­mag K0 star, the veloc­
ities are measured with a typical precision of 500-650 m s -1 .
Due to the comparatively long period of the system, the velocity
amplitudes are small. Consequently, for a significant part of the
orbit, the spectral lines of the components are severely blended.
Radial velocities of GJ 765.2 were also measured by
Tokovinin (1994) on the 0.7 m telescope at Moscow University
with another correlation scanner, RVM, leading to the first or­
bit calculation and now covering the period from 1986 to 2004.
However, the accuracy of this data is somewhat inferior to
CORAVEL, so we decided to use only CORAVEL velocities in
our final orbital solution. For completeness, the RVM velocities
are nevertheless given in Table 2 (marked with double asterisks).
3. Orbital solution, masses of the components
and the parallax
The combined orbit was determined using the ORBIT code of
Tokovinin (see Forveille et al. 1999, for comments). The pro­
gram performs a least­squares adjustment to all available ra­
dial velocity and relative astrometry observations, with weights

Y. Y. Balega et al.: Parameters of GJ 765.2 637
inversely proportional to the square of their standard errors.
The solution is found simultaneously for the 10 elements of
the astrometric­spectroscopic orbit, where the first seven are the
usual elements in a visual orbit, and the other three are the radial
velocity amplitudes and the centre­of­mass velocity of the sys­
tem. All position angles have been transformed to the equinox
2000.0 to correct for precession. The speckle data were collected
in the period 1993-2006, which corresponds to one revolution
of the pair.
In total, the astrometric data sets cover almost 3 cycles of the
system. The combination of the old visual observations and the
new speckle data improves the orbital solution because they pro­
vide an extended time coverage. However, all but two eyepiece
micrometer data points for GJ 765.2 show residuals more than
3 times their estimated errors. In addition, a systematic bias in
the visual measurements of # was found compared to the speckle
data. We do not know the origin of these errors, but it is extreme
di#culty to obtain visual observations at the resolution limit of
the telescope. Therefore, we exclude all visual measurements in
the orbit calculation -- they are included here only to complete
the list.
Our orbital solution uses only speckle measurements to­
gether with the radial velocities from CORAVEL. The radial
velocities near conjunctions, a#ected by line blending, were ex­
cluded from the analysis. The remaining velocities were care­
fully analyzed to reveal systematic errors or highly deviating
measurements. As a consequence, only 49 velocities of the
brighter component and 43 of the fainter one were used in the
following analysis. Figure 1 depicts the radial velocity orbit of
GJ 765.2. We show all our measurements in the figure, includ­
ing those which were not used in the orbital solution. Rejected
observations are marked with an asterisk in Table 2.
A combined speckle­spectroscopic solution is given in
Table 3. The last four positions in the table show the rms residu­
als of the measurements from the orbit. A graphical representa­
tion of the newly determined orbital ellipse and the observations
are shown in Fig. 2, with the primary component at the origin.
The motion of the secondary is direct (counter­clockwise), and
the plane of the true orbit lies close to the line of sight. The po­
sition
angle# of the ascending node is defined taking into con­
sideration the radial velocity of the secondary with respect to the
primary.
The visual measurements of Muller are given in the figure
for illustrative purposes only. To make angles consistent with the
11.919 yr period of the system, we have reversed the quadrants
of two visual observations: 1979.58 and 1991.60. Four erroneous
points of Muller (1976.77, 1980.62, 1981.53, and 1989.75) are
not presented. Unusual trends are seen in the # residuals of visual
observations displayed in the figure: all of Muller's visual points
are shifted, on average, by 10 # clockwise. It appears likely that
his position angles include a systematic error, which can proba­
bly be explained by the high declination of this star.
The orbital parameters in Table 3 and the measured magni­
tude di#erences allow us to determine the main physical prop­
erties of GJ 765.2. The total mass of the system, resulting from
the combined orbital solution, is 1.594 ± 0.053 M # . The mass
ratio is q = 0.92 ± 0.03. The masses of the primary and sec­
ondary components are M A = 0.831 ± 0.020 M # and M B =
0.763 ± 0.019 M # , respectively. Mass errors result from the er­
rors of the orbital elements. The relative errors of the primary's
and secondary's component mass estimates are 2.4% and 2.5%,
respectively.
