First photometric investigation of OGLE-SMC-ECL-2063: A low-metallicity massive contact binary in the SMC

Abstract

1 Introduction

The binary system OGLE-SMC-ECL-2063 has galactic coordinates of |$l = {302{_{.}^{\circ}}96}$| and |$b = -{43{_{.}^{\circ}}74}$|⁠. It was discovered by The Optical Gravitational Lensing Experiment (OGLE, Udalski et al. 1998). This system was classified as an early B-type system (Wyrzykowski et al. 2004) and as a contact eclipsing binary (Pawlak et al. 2016). In the present paper, we analyze OGLE light curves and investigate the period variation using all available data. The structure and evolutionary state of OGLE-SMC-ECL-2063 are discussed using the result of photometric solutions and the period change.

OGLE used the 1.3 m Warsaw University Telescope at Las Campanas Observatory in Chile to observe the Milky Way and the Small and Large Magellanic Clouds (SMC and LMC), and discovered thousands of eclipsing binary stars. There are more than 48000 eclipsing and ellipsoidal binary systems in Magellanic System to be found in OGLE collections (Pawlak et al. 2016). Two optical photometric bands, Johnson V and Cousins I bands, are contained by the observations; the I band is the default, with about 15 times more epochs than the V band. These light curves are confirmed by experts and divided into different types such as contact or semi-detached binary stars. Among all 48605 eclipsing binaries, only 628 are classified as contact binaries while 131 of them are in the SMC. This amount is obviously much less than the true amount of those in the SMC, and this is one of the reasons why binaries in the Milky Way are studied well while those in the SMC are rarely studied.

The period of OGLE-SMC-ECL-2063 is |${0{_{.}^{\circ}}6317643}$| and its V − I color index is −0.199 mag(not fixed). These show that OGLE-SMC-ECL-2063 is an early-type contact binary which might have a big fill-out factor due to its short period. Some other examples include V758 Cen (Lipari & Sistero 1985), V701 Sco (Bell & Malcolm 1987), V593 Cen (Lapasset et al. 1988), RZ Pyx (Zhao et al. 2018a), and BH Cen (Zhao et al. 2018b). Contact binaries are quite important in star evolution: for both components of a contact binary have filled its critical Roche lobe which makes it completely different from single stars. The evolution of both components is influenced by each other due to their interaction. Research shows that over |$70\%$| of all massive stars will exchange mass with their companion (Sana et al. 2012). We expect OGLE-SMC-ECL-2063 to be a system with great interaction which may lead to an explosion in the end.

The formation of massive binary stars is still unsolved, while the SMC gives us a condition to study the difference between the binaries in different natural conditions, because the value of Fe/H in the SMC is smaller than that in the Milky Way. In this research, we analyzed the light curves with the Wilson–Devinney (WD) method and studied the O − C curve using data over a 19-year period. We obtain the physical parameters of OGLE-SMC-ECL-2063 and a third body that may exist. We hope this research, and further research of binaries in the SMC, could give us more and more knowledge about the formation of massive binaries.

2 Observations

Now we have I- and V-band light curves from OGLE II, III, and IV, and BVR light curves from the 1 m telescope at the South African Astronomical Observatory. We only use the I-band data from OGLE since the V-band data are not sufficient for analysis. We plotted the light curves using the phase given by Pawlak et al. (2016). The 1 m telescope light curves are shown in figure 1a. In differential photometry, Var-Com means the magnitude of the variable star (OGLE-SMC-ECL-2063) minus the magnitude of the comparison star, and Com-Check is the comparison star minus the check star. Figure 1b is the light curve given by OGLE IV. The light curves show typical eclipsing W Ursae Majoris (EW)-type variation. Both maxima and minima are almost equal.

Fig. 1.

(a) Light curves observed at the South African Astronomical Observatory; different symbols represent different observation days. (b) Light curves collected from the OGLE IV; the open triangles and circles represent the V and I_C bands.

Open in new tabDownload slide

3 Orbital period investigation of OGLE-SMC-ECL-2063

As we know, the research of the period variation of a binary system is an important part of studying its evolutionary states and dynamic evolution process. We can get more information about the period changes from the O − C (observational times of light minimum − calculated times of light minimum) curves directly. Using the light curves from the 1 m telescope, we derived the minima times of OGLE-SMC-ECL-2063, but we cannot use the OGLE data directly since there are fewer than 10 data points in one period, as shown in figure 2, which is not enough for parabola fitting method. To solve this problem we have to take the average of the light curve. We cut the whole long time light curve into several sectors, usually around 300 days per sector, to make sure there are enough data points for fitting, usually more than 100 points in one sector. Then we convert the HJD to the phase so we can derive the minimum by the parabola fitting method, just as shown in figure 2. As a result, using the delta phase we can get an average minimum time of the sector. All eclipsing times and their errors are listed in table 1. These data can be very helpful in analyzing the orbital period changes and studying the mass transfer. This kind of method has also been used by Li et al. (2022b, 2022c) to calculate many minima.

