Two additional members of a newly identified group of pulsating pre-He white dwarfs

ABSTRACT

The VLT/UVES (Very Large Telescope/Ultraviolet and Visual Echelle Spectrograph) spectroscopic and Transiting Exoplanet Survey Satellite (TESS) photometric observations provide a unique opportunity to directly study the physical properties of binary stars. Through careful examination of these observations, the essential characteristics of the eclipsing components were revealed. The primary components are located within the overlapping main-sequence region of the |$\delta$| Sct and |$\gamma$| Dor variables, while the secondary components closely match the low-mass white dwarf models. Multifrequency analyses were performed on the residual TESS data after removing the binarity effects. The frequencies in the range of 230–460 |$\mu {\rm Hz}$| are attributed to |$\delta$| Sct pulsations that come from the primary stars of the systems. On the other hand, the frequencies of 1160–2890 |$\mu {\rm Hz}$| are considered to be oscillations of pre-He WDs. The investigated systems fall outside (hotter side) of the theoretical instability strip while positioned in the empirical instability strip. Increasing number of pre-ELMVs (Extremely Low-Mass Variables) discovered to have higher |$T \rm _{eff}$|s than theoretical models predicted and this could be caused by the different He abundances in the driving zone originated from different binary evolution scenarios.

1 INTRODUCTION

White dwarfs (WDs) are the ultimate remnants of stars that had original masses of up to approximately 10 M|$_{\odot }$|⁠, which accounts for 95 per cent of all stars in our galaxy (Althaus et al. 2010; Córsico et al. 2019; Saumon, Blouin & Tremblay 2022). A significant number of WDs are concentrated around a mass of approximately 0.6 M|$_{\odot }$| and have CO cores and hydrogen-rich envelopes. According to Kilic et al. (2007), the minimum mass for a WD that can be generated from the evolution of a single star is estimated to be between 0.3 and 0.45 M|$_{\odot }$|⁠, taking into account the age of the universe. On the other hand, the distribution of stellar remnants suggests that there are a significant number of extremely low-mass (ELM) WDs less than 0.3 M|$_{\odot }$| (Kleinman et al. 2013; Kepler et al. 2017). These objects’ masses are insufficient to maintain the burning of their helium cores. The ELM WDs are believed to be potential outcomes of binary star evolution resulting from either stable or unstable mass transfer (Istrate et al. 2016a; Calcaferro, Althaus & Córsico 2018; Li et al. 2019). Observationally, their companions are A/F main-sequence (MS) stars.

EL CVn-type stars are a type of eclipsing binaries (EBs) that consist of an ELM WD precursor (pre-He WD) and an A/F dwarf (Maxted et al. 2014a). As noted by Lagos et al. (2022), the orbital periods of their MS binary precursors are primarily expected to be less than approximately 3 d. The light variations of the EL CVn binaries exhibit total eclipses during the primary minima due to the occultation of the pre-He WDs. Additionally, there are ellipsoidal variations in the shape of the stars outside the eclipses, resulting from the tidal deformation of the MS stars. Over 80 EL CVn-like EBs have been identified using different ground- and space-based photometric surveys. These surveys include studies conducted by van Kerkwijk et al. (2010), Rowe et al. (2010), Maxted et al. (2013, 2014b), Faigler et al. (2015), Rappaport et al. (2015), Guo et al. (2017), van Roestel et al. (2018), and Wang et al. (2018). Their orbital periods, denoted as P|$_{\rm orb}$|⁠, vary between 0.46 and 23.9 d, with most having a P|$_{\rm orb}$| of 3 d.

The quantity of EL CVn candidates is progressively rising; however, aside from six double-lined EBs (WASP 0247−25; Maxted et al. 2013), (WASP 1628 + 10; Maxted et al. 2014b), (KIC 9164561; Zhang et al. 2016), (TIC 160081043, TIC 408351887, and TIC 192990023; Çakırlı, Hoyman & Özdarcan 2024) the majority have no or inadequate spectroscopic evidence to accurately determine their physical characteristics. Certain pulsations can be observed in these systems, including |$\delta$| Sct and/or |$\gamma$| Dor variables in the A/F primary components, as well as very short-period oscillations lasting a few hundred seconds in the pre-He WD companions. Pulsating components in EL CVn-type systems offer great potential for in-depth investigations of extra low-mass WDs and intermediate-mass MS stars due to the significant combination of their asteroseismology and binary characteristics. This research specifically examines two EL CVn-type binaries, namely TIC 65448527, and TIC 54957535, which were shown to have a double-lined EBs. We employ a comparable methodology to prior research (see to Çakırlı et al. 2024) in this study.

