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ORBIT, DYNAMICAL MASS, AND MK TYPE OF VISUAL BINARY WOR 2
V. S. Tamazian, 1
J. A. Docobo, 1
N. D. Melikian, 2,3
Y. Y. Balega, 4
and A. A. Karapetian 2,3
Received 2005 August 13; accepted 2005 September 1
ABSTRACT
On the basis of new speckle measurements with the 6 m telescope of the Special Astrophysical Observatory (Russia)
and Hipparcos astrometry, an improved orbital solution with a period of P ® 24:1 yr for the visual binary WOR 2 is
obtained. The dynamical mass of the system is 1:40 # 0:25 M# . Differential photometry (#m ® 0.55 mag) allowed
us to estimate the luminosity of individual components (M ® ”8:0 and +8.6 mag), which in turn led to individual
masses of 0:65 and 0:61 M# , in good agreement with the systemic mass. The slit spectra obtained with the 2.6 m
telescope of the Byurakan Astrophysical Observatory (Armenia) show that in the combined light WOR 2 is a K6 dwarf,
whereas individually the components according to their luminosities are likely to be K6--K7 and M0 dwarfs. The
equivalent width of the H# absorption line (0.9 8) is concordant with previous data, indicating the overall stability
of this system.
Key words: astrometry --- binaries: visual --- stars: individual ( WOR 2)
1. INTRODUCTION
The duplicity of WOR 2 (WDS 02288 ” 3215 ® HIP 11542 ®
Gl 99), with a separation between components of 0B26 and a magí
nitude difference of 0.6 mag, was discovered in 1959 by Worley
(1960). Three years earlier, WOR 2 was spectroscopically found
to be an M0p dwarf by Vyssotsky (1956; Vys 393). The same
dM0p type was reported by Bidelman & Lee (1975), but Reid
et al. (1995) have recently classified it as a K7 dwarf. Its brightí
ness, V ® 9:57, was recently measured by Salim &Gould (2003),
and the Washington Double Star Catalog ( Mason et al. 2003)
assigns V ® 10:2 and 10.5 to the individual components. The
Hipparcos parallax, # ® 38:71 # 2:17 mas, places this star at a
distance of 25.8 pc.
In spite of its brightness and convenient position on the
northern sky (# ® ”31 # ), this star was unevenly observed astroí
metrically. There are no reported observations between 1968 and
1974, or from 1991 until our recent observation in 2004.
The first orbit, with a period of 18.9 yr, was calculated by Baize
(1986), who promptly changed it to an orbit of 23 yr (Baize 1991)
due to a discrepancy with the first ever speckle measurement of
this star ( Balega et al. 1989) with the 6 m telescope of the Speí
cial Astrophysical Observatory (SAO; Russia). Since then, a
new speckle observation by Balega et al. (1994) and Hipparcos
astrometry ( Perryman et al. 1997) data have been published. In
addition, a new speckle measurement and differential photomí
etry obtained with the 6 m telescope are reported in this paper.
These additional highíprecision data allow us to calculate an
improved orbit.
Apart from the orbit calculation, in view of somewhat disí
crepant spectral classification several slit spectra were obtained
with the 2.6 m telescope of the V. Ambartsumian Byurakan Así
trophysical Observatory ( BAO; Armenia) in order to verify the
combined spectral type of WOR 2.
2. ASTROMETRIC OBSERVATIONS AND ORBIT
2.1. New Speckle Measurement, Differential
Photometry, and Data Set
The speckle measurement of WOR 2 was carried out on 2004
December 28 with the 6 m telescope of SAO with the speckle
camera and an intensified 1280 ; 1024 pixel CCD coupled with
the Sí25 photocathode. The image motionícompensated seeing
( FWHM) during the observations was 1B0--1B5, and a filter with
center wavelength and bandwidth of 800 and 110 nm, respecí
tively, was used. Usually, this system allows us to observe binary
components as faint as 15.0 mag in optical wavelengths with a
dynamic range of about 4.0--5.0 mag. The diffractionílimited
resolution is about 22 mas.
The relative position and the magnitude difference #m are
derived from the ensembleíaveraged power spectrum. A doubleí
slit pupil mask and interferometric binaries with slow orbital
motion are used for calibration. More details regarding the obí
servation and reduction procedure can be found in Balega et al.
