Asteroseismology of SX Phe stars in binary systems: constraining the parameters and formation history of DY Pegasi

Asteroseismology of SX Phe stars in binary systems: constraining the parameters and formation history of DY Pegasi Wojciech Niewiadomski, Jadwiga Daszyńska-Daszkiewicz, Przemysław Walczak Instytut Astronomiczny, Uniwersytet Wrocławski, Poland SEISMIC MODELING WITH SINGLE EVOLUTION SEISMIC MODELING WITH BINARY EVOLUTION The upper panel shows the position of seismic models of DY Peg on the HR diagram. The median values of the parameters of these models are given in the table on the left, whereas their distributions are shown in the histograms on the right (for ξt = 4 km s-1). The age of DY Peg from the seismic modelling with single evolution is about 1.8 Gyr. In all models both radial modes are excited (the instability parameter 𝜼 is positive – the bottom middle and right panels). DY Pegasi is one of a few field SX Phoenicis stars. It pulsates in the two radial modes and a few nonradial modes. The star is a blue straggler star (BSS) and its colour, metallicity, and kinematics indicate that it is a member of the thick-disk population. DY Peg is also in a binary system, most probably with a white dwarf companion. If so, the most likely channel for the formation of DY Peg as BSS is through wind Roche-lobe overflow (WRLOF). First, we performed seismic modelling of DY Peg based on single evolution calculations. We constructed the models which fit the observed frequencies of two radial modes and have the effective temperature and luminosity within the error box. Observational constraints on metallicity, rotation and radius from the infrared photometry were also included. We derived the seismic values of mass, metallicity, hydrogen abundance, rotation, efficiency of envelope convection and the extent of convective core overshooting. In the next step, using the MESA binary module, we calculated the binary evolution of the system assuming the white dwarf mass to be 0.6 M☉, the orbital period of about 42 years and eccentricity e=0.24. Based on the binary evolution models, we constructed seismic models of DY Peg and compare their properties with those obtained with a single evolution calculations. ACKNOWLEDGEMENTS: the work was financially supported by the Polish National Science Centre grant 2023/50/A/ST9/00144 DY Peg was observed by TESS in Sector 56. We used 200 s cadence PDCSAP flux data to extract pulsation frequencies. All frequencies with a signal-to-noise ratio (S/N) greater than 5.0 were considered as significant. The noise level was estimated as the mean amplitude within a 1 d⁻¹-wide window centred on each frequency. We used an algorithm based on the fast Fourier transforms for non-equally spaced data (e.g., Leroy 2012) and proceeded the standard pre-whitening procedure. The panel on the right shows the periodograms for the original data, after subtracting 3 frequencies, and after subtracting 24 frequencies. We found 8 independent frequencies, among which 𝛎1=13.712437(4) d⁻¹ and 𝛎2=17.6995(2) d⁻¹ were identified as the fundamental radial mode and the first radial overtone, respectively. The remaining six can only be associated only with nonradial modes. The table gives the whole set of the extracted frequencies from the TESS data. PULSATION FREQUENCIES OF DY PEG FROM TESS Nearly 70 years of observations of DY Peg have revealed a secular decrease in its dominant pulsation period. Deviations in the observed times of maxima from the expected trend suggest the presence of a stellar companion, likely a white dwarf, producing a light-time effect. The radius of the primary was estimated to be 2.09±0.25 R☉ using the Baade–Wesselink method (Wilson et al. 1998), in good agreement with the value of 2.1±0.1 R☉ obtained from limb-darkened disk angular diameter from the infrared photometry (Cruzalèbes et al. 2019) and the distance derived from the Gaia DR3 parallax. Metallicity was estimated to be [m/H] = –0.8 (Burki & Meylan 1986, Hintz et al. 2004). The projected rotational velocity is 23.6 km s⁻¹ (Solano et al. 1997). Close binary systems can undergo mass transfer at various evolutionary stages of the donor: during the main-sequence phase (Case A), after the main sequence (Case B), or during the asymptotic giant branch (AGB) phase (Case C). In widely separated systems, where the AGB star does not fill its Roche lobe, mass can still be efficiently transferred through a cold stellar wind from the evolved donor to the companion, in a manner analogous to the classical Roche-lobe overflow. This mechanism is known as wind Roche-lobe overflow (WRLOF), called also Case D. We conducted binary evolution modeling of DY Peg using the MESA binary module with the implementation of WRLOF by Sun et al. (2024). We assumed the initial orbital period Porb= 10 000 days and aimed to get the observed value Porb= 15 425 days (Xue et al. 2020), at the end of mass transfer. After reaching this value of Porb, further evolution of the acceptor was computed with the MESA code for single-star evolution. The panels below illustrate the evolution of the orbital period (top) and masses of the acceptor and donor (bottom) for different pairs of their initial masses. We constructed seismic models of DY Peg with binary-evolution computations. The top panel below presents the Petersen diagram for a few models of the acceptor. The horizontal and vertical lines mark the observed values of 𝛎1 and 𝛎1/𝛎2. The bottom panel shows the corresponding evolutionary tracks on the HR diagram compared with the error box of DY Peg. The internal profiles of hydrogen X, helium Y (top) and metallicity Z (bottom), of two models with the same current mass and surface abundances but having different evolution history, , i.e., single vs binary. Both models match the dominant frequency of DY Peg. Monte Carlo simulations combined with Bayesian inference were used to determine the stellar parameters of DY Peg. Evolutionary models were computed using the Warsaw–New Jersey evolutionary code (Paczyński, 1969; Pamyatnykh, 1999). We adopted the OPAL opacities (Iglesias&Rogers, 1996), solar chemical mixture of Asplund et al. (2009), and the OPAL2005 equation of state (Rogers&Nayfonov 2002). Linear non-adiabatic pulsations were calculated using the code of Dziembowski (1977). We fitted the observed frequencies of two radial modes, 𝛎1=13.71243 d−1 and 𝛎2 =17.6995 d−1, the effective temperature and luminosity, as well as the photometric amplitudes and phases in the Strömgren uvby system for 𝛎1. NEMO model atmospheres were used for various microturbulent velocities ξt. We considered the whole range of effective temperature found in the literature, i.e., (6750, 8350) K. The luminosity log L/L⊙ = 1.07(5) was derived from the StarHorse2 distance (based on the Gaia DR3 parallax) and the bolometric correction from Kurucz models.