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ISSN 1990-3413, Astrophysical Bulletin, 2007, Vol. 62, No. 2, pp. 111­116. c Pleiades Publishing, Ltd., 2007. Original Russian Text c E.V.Malogolovets, Yu.Yu.Balega, D.A.Rastegaev, 2007, published in Astrofizicheskij Byulleten, 2007, Vol. 62, No. 2, pp. 124-130.

Nearby Low-Mass Triple System GJ 795
E. V. Malogolovets, Yu. Yu. Balega, and D. A. Rastegaev
Special Astrophysical Observatory of the Russian AS, Nizhnij Arkhyz, 369167 Russia
Received November 3, 2006; in final form, December 4, 2006

Abstract--We report the results of our optical speckle interferometric observations of the nearby triple system GJ 795 performed with the 6 m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences with diffraction-limited angular resolution. The three components of the system were optically resolved for the first time. Position measurements allowed us to determine the elements of the inner orbit of the triple system. We use the measured magnitude differences to estimate the absolute magnitudes Aa Ab B and spectral types of the components of the triple: MV =7.31±0.08, MV =8.66±0.10, MV =8.42±0.10, SpAa K5, SpAb K9, SpB K8. The total mass of the system is equal to MAB =1.69±0.27M . We show GJ 795 to be a hierarchical triple system which satisfies the empirical stability criteria. PACS numbers : 97.80.Kq DOI: 10.1134/S1990341307020022

1. INTRODUCTION According to the most recent concepts, stars form in small groups and clusters. The disruption of such groups results in the formation of both multiple systems and single stars. Stars in triple and more complex multiple systems make up for more than 20% of the Milky-Way population. The study of their dynamical and physical parameters is necessary for understanding the process of star formation as a whole. However, the now available observational data are insufficient for testing the theories of formation and evolution of multiple stars. We do not yet entirely understand the initial conditions and mechanisms of multiple star formation. The issues that still remain unclear include the conservation of angular momentum in the process of star formation; the dynamical stability of multiple systems with more than three stars; the effect of tidal interactions on the dynamical evolution of multiple systems; the distribution of orbital periods, eccentricities, component mass ratios, and correlations between these parameters; mutual orientations of the orbital planes in multiple systems, etc. Of special interest is the study of multiple systems with low degree of hierarchy with comparable orbital periods and semimajor axes. The Orion Trapezium -- a small cluster of very young and massive stars -- is the most well known dynamically unstable multiple system. The disruption time scale of the Trapezium is estimated at 104 - 106 years [1]. Main-sequence stars are also found in a number of systems that are potentially dynamically unstable [2­4]. The stability criteria for multiple stellar systems were analyzed by

[5­10] and other authors. However, the conclusion about the dynamical instability of a particular system is often disproved when its orbital elements are refined. The triple system ADS 16904 with the periods of the inner and outer orbits equal to 15 and 150 years, respectively, is an example [11]. According to all known criteria, the state of this system must be close to instability [12]. However, new interferometric measurements including the data obtained with the 6 m Bolshoi Azimuthal Telescope (BTA) of the Special Astrophysical Observatory of the Russian Academy of Sciences indicate that the actual period of the outer orbit in this triple is twice longer and hence the system must be dynamically stable. So far, no systems with main-sequence components have been found that could be securely classified as dynamically unstable. Known candidate objects with low orbit hierarchy, which therefore should be viewed as possible dynamically unstable multiple systems, include the nearby (d 16 pc) triple star GJ 795 (HD 196795 = Hip 101955, =20h 39m 38s , =+04 58 19 ,epoch 2000.0). Its integrated spectral type corresponds to that of a K5V star. For decades, GJ 795 has been known as the visual pair Kui 99 [13] with a period of 40 years. During his spectroscopic survey of visual binaries with the CORAVEL radial-velocity scanner, Duquennoy [14] found GJ 795 to contain a hitherto unknown spectroscopic subsystem with very low amplitude of radial-velocity variations. He concluded that the companion is bound to the main component of the binary and computed a preliminary model
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of the system by combining photometric and spectroscopic data with the computed orbital elements. At the same time, the inclination of the inner orbit of the triple was estimated based on the assumed component masses exclusively. The strongly inclined outer orbit also remained highly uncertain. To refine the pattern of component motions in GJ 795, this system was put in 1998 into the list of program stars for speckle interferometric observations with the BTA 6 m telescope. In this paper, we report the results of our speckle interferometric observations of the relative measurements of components of GJ 795 and their differential photometry, and determine the parameters of orbital motion of stars and their dynamic masses. In conclusion, we discuss the dynamical stability of the system. 2. OBSERVATIONS AND DATA ANALYSIS We performed speckle interferometric observations of GJ 795 with the new facility mounted on the BTA 6 m telescope [15]. Its detector consists of a fast 1280â1024 Sony ICX085 CCD combined with a three-camera image-tube converter with electrostatic focusing. We recorded speckle interferograms in the visible part of the spectrum with exposures ranging from 5 to 20 milliseconds. Table 1 lists the log of observations, which gives for each measurement the date of observation (as a fraction of Besselian year); seeing in arcsec; the number of speckle interferograms in the series; filter parameter / in nm, where and are the central wavelength and half-bandwidth, respectively. We determined the relative component positions and magnitude differences from the power spectra of the speckle interferograms averaged over the series [16]. The accuracy of the measured position parameters is 0.2­4.0 and 1­4 milliarcsec for position angle and angular separation, respectively. Measurement errors depend on a number of parameters: component separation, magnitude difference, and seeing . The accuracy of the magnitude differences inferred from reconstructed power spectra depends on the same parameters. For objects in the mV =8­10 magnitude interval it usually varies from 0.05 to 0.2. We use bispectral analysis of the interferogram series to perform complete reconstruction -- including that of modulus and phase -- of the images [17, 18]. Figure 1 shows the reconstructed image of the triple star GJ 795 based on observations made in 1998. 3. ABSOLUTE MAGNITUDES AND SPECTRAL TYPES As we already mentioned in the Introduction, Duquennoy [14] carried out a detailed study of the
Fig. 1. The 610/20 nm image of GJ 795 (1998.77) reconstructed using bispectral analysis. Artefacts surrounding the point sources are due to various types of noise. North is at the top and East on the left.