Our focus is solely on discovering new pulsating pre-He-WDs. The presence of additional stars with clearly defined asteroseismic features allows us in refining the accuracy of the instability strip. Córsico et al. (2019) proposed that they represent a new class of pulsating stars, utilizing the |$T \rm _{eff}$|-|$\log g$| distribution of their stars. At the same time, various authors (e.g. Jeffery & Saio 2013; Córsico et al. 2016) investigated the seismic characteristics of pre-ELM WDs. The authors found that pre-ELM WDs are capable of pulsating in both radial and non-radial p and g modes. The |$\kappa -\gamma$| mechanism causes these modes, primarily functioning within the He|$^+$|–He|$^{++}$| ionization zone. One can explore their internal structure using the methods of asteroseismology (e.g. Istrate, Fontaine & Heuser 2017). Pulsation EL CVn-type binaries hold a significant and distinctive position in enhancing our comprehension of the formation and evolution of pre-ELM WDs. Their binarity enables us to evaluate their physical parameters, including mass and radius. Nevertheless, the precise characteristics of pulsating EL CVn stars are still not fully understood because of the existence of several objects.

These systems are previously identified as EB stars with light curves of the EL CVn type, as described by Maxted et al. (2014a). However, no comprehensive investigation or classification of their Roche geometry based on models has been conducted thus far. Thus, our study enhances the existing collection of pre-He WDs with accurately measured absolute stellar characteristics, and increases the overall count of known pulsating pre-He-WDs by almost 25 per cent. Their physical and geometric properties are determined through the analysis of both photometric and spectroscopic data.

The selected systems have been subjected to data collection, including time-series TESS data and high-resolution spectroscopic data (see to Section 2). This data will be utilized to conduct thorough atmospheric and photometric modelling (Section 3) and accurately determine the stellar parameters. In Section 4, we present the evolutionary models that we employed. Section 5 provides a comprehensive analysis of the pulsation characteristics of our samples. We evaluate the similarities and differences between our samples and the known EL CVn binaries. The study ends with a discussion of some notable outcomes, which will be provided in Section 6. The errors of the parameters in all tables of the present study are indicated in parenthesis next to the values and represent the last digit(s).

2 DATA

2.1 Photometry

Transiting Exoplanet Survey Satellite (TESS) Science Processing Operations Centre (Jenkins et al. 2016, SPOC) observed the target TIC 65448527 and TIC 54957535 in 20 and 120 s cadence modes during Sectors 4–61 of the mission. Table 1 summarizes the TESS observations for each system as we were able to retrieve the light curves of two targets from the Mikulski Archive for Space Telescopes (MAST)¹ archive by making use of the lightkurve module under python environment (Lightkurve Collaboration 2018). Ricker et al. (2015) have given detailed explanations regarding TESS spacecraft and camera. In Section 3.3, we present the resulting light curves for both stars. The light curves exhibit a primary eclipse with a boxy shape and sinusoidal modulation occurring outside of the eclipses. These characteristics are commonly observed in EL CVn-type binaries. It is suggested that there may be new EL CVn systems exhibiting multiperiodic pulsations. The subsequent sections will address this topic.

2.2 Spectroscopy

The high-resolution optical spectra used in this study were obtained from the European Southern Observatory (ESO) Science Archive Facility.² Observations were conducted using the Ultraviolet and Visual Echelle Spectrograph (UVES; Dekker et al. 2000) on the ESO VLT/UT2 (Very Large Telescope/Unit Telescope 2) telescope, also known as Kueyen,³ located in Paranal, Chile. These observations were made via the Fibre Large Array Multi Element Spectrograph system, which has a resolution of approximately 50 000. Our spectroscopic analysis utilized the 1D spectra that were calibrated for wavelength by ESO personnel using dedicated pipelines as part of the 086.D-0194(A) and 094.D-0027(A) programmes.