The distance determined to GJ 765.2, based on our or­
bital solution, is 32.23 ± 0.52 pc, corresponding to an orbital
Fig. 1. CORAVEL radial velocity orbit of the GJ 765.2 AB system.
Filled triangles represent measurements of the primary star; the filled
squares correspond to the secondary.
Table 3. Speckle­spectroscopic orbital solution for GJ 765.2.
P(yr) 11.919 ± 0.003 K A (km s -1 ) 7.40 ± 0.09
T 1993.150 ± 0.004 K B (km s -1 ) 8.05 ± 0.08
e 0.240 ± 0.003 V 0 (km s -1 ) --3.73 ± 0.05
a(mas) 189 ± 2 # # ( # ) 2.0
i( # ) 80.2 ± 0.2 # # (mas) 2.0
# asc ( # ) 293.0 ± 0.6 # RVA (km s -1 ) 0.40
#( # ) 250.0 ± 0.1 # RVB (km s -1 ) 0.32
parallax # orb = 31.0 ± 0.5 mas. This value is approximately 7%
smaller than the Hipparcos parallax, # hip = 33.28 ± 0.69 mas.
The nonlinear relative motion of the components during the
Hipparcos mission was not properly taken into account in the
data reduction and could a#ect the measured parallax. The error
of the Hipparcos parallax value in the case of GJ 765.2 is prob­
ably underestimated and should be increased by a factor of 2
or 3. Similar discrepancies for other Hipparcos binaries were
also mentioned by Shatskii & Tokovinin (1998), Tokovinin et al.
(2000) and Balega Y. et al. (2002). At the distance of the system,
the semi­major axis of the orbit is 6.1 AU.
4. Luminosities, metallicity and T eff
The mean speckle magnitude di#erence at 545 nm is #m =
0.65±0.03, but because the components are similar in brightness,
there is no significant di#erence in #m between our spectral win­
dow and the V band. To derive the system's V magnitude, we
have used the Hipparcos Hp and the Tycho B T and V T photom­
etry (ESA 1997) as the most uniform and accurate collection of
photometric measurements of the star. The Hp and Tycho magni­
tudes from the catalog were transformed to the Johnson's system
using the relations (Hp-V Johnson ) versus (V-I Cousins ) and V Johnson
versus V Tycho for K­type stars. The average from the Hipparcos
and Tycho photometry value, m V = 8.059, was used in com­
bination with the orbital parallax to derive absolute component
magnitudes, M A
V = 5.99 ± 0.04 and M B
V = 6.64 ± 0.05, where the
uncertainties include the contribution from the distance error.
The metallicity of GJ 765.2 is not well constrained at this
point. Based on the GJ 765.2 proximity to the Sun and since its
space motion indicates a disk population, one can expect that
GJ 765.2 has elemental abundances near solar values. The only

638 Y. Y. Balega et al.: Parameters of GJ 765.2
Fig. 2. Apparent ellipse representing the orbital elements for GJ 765.2.
The BTA speckle interferometric data are indicated by filled circles,
the speckle interferometric measurement performed by Mason et al. in
2001.499 is shown by an open circle, data from visual observers are
given by open squares, and the Hipparcos measurement is shown as an
open triangle. Residual vectors for all measurements are plotted, but in
the case of speckle observations they are smaller than the points them­
selves. The orbital motion direction is indicated by an arrow. The solid
line shows the periastron position, while the dot­dashed line represents
the line of nodes. The dashed circle around the position of the primary
has an angular radius of 0.02 ## corresponding to the di#raction limit of
the 6 m telescope in the V band.