Table 1. Log of speckle observations Date 1998.7741 1999.8206 2000.8752 2001.7522 2002.7986 2003.9272 arcsec 1 2 1.5 2 2 3-5 1 1 1 2004.8232 1.5 700 1500 1000 1500 1500 1500 2000 2000 2000 2000 N / nm 610/20 610/20 600/30 545/30 850/75 600/30 545/30 700/30 800/110 600/30

radial-velocity variations of primary component A of the visual binary KUI 99 with the CORAVEL radial-velocity scanner. He detected no traces of the fainter star B in the spectra. On two nights in 1985, significant variations were observed in the profile of the correlation minimum that were due to the contribution of component Ab to the total flux. The resulting radial-velocity curve was used to determine the orbit of inner binary Aab with a period of P =920.2 days and eccentricity e=0.747. The preliminary model of the system, which included all three components, assumed a total mass and parallax of MAB =1.62±0.27M and =64±5
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NEARBY LOW-MASS TRIPLE SYSTEM GJ 795 Table 2. Differential speckle interferometry of GJ 795 Date BY Component m vector / Reference nm 1.09 0.05 610/20 0.88 0.05 1.14 0.03 610/20 0.94 0.03 1.30 0.06 600/30 1.02 0.06 1.35 0.06 545/30 1.11 0.06 0.92 0.06 850/75 0.68 0.06 1.42 0.05 600/30 This paper 1.27 0.05 [35] [35] [34] [16]

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emission level in the H and K Ca II lines [25] imply that this star should be classified as a Galactic-disk object with the age of 2­3Gyr. 4. ORBITAL PARAMETERS AND TOTAL MASSES The motion of components in a triple system can be subdivided into two components: the motion about the center of mass of the inner binary and the motion of the outer component about the common center of mass. The orbit of the outer system AB was computed by a number of authors from visual micrometric measurements [19, 26]. Its main parameters are: a period P of about 40 years; small eccentricity e, and high inclination with respect to the sky plane (i 85 ). Soderhjelm [23] refined the orbital elements of the pair AB by combining the data of ground-based observations with Hipparcos astrometry. He inferred a total mass of MAB =2.26±0.36M , which exceeds significantly the mass estimated by Duquennoy [14] based on spectroscopic and visual data. Despite the use of Hipparcos astrometry, the outer orbit remains uncertain, mostly because of its high inclination. We determined the preliminary orbital parameters of the subsystems of GJ 795 with allowance for new speckle interferomeric measurements based on the Fourier transform of equations of motion [27]. At the next stage, we refined the orbital elements via differential correction based on the least squares method (see comments in [28]). We adopted early visual and several interferometric measurements from the Washington Catalog of Binary Stars [29]. We set the weights of speckle observations made with the BTA 6 m telescope to be 10 times higher than those of the visual and interferometric observations made with other telescopes. The main reason why we attributed such low weight factors to earlier data is that they did not allow for the binary nature of component A, resulting in significant systematic errors. We computed the orbit of the inner binary Aab based exclusively on the data of interferometric observations made with the BTA 6 m telescope. Seven measurements span over about 2.5 periods along the apparent ellipse of the orbit (Fig. 2). An attempt to use radial velocities from [14] to construct a combined orbit resulted in increased errors of the inferred orbital elements. This is due to the combined effect of small radial velocities of Aab system, small inclination of the inner orbit to the sky plane, and systematic errors in radial-velocity measurements due to the influence of the distant component B. To convert the motion of component B to the center-of-mass frame of the inner binary Aab, we set the mass ratio equal to qin =0.8 based on the empirical