3 ANALYSIS

3.1 Radial velocity measurements and orbital solutions

The radial velocity of the host star undergoes temporal variations in a binary system due to the presence of a companion star. Through careful analysis of the radial velocity data, valuable insights can be gained regarding the relative masses of the host and companion, as well as important orbital parameters such as period and eccentricity. In this section, we will explain the method of establishing the inference of radial velocity measurements within a Markov Chain Monte Carlo (MCMC; Goodman & Weare 2010) framework. This method has been widely used in astrophysics for searching, optimizing, and sampling probability distributions. We used the normalized spectra and adopted the spectrum radiative transfer code (Gray & Corbally 1994), and the stellar atmospheric model atlas9. Castelli model atmospheres (Castelli & Kurucz 2003), and the line lists provided alongside the spectrum code. These were modified to be compatible with ispec software (Blanco-Cuaresma et al. 2014). We specified a range of parameters for the synthesized spectra, including |$T \rm _{eff}$|⁠, |$\log g$|⁠, [M/H], |$v\sin i_{\rm obs}$|⁠, |$V_r$|⁠, and |$\mathrm{ lf}$| (light fraction). Here, |$T\rm _{eff}$|⁠, |$\log g$|⁠, and [M/H] denote the atmosphere properties of the star, namely the effective temperature, surface gravity, and metal abundance, respectively. Both the rotation and the radial velocity of the star are denoted by the symbols |$v\sin i_{\rm obs}$| and |$V_{\rm r}$| respectively.

We obtained the normalized spectra of single stars using ispec based on these parameters. We merged the synthetic spectra of two individual stars without introducing any additional noise to generate binary spectra. Upon creating the synthetic spectra for each individual component, we started the process of measuring the radial velocity. In order to do this, we identified the spectral areas that were not influenced by the telluric lines, and we found that both of the components were able to be recognized with relative ease. Through the use of these areas, we were able to crop the spectra that previously were seen. The synthetic composite spectra were created by adjusting the components’ synthetic spectra based on their expected radial velocities. The light contributions obtained from light-curve solutions were used to scale the spectra. The observed and theoretical spectra were then compared to determine how well they corresponded. The MCMC algorithm allowed for flexibility in adjusting the radial velocity of the components in order to find the optimal fitting solution. The algorithm assumes that the likelihood function for this process is represented by |$\rm ln(p)$| = |$\chi ^2$|/2. The MCMC solutions are executed using 24 walkers, with each walker taking 5000 steps for every observed spectrum.

Fig. 1 shows example corner plots that illustrate the MCMC solutions of the systems. The radial velocities are obtained by examining the sample data of each solution and determining the lower error, median value, and upper error based on the 3rd, 50th, and 97th percentiles. The measured radial velocities for each system are displayed in Table B1.

It is evident from the spectroscopic variations that the absorption lines undergo periodic changes, aligning with the orbital period of the system. An exemplary demonstration of this principle may be seen in the observed spectrum of all systems. Fig. 2 clearly demonstrates the spectroscopic variation through the multitude of absorption lines for the components. The periodic shift of the isolated absorption lines profiles across numerous consecutive runs is also illustrated in Fig. 2, where the absorption lines from the systems are clearly distinguished and displaced along the orbital phases. Furthermore, the right panel of Fig. 2 displays the measured radial velocities with the corresponding radial velocity model that has been fitted. It seems that all the stars that have undergone spectrum analysis have completed a full cycle, to different extents. However, the reliability of analysis is not affected in any way by the fact that there are intervals between each step.

By measuring the radial velocities of the components, we are able to determine the orbital solutions of each system. This is done using the MCMC algorithm, which efficiently explores parameter space and provides probability distributions of orbital parameters. We utilize the emcee code, which is a python version of the Goodman–Weare affine invariant (Goodman & Weare 2010) MCMC ensemble sampler developed by Hogg & Foreman-Mackey (2018). The data, the prior distributions of the model parameters, the likelihood function, and the beginning locations of the random walkers are the key elements that are used to enter the code into the computer. Before delivering the posterior distributions of model parameters as outputs, the algorithm first determines the likelihood of various solutions, then executes jumps and explores the parameter space for a certain number of steps, and then returns the results. The solution was performed with the assumption that the likelihood function was |$\rm ln(p)$| and several parameters including orbital eccentricity (e), argument of periastron (⁠|$\omega$|⁠), radial velocity amplitude of the components (⁠|$K_{1,2}$|⁠), radial velocity of the centre of mass (⁠|$V_{\rm \gamma }$|⁠), and arbitrary phase shift (⁠|$\phi _{\rm shift}$|⁠) were considered as adjustable. The orbital period (P) and mid-time of the primary minimum (⁠|$T_0$|⁠) were obtained from light-curve solutions and remained constant throughout. The MCMC solutions are executed with 48 walkers, each taking 10 000 steps per walker for every system. The corner plots for each solution can be found in Fig. 3, while the fitted parameters and other derived quantities for the best-fitting model are provided in Table 3. The parameter determination and error estimation method for the radial velocities were applied in the same manner. The sample sets were calculated using the final MCMC samples to determine the parameters and errors.

