Discoveries and Properties of EL CVn-type Binaries in the TESS Survey

EL CVn-type binaries are a distinctive class of eclipsing binary systems, comprising an A/F-type or B-type main-sequence (MS) star and a low-mass ($\sim 0.15$-$0.33\rm{M}_{\odot}$) pre-helium white dwarf (pre-He WD) (Maxted et al., 2011, 2014). These systems are the post-mass transfer remnants of close binary evolution, typically formed through stable mass transfer initiated by Roche-lobe overflow (RLOF) (Chen et al., 2017). During this process, the progenitor of the pre-helium white dwarf, originally the more massive star, evolves into a red giant and transfers its outer envelope to its companion, leaving behind the exposed core of a stripped red giant (van Kerkwijk et al., 2010; Maxted et al., 2011). This evolutionary pathway not only sheds light on the terminal phases of low-mass star evolution, but also offers a valuable laboratory for studying the dynamics of mass transfer in close binary systems.

The EL CVn-type binaries with smaller and hotter pre-He WD secondaries exhibit distinct features in time-domain photometric observations. In the folded light curve, such systems are characterized by a deeper secondary eclipse, where the pre-He WD is eclipsed by the MS star, displaying a ”boxy” shape with steep ingress and egress phases and a flat-bottomed minimum. In contrast, the primary eclipse, caused by the transit of the pre-He WD across the MS star, is notably shallower. Recent photometric surveys have significantly expanded the number of known EL CVn-type binaries. And approximately 80 such systems were detected in the WASP (Wide Angle Search for Planets, Maxted et al. 2011, 2014; Luo 2020; Lee et al. 2020; Hong et al. 2021; Kim et al. 2021; Lee et al. 2022b, a), Kepler (van Kerkwijk et al., 2010; Breton et al., 2012; Carter et al., 2011; Breton et al., 2012; Rappaport et al., 2015; Guo et al., 2017; Zhang et al., 2017, 2019), PTF (Palomar Transient Factory, van Roestel et al. (2018)), TESS (Transiting Exoplanet Survey Satellite, Wang et al. 2020a; Peng et al. 2024; Çakırlı et al. 2024) and Gaia (Gaia Collaboration et al., 2023a). In addition, for EL CVn systems with smaller and cooler pre-He WD secondaries, the beaming, ellipsoidal, and reflection effects are observed along with primary and secondary eclipses. These systems have also been identified in the Kepler survey (Faigler et al., 2015).

To rigorously test theoretical models of white dwarf cooling and binary evolution, precise measurements of the effective temperatures, luminosities, masses, and radii of EL CVn-type binaries are essential. Among the discovered $\sim$80 systems, only about half have had their full set of parameters, including masses and radii, determined. The further analysis of some systems has been hindered by the lack of complete light curves, limiting our ability to derive critical parameters. Moreover, only a limited number of these systems have been subjected to multi-epoch spectroscopic observations (Maxted et al., 2011; Wang et al., 2020b; Çakırlı et al., 2024), which are essential for obtaining accurate dynamical masses and refining our understanding of their evolutionary pathways.

Since 2018, the TESS survey has provided high-precision, continuous, and long-duration photometric observations, enabling the study of binary systems across nearly the entire sky. To date, more than 10,000 eclipsing binaries have been identified using TESS data (IJspeert et al., 2021; Prša et al., 2022; Howard et al., 2022; Chen et al., 2022) (Gao et al., in prep). Furthermore, data from Gaia (Gaia Collaboration et al., 2023b, c; Zhang et al., 2023) and LAMOST have provided highly accurate astrometric and atmospheric parameters for millions of stars within the Galaxy. Additionally, large multi-band photometric surveys such as GALEX (Galaxy Evolution Explorer; Bianchi et al. 2014), 2MASS, the Wide-field Infrared Survey Explorer (WISE; W1 and W2; Wright et al. 2010), SkyMapper (Onken et al., 2019), SDSS (York et al., 2000; Albareti et al., 2017), and APASS (AAVSO Photometric All-Sky Survey; Henden & Munari 2014) have contributed additional photometric data across multiple wavelengths, enabling a comprehensive investigation of EL CVn-type binaries and more precise parameter determination.

In this paper, we first conduct a search for EL CVn-type systems with smaller and hotter pre-He WD secondaries in the TESS survey. We then combine the astrometric and atmospheric parameters from Gaia and LAMOST to derive the physical parameters of the identified EL CVn binaries. Finally, we analyze the properties of these systems and discuss the mechanisms driving their evolution. The structure of the paper is as follows: Section 2 describes the reduction of the observational data from the TESS survey. Section 3 details the identification process for EL CVn-type binaries. In Section 4, we present the methods used to determine the parameters of the identified systems. Section 5 discusses the properties and evolutionary pathways of the EL CVn binaries. Finally, Section 6 provides a summary of our findings.