published value can be found in the catalog of stellar metallic­
ities (Zakhozhaj & Shaparenko 1996). They used the relation
between the metallicity and UV excess for the late­type stars
of the MS (Suchkov et al. 1987), together with the UBV pho­
tometry from the Catalogue of Nearby Stars (Gliese & Jahreiss
1991), to find [Fe/H] = -0.20. However, this method is only
suitable for survey purposes, not for astrophysical analysis. To
specify the [M/H] value, we placed the GJ 765.2 AB system on
the observing program at the moderate resolution Main Stellar
Spectrograph mounted on the 6 m telescope. The CCD spectrum
was obtained in 2005.64 at the orbital phase 0.0472 using the
resolution #/## = 18 000 with the S/N ratio about 300 in the
spectral region 4380-4630 å. At the given phase the radial ve­
locity di#erence between the components was about 0.9 km s -1 ,
which is below the resolution limit of the spectrograph. We used
Kurucz's model atmospheres (Kurucz 1992), T e# = 5000 K,
and log g = 4.5 to estimate the metallicity from the compar­
ison with the synthetic spectra. The adapted value, [M/H] =
-0.35 ± 0.15 dex, is in agreement with the above­mentioned
photometric estimate. Low accuracy of the metallicity estimate
is explained by the short length of the spectrum used and the
complexity of the spectrum modelling due to line blending.
Individual luminosities of the components in the infrared
can be determined from measured intensity ratios in the J and
K bands and the combined m J and m K magnitudes for GJ 765.2,
available from the 2 MASS Catalog (Skrutskie et al. 1997).
These, combined with the orbital parallax value, yield abso­
lute J and K magnitudes of the components, which are given
in the generalized Table 4 together with the (V - K) and (J - K)
color indices. The infrared color indices for the components al­
low for an estimate of the e#ective temperatures, which is nearly
independent from the adapted [Fe/H] value. Using the color­
temperature calibration by Alonso et al. (1996) and the metallic­
ity value [Fe/H] = -0.35, we adopt the following values of the
temperatures for the GJ 765.2 components: T A
e# = 5000±120 K,
T B
e# = 4770±150K and T A
e# = 5120±160K, T B
e# = 4615±190 K,
correspondingly from the (V - K) and (J - K) color indices.
The error of these estimates comes from the speckle photometry
errors and temperature calibration errors (#2%). In the following
Table 4. Summary of the main physical parameters of GJ 765.2.
Parameter Primary Secondary
Mass (M # ) 0.831 ± 0.020 0.763 ± 0.019
log (M/M # ) -0.0804 ± 0.0104 -0.1175 ± 0.0108
m V 8.54 ± 0.02 9.19 ± 0.04
M V 5.99 ± 0.04 6.64 ± 0.05
L/L # 0.40 ± 0.02 0.26 ± 0.02
M bol 5.71 ± 0.05 6.17 ± 0.06
J magnitude 4.40 ± 0.09 4.94 ± 0.22
K magnitude 3.92 ± 0.09 4.34 ± 0.22
(V - K) 2.07 ± 0.10 2.30 ± 0.23
(J - K) 0.48 ± 0.13 0.60 ± 0.32
T e# (K) 5060 ± 130 4690 ± 160
log T e# 3.702 ± 0.011 3.670 ± 0.015
Spectral type K1V K3V
[M/H] --0.35 ± 0.15
analysis, we will use the average estimates of the temperature,
namely, T A
e# = 5060 ± 130 K, T B
e# = 4690 ± 160 K.
The inferred bolometric luminosities of each star are L A =
0.40±0.02 L # and L B = 0.26±0.02 L # . Bolometric magnitudes,
M A
bol = 5.71 ± 0.05 and M B
bol = 6.17 ± 0.06, are determined us­
ing the average estimates of the temperatures and the bolometric
corrections from Flower (1996). We summarize the astrophysi­
cal parameters for the GJ 765.2 system in Table 4.
5. Age and MLR
To compare the inferred parameters of the GJ 765.2 compo­
nents with evolutionary tracks, it is necessary to know the
age of the system. Three indicators, kinematics, chromospheric
activity and metallicity, can be used to estimate the ages of
K dwarfs. The existing data lead to contradictory age values
for GJ 765.2. Montes et al. (2001) identified GJ 765.2 as one
of 34 possible members of the Castor moving group with an
age of 200 Myr. They found that the position of the star in the
velocity space, (U, V, W) = (-23.5, -10.2, -16.6) km s -1 (cor­
rected due to the solar motion the value is (U, V, W) = (-13.5,
-5.0, -9.4) km s -1 ), corresponds to the location of this young
group in the (U, V) and (W, V) planes. However, the authors did
not account for the presence of the secondary star and used an
inexact value of its center of mass velocity. With our veloc­
ity value, V 0 = -3.73 km s -1 , and the orbital parallax value,
# orb = 31.0 ± 0.5 mas, the Galactic space­velocity components
become:
(U, V, W) = (-17.83±0.58, -0.99±0.18, -8.74±0.31), total
velocity V Total = 19.9 km s -1 .