3.2 Atmospheric parameters

The methodology we employ is exactly the same as the one used in earlier works on pre-He WDs (Çakırlı et al. 2024). In brief, our code utilizes ispec subroutines (Blanco-Cuaresma et al. 2014; Blanco-Cuaresma 2019) and pre-generated synthetic spectrum libraries provided alongside the ispec code to develop a synthetic spectrum for each component. It is written in the python programming language. The spectra are shifted based on the radial velocity of each component and then scaled to their contribution to the total luminosity. This process ultimately produces a composite spectrum. This synthetic composite spectrum can be generated to cover the entire observed spectrum, or limit in certain segments to reduce computing time and improve solutions.

The sampling of a significant number of parameters was necessary to conduct a thorough examination of the systems. The spacious corner plots clearly show the posterior distributions, highlighting the 2D cross-sections. Fig. 3 depicts an instance of this plot. It can be challenging to determine how thoroughly the MCMC walkers have explored the posterior distribution. However, we can evaluate the advancement of these MCMC runs using particular heuristic measures. The advantages and limitations of the strategies mentioned above are extensively analysed by Çakırlı, Özdarcan & Hoyman (2023).

Fig. 4 depicts the findings from our analysis of the samples. By utilizing the exceptional UVES spectra, we have successfully achieved precise classifications for every system listed in Table 2.

3.3 Light-curve modelling and absolute parameters

To analyse the TESS light curves and radial velocities derived from UVES spectra of the two EBs, we used Wilson–Devinney EB modelling code (Wilson & Devinney 1971), which is implemented in the fortran programming language. To efficiently and promptly implement the Wilson–Devinney code, we employ the python framework PyWD2015 (Güzel & Özdarcan 2020), which offers a graphical user interface for the 2015 version of the code (Wilson & Van Hamme 2014). Due to a typical EL CVn-type light curves observed in Sectors 14-31-34-61, we conducted a simultaneous fitting of the complete sets of light curves for all systems. In this paper, we define the luminous, more massive, primary star as star 1 and the hotter less-massive component as star 2. The temperatures of star 1 remained constant throughout the operation, thanks to the data obtained from the atmospheric analysis in previous section. The assumptions of circular orbit (e = 0) and synchronous rotation (⁠|$F_1$| = |$F_2$|⁠) for both binary systems are reasonable derived from their radial velocities. We adopted the TESS-band limb-darkening coefficients (⁠|$x_T$|⁠, |$y_T$|⁠) and the bolometric ones (⁠|$X_{bolo}$|⁠, |$Y_{bolo}$|⁠) from Claret (2000) and van Hamme (1993), respectively. The initial approach involved utilizing the standard gravity brightening coefficients (g|$_1$| = |$g_2$| = 1; Lucy 1967) and bolometric albedos (⁠|$A_1$| = |$A_2$| = 1; Ruciński 1969) for radiative atmospheres. Nevertheless, the light-curve residuals continue to exhibit noticeable fluctuations. The light-curve fit is significantly enhanced when |$g_1$| and |$A_1$| are allowed to vary as free parameters. We made adjustments to the bolometric albedo and gravity brightening coefficient of star 1. We kept |$g_2$| and |$A_2$| at their default values as they have minimal impact on the higher temperature of the secondary star with T|$_{\rm eff}$||$>$| 8000 K. The adjustable parameters encompassed various factors such as the orbital semimajor axis (a), centre-of-mass velocity (V|$_{\gamma }$|⁠), orbital eccentricity (e), longitude of periastron (⁠|$\omega$|⁠), phase shift (⁠|$\mathrm{ pshift}$|⁠), mass ratio of the system (q = M|$_2$|/M|$_1$|⁠, where M|$_1$| and M|$_2$| denote masses of the primary and the secondary components, respectively), inclination of the orbital plane (i), effective temperature of the secondary component (T|$_2$|⁠), dimensionless potentials (⁠|$\Omega _{1,2}$|⁠), and luminosity of the primary component (⁠|$L_1$|⁠). In the case of circular orbit, we drop e, |$\omega$|⁠, and |$\mathrm{ pshift}$| from the adjustable parameter list and keep them fixed to zero.

