PHOTOMETRIC STUDY OF THE POSSIBLE COOL QUADRUPLE SYSTEM PY VIRGINIS

Until now, it has been unclear how W UMa overcontact binaries form. Many investigations (e.g., Huang 1966; Mestel 1968; Vilhu 1982; Guinan & Bradstreet 1988; Eggen & Iben 1989; Bradstreet & Guinan 1994) have shown that W UMa binaries are formed from initially detached binaries with periods less than five days through angular momentum loss (AML) via magnetic torques from stellar winds. One mechanism for the formation of these initially tidal-locked detached systems is the angular momentum transfer within multiple systems (e.g., Tokovinin 2004) during the Kozai oscillation (Kozai 1962). Therefore, searching for and studying the companion-star environment of W-UMa-type systems can provide valuable information of their formation and evolution.

The light variability of PY Vir (=GSC 4961-667) was discovered by Wils & Dvorak (2003) in Stardial images. They identified this star as an eclipsing variable of W- UMa-type and published the earliest photoelectric minima of this system. PY Vir is also known to be an X-ray source (1RXS J131032.4-040934). Rucinski et al. (2008) published the first spectroscopic study of this system. They classified the spectral type of the system as K2V and derived its spectroscopic mass ratio as 0.773 ± 0.005. Moreover, they found a spectroscopic third component in the system. Based on their observations, they obtained the radial velocities of this third body, which varied from −32.9(± 4.1) km s⁻¹ to −23.3(± 3.7) km s⁻¹ in about 320 days. Thus, they suggested that the third body may be a binary itself or a closer low-mass star with fast orbital motion.

After the investigation of Rucinski et al. (2008), Deb & Singh (2011) presented the light-curve analysis of V-band observations of this binary star obtained by the All Sky Automated Survey (ASAS; Pojmanski 1997, 2002). They concluded that PY Vir belongs to a marginal contact binary with the primary component (the massive one) filling its critical Roche lobe (RL) and the secondary one nearly filling its critical RL. Meanwhile, they derived a higher effective temperature for the secondary component (the less massive one). This suggests that PY Vir is a W-type marginal contact system. Until now, 16 high-precision CCD times of minimum light have been published, which can be used to analyze its period behavior. In the present paper, combining the results of the period investigation and photometric and spectroscopic solutions, we discuss the structure and evolutionary state of this cool system.

We carried out new photometric observations of PY Vir, which was observed on 2012 January 7, 29, 31, and April 23 with DW436 2048 × 2048 CCD attached to the 60 cm Cassegrain reflecting telescope of Yunnan Astronomical Observatory of Chinese Academy of Sciences (YNAO). Its field of view at the Cassegrain focus is about 12 × 12 arcmin². During the observation, the integration times were set to be 80 s 50 s, 25 s, and 20 s for BV(RI)_c wavelengths, respectively. GSC 4961-00268 (α₂₀₀₀ = 13:10:19.3, δ₂₀₀₀ = −04:06:52.2) and GSC 4961-00492 (α₂₀₀₀ = 13:10:37.9, δ₂₀₀₀ = −04:05:36.8) were chosen as comparison and check stars, respectively. These two stars are near the target and have similar brightnesses. Image reductions were done with the IRAF package. With these observed data, complete CCD BV(RI)_c light curves of PY Vir were obtained and plotted in Figure 1. The original data can be found in Table 1.

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As one can see from Figure 1, there are unequal minima depths and unequal maxima heights in the multi-color light variations of PY Vir. The differences in the light levels in the four bands are tabulated in Table 2. The errors between the differential magnitude of the check star and the comparison star for each band are also listed in the last line of this table, which indicates that our measurements have relatively higher precision with a mean error of about 0.012 mag. As pointed out by Qian et al. (2005), using different methods, i.e., Kwee & Van Woerden (1956) or the parabolic fitting method, the determined minimum values have only slight differences, which are usually much smaller than the scatter of the O − C residuals. Moreover, the light levels around the minima of PY Vir are symmetric, so we use a quadratic polynomial fitting method to determine the times of minimum light, and five newly determined minima times are derived based on our observations.

