Semi-analytical Expression of G-mode Period Spacing: The Case of Brunt–Väisälä Frequency with Not a Jump but a Ramp

Abstract

To decipher complex patterns of gravity-mode period spacings observed for intermediate-mass main-sequence stars is an important step toward a better understanding of the structure and dynamics in the deep radiative region of the stars. In this study, we apply the JWKB approximation to derive a semi-analytical expression of the g-mode period spacing pattern, for which the gradient in the Brunt–Väisälä frequency is taken into account. The formulation includes the term P −1 B ⋆, where P and B ⋆ represent the g-mode period and degree of the structural variation, the latter of which especially is related to the steepness of the gradient of the Brunt–Väisälä frequency. Tests with one-dimensional stellar models show that the semi-analytical expression derived in this study is useful for inferring the degree of the structural variation B ⋆ with an accuracy of ∼10 % in the case of relatively massive intermediate-mass models with the mass M larger than 3 M ⊙. The newly formulated expression will possibly allow us to put further constraints on, e.g., mixing processes inside intermediate-mass main-sequence g-mode pulsators such as β Cep, SPB, and γ Dor stars that have been principal targets in asteroseismology.