A Study of Twelve Potential Merger Candidate Contact Binary Systems

As the number of identified contact binary systems grows with new discoveries from an ever growing number of sky surveys, the interest in their investigation has also increased. The confirmation of Nova 2008 Sco (V1390 Sco) as a red nova resulting from the merger of contact binary components (Tylenda et al., 2011) has also intensified interest in the investigation of orbital stability of contact binary systems (Wadhwa et al., 2021; Gazeas et al., 2021; Christopoulou et al., 2022; Liu et al., 2023). Theoretical models of contact binary evolution predict a likely merger event leading to a rapidly rotating cool giant star as the final outcome (Soker & Tylenda, 2003; Eggleton, 2012; Stȩpień, 2011; Robertson & Eggleton, 1977). Although the predicted rate of Galactic merger events is high at once every 2 to 3 years, brighter events suitable for study are likely to be much rarer at once every 10 or more years (Kochanek et al., 2014).

Investigators such Rasio & Shapiro (1995), Li et al. (2007) and Arbutina (2007, 2009) have clearly shown that merger events are likely to occur when the mass ratio of the components is low. More recently Wadhwa et al. (2021) linked the instability parameters to the mass of the primary ($M_{1})$ and concluded that there is not one global minimum mass ratio at which merger will take place, rather the instability mass ratio can range from below 0.05 to above 0.2 for systems where $0.6M_{\sun}<M_{1}<1.4M_{\sun}$. Although a number of studies, each with a large (10 or greater) number of contact binaries with extremely low mass ratios, have recently been reported they did not identify any system that meet the instability criteria (Gazeas et al., 2021; Christopoulou et al., 2022; Li et al., 2022; Liu et al., 2023). Wadhwa et al. (2022a) recently linked the amplitude of totally eclipsing contact binaries with the mass ratio which when used in conjunction with estimates of the mass of the primary can result in the rapid identification of potentially unstable systems. They identified over 40 new potential merger candidates based on the analysis of survey photometric data. In this study we perform follow up ground based observations on nine systems identified by (Wadhwa et al., 2022a) and three other systems identified from the All Sky Automated Survey - Super Nova (ASAS-SN) (Shappee et al., 2014; Jayasinghe et al., 2020) using the criteria described in Wadhwa et al. (2022a). Basic identification data for each system is presented in Table 1. Almost all ground based surveys have been carried out using either small aperture telescopes or telephoto lenses. The angular resolution is therefore quite poor ranging from 9” to over 60” (Drake et al., 2017; Shappee et al., 2014; Jayasinghe et al., 2020; Thiemann et al., 2021; Pojmanski, 2002). The risk of potential blending of the survey light curves was highlighted by Wadhwa et al. (2022b) where a system thought to be of extreme low mass ratio and a potential merger candidate is in fact a high mass ratio system with no indications of orbital instability. Each system reported here was checked against $Gaia$ EDR 3 (Anders et al., 2022; Gaia Collaboration et al., 2022) to ensure there was no other star system brighter than 17th magnitude within 10” of the target. We perform light curve analysis and compare our results with reported data from survey analysis, in addition, we show that all systems described demonstrate features of orbital instability, have secondaries that are denser and most show evidence of chromospheric activity in the absence of star spots.

Having established an estimate for the mass of the primary the next (and only) other parameter required to determine potential orbital stability is the mass ratio of the system. In the absence of radial velocity measurements light curve analysis of contact binary systems can be successfully carried out if total eclipses are present (Terrell & Wilson, 2005). One of the input parameters for such analysis is the temperature of the primary component ($T_{1}$). There is no standard method for assigning the value for the temperature of the primary. Colour based estimations have been the mainstream, however these have proven troublesome, for example the ViziR database reports a range of over 3000K for one of our targets (V396 Lup). Given the lack of a standard approach many investigators (see e.g. Zhou et al., 2018; Chang et al., 2022; Guo et al., 2022) are now moving to low resolution spectra (where available) to aid in determining the primary’s temperature. To this end for this study we acquired spectra using the LCO network of 2m telescopes equipped with FLOYDS spectrograph, a cross-dispersed, spectrograph with variable resolution of R=400 to R=700 for 10 of the systems. The reduction pipeline for the FLOYDS spectral data is fully automated and described in detail on the LCO website (https://lco.global/documentation/data/floyds-pipeline/ - accessed 14/1/2023). For A0514 we used the published spectral data (Cannon & Pickering, 1993). We were unable to obtain a spectrum for A2044 due to technical reasons during the allotted time. All FLOYDS spectra were visually compared to standard library spectra of main sequence stars (Jacoby et al., 1984; Pickles, 1998) to determine the spectral class for each system. Representative FLOYDS spectra and matching library spectra are shown in Figure 1.

