PERIOD CHANGES AND FOUR-COLOR LIGHT CURVES OF THE ACTIVE OVERCONTACT BINARY V396 MONOCEROTIS

The light curves of V396 Monocerotis are continuous and sine-like. The primary minima are nearly as deep as the secondary minima. That is, V396 Mon has an EW-type light curve and was classified as a W Ursae Majoris eclipsing binary in the General Catalogue of Variable Stars (Kholopov 1985). A photographic light curve, times of light minimum, and ephemeris were given by Wachmann (1964). Subsequently, additional times of minimum were published by Hoffmann (1983) and the Swiss Astronomical Society (BBSAG). Subsequently, BV light curves that were observed in 1999, photoelectric solutions, and a period analysis were published by Yang & Liu (2001). Their conclusions were that V396 Mon is a W-type W UMa contact binary with a mass ratio of 0.402 and a cool spot on the secondary component which causes asymmetry of the light curves. Soon afterwards, Gu (2004) observed the O'Connell effect (O'Connell 1951) to become very weak compared with that in Yang & Liu's (2001) observation; he attributed this to starspot activity.

Generally, magnetic activity leads to an alternate period change of a close binary (e.g., Applegate 1992; Lanza et al. 1998). However, in Yang & Liu's (2001) period analysis they did not find the expected variations owing to lack of times of light minimum data. Qian has published a series of papers discussing the long-term period variation of contact binary stars (i.e., Qian 2001a, 2001b, 2003). His result is that this kind of variation may correlate with the mass of the primary component (M₁) and the mass ratio of the system (q). His statistical critical mass ratio q is 0.4. When q>0.4, the secular period increases, and decreases when q < 0.4. V396 Mon is important because its mass ratio is around 0.4. According to Qian, such systems should be unstable and oscillate around the critical mass ratio. Therefore, V396 Mon has become one of the monitoring targets in our contact binary observation program running at Yunnan Observatory.

We carried out new CCD photometric observations of V396 Mon in the BVRI bands on 2009 November 16 and 17, using the 1024 × 1024 PI1024 BFT camera attached to the 85 cm telescope at the Xinglong Station of the National Astronomical Observatories of Chinese Academy of Sciences. The filter system was a standard Johnson–Cousins–Bessel multicolor CCD photometric system built on the primary focus (Zhou et al. 2009). The effective field of view was 165 × 165. The integration time for each image was 20 s. 2MASS06382732+0340193 and 2MASS06385506+0339462 were chosen as comparison star and check star, respectively. These two stars are close to the target and have similar brightness. PHOT (measure magnitudes for a list of stars) of the aperture photometry package of IRAF was used to reduce the observed images, including a flat-fielding correction process. From the observation we obtained BVRI light curves. The original data are listed in Tables 1–4. After calculating the phase of the observations with the equation 2, 455, 153.3614 + 0.39634359 days × E, the light curves are plotted in Figure 1. In this figure, it is seen that the data over two days merged smoothly and the light variation is of EW type. The magnitude difference between the comparison star and the check star is a constant, indicating the authenticity of the variations of the curves of V396 Mon. Since the light levels around the minima are symmetric, a quadratic polynomial fitting method was used to determine the times of light minimum by the least-squares method. Our new epochs of light minima are listed in Table 5.

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The light curves in the V band obtained by Yang & Liu (2001) in 1999 and by the authors in 2009 are plotted in Figure 2. As shown in this figure, the light curves changed between 1999 January and 2009 November. The light curves observed in 2009 November are symmetric, while those obtained in 1999 January are asymmetric; they exhibit a typical O'Connell effect and show a much deeper primary minimum. A similar phenomenon was found by Qian et al. (2006) when they analyzed a deep, low mass ratio over contact binary system, AH Cancri. They did not attempt any interpretation at the time, but we are convinced that the changes in the light curves are caused by some cool star spots on the surface of the components. A cool star spot, or several, can make the primary minimum much deeper, which was confirmed by Yang and Liu's photometric solutions. Later, the spot disappeared, which was verified by the photometric solutions of Gu (2004) and us. The present cool spots will greatly alter the light curves, even strongly affecting the results of the photometric parameters.