With these new (U, V, W) values, GJ 765.2 no longer fits the
position of the Castor moving group, (-10.7, -8.0, -9.7) km s -1 ,
V T = 16.5 km s -1 , in the (U, V) plane (Barrado y Navascues
1998), while for its position in the (W, V) plane it can be as­
sociated with the Ursa Major supercluster. Therefore, following
the specified space velocity components, GJ 765.2 must be dis­
carded as a possible member of the Castor young moving group.
Stellar age can be estimated from its space velocities using
Grenon's (1987) kinematic age parameter,
f =
1
300
# U 2 + 2.5V 2 + 3.5W 2 .
It is based on the assumption that all stars sharing the
same f value should have the same age. For GJ 765.2, Grenon's
parameter value is 0.08, which means that the star belongs to the

Y. Y. Balega et al.: Parameters of GJ 765.2 639
Fig. 3. The mass­magnitude relation in the V band for the mass range
0.6-0.9 M # . The filled circles are the components of GJ 765.2. The
asterisks represent the components of eclipsing double­lined spectro­
scopic binaries; the open circles show the components of astrometric
double­lined spectroscopic binaries. The two curves are 5 Gyr theoret­
ical isochrones from Bara#e et al. (1998) for metallicities [M/H] = 0.0
and [M/H] = -0.5.
young­to­intermediate age group of the thin disk population (age
less than 3-4 Gyr).
The slightly enhanced CaII chromospheric emission of
GJ 765.2 also counts in favour of its young age. The star was
included in the Young et al. (1989) compilation of the measured
Ca II H and K fluxes with the empirical #S # index equal to 0.32.
This value is slightly higher than the typical value for most late­
type MS stars (#S # = 0.25). It should be noted, however, that a
small increase of the #S # emission can be caused by the binary
nature of the star.
On the other hand, in his survey of the chromospheric emis­
sion and rotation among solar­type stars in the solar neighbor­
hood, Soderblom (1985) gives the following ratio of the CaII H
and K flux to the stellar bolometric flux for GJ 765.2: log RHK =
-4.59. It corresponds to relatively low chromospheric activity
of a typical late­type MS star. The chromospheric CaII emission
flux in G and K stars is proportional to their rotation rates. It fol­
lows from the same paper that GJ 765.2 rotates #50% faster than
most stars at (B -V) = 0.88;
namely,# /# # = 0.91. At the same
time, this value is about 3 times lower than for Hyades late­type
members. Following the ``activity­age'' relation, RHK # t 1/2 , the
age of GJ 765.2 should be close to 4 Gyr. A low X­ray lumi­
nosity of 8.4 â 10 27 erg s -1 (HÝnsch et al. 1999), which is at­
tributed to magnetically heated coronae of the components, also
gives evidence of its considerable age. We therefore conclude
that GJ 765.2 is a middle­age system of the thin disk.
The location of the GJ 765.2 components in the mass­
magnitude diagram is shown in Fig. 3. Added in the figure
are two theoretical isochrones for the age 5 Gyr from Bara#e
et al. (1998) for two metallicity values, [M/H] = 0.0 and
[M/H] = -0.5. The location of the GL 765.2 components in the
``mass­M V '' diagram can be compared with other well­studied
binaries of the same mass regime. The components of binaries
display a broad spectrum of ages, chemical compositions, and
evolutionary stages.
In a search for possible faint physical or common proper­
motion companions associated with the GJ 765.2 binary system,
we extracted all stars from the 2MASS Point Source Catalog
within a 5 arcmin radius of the star and plotted them on the
(J, J -K) color-magnitude diagram. None fall close to the main
sequence corresponding to the distance to the star, so we are
confident that GJ 765.2 is a binary, not a triple.