Table 2. The Differences of Light Levels in the Light Curves of PY Vir

	ΔB	ΔV	ΔR	ΔI
Max.I–Max.II (m0.25 − m0.75)	0036	0019	0014	−0002
Min.I–Min.II (m0.0 − m0.5)	0.068	0.063	0.062	0.050
Min.I–Max.I	0.482	0.457	0.416	0.398
Min.II–Max.II	0.450	0.413	0.368	0.350
EC-CH	0.014	0.013	0.012	0.010

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Using the 2003 version of the Wilson–Van Hamme code (Wilson & Devinney 1971; Wilson 1979, 1990, 1994; Wilson & Van Hamme 2003), we analyzed the complete BV(RI)_c light curves of PY Vir obtained on 2012 January 29 and 31. The spectral type of PY Vir is K2V (Rucinski et al. 2008), so we assumed an effective temperature of T₁ = 4830 K for the primary component (the star eclipsed at primary minimum). The gravity-darkening coefficients g₁ = g₂ = 0.32 (Lucy 1967) and the bolometric albedo A₁ = A₂ = 0.5 were used, which correspond to the convective envelopes of both components. The mass ratio q was fixed to the spectroscopic mass ratio 0.773 obtained by Rucinski et al. (2008). Bolometric and bandpass square-root limb-darkening parameters were taken from Van Hamme (1993). The adjustable parameters were as follows: the inclination, i, the mean temperature of star 2, T₂, the monochromatic luminosity of star 1, L_1B, L_1V, L_1R, and L_1I, and the dimensionless potentials of star 1 and star 2, Ω₁ and Ω₂.

We performed a differential correction using different modes, i.e., mode 2 (detached model), mode 3 (contact model), mode 4 (semi-detached model with lobe-filling primary), and mode 5 (semi-detached model with lobe-filling secondary). After a lot of runs, we find that it could converge to either a contact model (mode 3) or a semi-detached model (mode 4 and mode 5). Three group photometric solutions were reported in Table 3. The quality of the fit is judged by sums of the square of the deviations between observed and fitted data points (Σ), which are listed in the last line of Table 3. From this table, we can see that the minimum Σ is achieved at both mode 3 and mode 5. Actually, the solutions of mode 5 show that the primary component reached its critical RL with the uncertainty of Ω₁ (column 4) taken into account. Also the degree of overcontact of mode 3 (column 2) is very low (0.3%) with an uncertainty of 2.1%. All of this implies a marginal contact characteristic of PY Vir. The corresponding synthetic light curves of mode 3 were shown in Figure 2 with solid lines. The residuals (i.e., the observed-minus-calculated light curves) from this model are also shown in the lower panel of this figure.

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Table 3. Photometric Solutions of PY Vir

Parameter	Mode 3	Mode 4	Mode 5
g1 = g2	0.32	0.32	0.32
A1 = A2	0.5	0.5	0.5
i (deg)	69.53(13)	86.71(80)	69.56(12)
T1 (K)	4 830	4 830	4 830
T2 (K)	4 702(7)	4 861(14)	4 703(7)
q	0.773	0.773	0.773
Ωin	3.3706	3.3706	3.3706
Ω1	3.3691(36)	3.3706	3.3707(67)
Ω2	3.3691(36)	5.7133(468)	3.3706
$\frac{L_{1I}}{L_{1I}+L_{2I}}$	0.6004(7)	0.8550(3)	0.6003(9)
$\frac{L_{1R}}{L_{1R}+L_{2R}}$	0.5823(8)	0.8426(4)	0.5821(11)
$\frac{L_{1V}}{L_{1V}+L_{2V}}$	0.6023(9)	0.8506(3)	0.6020(12)
$\frac{L_{1B}}{L_{1B}+L_{2B}}$	0.6127(11)	0.8495(4)	0.6124(13)
r1(pole)	0.3779(5)	0.3777(13)	0.3777(9)
r1(side)	0.3984(6)	0.3981(14)	0.3981(11)
r1(back)	0.4284(8)	0.4281(15)	0.4281(16)
r2(pole)	0.3350(5)	0.1676(17)	0.3348(15)
r2(side)	0.3509(6)	0.1685(17)	0.3507(16)
r2(back)	0.3827(9)	0.1699(18)	0.3812(18)
Degree of overcontact f(%)	0.3(2.1)
Σ	0.015	0.021	0.015