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The first orbital period analysis of V396 Mon was given by Yang & Liu (2001). They collected 30 light minima and yielded a corrected ephemeris,

$$\begin{eqnarray} {\rm Min. I}&=&2{,}451{,}199.0715(\pm 0.0006)\nonumber \\ & &+0.3963410(\pm 0.0000007)\;{\rm days}\times {E}. \end{eqnarray} \tag{ 1 }$$

Over time, more and more minima of V396 Mon were obtained by various observers. We collected all available visual, photoelectric, and CCD times of light minimum, and we list them in Table 6. We adopted the ephemeris 2,455,153.3614+0.39634498 days × E to modify its period, where 2,455,153.3614 is one of our times of light minimum and 0.39634498 is found in the General Catalogue of Variable Stars (Samus et al. 2004). In the calculations, the weight of the visual data is set as 1, while that of the other data is set as 8. A new corrected linear ephemeris was obtained:

$$\begin{eqnarray} {\rm Min. I}&=&2{,}455{,}153.3766(\pm 0.0035)\nonumber \\ & &+0.39634359(\pm 0.00000010)\;{\rm days}\times {E}. \end{eqnarray} \tag{ 2 }$$

The (O − C) values with respect to the linear ephemeris are listed in the fifth column of Table 6. The corresponding (O − C)₁ diagram is displayed in Figure 3.

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The general (O − C)₁ trend of V396 Mon shown in Figure 3 indicates a continuous period decrease. However a long-term period decrease alone (dashed line in Figure 3) cannot adequately describe the (O − C)₁ curve; a period oscillation exists. Assuming that the period oscillation is cyclic, then, based on a least-squares method, a sinusoidal term was added to the quadratic ephemeris to give a better fit to the (O − C)₁ curve (solid line in Figure 3). The result is

$$\begin{eqnarray} {\rm Min. I}&=&2455153.3763(\pm 0.0053) \nonumber \\ & & +0\mbox{$.\!\!^{\mathrm d}$}39634132(\pm 0.00000038)\times {E}\nonumber \\ & &-4.65(\pm 0.59)\times {10^{-11}}\times {E^{2}}\nonumber \\ & &+0.0160(\pm 0.0009)\sin [0\mbox{$.\!\!^\circ $}00921\times {E}\nonumber \\ & &-65\mbox{$.\!\!^\circ $}5(\pm 12\mbox{$.\!\!^\circ $}2)]. \end{eqnarray} \tag{ 3 }$$

With the quadratic term included in this equation, a secular period increase rate is determined: dP/dt = −8.57 × 10⁻⁸ days yr⁻¹.

The (O − C)₁ values, taking account of the quadratic ephemeris in Equation (3), are shown in Figure 4. Although the visual data show large scatter, most of the photoelectric and CCD data lie close to the fitting line; an oscillation is seen in this figure. We have the relation,

$$\begin{equation} \omega =360^{\circ }P_{e}/T, \end{equation} \tag{ 4 }$$

where P_e is the ephemeris period (0.39634359 day); the period of the orbital period oscillation is determined to be T₃ = 42.4 yr.

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V396 Mon is a neglected but important system. Yang & Liu (2001) determined its photometric solutions. They found the mass ratio q to be 0.402 and the fill-out factor f to be 5%, including a dark spot on the secondary component. But soon afterwards, Gu (2004) found that the spot had disappeared. He derived a mass ratio of 2.937 (0.340).

To obtain initial input parameters, a q-search method with the 2003 version of the W-D program (Wilson & Devinney 1971; Wilson 1990, 1994; Wilson & Van Hamme 2003) was used (Figure 5). We fixed q to be 0.3, 0.4, 0.5 and so on, as Figure 5 shows. It can be seen that there are two lower points and the best value is around q = 2.5 (0.4), which is very close to the photometric value q = 0.402 (Yang & Liu 2001).

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Throughout the calculation the same temperature for star 1 (the star eclipsed at the primary minimum) as that used by Yang & Liu (2001) (T₁ = 6210 K) was chosen. The bolometric albedo A₁ = A₂ = 0.5 (Rucinski 1969) and the values of the gravity-darkening coefficient g₁ = g₂ = 0.32 (Lucy 1967) were used, which correspond to the common convective envelope of both components. Logarithm limb-darkening coefficients were used, taken from Claret & Gimenez (1990). We adjusted the mass ratio (q), the orbital inclination (i), the mean temperature of star 2 (T₂), the monochromatic luminosity of star 1 (L₁), and the dimensionless potential of star 1 (Ω₁ = Ω₂, mode 3 for contact configuration). Like Gu (2004)'s light curves, our multicolor light curves showed no O'Connell effect. Period analysis indicated that the period oscillation may be caused by a light-time effect of a tertiary component, so we tried to adjust the parameter l₃ in the W-D code. However, the numerical third light calculated by the program tended to negative values. Therefore, in our final results we set the third light equal to zero. The photometric solutions are listed in Table 7 and the theoretical light curves computed with those photometric elements are plotted in Figure 6. The geometrical structure of V396 Mon is displayed in Figure 7.