For this study we use the mean ($\pm{SD}$) of four estimates for the temperature of the primary. We estimate effective temperature of the primary based on our extinction corrected value of $B-V$, the observed spectral class, the 2MASS $J-H$ colour and the reported value from the GAIA third data release all adjusted to the nearest 10. For consistency we use the April 2022 update tables of Pecaut & Mamajek (2013) for colour and spectral calibrations. Summary of the spectral class, temperatures and the adopted mean value of the four calibrations is presented in Table 4. In the case of A2044 where no spectral observations were available we adopt the mean of the two colour calibrations and the GAIA estimate.

The 2013 version of the Wilson-Devinney (WD) code with Kurucz atmospheres (Wilson, 1990; Kallrath et al., 1998; Nelson, 2021) was used to obtain the photometric solution for each system. As all systems show total eclipses accurate photometric solutions are possible and as there was no significant asymmetry at maximum brightness (i.e no significant O’Connell Effect) only unspotted solutions were obtained. As the effective temperature of the primary is less than 7200K in all cases, the gravity coefficients were set as $g_{1}=g_{2}=0.32$, and bolometric albedoes as $A_{1}=A_{2}=0.5$. Logarithmic (Nelson & Robb, 2015) limb darkening coefficients were interpolated from the 2019 update of van Hamme (1993).

Simultaneous solutions were obtained for both the V and R band in all cases. Mass ratio ($q$) search grid method was used to find the best solution for a range of fixed mass ratios from 0.05 to 20. The initial search was performed with mass ratio increments of 0.1 up to $q=1$ and then 0.2 up to $q=10$ and 0.5 increments up to $q=20$. The search was then refined near the best solution in increments of 0.05 and finally in increments of 0.01. During the search procedure the orbital inclination ($i$), the surface potential, temperature of the secondary component ($T_{2}$) and the dimensionless luminosity of the primary ($L_{1}$) were the adjustable parameters and all of which were adjusted between each iteration. The iterations were carried out until the suggested adjustment for all adjustable parameters was less than the reported standard deviation. During the last iteration the mass ratio was also made a adjustable parameter.

To determine the effects of the variable temperature of the primary each system was further modelled with mass ratio increments of 0.01 around the mean temperature solution with the temperature of the primary adjusted both to the upper and lower limits reported in Table 4. As has been well established the light curve shape of contact binaries is almost completely due to the system geometry with the degree of contact, mass ratio and inclination being the major contributors (Rucinski, 1993, 2001). The shape of contact binary light curves places a tight constrain on the component temperature ratio ($T_{2}/T_{1}$) but not on individual component temperatures (Rucinski, 1993; Sun et al., 2020). With change in $T_{1}$ we expected change in $T_{2}$ but no significant change in the geometric parameters. This proved to be the case with the light curve solution converging to the same mass ratio regardless of the input value of $T_{1}$ except in the case of A1846 where the mean $T_{1}$ solution converged at $q=0.151$ and the higher $T_{1}$ solution converged at $q=0.150$. Similarly the inclination variation between high, mean and low values for $T_{1}$ were within 0.5^∘ and within the reported standard deviations reported by the WD software. The dimensionless potential and the geometric mean of the fractional radii again varied minimally. Although the errors in geometric parameters were small with change in temperature of the primary they were propagated to the mean solution reported. Apart from the mass ratio and fractional radii (reported to two decimal places) no other parameter resulting from modelling of the light curve is further used in this study. We report light curve solution parameters pertinent to this study in Table 5 with errors propagated relative to the input errors in $T_{1}$. Fitted and observed light curves are illustrated in Figure 2.

