BVR_cI_c Observations, Third-body Orbital Study, and Analysis of the UV Leo-type, Pre-W UMA Binary V642 Virginis

In this second study of a UV-Leo-type binary, begun with V1123 Persei (Samec et al. 2020), we note that polar spots flatten out the tops of the light curves, causing them to rise toward one of the minima as seen in the All-Sky Automated Survey for Supernovae (ASAS-SN) curves (Figure 2) and to a lesser degree in Hoffman's curves shown in Figure 1.

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It was identified in a study of orbital period changes that only 2% of 13,927 eclipsing binary candidates had sinusoidal period changes (Lohr et al. 2015). The binary was listed in the 81st Name List of Variable Stars, Part I (Kazarovets et al. 2015). The International Variable Star Index (AAVSO) gives a J–K = 0.75, a B–V of 1.08, and a V magnitude range of 13.06–13.89.

An earlier study of BVRI light curves was published of NSVS 10441882 (V642 Vir; Bin et al. 2019; this paper was found after we had completed our analysis so their results may be compared to the values given here.) They identified it as well-detached eclipsing binaries with inclinations of 85° and mass ratios (from a q-search) of q = 0.94. Their sparce O − C diagram gave a circular third-body orbital variation with a 17-year period with an amplitude of 0.0035 days. This gave a mass of the third body of at least 0.12 M_⊙.

The systems distance is 185 ± 17 pc, as determined from Gaia DR2. In addition, observations of the system are continuously being undertaken by the Super Nova Search Program of Ohio State (ASAS; Shappee et al. 2014; Kochanek et al. 2017). See Figure 2. Note that the variable maxima following the secondary eclipse points to the presence of polar spot activity. This increase in maxima occurs after 2014. In addition, our curves do not show the rising curves before the secondary eclipse but are nearly level from phase 0.25–0.4. The ephemeris given at the site (2020) is

$$\begin{eqnarray}&&\mathrm{HJD}=2457846.8578{\rm{d}}+0.5166446\,\times \,E.\end{eqnarray} \tag{ 1 }$$

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The initial presentation of this study was presented at the American Astronomical Society Meeting 237 (Chamberlain et al. 2021).

Our 2020 Johnson–Cousins BVR_cI_c light curves were taken on 2020 April 16, 17; May 23, 24; and June 7 at the Dark Sky Observatory in North Carolina, USA, with the 0.81 m reflector of Appalachian State University at Philips Gap, North Carolina, USA, with a thermoelectrically cooled (−25.0°C to −32.5°C) 2 K × 2 K Apogee Alta by D. Caton with standard B,V,R_c , and I_c filters. Individual observations included 384 in B, 402 in V, 406 in R_c, and 401 in I_c. The probable error of a single observation was about 0.01 mag in ΔB, 6 mmag in ΔV and ΔI_c, and 0.015 mag in ΔR_c. The observations are given in Table 1. Table 2 gives information on the photometric targets. The variable (denoted as V), has a position of (α(2000) = 04^h01^m 58.83, δ(2000) = +13°49'320) ICRS], J–K ≈ 0.75, a parallax of 2.53 ± 0.03 mas, and a distance of 185 ± 17 pc as determined from Gaia DR2. The comparison star was denoted as C, and has a position of [α(2000) =13^h29^m564867, ICRS]. The check star (denoted CH) has a position of [α(2000) = 13^h30^m 15.0184986385 s, δ(2000) =13^d 55' 06545339063, ICRS], δ(2000) = +13^d56'11900 ICRS. The finder chart is given as Figure 5 with the variable star (V), comparison star (C), and check star (CH) shown.

The first nights the C-CH values were variable so we changed our observations from V-C to V-CH. This resulted in larger than normal Δ(B–V) values. Rather, V-CH values stayed constant throughout the observing run with a precision of about 1% or better. Exposure times varied from 120 s in B, 40 s in V, and 20 s in R_c and I_c depending on the count needed to obtain 1% photometry. Figures 3 and 4 show the light curves taken from 2020 April 17 and May 24.