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Table 7. Photometric Solutions for V396 Mon

Parameters	Photometric Elements	Errors
g1 = g2	0.32	Assumed
A1 = A2	0.50	Assumed
x1bolo = x2bolo	0.644	Assumed
y1bolo = y2bolo	0.231	Assumed
x1B = x2B	0.817	Assumed
y1B = y2B	0.215	Assumed
x1V = x2V	0.728	Assumed
y1V = y2V	0.269	Assumed
x1R = x2R	0.635	Assumed
y1R = y2R	0.276	Assumed
x1I = x2I	0.543	Assumed
y1I = y2I	0.263	Assumed
T1	6210 K	Assumed
q	2.554	±0.004
Ωin	6.0187	⋅⋅⋅
Ωout	5.4076	⋅⋅⋅
T2	6121 K	±3 K
i	89654	±0.863
L1/(L1 + L2)(B)	0.3194	±0.0007
L1/(L1 + L2)(V)	0.3146	±0.0006
L1/(L1 + L2)(R)	0.3119	±0.0164
L1/(L1 + L2)(I)	0.3099	±0.0005
Ω1 = Ω2	5.9032	±0.0074
r1(pole)	0.2898	±0.0007
r1(side)	0.3034	±0.0008
r1(back)	0.3428	±0.0015
r2(pole)	0.4429	±0.0006
r2(side)	0.4750	±0.0008
r2(back)	0.5049	±0.0010
f	18.9%	±1.2 %
∑(O − C)2i	0.000005618

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V396 Mon is a W-type marginal contact binary with a reliable photometric mass ratio of 2.554 and a fill-factor of 18.7%. The mass ratio of 1/2.554 = 0.392 is close to that of Yang & Liu (2001)'s result of 0.402, but the fill-factors of the two results are significantly different (18.7% ± 1.2% and 4.7% ± 5.0%, respectively). The reasons are the system's period decrease, the model's unreliability in the sense of probable errors, and the substantial changes in the system over a decade. First, a long-term period decrease cannot cause such large variations. The timescale for this to happen is at least several million years, which is much longer than a decade. So it is impossible to see clear changes in a systematic fashion in so short a time. Second, although the models are simple, prevailing practice tells us that the errors should not be so large. The third reason is the main one: the appearance of the cool spot strongly affects the results of the photometric parameters. Two different light curves should have two different photometric solutions. Yang & Liu's (2001) light curves contain a star spot, which impacts on the solutions of the internal physical parameters. Moreover, the error in their fill-factor is 5%, indicating that the relative error is 106.3%, much bigger than our 6.3%. The disappearance of the cool spots enables the light curves to restore their original appearance. Hence, we think our results uncover the physical parameters and are more reliable than Yang and Liu's.

Although no spectroscopic elements have been published for this binary system, their absolute parameters can be estimated. Assuming that the primary components are normal main-sequence stars, we can estimate their masses as 0.36 and 0.92 M_☉, corresponding to the results of the W-D code. Combined with the system's photometric solutions and period, we then estimate its absolute parameters (R₁ = 0.84 R_☉, R₂ = 1.27 R_☉; L₁ = 0.947 L_☉, L₂ = 2.043 L_☉). The evolutionary status of the components can be inferred from their mean densities (see, for example, Mochnacki 1981, 1984). Using the following formulae (Kopal 1959),

$$\begin{equation} \overline{\rho _1}=\frac{0.079}{V_1(1+q)P^2},\quad \overline{\rho _2}=\frac{0.079q}{V_2(1+q)P^2}, \end{equation} \tag{ 5 }$$

where V_1,2 are the volumes of the components using the separation A as the unit of length, we determine the mean densities (ρ₁, ρ₂) of the two components to be 1.112 ρ_☉ and 0.809 ρ_☉. The corresponding logarithms of the mean densities are 0.046 and −0.092, which are lower than those of zero-age main sequence (ZAMS) stars of the same spectral type, especially for the less massive components. This indicates that the components in both systems have already moved away from the ZAMS line to a greater or lesser extent.