6. Summary
The overall goal of this study is to improve our knowledge
about the lower MS MLR where eclipsing binaries are missing;
more precisely, in the mass region of 0.6-0.9 M # . CORAVEL
radial velocities were combined with 17 speckle interferomet­
ric observations and one Hipparcos measurement to obtain an
astrometric­spectroscopic solution for the system, yielding di­
rect mass determinations and an orbital parallax. The result­
ing masses are M A = 0.831 ± 0.020 M # and M B = 0.763 ±
0.019 M # . The formal errors of 2.4 and 2.5% put this result into
a category of only 12 systems (17 components) in the mass range
of 0.6-0.9 M # that have mass uncertainties similar to or better
than ours. The components of GJ 765.2 are su#ciently di#erent
in mass to provide a good test of models.
Our orbital parallax is 7% lower and #50% more precise than
the direct Hipparcos trigonometric parallax. Together with the
di#erential speckle magnitudes, this implies absolute V magni­
tudes of the stars, M A
V = 5.99 ± 0.04 and M B
V = 6.64 ± 0.05.
The result illustrates the accuracy attainable from a speckle­
spectroscopic orbit when the parallax measurement error is
included.
The temperatures of the components, resulting from the V, J
and K speckle magnitude di#erences, are: T A
e# = 5060 ± 130 K,
T B
e# = 4690 ± 160 K. Correspondingly, they belong to spectral
types K1 and K3. The metallicity of the system was roughly es­
timated from the 6 m telescope moderate resolution spectrum:
[M/H] = -0.35 ± 0.15 dex. Available age indicators, chromo­
spheric activity, and metallicity classification suggest that the
system is 3-4 Gyr old. Recent evolutionary models show good
agreement with the location of the GJ 765.2 components in the
mass­luminosity diagram in the V band.
Acknowledgements. We are grateful to I. I. Romanyuk and E. A. Semenko for
providing the original spectrum of GJ 765.2 and for their helpful comments,
particularly their analysis of the star's metallicity. This project required exten­
sive observations at the SAO 6 m BTA telescope and the Haute­Provence 1 m
telescope, and we would like to thank the technical personnel of both observato­
ries for their assistance. The speckle interferometry program at the 6 m telescope
has been partly supported by the Russian Foundation for Basic Research through
grant No. 04­02­17563a. The publication has made use of the SIMBAD database,
operated at CDS in Strasbourg, France, and the Washington Double Star Catalog
(http://ad.usno.navy.mil/wds).
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Y. Y. Balega et al.: Parameters of GJ 765.2, Online Material p 1
Online Material

Y. Y. Balega et al.: Parameters of GJ 765.2, Online Material p 2
Table 1. Astrometric measurements, their deviations from the ephemerides, and di#erential magnitudes for GJ 765.2.
Epoch # # ## ## #m #/##, nm Reference
1971.570 275.6 0.170 --14.9 --0.007 0.7 Muller a
1971.670 280.0 0.210 --11.0 0.029 0.7 Muller a
1972.650 288.6 0.200 --7.1 0.000 Muller a
1973.580 296.6 0.190 --3.6 0.010 Muller a
1974.560 291.0 0.130 --16.3 --0.003 Muller a
1974.600 Heintz a
1975.530 Heintz a
1976.770 180.0 0.140 113.1 0.088 0.7 Muller a
1977.520 Muller a
1979.580 296.3 0.170 184.2 0.003 0.7 Muller a
1980.620 349.4 0.190 228.4 0.075 0.7 Muller a
1980.660 Muller a
1981.530 10.5 0.160 --164.7 0.132 0.7 Muller a
1983.070 287.0 0.180 --0.7 0.028 Muller a
1984.550 286.2 0.220 --9.4 0.020 Muller a
1989.750 189.8 0.180 91.6 0.063 Muller a
1991.250 116.0 0.159 5.4 --0.10 0.68 ± 0.28 V Hp ESA a
