Study of the low-order Δν–ρ¯ relation for moderately rotating δ Scuti stars and its impact on their characterization

Abstract

ABSTRACT The large separation in the low-radial order regime is considered as a highly valuable observable to derive mean densities of δ Scuti stars, due to its independence with rotation. Up to now, theoretical studies of this Δν–${\bar{\rho}}$ relation have been limited to 1D non-rotating models and 2D pseudo-evolutionary models. The present work aims at completing this scenario by investigating quantitatively the impact of rotation in this relation on a large grid of 1D asteroseismic models representative of δ Scuti stars. These include rotation effects on both the stellar evolution and the interaction with pulsation. This allowed us to compute the stellar deformation, get the polar and equatorial radii, and correct the stellar mean densities. We found that the new Δν–${\bar{\rho}}$ relation for rotating models is compatible with previous works. We explained the dispersion of the points around the linear fits as caused mainly by the distribution of the stellar mass, and partially by the evolutionary stage. The new fit is found to be close to the previous theoretical studies for lower masses ($1.3\!-\!1.81\, \mathrm{M}_{\odot }$). However, the opposite holds for the observations: For the higher masses ($1.81\!-\!3\, \mathrm{M}_{\odot }$), the fit is more compatible with the empirical relation. To avoid such discrepancies, we provided new limits to the fit that encompass any possible dependence on mass. We applied these results to characterize the two well-known δ Scuti stars observed by CoRoT, HD 174936 and HD 174966, and compared the physical parameters with those of previous works. The inclusion of rotation in the modelling causes a tendency towards greater masses, radii, and luminosities, and lower density values. Comparison between Δν and Gaia’s luminosities also allowed us to constrain the inclination angles and rotational velocities of both stars. The present results pave the way to systematically constrain the angle of inclination (and thereby the actual surface rotation velocity) of δ Scuti stars.