m

1998.7741 Aa-Ab Aa-B 1999.8206 Aa-Ab Aa-B 2000.8752 Aa-Ab Aa-B 2001.7522 Aa-Ab Aa-B Aa-Ab Aa-B 2004.8232 Aa-Ab Aa-B

mas, respectively. This model also made use of the empirical "mass ­ luminosity" relation for K6V (Aab) and K9V(B) type stars and a highly uncertain visual orbit of the outer pair AB [19]. According to Hipparcos [20] data, the trigonometric parallax of GJ 795 differs significantly from the above value (Hip =53.82±2.21 mas). However, Hipparcos trigonometric parallaxes for binary and multiple stars are known to be potentially fraught with extra errors due to wrong correction of component orbital motions in the process of Hipparcos data reduction [21, 22]. Soderhelm [23] corrected the parallax for the effect of the orbital motion of the pair AB: Hip =58.8±2.1 mas. The corrected Hipparcos parallax agrees within the quoted errors with that given by Duquennoy [14]. We performed differential speckle photometry of the system with the BTA 6 m telescope and list the results in Table 2. We set the V -band magnitude differences equal to mAaAb = 1.35 ± 0.06 and mAaB = 1.11 ± 0.06, respectively, implying, given the corrected parallax, the absolute magniAa Ab tudes of MV = 7.31 ± 0.08, MV = 8.66 ± 0.10, B and MV = 8.42 ± 0.10, respectively. These absolute magnitudes correspond to the spectral types of SpAa K5, SpAb K9, and SpB K8, respectively. The above spectral types agree well with the color index B - V =1.24 [24]. The space velocity components (U, V , W )=(-75.5, -19.7, -42.3) [24] and low
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(a) (b)

Fig. 2. Relative ellipses of the orbits of the triple system GJ 795: (a) orbit of binary Aab, (b) orbit of binary AB. The filled circles show the speckle interferometric observations made with the BTA 6 m telescope; the solid line shows the position of the periastron, and the dotted-and-dashed line, the line of nodes. The radius of the dashed circle is equal to 20 mas. Position parameters of component B are converted to the center-of-mass frame of binary Aab.

Table 3. Parameters of the inner and outer orbits in the triple system GJ 795

Table 4. Position parameters and residuals of the measurements of the triple system GJ 795
Subsystem Epoch (O - C ) (O - C ) degrees 0.3 -0.5 0.4 -0.2 0.5 0.9 -0.3 -0.3 -0.5 -0.1 0.2 -0.2 0.0 2.3 0.6 0.6 0.1 -0.2 -0.4 0.3 mas -2 1 1 0 1 2 -1 1 1 0 2 1 1 1 -2 0 -3 1 1 -1

Aab P, years T e a, mas i


AB 39.4±0.2 1975.0±0.3 0.06±0.01 820±30 86.9±0.1 128.5±0.2 212±2 0.8 1

2.51±0.01 2000.55±0.01 0.620±0.006 120±2 18±3 174±11 87±11 0.5 1

degrees mas Aab 1998.7741 55.0 161 164 108 185 186 98 172 174 174 164 358 234 108 48 45 153 286 289 289 390

1999.8206 105.7 2000.8752 2001.7522 2001.7522 20.8 78.2 78.5





2002.7986 150.3 2003.9272 2003.9272 2003.9272 61.9 61.9 61.7



"mass ­ MV " relation of [30] and absolute magniAa Ab tudes MV =7.3 and MV =8.7. We give the elements of the outer and inner orbits in Table 3. We list all position measurements made with the BTA 6 m telescope and the corresponding residuals in Table 4. The orbital parameters of the inner binary Aab agree well with those of the spectroscopic orbit by Duquennoy [14] and those of the outer binary AB, with the refined orbit of Soderhelm [23]. It is remarkable that the preliminary estimates of the inclination and semimajor axis of the inner orbit obtained by Duquennoy [14] based on published empirical "mass ­ luminosity" relations coincided exactly with their true values inferred from the results of our interferometry. Let us now determine the angle between the

2004.8232 105.2 AB 1998.7741 135.4 1999.8206 139.1 2000.8752 153.2 2001.7522 238.5 2001.7522 236.8 2002.7986 292.5 2003.9272 300.3 2003.9272 300.0 2003.9272 299.8 2004.8232 303.1