Fig. 2.

Eclipse time of OGLE-SMC-ECL-2063 obtained from OGLE IV. The upper panel shows the time series and the lower panel shows the orbital phase light curve with the fitting parabola around the time of minimum.

Open in new tabDownload slide

Fig. 3.

O − C diagrams of OGLE-SMC-ECL-2063 fitted with an eccentric orbit and a circular orbit. The dot-dashed lines are parabolic changes. The solid lines refer to upward parabolic plus cyclic variation in the upper panels, and to the cyclic variation alone in the middle panels.

Open in new tabDownload slide

4 Light-curve analysis

The light curves of OGLE-SMC-ECL-2063 from OGLE and the 1 m telescope were analyzed separately with the software program Wilson and Devinney (2013 version) (Wilson & Devinney 1971; Wilson 1990, 2012; van Hamme & Wilson 2003; Wilson & Wyithe 2003). We derived the V − I color index of the OGLE data and the reddening map of Magellanic clouds (Skowron et al. 2021) as V − I = −0.221 mag, which means the primary component is a B5 type star. From Cox (2000) we can estimate that the effective temperature of the primary component is T₁ = 15200 K. Also, the gravity darkening coefficients were given as 1.0 for both stars (Lucy 1967) and the bolometric albedo as 1.0 for both stars (Ruciński 1969). Bolometric and bandpass square-root limb-darkening parameters are given by van Hamme (1993). Mode 3 (the contact mode) was chosen to approximate the contact configuration. The adjustable parameters include the inclination i, the mean temperature of star 2 T₂, the dimensionless potentials ω₁ and ω₂ of each component, the mass ratio q, and the monochromatic luminosity of the primary component.

We use the q-search method (Zhang & Qian 2013; Zhou & Soonthornthum 2019; Liu et al. 2020; Li et al. 2022a) to determine the mass ratio of the binary and constrain the temperature of the primary star. The result of temperature constraint is shown in figure 4. We get T₁ = 14000 with the lowest residual, so this should be close to the true temperature, and we get our final result with this T₁. For each q, the calculation starts at mode 3. Different light curves, the OGLE IV and the 1 m telescope data, give the same result that the minimum of the binary is around q = 0.900. The final solution and the observed light curves were plotted in figure 5. Since we found that a period oscillation may exist in OGLE-SMC-ECL-2063, according to the orbital period investigation in section 3, we made l₃ an adjustable parameter to add a third light to the calculation. The result of the q-search is shown in figure 6; the value of the parameters are shown in table 3; the morphology of the system is shown in figure 7. In the table, the radii are shown in the form of fractions of the semimajor axis, R₁ and R₂ refer to the equivalent volume radii, and the fill-out factor f refers to the degree of contact. The degree of contact is f = (Ω_in − Ω_star)/(Ω_in − Ω_out), in which Ω_star refers to the modified dimensionless potential of the star surface, while Ω_in and Ω_out means the dimensionless potential of the inner and outer Roche lobes, respectively.

Fig. 4.

Residuals in different temperatures.

Open in new tabDownload slide

Fig. 5.

(a) Theoretical (solid line) and observational (open symbols) light curves obtained from the 1 m telescope (offset for B, V, and R from top to bottom). (b) I band from the OGLE IV. The solid line represents the theoretical light curve. The lower panels are the corresponding residuals. (c) OGLE V-band (blue triangles) compared with the WD result of the 1 m telescope V-band (solid line).

Open in new tabDownload slide

Fig. 6.

q-search of OGLE-SMC-ECL-2063. The circles represent the residuals of 1 m light curves; the squares represent that of the light curve from OGLE and its values have been subtracted by 0.000415.

Open in new tabDownload slide

Fig. 7.

Morphology of OGLE-SMC-ECL-2063.

Open in new tabDownload slide

5 Results and discussion

We cannot determine the absolute parameters of the system directly since no spectroscopic elements have been published. We can estimate the primary mass to be 5.23 M_⊙ corresponding to its effective temperature assuming that it is a normal main-sequence star (Cox 2000). Since the mass ratio is 0.900, we can derive that the mass secondary component is 4.71 M_⊙.

Fig. 8.

Observation field of OGLE.

Open in new tabDownload slide

Acknowledgements

This work is partly supported by the Chinese Natural Science Foundation (Nos. 11933008, 11873017, 11903076) and the basic research project of Yunnan Province (Grant Nos. 202201AT070092, 202001AT070051). This study is based on data collected with the South Africa 1 m telescope at the South African Astronomical Observatory. This paper makes use of online data 〈https://cdsarc.cds.unistra.fr/viz-bin/cat/J/AcA/66/421〉 provided by Pawlak et al., and the authors thank Pawlak et al. for providing an opportunity to study the evolution of massive binaries in the SMC. We would like to thank the OGLE team for making all of their databases easily publicly available.

References