(2002) and remain essentially unchanged.
In total, astrometric observations of WOR 2 cover a timespan
of about 50 yr and comprise 17 visual and speckle interferometí
ric measurements and differential photometry data taken from
the Washington Double Star Observations Catalog ( Mason et al.
2001), the Fourth Catalog of Interferometric Measurements of
Binary Stars ( Hartkopf et al. 2004), the Second Photometric
Magnitude Difference Catalog ( Mason & Wycoff 2003), and
elsewhere in the literature.
Both astrometry and differential photometry data are given in
Table 1. The first six columns list (1) observation epoch, (2) type
of measurement (visual or interferometric), (3) magnitude differí
ence #m, (4) position angle, (5) separation, and (6) the reference
from which the astrometric data were taken. Columns (7)--(10) list
(O # C ) residuals in # and # relative to our orbit and that of Baize
(1991). Position angles are corrected for precession to refer them
to the J2000.0 equinox. The last row gives the rms of residuals in
# and #, which are the indicators used to compare the orbits. The
measurements' accuracy is presented if given in the original paper.
2.2. Orbit and Dynamical Mass Calculation
The method elaborated by Docobo (1985) was used to get the
orbital solution. It is briefly summarized in Docobo et al. (2000)
and Tamazian et al. (2002).
1
Observatorio Astrono Òmico Ramo Òn MarÐÒa Aller, Universidade de Santiago
de Compostela, Avenida das Ciencias s/n, Santiago de Compostela, Spain;
oatamaz@usc.es, oadoco@usc.es.
2 Byurakan Astrophysical Observatory, 378344 Byurakan, Aragatsotn Region,
Armenia; nmelikia@bao.sci.am, akarapet@bao.sci.am.
3 Isaac Newton Institute of Chile, Armenian Branch, Byurakan, Armenia.
4 Special Astrophysical Observatory, Nizhnij Arkhyz, KarachaiíCherkasia
369167, Russia; balega@sao.ru.
2847
The Astronomical Journal, 130:2847--2851, 2005 December
# 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A.

Initially, each measurement is weighted according to observaí
tional criteria such as telescope aperture, technique, and number
of combined measurements ( Docobo & Ling 2003). A family of
Keplerian orbits are then generated whose apparent orbits pass
through three base points that are assumed to be either the most
reliable measurements or positions belonging to the areas with
maximum observational likelihood. Simultaneously, O # C reí
siduals in both # and # are determined for these orbits. Then the
orbit with the smallest weighted rms values for both observed
parameters (# and #) is selected. Usually, the orbit with the
smallest rms values in # is not exactly the same as the orbit with
the smallest rms values in #. Therefore, a number of orbital soí
lutions between these two minimal solutions are determined.
The orbital solution with the smallest O # C residuals is seí
lected as the best fit, and the range of orbits is used to charací
terize the uncertainties in the orbital elements. Over this range of
orbital solutions, all orbital elements are computed simultaneously
and independently to ensure a proper error estimation for each
( Tamazian et al. 2002). The range of orbital solutions typically
corresponds to O # C residuals at #(1--2) #.
Our orbit was initially announced in Docobo & Tamazian
(2005) and is graphically represented in Figure 1. Table 2 lists the
orbital elements with their corresponding standard errors (and
system mass) both for our orbit and for that of Baize (1991), and
Table 3 contains ephemerides up to 2016.0. For the reader's coní
venience, the ephemerides for 2009, 2010, and 2011 are given with
0.25 yr intervals to better describe the rapidly changing separation.
