THE FIRST MULTI-COLOR PHOTOMETRIC STUDY OF THE NEAR-CONTACT BINARY AS SERPENTIS

Near-contact binaries (NCBs) have been defined by Shaw (1994) as systems with periods of less than one day, showing tide interaction and facing surface less than 0.1 orbital radius apart. This subclass of close binaries is interesting due to its marginal characteristic. They can be intermediate objects between the stage of detached or semi-detached binary systems and that of contact binary systems. In the 4th edition of the General Catalogue of Variable Stars (GCVS) (Kholopov et al. 1987), AS Ser is classified as a short-period EB-type eclipsing binary system of the F2 spectral class. It was also listed in the table of Shaw (1994) as a near-contact system. We thus list it as one of our observed targets to study near-contact binaries.

The light variation of the eclipsing binary system AS Ser was discovered by Hoffmeister (1935). Since then, neither complete light curves nor spectroscopic data for this system have been published in the literature; only some times of light minimum are available. In 2005 and in 2008, we observed this neglected system and obtained complete CCD light curves in the B, V, and R bands, with the 1.0 m Cassegrain reflecting telescope at the Yunnan Observatory in China. In order to understand the geometrical structure and evolutionary state of this eclipsing binary system, the light curves are analyzed with the Wilson–Devinney (WD) synthetic method. Combining the photometric solutions with the period change, the structure and the probable evolutionary state of AS Ser are discussed.

AS Ser (α₂₀₀₀ = 15:38:49.01; δ₂₀₀₀ = 02:15:30.5) was observed in the B, V, and R bands on 2005 April 9, 23, and May 4 with the PI1024 TKB CCD photometric system attached to the 1.0 m Cassegrain reflecting telescope at the Yunnan Observatory in China. Its effective field of view at the Cassegrain focus was about 6.5 × 6.5 arcmin². During the observation, the integration time for each image was 120 s and B, V, and R filters close to the Johnson UBVRI system were used (Yang & Li 1999). Image reductions were done using the IRAF package, and the observed data in three bands are listed in Tables 1–3 and plotted in Figure 1. Comparison (α₂₀₀₀ = 15:38:41.35, δ₂₀₀₀ = 02:13:56.9) and check stars (α₂₀₀₀ = 15:38:51.98, δ₂₀₀₀ = 02:13:53.1) were chosen near the target. As one can see from Figure 1, AS Ser displays total eclipses. The shape of its light curve is typically a β Lyr type with an unequal height at two maxima (maximum II slightly brighter than maximum I), i.e., the O'Connell effect. Furthermore, a deeper minimum II in the R band than in the other two bands can be clearly seen in Figure 1. All these characteristics imply that this system has a strong tidal interaction and its secondary component may be a late-type star due to its radiation concentrating on longer wavebands. The differences in the light levels in the three bands are shown in Table 4. To investigate the period variation of this target, we again observed it using the same photometric system and telescope on 2008 January 4 and obtained an R-band light epoch of 2454,470.4391(±0.0002).

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Table 4. The Differences in Light Levels in the Light Curves of AS Ser

	ΔB	ΔV	ΔR
Max. I−Max. II(m0.25 − m0.75)	−0 036	−0 016	−0 016
Min. I−Min. II(m0.0 − m0.5)	0.509	0.425	0.367
Min. I−Max. I	0.670	0.589	0.566
Min. II−Max. II	0.125	0.149	0.183

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The times of light minimum of AS Ser have been compiled by Kreiner et al. (2000) and some of them, published in Beobachter der Schweizerischen Astronomischen Gesellschaft (BBSAG) Bulletins, have been collected at the Eclipsing Minimum Database (available at http://nac.oa.uj.pl/ktt/ktt.html). Recently, six new photoelectric and CCD observations were obtained by Agerer & Hüebscher (2002), Nelson (2005), Dvorak (2006), and ourselves. All available photographic (ph), visual (v), photoelectric (pe), and CCD minima times are listed in Table 5. With the following ephemeris given by Kreiner et al. (2000):

$$\begin{equation} {\rm Min. I}={\rm HJD}2452500.1345+0^{\rm d}.4662339\times {E}, \end{equation} \tag{ 1 }$$

the O − C values for those times are computed and listed in Columns 5 and 12 of Table 5. The corresponding O − C curve is plotted in the upper panel of Figure 2, where the open circles stand for photographic and visual observational data and the dots for photoelectric and CCD observations.