1991.600 286.7 0.160 173.9 --0.005 Muller a
1993.351 151.7 0.035 --5.2 0.000 Balega et al. a
1993.844 264.7 0.052 5.7 0.008 Balega et al. a
1994.713 285.1 0.129 --0.2 --0.002 0.49 ± 0.07 656/30 SchÆller et al. a
1997.789 303.0 0.166 0.6 0.001 0.42 ± 0.20 2165/328 SchÆller et al. a
1997.789 303.3 0.166 0.9 0.001 0.47 ± 0.20 1238/276 SchÆller et al. a
1998.777 311.3 0.111 --0.6 0.001 0.67 ± 0.03 545/30 Balega et al. a
1999.813 348.3 0.046 --0.6 --0.001 0.76 ± 0.08 610/20 Balega et al. a
2000.878 80.8 0.068 0.3 0.000 0.63 ± 0.03 545/30 Balega et al. (2006)
2001.499 96.9 0.110 1.1 0.003 Mason et al. a
2001.752 99.3 0.122 0.0 0.000 0.56 ± 0.03 750/35 Balega et al. (2006)
2001.837 100.2 0.128 --0.1 0.002 0.61 ± 0.05 1238/276 This paper
2002.801 108.3 0.165 0.0 0.000 545/30 This paper
2002.801 107.8 0.165 --0.5 0.000 600/20 This paper
2002.801 107.9 0.163 --0.4 --0.002 700/33 This paper
2002.801 107.8 0.163 --0.4 --0.002 850/75 This paper
2004.815 126.8 0.082 --0.9 0.001 600/20 This paper
2006.438 282.6 0.115 --0.4 0.001 545/30 This paper
a Data extracted from the Washington Double Star Catalog (http://ad.usno.navy.mil/wds).

Y. Y. Balega et al.: Parameters of GJ 765.2, Online Material p 3
Table 2. Radial velocities and residuals for GJ 765.2.
HJD Date RV A RV B (O--C) A (O--C) B Orbital
(km s -1 ) (km s -1 ) (km s -1 ) (km s -1 ) phase
45 533.464 1983.541 3.20 --10.26 0.32 0.66 0.1935
45 543.442 1983.569 3.29 --10.82 0.38 0.13 0.1958
45 584.358 1983.681 3.54 --10.68 0.56 0.35 0.2052
45 620.282 1983.779 3.28 --10.65 0.25 0.43 0.2134
45 868.576 1984.459 2.55 --11.71 --0.33 --0.79 0.2705
45 969.299 1984.735 2.53 --10.67 --0.11 --0.01 0.2937
45 976.299 1984.754 3.76 --10.15 1.14 0.49 0.2952 #
46 221.544 1985.425 3.23 --8.73 1.50 0.94 0.3515 #
46 245.572 1985.491 2.07 --9.47 0.45 0.08 0.3571
46 248.490 1985.499 2.48 --9.47 0.87 0.07 0.3577
46 249.499 1985.502 1.30 --9.38 --0.31 0.16 0.3580
46 253.481 1985.513 2.01 --9.80 0.42 --0.28 0.3589
46 270.524 1985.559 0.98 --10.07 --0.53 --0.64 0.3628
46 274.450 1985.570 1.90 --9.49 0.41 --0.08 0.3637
46 278.452 1985.581 2.31 --9.28 0.83 0.11 0.3646
46 279.484 1985.584 1.86 --9.54 0.39 --0.15 0.3649
46 280.448 1985.586 1.64 --9.62 0.17 --0.24 0.3650
46 332.329 1985.728 1.00 --9.50 --0.22 --0.38 0.3770
46 561.621 1986.356 1.43 --7.50 1.40 0.32 0.4297 #
46 632.431 1986.550 --0.14 --7.37 0.24 0.01 0.4459
46 632.364 1986.550 --0.20 --6.37 0.19 1.00 0.4459 ##
46 645.375 1986.586 --0.98 --7.28 --0.52 0.01 0.4489 ##
46 985.539 1987.517 --1.08 --5.64 1.49 --0.65 0.5271 #
47 012.343 1987.590 --4.26 --4.26 --1.51 0.54 0.5332 ##
47 029.397 1987.637 --2.61 --6.53 0.25 --1.85 0.5371 #
47 248.652 1988.237 --4.45 --2.28 --0.09 0.76 0.5875 #
47 350.511 1988.516 --6.26 --1.63 --1.18 0.63 0.6109 #
47 728.543 1989.551 --7.81 0.89 0.02 0.16 0.6977
48 079.441 1990.512 --9.69 2.72 0.54 --0.63 0.7783 ##
48 088.539 1990.537 --10.27 2.89 0.02 --0.51 0.7804
48 105.415 1990.583 --10.26 2.53 0.13 --0.99 0.7843 ##
48 109.377 1990.594 --10.02 2.71 0.39 --0.84 0.7852 ##
48 121.444 1990.627 --10.24 3.46 0.24 --0.15 0.7880
48 140.329 1990.679 --10.45 3.56 0.14 --0.17 0.7923
48 229.235 1990.922 --10.85 3.93 0.20 --0.30 0.8127
48 229.235 1990.922 --11.99 3.17 --0.94 --1.07 0.8127 ##
48 166.274 1990.750 --10.54 3.60 0.19 --0.30 0.7983 ##
48 458.426 1991.549 --10.79 4.39 0.94 --0.59 0.8653 ##
48 459.563 1991.553 --11.08 4.85 0.64 --0.12 0.8657
48 473.374 1991.590 --11.54 4.97 0.19 0.00 0.8688

Y. Y. Balega et al.: Parameters of GJ 765.2, Online Material p 4
Table 2. continued.