3. MK CLASSIFICATION
Awellídefined homogeneous set of spectral types in the revised
MK system (Keenan 1987) is a key element in the determination
TABLE 1
Measurements, (O # C ) Residuals, and rms Values
This Paper Baize (1991)
Date
(1)
V/ I a
(2)
#m
(3)
# # #
(4)
# # #
(mas)
(5)
Reference
(6)
(O # C ) #
(deg)
(7)
(O # C ) #
(mas)
(8)
(O # C ) #
(deg)
(9)
(O # C ) #
(mas)
(10)
1959.72..................... Vis 0.6 105.5 260 1 #0.3 0 #1.7 #7
1960.84..................... Vis 115.6 150 2 +3.5 #5 +2.7 #39
1964.696................... Vis 0.2 275.8 260 3 #2.5 +5 +7.3 +91
1966.509................... Vis 0.2 283.1 280 3 #0.4 #10 4.3 +29
1966.909................... Vis 0.3 281.6 b 220 4 #3.1 #63 1.2 #34
1967.81..................... Vis 287.8 240 5 +0.3 #12 3.6 +1
1968.308................... Vis 0.1 287.2 260 3 #2.3 +31 +0.5 +40
1968.95..................... Vis 287.6 200 6 #5.2 +6 #3.1 +13
1974.867................... Vis 91.7 240 7 +3.8 +10 2.5 #21
1976.86..................... Vis 97.6 300 8 +3.9 #34 2.9 #50
1977.659................... Vis 0.4 94.6 330 9 #0.6 #35 #1.7 #41
1980.864................... Vis 0.3 100.0 380 9 0 #21 #2.2 +26
1983.97..................... Vis 101.8 270 10 #4.7 +24 #12.1 +92
1986.6464................. Int 251.2 # 2.0 b 63 # 2 11 0 0 1.1 #24
1989.8075................. Int 281.4 # 1.0 290 # 3 12 0 0 +1.4 +36
1991.25..................... HIP 282.0 # 0.5 271 # 1 13 #3.5 #4 #4.4 +48
2004.9903................. Int 0.55 100.0 # 0.4 399 # 2 14 0 0 #4.9 +91
rms............................ 2.1 22.0 3.8 48.9
a Type of measurement: Vis, visual; Int, interferometric; HIP, from Hipparcos.
b Quadrant changed.
References.---(1) Worley 1960; (2) Worley 1971; (3) Worley 1972; (4) Walker 1971; (5) Couteau 1968; (6) Couteau 1970; (7) Worley 1978; (8) Heintz 1978;
(9) Worley 1989; (10) Couteau 1985; (11) Balega et al. 1989; (12) Balega et al. 1994; (13) Perryman et al. 1997; (14) this paper.
Fig. 1.---Apparent orbit of WOR 2 (the scales on both axes are in arcseconds).
Each measurement is connected to its predicted position by an O # C line. The
dashed line passing through the primary star is the line of nodes. The points and
stars represent visual and speckle measurements, respectively.
TABLE 2
Orbital Elements and System Mass
Element This Paper Baize (1991)
P (yr) ................................ 24.07 # 0.5 23.0
T ....................................... 1987.35 # 3 1988.8
e........................................ 0.296 # 0.02 0.22
a (arcsec).......................... 0.361 # 0.005 0.32
i (deg)............................... 82.9 # 4 80.4
# (deg) ............................. 100.6 # 7 99.5
! (deg) ............................. 122.5 # 10 158.0
System mass (M # ) ........... 1.40 # 0.25 1.07
TAMAZIAN ET AL.
2848 Vol. 130

of the fundamental stellar properties, the luminosity function, and
the massíluminosity relation, which are poorly known at the lower
end of the HíR diagram. The MK types for many visual binaries,
estimated on the basis of the prism surveys, are often subject to
change after a more careful study of the slit spectra. Obtaining MK
types on the basis of the slit spectra is a significant problem (Gray
et al. 2003).
3.1. Spectral Observations
Several spectra for WOR 2 were obtained at the 2.6 m teleí
scope of the BAO on 2004 September 2 with SCORPIO, which
is a multiregime, prime focus focal reducer for observing both
starlike and extended objects. On the 2.6 m telescope, SCORPIO
is used in combination with a 2K ; 2K Lick3 CCD based on a
2063 ; 2058 Loral system, with elements of 15 #m 2 size and a
readout noise of #5 e #1 . The resulting field of view is 14 0 ; 14 0 ,
and the spatial resolution is 0B42 per element. In the spectrosí
copy mode, a grism with a 600 lines mm #1 grating (with a reí
sulting linear dispersion of 1.7 8 per element and resolution of
3.5--4.0 8) covering the spectral range #4100--7500 8was used.
Since the components' separation in the WOR 2 system is less
than 1B0, the spectrometer slit of size 2B0 ; 6A0 contained both
stars.