Orbital stability and potential merger of contact binary systems has received considerable attention recently (Wadhwa et al., 2021; Christopoulou et al., 2022; Liu et al., 2023). Wadhwa et al. (2021) developed new relationships linking the mass of the primary, the degree of contact and the instability mass ratio ($q_{inst}$). Following their methodology, and adopting the values of the gyration radii of the components as described, we calculated $q_{inst}$ for each system for fill-out factor values of 0 and 1 (Table 5). This provides a range of mass ratios where orbital instability is likely. As noted by Christopoulou et al. (2022) a small uncertainty in the estimation of the mass of the primary propagates to a significant uncertainty in the estimation of orbital instability parameters. This is confirmed by this study where the mean mass of the primary components of the systems presented in this study is $1.06M_{\sun}$. At this mass the instability mass ratio range for fill-out factor 0 to 1 extends from 0.094 to 0.109. A 10% change in the mass of the primary (either above or below) results in a greater than 17% change in the instability mass ratio range. Thus for the purpose of this study we consider any system where the mass ratio is within 17% of the maximum instability mass ratio to be potentially unstable. Based on this criteria ten of the twelve systems lie within the instability mass ratio range taking into account reported errors. One (A1846) is within 7% and one (A2348) 17% of the maximum instability mass ratio. We note that the distance estimation of A2348 has a reported error near 10% so we consider it reasonable to include the system as potentially unstable. The instability mass ratio ranges are summarised in Table 5.

Manual analysis of the survey photometric data for 9 of the systems presented here was reported by Wadhwa et al. (2022a). The survey data mass ratio estimate was within 10% of the mass ratio based on dedicated observations except in the case of A2044 and A2132 where the survey data estimates of the mass ratio were 20% and 12%, respectively, below the values reported here.The findings confirm that generally survey photometric data provides a good starting point in the selection of potential low mass ratio systems and merger candidates. Wadhwa et al. (2022a) found that all 9 of the common systems could be regarded as potential merger candidates as their estimation of the mass of the primary was based on $J-H$ calibration. Looking at the two candidates in our report A1846 and A2348 which are just outside the instability range, have $J-H$ calibrated mass of the primary, 0.89 and 1.07, respectively, both lower than the combined with distance estimation used in this study. If the single colour estimation was used than the 2 would fall within the instability range.

Photometric observations and light curve solution of twelve low mass contact binary systems is presented. All were found to be of extreme low mass ratio ranging from 0.072 to 0.15. Compared to theoretical parameters all have a mass ratios indicative of likely orbital instability and are likely merger (red nova) candidates. Regular high cadence future observations are encouraged to accurately determine period variations and brightness changes which maybe an indicator of impending merger (Tylenda et al., 2011). A thorough study of orbital behavior of contact binaries have been performed recently by Zhang & Qian (2020); Poro et al. (2022); Loukaidou et al. (2022). The first and the last paper discuss in particular the systems close to the orbital period cut-of. Ultra-short period systems seem to have generally stable orbits and do not show evidence of significant period decrease. From the viewpoint of Darwin instability, this is understandable, since these are not such a low-mass ratio systems and it may take a long evolutionary time for ultra-short contact binaries to reach an extremely low mass ratio and become dynamically unstable (Loukaidou et al., 2022).

Review of some astrophysical characteristics confirm similarity with other contact binary systems with the secondary considerably brighter and larger than main sequence stars of similar mass. In addition, the secondary in all cases is significantly denser than the current primary. Chromospheric activity in contact binary is usually detected as a variation in the two maxima from the light curve due to starspots. As we have shown in this study non-photospheric markers probably can detect such activity without typical light curve features. Another high energy feature of excess chromospheric/magnetic activity is X-Ray emissions (Gondoin, 2004). Only a small fraction of contact binary star systems are X-ray sources (Liu et al., 2022) such that presence of X-Ray emissions can be taken as a marker of increased magnetic activity and potential indicator for an increased loss of angular momentum and orbital instability. Seven of twelve systems reported have been catalogued as having X-Ray emissions (Liu et al., 2022). Also, as noted above the FUV magnitude can be used as a marker for chromospheric activity. Another interesting point of note is how much brighter relative to main sequence stars are the contact binaries in the FUV band. Findeisen & Hillenbrand (2010) have estimated the absolute FUV magnitudes ($M_{\rm FMS}$) for single main sequence stars from B8 to M2 spectral types. For the six systems from our sample with FUV magnitude we find that all systems are between 0.5 and over 3.0 magnitude brighter in the FUV band relative to their main sequence counterparts.

Progress in the detection and monitoring of potential contact binary merger candidates is rapidly progressing. There now exists a theoretical framework to determine the potential for merger from the estimate of the mass of the primary and the mass ratio of the system (Wadhwa et al., 2021). Models and techniques have been developed to rapidly select potential merger candidates from survey photometry (Wadhwa et al., 2022a). However, follow up dedicated observations are required due to the low resolution of most survey data (Wadhwa et al., 2022b).