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Four times of minimum light were determined from our present observations, which include two primary eclipses and two secondary eclipses: HJD Min I = 2458955.57893 ± 0.00039, 2458955.83742 ± 0.00023 and HJD Min II =2458956.61203 ± 0.00007, 2458955.87052 ± 0.00041. In addition, 12 TESS (Vanderspek 2019) timings were calculated, and four ASAS (Super Nova Search Program of Ohio State). The data was in mid-point solar system barycentric Julian Dates. Also, some low light timings were determined and were given low or zero weights. Since 2008, the system was also observed during 63 nights at the Ondřejov Observatory, Czech Republic. The Mayer 0.65 m (f/3.6) reflecting telescope with the G2-3200 CCD camera and photometric R filter was used. A standard calibration (dark frame, flat field) was applied to the obtained CCD frames. Time series were constructed by computing the magnitude difference between the variable and nearby comparison and check stars. The new times of primary minima and their errors were generally determined by fitting the light curve by Gaussians or polynomials of the third or fourth order using the least-squares method. These timings, determined by co-authors M.W., H.K., P.Z., and K.H., were included along with others from the literature in our period study. A total of 88 timings covering nearly 22 years were used in the period study. From these we determined the linear and quadratic ephemerides:

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{JD}\,\mathrm{HELMINI} & = & 2451274.61613(93)d\\ & & +\ 0.516644892(75)\times E,\end{array}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{JD}\,\mathrm{HELMINI} & = & 2451274.63059(46)d+\\ & & 0.516641337(91)d\times E\\ & & +\ 0.000000000185(5)\times {E}^{2}.\end{array}\end{eqnarray} \tag{ 3 }$$

However, an oscillation was discovered in the linear residuals. This was used to determine that a third body is orbiting the binary. The residuals and the orbital fit are displayed in Figure 6. The initial residuals were calculated from JD HELMIN I = 2451274.6257 d+0.516644 XE (Wolf et al. 2020).

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The quadratic fit is displayed in Figure 7.

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The results of the eccentric calculation of the orbit of the third body (e = 0.41) yield light time residuals with an amplitude of 0.0051 days and an orbital period of 20.07 yr (see Figure 6.) This results in a mass ratio of 0.125 for the third body compared to the mass of the binary. Table 3 contains the O − C residuals for the three calculations: the orbital, linear and quadratic ephemerides. For a calculation of the light-time effect, the suitable equations presented by Mayer (1990) were used. The phased light curves using the Equation (1) follow as Figures 8 and 9.

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Mean light-curve characteristics (averages at quadrature and critical differences) are given in Table 4. The curves are of good photometric precision, averaging about 1% precision. We summarize them here. The amplitudes of the light curves vary from 0.80–1.05 mag in I to B. The curves reach a maximum at 0.25 and stay fairly level until phase ∼0.4, then they fall into eclipse. The curves then go back to about the same magnitude at phase ∼0.6 and then decrease ∼0.1 mag and drop into the primary eclipse. The differences in the depths of the minima are large, 0.253–0.525 mag in I to B, indicating noncontact light curves. The B–V color curves fall about 0.07 mag at phase 0.0, however they rise about 0.08 mag at phase 0.5, which indicates that the primary component is underfilling its Roche lobe. In normal light curves, this indicates that the primary component is not filling its Roche Lobe. Indeed, the synthetic light-curve solution indicates a well-detached binary.

The 2MASS, J–K = 0.749 ± 0.046 and the APASS B–V = 1.085, E(B–V):0.022 for the binary. The temperature for such a system is ∼4250K. Gaia EDR3 gives a parallax of 5.467 ± 0.016 mas (for a distance of 183 ± 1 pc).