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We take a weight of 1 for photographic and visual observational data and 8 for the photoelectric and CCD observational data. Then, by means of the least-squares method, the following ephemeris is obtained:

$$\begin{equation} {\rm Min. I}={\rm HJD}2454470.4406+0^{\rm d}.4662346(1)\times {E}, \end{equation} \tag{ 2 }$$

which gives a more precise period and can be used to predict the epochs of light minimum. The linear fitting curve (dashed line) is plotted in the upper panel of Figure 2 and the residuals (which are listed in Columns 6 and 13 of Table 5) of this fit are shown in the bottom panel. From the bottom panel, one can see that the photoelectric and CCD residuals display a trend of period variation. Thus, we fit these residuals with the least-squares method and derive the following equation:

$$\begin{eqnarray} (O-C)_{1}&=&0.0010(\pm 0.0001)+0^{\rm d}.0049(\pm 0.0009) \sin [0.^{\circ }039\nonumber \\ &&\times {E}-47.^{\circ }5(\pm 10.^{\circ }5)]. \end{eqnarray} \tag{ 3 }$$

The sinusoidal term reveals that a periodic oscillation with an amplitude of 0.0049  days and a period of 11.8  years may exist. The corresponding fitting curve is shown in the bottom panel of Figure 2.

CCD observations, 91 in the B band, 95 in the V band, and 93 in the R band for AS Ser, are analyzed with the latest version of the WD program (Wilson & Devinney 1971; Wilson 1979, 1990, 1994; Wilson & Van Hamme 2003).

According to the spectral type of F2 for AS Ser (from GCVS, Kholopov et al. 1987), we assume an effective temperature of T₁ = 7 000 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 are used, corresponding to the convective envelope of this binary system. Bolometric and bandpass square-root limb-darkening parameters are taken from the table of Van Hamme (1993). The adjustable parameters are the inclination, i, the mean temperature of star 2, T₂, the monochromatic luminosities of star 1, L_1B, L_1V, and L_1R, and the dimensionless potentials of star 1 and star 2, Ω₁ and Ω₂.

To get a reliable mass ratio, q, the solutions for several assumed values of the mass ratio q (q = 0.25, 0.3, 0.35, 0.4, 0.5, 0.6) are obtained. For each q, the calculation starts at mode 2 (the detached mode). The sums of weighted square deviations ΣW_i(O − C)²_i for all the assumed values of q are shown in the upper panel of Figure 3. There is a nearly flat segment on the bottom from q = 0.3–0.35, which makes it difficult to find a proper q. We thus add the inclination, i, as a second dimension for the search. For several fixed i (i = 80°, 81°, 82°, 83°, 84°, 85°, 86°, 87°, 89°, 90°, which correspond to the total eclipse of AS Ser), the minimum Σ is achieved at q = 0.31 and i = 86°, which can be clearly seen in the lower panel of Figure 3. Therefore, we perform a differential correction so that it converges by choosing q = 0.31 and i = 86° as the initial values and by making q and i adjustable parameters. We find that it could converge to either of mode 4 (semi-detached mode with lobe filling primary, SD1) and mode 5 (semi-detached mode with lobe filling secondary, SD2). Actually, the two components reached their critical Roche lobes with the uncertainties of Ω₁ (Columns 3 and 4) and Ω₂ (Column 2) taken into account. This implies the marginal characteristic of AS Ser. The derived photometric parameters are listed in Table 6. In Table 6, Column 3 is the parameters with the minimum value of Σ without a spot; we will take them as our final solutions for further calculations. The solid lines in Figure 4 show the theoretical light curves computed with the parameters of Column 3.

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It is obvious that the observed light curves are asymmetric with maximum I slightly brighter than maximum II. This phenomenon of unequal heights at two maxima in the light curve, i.e., the O'Connell effect, exists generally in marginal contact binaries, such as KQ Gem (Hilditch et al. 1998), V432 Per (Yang & Liu 2002), and CN And (Çiçek et al. 2005). To interpret the observed asymmetry, we have therefore used an SD2 model with a cool spot on the secondary component, consistent with its late-type nature (effective temperature ∼4565 K). After many runs, we obtained the solution reported in the fourth column of Table 6. The spot parameters are latitude, φ, longitude, θ, angular radius, r_s, and the temperature factor, T_s/T_* (where T_s is the temperature of the spot and T_* is the local effective temperature of the adjacent photosphere). The corresponding synthetic light curves and the configuration of AS Ser with a spot are shown in Figure 4. Clearly, the addition of a spot gives a better fit to the observed light curves though it still has some deviation. Considering the marginal characteristic, we tried adding a hot spot close to the neck of the binary but failed to reach converged solutions.

According to the orbital period investigation in Section 3, we suspected that a period oscillation may exist in AS Ser. Therefore, we tried adding a third light (i.e., we made l₃ an adjustable parameter) to the calculation. The corresponding solutions are listed in Columns 5 and 6 and displayed in Figure 5 which show an improvement in the fitting of the light curves. As Maceroni & van't Veer (1993) pointed out that the spot determination by photometry alone is unreliable due to the uniqueness of the spotted solutions, the parameters with a spot shown in Table 6 are tentative. In the following analyses, we will adopt the parameters without spots for calculation and presentation.