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orbital planes: cos = cos iout cos iin +sin iout sin iin cos(out - in ), (1)

where iout and iin are the tilt angles of the orbit of the outer and inner binaries with respect to the sky plane, respectively; out and in are the longitudes of the ascending node of the outer and inner binaries, respectively. We now use the angle values from Table 3 to obtain =74 . The dynamic mass of the inner binaries as inferred from the orbital parameters and the corrected Hippar cos parallax of Hip =58.8±2.1 mas [23] is equal to MAab =1.28±0.15M . The mass of the entire system GJ 795 computed using the orbital parameters of binary AB is equal to MAB =1.69±0.27M . According to Lang [31], the individual masses of stars in the system as inferred from their absolute magnitudes are equal to: MAa =0.67M , MAb =0.57M , MB =0.54M . The above estimates imply a mass of MAab =1.24M for Aab binary and a total mass of MAB =1.78M for the entire system, which are consistent within the quoted errors with the total masses inferred using orbital parameters. 5. HIERARCHY OF ORBITS AND THE KOZAI MECHANISM OF OSCILLATIONS The ratio of the orbital periods of the components of the system is equal to Pout /Pin =15.7, and hence the system is weakly hierarchical and its components form a single gravitationally bound system. Let us now try to estimate its dynamical stability using empirical criteria and criteria based on numerical simulations. According to one of such criteria suggested by Tokovinin [32], the system is stable if the following inequality is satisfied: T= Pout (1 - eout )3 > Tc , Pin (2)

Like in the case of empirical estimate, the value of this parameter, F =6.42, exceeds the critical level of Fc =5.46. However, these criteria should be used with much caution when applied to systems with orthogonal orbits. The semimajor axes of the outer and inner binaries are equal to aout 14 AU and ain 2 AU, respectively. The apoastron distance of the inner binary is equal to 3.2 AU. The eccentricity of the outer orbit is close to zero and therefore components of the triple are never at comparable distances from each other. Theoretical studies on the dynamics of multiple systems show that in the case of large angles between the orbital planes the inner and outer binaries [33] exchange angular momentum. This mechanism triggers periodic variations (Kozai oscillations) of the eccentricity of the inner orbit, ein , and angle between the orbital planes. The quantity (1 - e2 )cos2 = const remains constant in this in process. The following formula gives the period of Kozai cycle: Pkoz
ai 2 Pout /Pin (1 - eout )3/2 .

(4)

The period of Kozai oscillations for the triple star GJ 795 is equal to only 560 years. We may try to directly observe Kozai oscillations of the orbital parameters of binary Aab over several years of interferometric observations. 6. CONSLUSIONS We use speckle interferometric observations made in 1998­2004 with the BTA 6 m telescope to compute accurate visual orbits for the outer and inner binaries of the triple star GJ 795. This triple system belongs to the disk component of the Galaxy and is 2­3Gyr old. Differential photometry of the components of this system made it possible to construct a complete model of GJ 795, which agrees well with modern empirical and theoretical relations. The absolute magnitudes Aa of the components are equal to MV =7.31±0.08, Ab =8.66±0.10, and M B =8.42±0.10 and they corMV V respond to the spectral types of SpAa K5, SpAb K9, and SpB K8, respectively. The orbital periods are equal to 2.51 and 39.4 years for the inner and outer binaries, respectively. The angle between the planes of the inner and outer orbits is equal to =74 . The total dynamiMAB = cal masses MAab =1.28±0.15M and 1.69±0.27M are consistent with the estimated spectral types of the components. We use the available empirical and theoretical stability criteria to conclude that GJ 795 is a gravitationally bound stable hierarchical system. For objects of

where Pout and Pin are the orbital periods of the outer and inner binaries, respectively; eout , the eccentricity of the orbit of the outer binary, and Tc is the critical instability value, which is equal to 5. The stability parameter for GJ 795 is equal to T13 and hence the system is stable. Based on numerical simulations, Harrington [9] proposed the following stability parameter for triple systems, which depends on the ratios of the semimajor axes of the outer and inner orbits, aout and ain ,and the eccentricity of the outer orbit: F= aout (1 - eout ) > Fc . ain (3)

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this type, the Kozai mechanism should be efficient, which causes oscillations of the orbital eccentricities and the angle between the orbital planes. During its lifetime, the triple star GJ 795, whose Kozai period is equal to Pkoz ai 560 years, must have undergone 106 such periodic perturbations. ACKNOWLEDGMENTS We are grateful to the night assistants at the 6 m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences for supporting the efficient work on the program. This work was supported by the Russian Foundation for Basic Research (grant no. 04-02-17563). REFERENCES
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