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From Figure 2, one can see that the theoretical light curves do not fit the observed ones very well, especially around the secondary maximum. The observed light curves are asymmetric, with the second maximum slightly brighter than the first maximum. This kind of phenomenon of unequal heights at two maxima in the light curve, i.e., the O'Connell effect (O'Connell 1951), also exists in some other late-type close binaries, such as AD Cnc (Qian et al. 2007), DV Psc (Zhang et al. 2010), WZ Cep (Zhu & Qian 2009), and DD Com (Zhu et al. 2010), which might be attributed to the manifestation of a chromospheric and a photospheric activity common in close binaries consisting of late-type components. Using a spots model can obtain the fits with flat residuals. However, spot determination by photometry alone is tentative because of the uniqueness of the spotted solutions. As suggested by Bonanos (2009), adding free parameters would improve the fit, but would not significantly change the masses and radii, so we choose our contact model as our final solution to calculate the absolute parameters of this system.

Combining our photometric solutions and spectroscopic elements derived by Rucinski et al. (2008), we can calculate the absolute physical parameters of PY Vir. Assuming an eccentricity e = 0, the mass of the components can be obtained from the expression (Kopal 1959, p.471)

$$\begin{equation} M_{1,2}\sin ^{3}i=1.0385\times 10^{-7}(K_{1}+K_{2})^{2}K_{2,1}P, \end{equation} \tag{ 1 }$$

where the orbital period is in days and semi-amplitudes are in km s⁻¹. The separation between the components can be given using Kepler's third law. Then all absolute parameters for PY Vir are calculated and shown in Table 4.

Our solutions show that PY Vir is a marginal contact binary, which is consistent with the results of Deb & Singh (2011). In addition, we derived the higher temperature of the primary component, which means PY Vir is an A-type marginal contact binary. This is different from the results of Deb & Singh (2011). Their results show PY Vir to be a W-type system. Some systems show an exchange between A type and W type, such as FG Hya (Qian & Yang 2005) and AH Cnc (Qian et al. 2006b). PY Vir maybe one of these systems exchanges from a W-type system to the present A-type system.

For investigating the period variations of PY Vir, we have collected all available times of minimum light of this target and listed them in Table 5 along with the timings obtained by us. The corresponding O − C values and circles E were calculated with the following ephemeris, and plotted in the upper panel of Figure 3. Those shown in the third column of the table are the types of eclipses, where "pri" refers to the primary minimum and "sec" to the secondary minimum:

$$\begin{equation} {\rm Min\,}I = {\rm HJD}2455956.29945+0\buildrel{\mathrm{d}}\over{.}311248\times {E}. \end{equation} \tag{ 2 }$$

Since all timings are derived from the CCD observational data, we used the same weight for all timings. Then, the following equation was obtained with a least-squares method:

$$\begin{eqnarray} O-C &=& {-}0.0034(\pm 0.0003)-0\buildrel{\mathrm{d}}\over{.}31124849(\pm 0.00000008) \nonumber \\ && {\times}\, {E}+0\buildrel{\mathrm{d}}\over{.}0075(\pm 0.0004) \sin [0\mbox{$.\!\!^\circ $}0587 \nonumber \\ && {\times}\, {E}-35\mbox{$.\!\!^\circ $}8(\pm 3\mbox{$.\!\!^\circ $}1)]. \end{eqnarray} \tag{ 3 }$$