HJD Date RV A RV B (O­C) A (O­C) B Orbital
(km s -1 ) (km s -1 ) (km s -1 ) (km s -1 ) phase
48 495.385 1991.651 --11.60 4.65 0.13 --0.33 0.8739
48 505.365 1991.678 --11.56 4.98 0.17 0.01 0.8762
48 565.258 1991.842 --11.27 4.96 0.39 0.07 0.8899
48 721.658 1992.270 --10.89 4.26 0.05 0.15 0.9258
48 738.472 1992.316 --12.88 1.87 --2.07 --2.11 0.9297 ##
48 843.483 1992.604 --12.09 1.50 --2.31 --1.36 0.9538 ##
48 853.415 1992.631 --10.59 2.84 --0.92 0.11 0.9561
49 099.638 1993.305 --5.65 --1.00 0.26 0.35 0.0127 #
49 172.446 1993.504 --3.68 --3.68 0.94 --0.92 0.0293 ##
49 184.498 1993.537 --5.34 --2.09 --0.92 0.89 0.0321 #
49 332.298 1993.942 --1.32 --5.93 0.63 --0.26 0.0661 #
49 457.571 1994.285 1.18 --7.80 1.36 --0.21 0.0949 #
49 504.568 1994.414 0.63 --8.16 0.25 0.04 0.1057
49 547.490 1994.531 0.62 --8.68 --0.22 0.02 0.1155
49 592.486 1994.654 1.35 --9.41 0.08 --0.24 0.1259
49 604.393 1994.687 1.23 --9.70 --0.15 --0.42 0.1286
49 917.511 1995.544 --7.20 3.80 0.2005 ##
49 921.480 1995.555 2.91 --10.75 --0.05 0.25 0.2014
49 945.413 1995.621 3.35 --10.89 0.35 0.16 0.2070
49 975.327 1995.702 --7.23 3.86 0.2137 ##
50 281.467 1996.541 2.09 --10.65 --0.66 0.13 0.2842
50 314.424 1996.631 2.28 --11.34 --0.39 --0.65 0.2917
50 324.388 1996.658 --6.57 4.09 0.2940 ##
50 341.309 1996.704 2.00 --11.19 --0.59 --0.59 0.2978
50 635.507 1997.510 --6.24 3.13 0.3654 ##
50 641.550 1997.526 --5.87 --17.82 --7.3 --8.47 0.3668 #
50 641.563 1997.527 1.52 --9.69 0.09 --0.34 0.3669
50 668.459 1997.600 --5.87 3.34 0.3730 #
51 050.419 1998.646 --4.66 2.31 0.4608 #
51 057.306 1998.665 --4.58 2.34 0.4623 ##
51 519.163 1999.929 --3.34 0.33 0.5684 ##
52 053.413 2001.392 --3.79 --4.30 0.6911 ##
52 211.214 2001.824 --2.30 --4.04 0.7274 ##
# CORAVEL measurements not included in the orbital solution. ## RVM measurements not included in the orbital solution.