The observed period variation of V396 Mon is very complex. Based on all available photoelectric and CCD eclipse times, the period changes of the contact binary star were discussed in the previous section. First, the orbital period was revised to be 0.39634359 days using the 118 visual, CCD, and photoelectric timings, listed in Table 6. Second, the general (O − C) trend revealed a long-term period decrease at a rate of dP/dt = −8.57 × 10⁻⁸ d yr⁻¹. In addition, a period oscillation (A₃ ∼ 00160) was discovered superimposed on the period decrease. If this period decrease is due to a conservative mass transfer from the more massive component to the less massive one, then with the absolute parameters derived in the present paper and using the well-known equation,

$$\begin{equation} \frac{\dot{P}}{P}=3\frac{\dot{M_2}}{M_2}\left(\frac{M_2}{M_1}-1\right), \end{equation} \tag{ 6 }$$

the mass transfer rate is estimated to be dM₂/dt = −4.26 × 10⁻⁸ M_☉ yr⁻¹. The negative sign implies that the more massive component M₂ is losing its mass. The timescale of mass transfer is $\tau \sim {M_2/\dot{M_2}}\sim 2.2\times {10^{7}}$ yr which is four times the thermal timescale of the more massive component. However, having considered the strong magnetic activity of the system (Gu 2004 and our discussions above), the long-term period decrease can be reasonably explained as the results of an enhanced stellar wind and angular momentum loss. Table 8 lists some contact binary systems that exhibit long-term period decreases.

We now address the short-term period oscillation with T₃ = 42.4 yr, A₃ = 0.0160 days. There are two main ways to interpret these observations: the Applegate mechanism and the light-time effect.

The Applegate mechanism says that the cyclic period change is caused by magnetic activity-driven variations in the quadrupole moment of solar-type components (e.g., Applegate 1992; Lanza et al. 1998). According to the formula (Lanza & Rodonò 2002; Rovithis-Livaniou et al. 2000),

$$\begin{equation} \frac{{\Delta }P}{P}=-9\frac{{\Delta }Q}{Ma^2}, \end{equation} \tag{ 7 }$$

$$\begin{equation} {\Delta }P=\sqrt{[1-{\rm {cos}}(2{\pi }P/P_3)]}\times A_3, \end{equation} \tag{ 8 }$$

we obtain the required quadrupole moments as ΔQ₁ = 1.41 × 10⁴⁹ and ΔQ₂ = 3.61 × 10⁴⁹ g cm². However, for active close binary stars, typical values range from 10⁵¹ to 10⁵² g cm². Therefore, the Applegate mechanism probably does not describe the short-term period changes in V396 Mon.

The most likely explanation of the period oscillation is that a light-time effect of a tertiary component causes this phenomenon. Using

$$\begin{equation} f(m)=\frac{4\pi ^{2}}{{\it G}T_3^{2}}\times (a_{12}^{\prime }\sin {i}^{\prime })^{3}, \end{equation} \tag{ 9 }$$

where a'₁₂sin i' = A₃ × c (where c is the speed of light), the mass function from the tertiary component can be computed using

$$\begin{equation} f(m)=\frac{(M_{3}\sin {i^{\prime }})^{3}}{(M_{1}+M_{2}+M_{3})^{2}}. \end{equation} \tag{ 10 }$$

Assuming the third body and the central system are coplanar, and taking the estimated physical parameters given in the first paragraph of this section, the mass and the orbital radius of the suspect third companion can be estimated. The smallest mass of a tertiary companion should be m₃ = 0.31 M_☉ with a septation of 14.2 AU. The luminosity of such a small M main-sequence star is only 0.026 L_☉, 0.87% of the whole system. This could explain why we did not find the third light in the W-D solutions.

In summary, V396 Mon is a middle mass ratio shallow contact binary. Although previous light curves showed evidence of spot activity, our current observations indicate a lack of any light-curve asymmetries. The periodic variation of its period changes is most likely caused by a third body, probably a small M star. To determine more accurately the absolute parameters of V396 Mon, a precise radial velocity curve must be obtained. If we can determine that its true mass ratio is indeed close to 0.4 (the 0.4 mass ratio argument of Qian), this binary system will become a particularly important system and will justify more intensive research.

This work is partly supported by Yunnan Natural Science Foundation (2008CD157), Chinese Natural Science Foundation (No. 10878012, 10973037, and No. 10903026), The Ministry of Science and Technology of the People's Republic of China through grant 2007CB815406, and The Chinese Academy of Sciences grant No. O8ZKY11001. New observations of the system were obtained with the 1 m telescope at Yunnan Observatory and the 85 cm telescope at Xinglong observation base. We are especially indebted to the anonymous referee who provided useful comments and helpful suggestions, which helped us to greatly improve the paper.