We observed at about the same zenithal distance spectroí
photometric standards ( Kharitonov et al. 1988) for both atmoí
spheric extinction correction and spectrograph response fitting
for different wavelengths. The spectra of some lateítype MK staní
dards from the list of Keenan &Yorka (1988) were also obtained
for comparison purposes. All stars were observed at less than
1.5 air masses, and we estimate our relative fluxes to be calií
brated on the order of 10% accuracy, well enough for classifií
cation purposes.
The standard ESO Munich Image Data Analysis System
environments were used for data reduction, including the subí
traction of bias, dark frames, and dome flats. The wavelength
dependence of the instrument profile was determined from single
lines in the comparison spectra and taken into account when
calculating the parameters of spectral lines.
3.2. Line Identification and Classification
The spectrum of WOR 2 is shown in Figure 2. A large numí
ber of absorption lines were identified, but strong representative
lines (some are marked in Fig. 2) were only used for classifií
cation purposes. When identifying the spectral lines we took into
consideration both wavelength coincidence and line intensity.
Different spectral atlases and libraries ( Yamashita et al. 1977;
Gunn & Stryker 1983; Jacoby et al. 1984; Kirkpatrick et al. 1991;
Goy et al. 1995; Allen & Strom 1995; Montes et al. 1997; Pickles
1998) were used for line identification. The standard criteria and
indications given by Keenan (1987), Jaschek & Jaschek (1987),
Keenan & McNeil (1989), Gray (1992, p. 431; 1994), Garrison
(1994), Malyuto et al. (1997), and Montes et al. (1997) were
followed for classification purposes.
The main features in the spectrum are the absorption lines Ca i
k4226, the G band, Fe i k5270, the Mg b triplet, MgH k4780 and
k5210, and NaD k5890 (typically the strongest feature for midíK
spectral type); several TiO bands (including a wellíobserved
broad feature at 6100--6400 8) were used to classify the spectrum.
As is seen from Figure 2, Ca i is rather strong, the G band
begins to dissolve into separate lines, MgH k4780 is still strong,
and TiO bands are visible but not yet strong. Apart from this,
metallic lines in general are rather strong, with Mg b and NaD
being the strongest spectral features. These properties and the
application of the aboveímentioned criteria allow us to classify
WOR 2 as K6 V, coinciding within the usual accuracy of one
subclass with the classification as K7 V by Reid et al. (1995).
4. DISCUSSION
Since its discovery, WOR 2 has practically covered two reví
olutions. In spite of the gaps in observations mentioned above,
the measurements covered the most distant positions of the secí
ondary. Due to the geometry of this system, these points corí
respond to the maximal curvature of the apparent orbit, thus
contributing decisively to the orbit's quality. Taking into account
the much larger weight of speckle measurements, these circumí
stances allow us to calculate a rather well defined orbit in spite
of a relatively small number of measurements.
An overview of (O # C ) residuals both in position angle
and separation shows that our orbit represents a substantial
TABLE 3
Ephemerides
This Paper Baize (1991)
Epoch
#
(deg)
#
(mas)
#
(deg)
#
(mas)
2006.00....................... 101.6 372 108.3 249
2007.00....................... 103.5 323 114.2 176
2008.00....................... 106.3 249 129.8 95
2009.00....................... 112.2 153 206.7 49
2009.25....................... 115.2 126 229.9 59
2009.50....................... 119.9 98 244.4 76
2009.75....................... 128.1 71 253.4 95
2010.00....................... 145.9 46 259.3 115
2010.25....................... 187.3 33 263.4 135
2010.50....................... 232.8 43 266.6 155
2010.75....................... 253.1 67 269.0 173
2011.00....................... 262.2 94 271.0 190
2011.25....................... 267.3 121 272.6 205
2011.50....................... 270.5 147 274.1 218
2011.75....................... 272.8 172 275.4 230
2012.00....................... 274.5 195 276.6 239
2013.00....................... 278.8 263 280.8 253
2014.00....................... 281.8 291 285.1 233
2015.00....................... 284.5 284 291.1 184
2016.00....................... 287.7 250 302.8 120
Fig. 2.---Spectrum of WOR 2. Several representative spectral lines are marked.