The fitted parameters for the best-fitting model and their uncertainties are given in Table 3. The theoretical light curves of TIC 65448527 and TIC 54957535, generated by the binary model, are plotted as dark solid lines in Fig. 5. The corresponding light residuals, calculated by using the observational data minus the final binary model, are displayed in the bottom of each panel.

The jktabsdim code (Southworth, Maxted & Smalley 2005) was utilized to ascertain the physical characteristics of the systems. The code utilized input parameters P, i, |$r_{1,2}$|⁠, |$K_{1,2}$|⁠, and |$T_{\rm eff1,2}$|⁠, along with their corresponding uncertainties listed in Table 3. The results obtained from the code are also displayed in same table at the bottom. The resulting parameters were utilized to position the components on the Hertzsprung–Russell (HR) diagrams in order to analyse their evolutionary status. The luminosity (L) and bolometric magnitudes (⁠|$M_{\rm bol}$|⁠) were derived by adopting |$T\rm _{eff}$|  = 5780 K and |$M\rm _{bol}$|  = + 4.73 for solar values.

jktabsdim can also estimate the distance to targets, using effective temperatures of two components, estimated metallicity, E(B − V) and apparent magnitudes via various calibrations. We used the interstellar reddening values E(B − V) to calculate the distance of the systems by using the remarkable approach to determine the average interstellar reddening values of E(B − V) is by analysing the Na i (D|$_2$| at 5889.951 Å, and D|$_1$| at 5895.924 Å) spectral lines, which are prominent in the stellar spectrum (Munari & Zwitter 1997). The average distance calculated for systems was consistent with all systems when utilizing the trigonometric parallax from the |$Gaia$| DR3 (Gaia Collaboration 2023).

4 EVOLUTIONARY STATUS

The formation channel of EL CVn binaries, as described in the literature (e.g. Chen et al. 2017), involves the birth of two MS stars with similar mass at a short orbital period of a few days. The star with more mass evolves faster and gets larger. As it moves on to the red giant branch, it reaches a point where it fills its Roche lobe and starts a stable mass transfer to the secondary star with a lower mass. This step continue until almost all of the outer envelope is transferred, which is known as R CMa-type binaries (e.g. Lee et al. 2016). The remaining part of the star, which was originally larger, has transformed into a pre-WD with a core made of helium and a surrounding envelope of hydrogen, weighing approximately 0.1–0.4 solar masses (Istrate et al. 2016a; Chen et al. 2017). The accretor has evolved into a rejuvenated MS star with a spectral type of A or F, which now holds the majority of the system’s luminosity. Henceforth, this binary system shall be classified as an EL CVn, provided that its orbital inclination results in the occurrence of eclipses.

Fig. 6 displays the positions of the MS and pre-helium WD components of our targets on Hertzsprung–Russell diagrams, alongside other EL CVn-type stars. The data set includes the evolutionary sequences of ELM WDs with masses ranging from 0.179 to 0.414 M|$_{\odot }$|⁠, and 0.155 to 0.176 M|$_{\odot }$|⁠, as provided by Althaus, Miller Bertolami & Córsico (2013) and Driebe et al. (1999), respectively. The 36 EL CVn-type binaries were discovered from the Palomar Transient Factory (PTF) photometric database by van Roestel et al. (2018). Nine EL CVn-type binaries have been studied by Çakırlı et al. (2024), while the other 12 stars have been extensively investigated by several researchers (Maxted et al. 2014a; van Roestel et al. 2018; Wang et al. 2018; Zhang et al. 2019; Cui et al. 2020; Kim et al. 2021; Lee et al. 2022; Peng, Wang & Ren 2024, 2024). In the figure, the open and filled symbols represent our targets MS and pre-He WDs, respectively. As one can see in the figure, MS component of the targets are located inside the region of the |$\delta$| Sct instability strips in the MS boundaries between the zero-age and the terminal-age MS. Based to the evolutionary theory of He WDs, the pre-He WDs undergo a nearly continuous increase in brightness as they transition from the MS, moving towards higher effective temperatures. Plus, for He WDs with a stellar mass greater than 0.18–0.20 M|$_{\odot }$|⁠, they undergo multiple thermonuclear carbon–nitrogen–oxygen (CNO) flashes before approaching the final cooling stage. Istrate et al. (2016b) provided a comprehensive overview of the history of the origins of ELM WDs, including a review of their formation and evolution.

