2025/11/26 by Yoshiki Hatta, Hatta, Yoshiki, T. Sekii +1
Physics and Astronomy · #Astronomy and Astrophysical Research #FOS: Physical sciences #Pulsars and Gravitational Waves Research #Solar and Stellar Astrophysics (astro-ph.SR) #Stellar, planetary, and galactic studies
paper · pdf · doi:10.48550/arxiv.2511.20948
openalex publication_date 2025/11/26 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28
Theoretical study of high-order gravity-mode period spacing (ΔPg) pattern is relevant for the better understanding of internal properties of intermediate-mass (1.5 M_\odot < M < 8 M\odot) main-sequence g-mode pulsators. In this paper, we carry out the first-order perturbative analysis to evaluate effects of a sharp, though not discontinuous, transition in the Brunt-Väisälä (BV) frequency on the ΔPg pattern. Such a finite-width transition in the BV frequency, whose scale height can be comparable to the local wavelength of gravity waves, is expected to develop in relatively low-mass (1.5 M_\odot < M < 3 M\odot) main-sequence stars, causing a bump in the second derivative of the BV frequency. Inspired by Unno et al.'s formulation, we treat the bump in the second derivative of the BV frequency as a small perturbation, which allows us to derive an analytical expression of the ΔPg pattern. The analytical expression shows that the amplitude of the oscillatory ΔPg pattern is determined by a weighted average of the bump in the second derivative of the BV frequency where the weighting function is given by the g-mode eigenfunction. Tests with low-mass (∼ 2 M_\odot) main-sequence stellar models show that the analytical expression can reproduce the ΔPg patterns numerically computed reasonably well. The results of our perturbative analysis will be useful for, e.g., improving semi-analytical expressions of the ΔPg pattern, which would enable us to investigate ΔPg patterns of SPB stars and γ Dor stars for inferring chemical composition profile and rotation rates.