The EL CVn binaries are characterized by a deeper, “boxy” secondary eclipse with a flat bottom. To identify this feature, we calculate the slope of the light curve. Due to the pulsations and the noise in the observation, at first, each original light curve is smoothed using Locally Weighted Scatterplot Smoothing (LOWESS), a technique commonly employed for data smoothing through locally weighted regression. During the smoothing process, 3% of the data points are utilized for each local regression. Fig.1 employs 6 EL CVn systems that provided by Wang et al. (2020a) and Peng et al. (2024) to illustrate the identification process. In the top panel of Fig.1, the TESS observation data is represented using a grayscale plot, where the intensity of each grid cell corresponds to the number of data points within that region. This approach replaces the direct visualization of individual data points, allowing for a more intuitive interpretation of the overall data distribution. The red solid line illustrates the LOWESS-smoothed light curve. In the bottom panel, the slope calculations of the LOWESS-smoothed light curves are depicted, with individual points also visualized as grayscale cells to enhance clarity. The analysis then focuses on the phase range between 0.4 and 0.6, as marked by the two vertical dashed gray lines in the bottom panel. Next, we identify the two points corresponding to the maximum and minimum slopes between phases 0.4 and 0.6. The number of data points between these two points is then counted. If more than 10 data points exist in this interval, and over 50% of them exhibit an absolute slope value of less than 0.2, the source is identified as a candidate EL CVn-type binary.

Subsequently, we apply additional selection criteria to further refine the sample. Specifically, we require the absolute difference between the depths of the two eclipses to be less than 0.15 mag and the eccentricity to be approximately zero (Peng et al., 2024). Additionally, we visually inspect the light curves of the candidate systems, excluding those displaying EW-type features. Given that the primary optical contribution in EL CVn-type binaries comes from A/F main-sequence stars, we refer to the color-magnitude diagram in Fig. 2. In Fig.2, the background depicts sources within 100 pc from Gaia DR3. Similar to Fig. 1, a grayscale plot is employed in place of individual points, with the intensity indicating stellar density within each grid region. The red plus sign markers indicate previously identified EL CVn systems (see Sec.LABEL:sec_intro). It is evident that most known EL CVn binaries are located on the A/F main sequence. To ensure consistency, we cross-match our candidates with Gaia DR3 using a 2 arcsec cone search and exclude stars with $e\_{\rm Plx}/\rm Plx>0.2$. Additionally, we remove candidates that do not lie within the A/F main sequence region of the color-magnitude diagram. Consequently, we identify 29 EL CVn candidates from TESS, of which 18 were previously known, and 11 are newly discovered, as represented by blue filled squares in Fig. 2. Among these, 17 systems have yet to have their parameters determined.

Fig. 3 illustrates the period distribution of the discovered EL CVn systems. The gray histogram represents the EL CVn binaries previously identified in the literature (see Sect.LABEL:sec_intro), while the red hatched histogram indicates the period distribution of the EL CVn binaries discovered in the TESS survey. In Fig. 3, the orbital periods of previously discovered EL CVn-type systems range from 0.464 to 23.8776 d. And it can be seen that the periods of our newly discovered targets range from 0.64 to 2.5 d, thereby supplementing the previously sparse sample of those $>$ $\sim$1 d. Next, we will proceed to determine the parameters of these EL CVn systems identified from the TESS survey.

In principle, using the light curves and astrometric data provided by TESS and Gaia, along with multi-band photometry, we can derive the stellar parameters for the EL CVn candidate sources. To illustrate our parameter-solving process, we use TIC 149160359 and TIC 416264037 (Wang et al., 2020a) as examples.

The period-mass distribution plays a crucial role in understanding the evolutionary channels of binary star systems. Mass-transfer models indicate a relationship between the mass of the WD and its final orbital period. To investigate this relationship, we analyze the mass-period distribution of EL CVn systems. Fig. 9 presents the period-mass distribution for EL CVn systems. In Fig. 9, the gray open circles represent the ELM white dwarf samples compiled by Li et al. (2019), while the red “plus” corresponds to the EL CVn samples from other literature (see Sec. LABEL:sec_intro). The blue open squares are the EL CVn candidates obtained from TESS survey. The red solid line is the period–mass relation proposed by Lin et al. (2011), and the black dashed lines indicate the ±10% uncertainties associated with this relation. Considering the observational uncertainties, it is evident that the new and previously known EL CVn systems are located near the red solid line and the two dashed lines, this alignment suggests that the EL CVn-systems evolve through the Roche lobe overflow (RL) channel and undergo stable mass transfer.

