Period–Luminosity Relationship for δ Scuti Stars Revisited

Abstract

The Gaia DR3 parallax approach was used to estimate the absolute parameters of 2375 $\delta$ Scuti stars from the ASAS catalog. The selected stars have a variety of observational characteristics, with a higher than 80\% probability of being $\delta$ Scuti stars. We have displayed all the stars in the Hertzsprung-Russell (H-R) diagram along with the $\delta$ Scuti instability strip, the Zero Age Main Sequence (ZAMS), and the Terminal-Age Main Sequence (TAMS). Then, we determined which fundamental and overtone modes each star belongs to using pulsation constant ($Q$) calculations. In addition, we evaluated the parameters in the $Q$ calculation equation using three machine learning methods, which showed that surface gravity and temperature have the greatest effect on its calculation. The Period-Luminosity ($P-L$) relationship of the $\delta$ Scuti stars was also revisited. Eventually, using least squares linear regression, we made four linear fits for fundamental and overtone modes and updated their relationships.