The corresponding fit curves are shown in the upper panel of Figure 3. The dashed line in this figure shows the improvement of the period to be 0.31124849 days. The solid line represents the fit by the sinusoidal term, which implies that a periodic variation was found in this O − C diagram, suggesting that a cyclic change exists with an amplitude of 00075 days and a period of 5.25 years. The residuals based on the ephemeris (Equation (2)) are plotted in the lower panel of Figure 3.

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Based on our new multi-color BV(IR)_c light curves, we derived the photometric solutions for PY Vir. We found that PY Vir is an A-type marginal contact binary system. Compared to the results of Deb & Singh (2011), PY Vir may be another system fluctuating between W and A types. Combining our photometric solutions and the spectroscopic elements derived by Rucinski et al. (2008), we obtained the absolute parameters of PY Vir.

By combining our newly acquired times of minimum light with those compiled from the literature, we found that the O − C diagram of PY Vir shows a cyclic period variation with a period of 5.22(± 0.05) years and an amplitude of 0.0075(± 0.0004) days. Since a spectroscopic companion was found in PY Vir by Rucinski et al. (2008), we consider that the cyclic period change discovered in the O − C diagram can be interpreted as the light–time effect via the presence of a third body. With the semi-amplitude of the O − C oscillation, the value $a_{12}^{\prime }\sin {i^{^{\prime }}}$ is calculated to be $a_{12}^{\prime }\sin {i^{^{\prime }}}=1.30$ AU. Then by using the following equation

$$\begin{equation} f(m)=\frac{(M_{3}\sin {i^{\prime }})^{3}}{(M_{1}+M_{2}+M_{3})^{2}} =\frac{4\pi ^{2}}{GT_{3}^{2}}\times (a_{12}^{\prime }\sin \,{i^{\prime }})^{3}, \end{equation} \tag{ 4 }$$

a mass function f(m) = 0.0804 M_☉ is determined for the assumed third body. The masses and the orbital radii of the third body for many values of the orbital inclinations (i') are computed and are shown in the left and right panels of Figure 4, respectively. We can estimate the minimal mass of the additional body to be m₃ = 0.79 M_☉ and the corresponding maximal orbital radius to be a₃ = 2.8 AU.

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To verify the presence of the third body, during the photometric solution we added a third light (i.e., we made l₃ an adjustable parameter), but l₃ is usually negative, indicating that the third body may be too faint relative to the eclipsing pair to contribute to the whole system. According to the analysis of Rucinski et al. (2008), the radial velocities of the third component changed from −32.9(± 4.1) km s⁻¹ in 2007 to −23.3(± 3.7) km s⁻¹ in 2008. Using the maximal orbital radius and the period of the third body derived from our investigation, we can estimate the maximal radial velocity of this third body to be 15.9(± 0.9) km s⁻¹, which is smaller than the values obtained by Rucinski et al. (2008), implying that the third component may be a binary itself. Therefore, PY Vir should be a quadruple system composed of two cool-type binary systems. Further observations are necessary to check these results.

The presence of the additional components may play an important role for the formation of the progenitors of W UMa systems by transferring angular momentum during the Kozai cycle (Kozai 1962). In that way, the progenitors can evolve to an overcontact configuration via magnetic braking. The situation of PY Vir resembles that of VZ Lib (Qian et al. 2008) and V899 Her (Qian et al. 2006a). It is possible that both the Kozai mechanism and magnetic braking can cause the additional binary to evolve into overcontact binaries, and to form a quadruple system consisting of two W UMa systems, just like the well-known BV and BW Dra system.

This work was partly supported by the Chinese Natural Science Foundation (Nos. 11133007, 10903026, 11003040, and 11103074).