Fig.10 shows the $T_{\rm eff}$ -$\log g$  diagram of the systems. In Fig.10, the colored solid lines represent the evolutionary tracks of Helium White Dwarfs (He WDs) with masses ranging from 0.145 to 0.335 $M_{\odot}$ (Li et al., 2019). The filled circles denote extremely low-mass (ELM) white dwarfs compiled by Li et al. (2019). The filled squares with black edges correspond to the EL CVn binaries identified from the TESS survey. The filled ”plus” symbols indicate EL CVn systems gathered from the literature, with those marked by black edges representing systems characterized by double-lined spectra and high-precision light curves. As shown in Fig. 10, the observational EL CVn systems are consistent with the evolutionary tracks of the models, further supporting the scenario of stable mass transfer. For the few outliers identified, the metallicity information would allow us to better constrain their parameters.

Furthermore, by comparing the theoretical evolutionary tracks with the observed data, it is evident that the He WDs in EL CVn systems are in an earlier evolutionary stage than typical ELM WDs. The white dwarfs in EL CVn systems have recently completed mass transfer and are still undergoing contraction, as indicated by their relatively higher surface gravity and lower effective temperature compared to standard ELM WDs. Over time, the pre-He WDs in EL CVn systems will cool, leading to an increase in both surface gravity and effective temperature until they align with the typical parameter range of ELM WDs. These EL CVn systems further support the stability of the mass transfer process, enhancing our understanding of the stable mass transfer channels that contribute to the formation of such white dwarfs.

EL CVn-type binaries are crucial for understanding the process of mass transfer in binary systems and the formation of extremely low-mass white dwarfs. In this study, we identified 29 EL CVn-type binary systems from the TESS eclipsing binary catalog (sectors 1-65). These systems consist of smaller, hotter pre-He WDs and more luminous A/F main-sequence stars, and they were selected based on their characteristic, deeper, “boxy” shaped secondary eclipses. Next, using light curves simulated by PHOEBE for EL CVn-type binaries, we trained a light curve fitting model with an MLP model to fit their light curves. This allowed us to determine the mass ratio ($q$), inclination ($i$), relative radii ($r_{1,2}$), and temperature ratio ($T_{2}/T_{1}$). With the effective temperature and radius ratios fixed, we then used the parallax provided by Gaia to calculate extinction and used it as a prior for fitting the SED to solve for the absolute effective temperature values of the two components. Based on the $T_{\rm eff}$ -$\rho$ relation of main-sequence stars, we derived their complete physical parameters, including mass and radius. The temperatures and masses obtained using this method align well with those derived from spectral data and dynamical mass measurements. Subsequently, we analyzed these systems in terms of mass-period and ELM WD evolutionary tracks. The results show that the observational data match the theoretical curves well and indicate that these systems have formed through stable mass transfer channels, consistent with Chen et al. (2017).

Additionally, in this study, we restrict our identification of EL CVn systems to those based on the 2-minute and 30-minute light curves obtained from the TESS survey. This catalog represents a subset of the total EL CVn systems in the TESS survey. Our current sample comprises approximately one-third of the EL CVn systems with complete parameters. Furthermore, the $T_{\rm eff}$ -$\log g$  diagram indicates that two additional cases have been identified, which exhibit relatively higher $\log g$  pre-He WDs. The identified EL CVn systems are significant for the study of binary mass transfer and the formation and evolution of white dwarfs. Recently, pulsations of EL CVn systems have also become a hot topic, and the discovery of these samples provides substantial observational support for the study of pulsations in EL CVn-type binaries. Furthermore, our method can be applied to identify additional EL CVn systems in the TESS survey by combining the EB catalogs from other ground-based surveys (e.g., ZTF, ASAS-SN) with the TESS light curves.

This work is supported by the National Natural Science Foundation of China (NSFC) with grant Nos.12288102, 12125303, 12090040/3, the National Key R&D Program of China (grant No.2021YFA1600401/ 2021YFA1600403), the NFSC (grant Nos.12303106, 12473034, 12103086, 12373037), the Postdoctoral Fellowship Program of CPSF (No.GZC20232976), Yunnan Fundamental Research Projects (grant Nos.202401AT070139, 202101AU070276), the International Centre of Supernovae, Yunnan Key Laboratory (No.202302AN360001) and the Yunnan Revitalization Talent Support Program—Science & Technology Champion Project (No.202305AB350003). This work is also supported by the China Manned Space Project of No.CMS-CSST-2021-A10. We acknowledge the TESS mission provided by NASA’s Science Mission Directorate. We also acknowledge the use of public TESS data from pipelines at the TESS Science Office and at the TESS Science Processing Operations Center. We thank the Gaia Data Processing and Analysis Consortium (DPAC) for their substantial contributions in producing and releasing high-quality data.