Fig. 6 shows that the position of the pre-He WD companion in our samples has shifted considerably from the constant luminosity phase of the evolutionary track. It is now located below the mass of 0.165 M|$_{\odot }$| and follows the model track after the CNO flashes have occurred. Although Althaus et al. (2013) and Istrate et al. (2016b) pointed out the challenges in detecting pre-He WDs during CNO flashes due to their fast evolution and lack of expected pulsations, our analysis revealed that the pre-He WD stars in the samples we studied exhibited clear pulsations. The pulsation of these stellar objects holds great importance within the framework of the nature of the pre-He WDs, regardless of their position on the HR diagram. Nevertheless, this scenario has the potential to give rise to a new region of instability as the pulsating pre-He WDs grow in number (Çakırlı et al. 2024). The pulsations of pre-He WDs presents a valuable opportunity for conducting comprehensive investigations into the internal structures of this particular type of star. It is achievable when precise frequencies and oscillation modes can be ascertained, particularly when there are strong observational constraints on the star’s mass, temperature, and luminosity.

5 PULSATIONAL CHARACTERISTICS

We performed a thorough frequency analysis by subtracting calculated binary models from the time-series TESS observations of systems, which included data with cadences of 20 and 120 s. We disregarded the data points collected during the eclipses to minimize the potential impact of any remaining binary signal on the residuals. We used the sigspec (Reegen 2007) software to detect and analyse important pulsation frequencies in the TESS data set. In order to determine the optimized values, we utilized a non-linear least-squares cosine fit to the remaining light curve. sigspec is an advanced code that detects the most important frequency within a certain range by employing a least-squares fitting method. It normalizes the sinusoidal pattern and performs significance calculations using residuals. During this process, a frequency analysis conducting, ranging from infinite in d|$^{-1}$| to a significance limit of sig|$\ge$| 5, which is considered the theoretical equivalent of a signal-to-noise ratio (S/N) of at least 4.0.

Subsequently, we conducted a search for potential combinations among frequencies. Frequency combinations were permitted for identification, provided that their results were consistent within a range of three standard deviations. Fig. 7 displays the frequencies of the prevailing period patterns for all systems. The results suggest that there are notable variations in power due to oscillations in pre-He WDs, occurring at a frequency of around 1040–3470 |$\mu {\rm Hz}$|⁠. The frequencies’ uncertainty have been computed using the methodology described in Kallinger, Reegen & Weiss (2008). The detailed frequency list is displayed in Table A1.

To ensure that the pulsational variability is not caused by a nearby contaminating star, we examined the images of the targets acquired from various sky surveys, including PanSTARSS⁴ (Panoramic Survey Telescope and Rapid Response System), Two Micron All Sky Survey (2MASS),⁵ Digitized Sky Survey (DSS),⁶ and X-ray Multi-Mirror Mission (XMM).⁷In addition, we obtained the target pixel file (TPF) for each object in order to examine the aperture and potential sources of contamination. Examining the TPFs is crucial due to the low brightness of our samples compared to the majority of TESS observations taken at 20 s and 2-min intervals. No evidence has been found to suggest that the light emitted by any stars, even those in densely populated areas, is tainted or blocked by any other source.

Fig. 8 displays the empirical instability strip, which is updated by two newly studied pre-He WDs in this study, as well as other pulsating pre-He WDs. The observed pulsating stars are plotted as a function of temperature and |$\log ~g$|⁠, along with the non-variables that have not yet shown any pulsational variation. Fig. 8 showcases two remarkable characteristics: a slender conical strip measuring 1550 K in width, along with both pulsating and non-pulsating pre-He WDs residing within the instability strip. The presence of non-pulsating stars in the middle of the strip challenges the empirical idea, even when considering the uncertainties in temperature that could explain the absence of pulsation near the edges. Additionally, it is worth mentioning that the distribution of pre-He WDs seems to be uneven along the strip. The features of this plot are influenced by several factors, including biases in candidate selection, non-uniform detection efficiency in the |$T_{\rm eff}$| - |$\log g$| plane, errors, and systematic effects in spectroscopic temperature and |$\log g$| calculations.