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Since no spectroscopic elements have been published, the absolute parameters of the system cannot be determined directly. Assuming that the primary component is a normal, main-sequence star, we can estimate its mass to be 1.5M_☉ corresponding to the spectral type F2 (Cox 2000). Combining the photometric solutions and the period, we can estimate the absolute parameters for this system, as reported in Table 7. One can see in Table 7 that the deduced luminosity and radius of the primary component agree well with those of main-sequence stars of the same mass, while the secondary component is overluminous and oversized compared with same-mass main-sequence stars. According to its mass, the secondary component may be an M0 star, which is consistent with the shape of the light curves discussed in Section 2.

With all available times of light minimum, the O − C residuals of AS Ser were analyzed and a new ephemeris was derived which gives a more precise period. The photoelectric and CCD times of light minimum show that the orbital period of the system oscillates with an amplitude of 0.0049 days and a period T = 11.8 yr. The oscillating characteristic of the O − C residuals may be the result of the light-time effect due to an additional body or might result from magnetic activity cycles in the two components. If the light-time effect is the reason, assuming that the orbit of the presumed third body is circular, we can obtain the mass function for the third body f(m) = 0.00439M_☉ using the following equation:

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

where a₁₂ is the distance between the close pair and the center of mass with respect to the third body. With the estimated absolute parameters listed in Table 7, we thus estimate the minimum mass of the additional body to be M₃ = 0.28M_☉ and the corresponding orbital radius around a₃ = 5.93 AU. Supposing that the third body is a main-sequence star, this mass corresponds to an M5 V star with an effective temperature about 3200 K and the absolute bolometric magnitude about 8^m fainter than that of the primary component (Cox 2000). Such a large difference makes the third body difficult to detect. The contribution of the tertiary component to the total light in the B, V, and R bands would roughly be 0.42 %, 1.08 %, 1.99 %, respectively, which are similar to the values derived from the WD code. This indicates that the orbital inclination of the third body should be close to 90°. Additionally, the luminosity contribution of the third light increases from the shorter wavelength (B) to the longer wavelength (R), which is consistent with the late-type property of the third body suggested by the period investigation.

As pointed by Pribulla & Rucinski (2006) and D'Angelo et al. (2006), most overcontact binaries exist in multiple systems, so the additional bodies may play an important role in the formation of overcontact binaries by transfer of angular momentum during the Kozai oscillation. NCBs are important transition targets between tidal-locked detached binary systems and W Ursae Major (W UMa)-type overcontact binaries. They have many common characteristics, such as continuum light variation, the O'Connell effect, and the existence of tertiary components. Some NCBs with a possible additional body are listed in Table 8 together with our newly derived one, AS Ser. If this is the case, the angular momenta of these systems may be eliminated due to the tertiary bodies and they will evolve into overcontact binaries in the future.

On the other hand, AS Ser is a short-period marginal contact binary with components possibly having a deep convection zone according to their spectral types F2 and M0. The rotational velocity is about 55 times faster than that of the Sun. Therefore, the high rotational velocity and deep convection zone of this system may lead to magnetic activity cycles (Applegate 1992; Lanza et al. 1998; Lanza & Rodonò 1999) in the two components, which is likely to be the reason for the period oscillation. However, the periodic oscillation found in the present study does not cover a complete period. It needs more precise times of light minimum to prove it.

Our photometric solutions indicate that AS Ser is a near-contact binary system with both components filling more than 99% of their Roche lobe. In other words, this system can be considered as a marginal contact binary within parameter uncertainties. The situation of AS Ser resembles those of KQ Gem (Hilditch et al. 1998), CN And (Çiçek et al. 2005), BL And, GW Tau (Zhu & Qian 2006), and UU Lyn (Zhu et al. 2007). They are important targets which lie in the rare phase predicted by the thermal relaxation oscillation (TRO) theory (e.g., Lucy 1976; Flannery 1976; Robertson & Eggleton 1977; Lucy & Wilson 1979). According to the TRO theory, W UMa systems must undergo oscillations around the state of marginal contact. Each oscillation comprises a contact phase followed by a semi-detached phase. When a system exhibits β Lyrae-type light-variation departures from EW light curves, a semi-detached phase with the more massive star filling the Roche lobe followed by a marginal-contact phase with poor thermal contact is to be expected. Therefore, AS Ser may be on the broken stage or at the beginning of the overcontact phase now, and it is a progenitor of a W UMa-type overcontact binary.

This work was partly supported by the Chinese Academy of Sciences (Grant No O8ZKY11001), Chinese Nature Science Foundation (Grant Nos 10433030 10573013, and 10778707), The National Key Fundamental Research Project through Grant 2007CB815406, and Yunnan Natural Science Foundation (Grant No. 2005A0059M), and has made use of the Eclipsing Binaries Minimum Database (available at http://www.oa.uj.edu.pl/ktt/krttk_dn.html). We are indebted to the many observers, amateur and professional, who obtained the wealth of data on this eclipsing binary system. We have used data observed with the 1.0 m telescope at the Yunnan Observatory.