The B, V, R_c, and I_c curves were pre-modeled with Binary Maker 3.0 (Bradstreet & Steelman 2002) and the fits were determined in all of the filter bands. The curves are at maximum before and just after eclipse and then fall about a tenth of a magnitude before they dip into secondary eclipse. David Bradstreet advised us for V1023 Per (see Samec et al. 2020) that this kind of curve happens when there is a prominent polar spot. Indeed, this inclusion resulted in a good fit to the curves. Another spot (a hot one) was used to clean up the asymmetries. Other than the spots, the result of the best fit was that of a well-detached eclipsing binary with fill outs of 75% and 86%, respectively, and a mass ratio of 0.88 for our hand modeling. The most important attribute of the model included a large, 64° polar dark spot (R.G.S. added an 18° equatorial hot spot). The polar dark spot was suggested by David Bradstreet (2020, private communication) when we modeled V1023 Per. The parameters were then averaged and put into a four-color simultaneous light-curve calculation using the 2016 Wilson–Devinney Program (W–D; Wilson & Devinney 1971; Wilson 1979, 1990, 1994, 2008, 2012, Van Hamme & Wilson1998; Van Hamme & Wilson 2007; Wilson et al. 2010; Wilson & Van Hamme 2014). The solution was computed in Mode 2 (detached). The third light was run for at least 25 iterations leading to negative nonphysical values (see later statement) so it was not explored further. The calculation converged to a firm solution. Both spots varied, but persisted. The reason for using Mode 2 was to allow the computation to determine the configuration. A q-search was calculated since the eclipse was not total. The best WD solution was at q = 0.954. Convective parameters, g = 0.32 and A = 0.5 were used throughout. The plot of the q-search versus the residual is given in Figure 10. However, it must be noted that, as our referee stated, the q value is not well constrained with no significant difference between q = 0.8 to about 1.1, which we reflect in the errors of the solution. This underlines the need for radial-velocity curve solutions.

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The parameters from this solution were input into a W–D final computation. The calculation converged to a solution. The solution was detached with fill outs of 76% and 78%. The inclination was 8687, which did not result in a time of constant light since the components were nearly identical in radii (back radii were r/a = 0.262). The two spots, one hot and one cool, survived the iterations. The polar cool spot was responsible for much of the odd light-curve characteristics. It had a radius of 68° with a t-factor (spot temperature/surface temperature) of 0.69. The dark spot was at −18° latitude, with a radius of 17° and a t-factor of 1.08. The full solution is given in Table 5, followed by the B,V and R,I normalized flux curves overlaid by the B,V,R, and I solutions in Figure 11 and 12. Next are the Roche-Lobe surface geometries of the binary at quadrature (see Figure 13).

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V642 Vir is a precontact W UMa binary in a well-detached configuration. Its spectral type is that of a cool-type binary with a surface temperature of 4250 K for the primary component. The secondary component has a temperature of ∼3932 K (K9V). The amplitude is 1.05–0.80 mag in B to I, respectively. The inclination of 869 does not result in a total eclipse due to the nearly equal radii of the components. The mass of the primary is on the order of 0.65 M_⊙ and the secondary is 0.56 M_⊙.The eccentric calculation of the orbit of the third body (e = 0.41) has an amplitude of ∼0.0051 days and an orbital period of 20.1 years. This gives a mass ratio of 0.125 for the third body giving a minimum mass of 0.15 M_⊙, assuming the masses given above or a spectral type of M5V. In the main binary, there is undoubtedly angular momentum loss. But the mass ratio of the binary will end as extreme and an instability will form when the mass of the secondary is small and coalescence will occur rapidly, probably resulting in a red novae event (Tylenda & Kamiński 2016).

The small ΔT in the components (∼318 K) and mass ratio near unity (0.9542 ± 0.0005) show that the stars are similar in spectral type (secondary ∼K9V). The period study of this precontact W UMa binary has a 22-year time duration. An oscillation in the residuals of the linear ephemeris reveals an elliptical orbit of a ∼M5V third body with a 21-year period. The binary has a total mass of ∼1.21 M_⊙ making it a precursor to a low-mass W UMa binary. For estimation, we used blackbody physics and the V luminosities to calculate the expected third light to be about 0.30 from continued third light runs. This was equal to the B third-light value (0.31), however the I value was 0.18 and the others were negative and therefore nonphysical, and third light was abandoned. Radial-velocity curves are needed to obtain absolute (not relative) system parameters.

R.G.S. would like to thank Daniel Caton for continuing to observe during the Covid-19 pandemic enabling this and other research to continue. In addition, the research of M.W. and P.Z. was supported by the project Progress Q47 Physics of the Charles University in Prague. H.K. and K.H. were supported by the project RVO 67985815.