The pre-He WDs exhibit only a few pulsation modes, characterized by small amplitudes (about 0.1–3 per cent) and periods ranging from 100 to 250 s. The variations in pulsation periods and amplitudes with temperature and |$\log g$| indicate that the detection efficiency is dependent on T|$_{\rm eff}$| and |$\log g$| as well. The distribution of pre-He WDs with these temperatures and |$\log g$| values can be determined by examining the area on the HR diagram. By calculating the width of the instability strip using the effective temperatures of the hottest and coolest pulsators, we can obtain a value that is not influenced by our perception of the shape of the pre-He WDs strip. However, due to the limited number of examples, it is currently difficult to ascertain whether the blue and red edges remain linear for extremely high mass or ELM, based on both our samples and the samples investigated by others.

After carefully analysing all available data, including a statistically significant and somewhat homogeneous set of 20 pre-He WDs (nine of which pulsated), we have accurately identified the new instability strip. The strip is easily recognizable with its distinct blue;

and the red edges;

We carefully considered all relevant variables in our approach. The dashed line for the blue and red edges in Fig. 8 illustrates this. Non-pulsating stars within the instability strip are also included in these edges. This also decreases the accuracy of the instability strip, resulting in a computed likelihood of the instability strip being pure of approximately 0.04 per cent. To better figure out the width and edges of the instability strip and to look into how pure it is, it is important to get higher S/N spectra of all the pulsating pre-ELMVs (Extremely Low-Mass Variables) and non-pulsating ones in the strip.

The pulsating pre-ELM WD components of TIC 54957535 and TIC 65448527 both exhibited pulsations with periods of 420.27 and 442.60 s, respectively, as was previously noted. The effective temperature and gravity of these stars place them slightly outside of the theoretical instability domain explained by Córsico et al. (2016, see fig. 1). These stars are situated near the boundary of the non-radial dipole (⁠|$\ell$| = 1) blue edge of the pre-ELMV instability domain. This positioning is attributed to the |$\kappa -\gamma$| mechanism acting in the He|$^+$|–He|$^{++}$| partial ionization region, as detailed in Córsico et al. (2016). They generated comprehensive models to clarify the reasons behind the incompatibility of the WASP J0247-25B and KIC 9164561 systems, which are inconsistent with the theoretical instability zone. The discussions related to these models have led to the conclusion that variations in He abundances may alter the position of the instability zone. It has been noted that the pulsation frequencies in the system may be activated if the WASP J0247-25B system, situated outside the instability zone and on the hotter side, exhibits higher He abundance than what the evolution models have predicted. Similarly, it has been observed that the pulsation frequencies of the KIC 9164561 system, which is located inside the instability zone, can be suppressed if it has a smaller He abundance than predicted by the models. The reason for these discrepancies in the models has been attributed to the possibility that the systems underwent a different evolution process than the binary star evolution models that were employed as initial models; for instance, they might have had different initial masses for their components and mass loss processes might have taken place at different times. It is possible that the two systems in this study and the two systems studied by Çakırlı et al. (2024; 1SWASPJ232812.74−395523.3, TYC 6051-1123-1) which are located outside the instability zone are pulsating due to processes similar to those predicted for the WASP J0247−25B system. Furthermore, Jeffery & Saio (2013) noted that as the hydrogen abundance diminishes, the instability zone moves towards higher temperatures and greater luminosities, reinforcing the prediction concerning the He abundance.

We can also compare the observed periods in these stars along with the ranges of excited periods for the sequences corresponding to the pre-WD model sequences Córsico et al. (2016, see fig. 8), identified based on their positions in the T|$_{\rm eff}$|–|$\log ~g$| diagram. Notably, our findings are closely match their theoretical computations.

Finally, the addition of two pulsating pre-ELMV WDs enhances the discoveries made by Maxted et al. (2014a) concerning a newly discovered category of pulsating stars in the later evolutionary stages of low-mass WDs. Recent discoveries of additional members within this category of pulsating stars, in addition to their analysis in relation to the existing theoretical framework, will allow us to bring more light on the evolutionary history of their progenitor stars.