The intensity is given in arbitrary units.
ORBIT OF WOR 2 2849
No. 6, 2005

improvement over the previous one. While the orbit's improveí
ment is mostly due to accurate speckle observations, the method
of calculation is also a key element. Data listed in Table 1 show
that much greater weight is given to speckle data (see details on
the weighting procedure in Docobo et al. 2000).
Quantitatively, the improvement is reflected in the quadratic
means of residuals (rms), which are significantly smaller than
those of the previous orbit (see Table 1). In particular, the rms
values in # and # for our orbit are equal to 2.1 and 22 mas, reí
spectively, whereas the same values for Baize's orbits are 3.8
and 49 mas.
Our orbit can probably be graded 2 (good orbit) according to the
scheme proposed by Hartkopf &Mason (2004). Usually, binaries
that have covered two revolutions are the best candidates to get the
maximal grade 1 (definitive orbit). However, the small number of
observations and their uneven coverage of the orbital arc suggest
that the definitive orbit for WOR 2 is yet to be determined.
From Table 3 one can see a rapid change in apparent sepaí
ration between 2009.75 and 2010.75, which can be measured
by the 6--8 class telescopes only. Should such measurements be
performed, the definitive orbit can probably be calculated.
The dynamical mass of the system, 1:40 # 0:25 M# , is
0:33 M# larger than that obtained from the Baize orbit. No
significant variation in this value should be expected, since the
limit is imposed by Kepler's third law. Moreover, when there
are no discrepancies regarding the temperature and luminosity
of the components, in principle, a small increase in the system's
mass reflects correctly the change of the combined spectral type
from M0 to K7.
It is worth noting, however, that the overall accuracy of the
dynamical mass determination for this binary (and many others)
is almost entirely conditioned by the low relative accuracy of the
parallax determination. Although an accuracy of less than 1% in
period and angular semimajor axis is obtained for a number of
binaries ( Mason et al. 1999), they are all strongly hindered by
the 3%--5% accuracy of parallaxes, which translates to a 10%--
15% error in mass determination. Such low accuracy is very far
from the theory requirements, so Hipparcos parallaxes in many
cases deteriorate the overall accuracy of the mass determination.
For example, should the parallax error be equal to zero, the
dynamical mass error is 0.082 M# (5.7%). At present, such a
value can still be used to fit certain theoretical tracks. As regards
further improvement of the orbit itself (and therefore the accuí
racy of the dynamical mass determination), more efforts should
be applied to get highíresolution measurements in the second
quadrant and, even more importantly, at the points of minimal
separation between components. Evidently, new postíHipparcos
data (from Gaia and the Space Interferometry Mission) are needed
to improve the situation, since the number of wellídetermined
orbits is rapidly growing.
Taking into account the 0.55 mag difference, as well as the
apparent brightness V ® 9:58 (Salim & Gould 2003) in the comí
bined light, we obtain 10.09 and 10.64 mag for the primary and
secondary components, respectively. With a distance of 25.83 pc,
these values lead to M ® ”8:03 and +8.58 mag as luminosity
estimates for the primary and secondary components, respecí
tively. The mass of each component can then be estimated using
the formula given in Henry et al. (1999):
log (#=#
# ) ® ”0:002456M 2
V # 0:09711M V ” 0:4365
where the mass is designated # to distinguish it from luminosity.
The masses 0.65 and 0:61 M# are obtained for the compoí
nents, and their sum, 1:26 M# , is in a good agreement with the
obtained dynamical mass. Apart from this, according to Schmidtí
Kaler (1982) the obtained luminosity corresponds approximately
to K7 and M0 dwarfs, concordant with our spectral classification.
Herbst & Miller (1989) measured the equivalent width of the
H# absorption in the spectra of WOR 2 as 0.85 8. Although our
spectra are not well suited to spectrophotometry, we estimated
the roughly similar value of #0.9 8, in a good agreement with
the above result. This is an indication of the overall photometric
stability of the system.
The authors would like to thank the referee, B. Mason, for
helpful comments. This paper was financed by research project
AYA2004í07003 of the Spanish Ministerio de Educacio Òn y
Ciencia.
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ORBIT OF WOR 2 2851
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