6 CONCLUSIONS

This paper is part of an ongoing series that focuses on the search and study of pre-ELMVs in TESS EBs. Based on the short-cadence TESS data from Sector 4 through 61, we found two new pre-ELMVs candidates. Kim et al. (2021) had previously conducted a study on one of these stars, specifically TIC 65448527, using only photometric data. The spectroscopy was performed using the high-resolution UVES spectra collected from the ESO Science Archive Facility. By analysing the spectra, we successfully derived radial velocity curves for both the primary star and the faint secondary star, representing the first instance of such measurements. An in-depth analysis of the spectrum enabled us to acquire accurate measurements of T|$_{\rm eff}$|⁠, |$\log ~g$|⁠, and the projected rotational velocity for both the primary and secondary components of the systems. The measured radial velocity data were solved alongside the TESS light curve and the orbital elements given in Table 3 were acquired. Based on the calculated models, it was confirmed that our program’s targets are EL CVn-type systems that have pre-ELMV components. The derived physical parameters of the more massive A-type primary stars show that they are somewhat evolved but still very close to the instability strip on the MS band when compared with the HR diagram. The less-massive components of the systems consist of pre-ELMVs, based on their absolute physical parameters. By comparing their cold degenerate radius (Nelson & Rappaport 2003), it becomes evident that they are thermally bloated, bearing a strong resemblance to the pre-ELMVs identified by the investigations. Based on our analysis, it is likely that the systems are EBs with pre-ELMVs, specifically EL CVn-type binaries.

In addition to the changes in light caused by eclipses, the residual light curves of the systems also exhibit short-period variations. The probability density function for the amplitude spectrum analysis of short-period variations in their light-curve residuals has been calculated using the sigspec program. The systems exhibit two distinct frequency concentration ranges in their amplitude spectrum: one ranging from 230 to 460 |$\mu {\rm Hz}$|⁠, and the other ranging from 1160 to 2890 |$\mu {\rm Hz}$|⁠. The pulsation signals in the low-frequency range can be observed during the two eclipses, despite the fact that the pre-ELMVs companion is entirely eclipsed by the A-type primary star between orbital phases 0.45–0.55. This implies that the intrinsic pulsations of the |$\delta$| Sct-type primary star are likely responsible for the independent frequencies between 230 and 460 |$\mu {\rm Hz}$|⁠. For the high-frequency signals, the situation is different. During the entire occultation of the pre-ELMVs component by the primary star, the pulsation signals in the second frequency region were barely identifiable. During its passage in front of the primary star, there appeared to be pulsation signals occurring between 1160 and 2890 |$\mu {\rm Hz}$|⁠. Therefore, we identify that the several pulsation signals, as indicated in Table A1, most likely originate from the pre-ELMVs component. Pre-He WDs may pulsate in p, g, or mixed modes (Córsico et al. 2016; Istrate et al. 2016b). These pulsations provide valuable insights into their inner structures and fundamental properties through the field of asteroseismology. Due to the fact that it offers the opportunity to directly determine the absolute physical parameters of the pulsators, a pure instability strip that is developed for this new class of pulsators has the potential to play a significant and one-of a-kind role in the method of understanding their formation and evolution. There is an increasing number of pre-ELMVs discovered to fall outside the blue edge of the theoretical predictions. This could be due to different He abundances in the driving zone than the model estimations which suggests distinct binary evolutionary origins. This constitutes an open problem to be investigated.

ACKNOWLEDGEMENTS

We thank the anonymous reviewer for their careful reading of our manuscript and their many insightful comments and suggestions. This research made use of data collected at ESO under programmes 086.D-0194(A) (PI: P. Maxted), and 094.D-0027(A) (PI: P. Maxted). This research has made use of ‘Aladin sky atlas’ developed at CDS, Strasbourg Observatory, France. The following internet-based resources were used in research for this paper: the NASA Astrophysics Data System; the SIMBAD database operated at CDS, as well as of the open-source python packages astropy, http://www.astropy.org (Astropy Collaboration 2013), healpy,http://healpix.sf.net (Górski et al. 2005), matplotlib (Hunter 2007), numpy (Harris et al. 2020), and pandas (Reback et al. 2020).

DATA AVAILABILITY

Photometric and spectroscopic raw data used in this paper are publicly available at the https://archive.stsci.edu/missions-and-data/tess, and http://archive.eso.org/cms.html archives.

Footnotes

REFERENCES

APPENDIX A: FREQUENCIES

APPENDIX B: RADIAL VELOCITY MEASUREMENTS OF TARGETS