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 the better understanding of the structure and dynamics in the deep radiative region of the stars. In this study, we apply 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 a term $P^{-1}{B}_{\star }$, where $P$ and $B_{\star }$ 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 1-dimensional stellar models show that the semi-analytical expression derived in this study is useful for inferring the degree of the structural variation $B_{\star }$ with accuracy of $\sim 10\%$ in the case of relatively massive intermediate-mass models with the mass $M$ larger than $3M_{\odot }$. 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 $\beta$ Cep, SPB, and $\gamma$ Dor stars that have been principal targets in asteroseismology.

20 pages, 15 figures, 1 table, accepted for publication in ApJ

References in corpus (20)

• Modules for Experiments in Stellar Astrophysics (MESA)
• Modules for Experiments in Stellar Astrophysics (MESA): Pulsating Variable Stars, Rotation, Convective Boundaries, and Energy Conservation
• Probing the properties of convective cores through g modes: high-order g modes in SPB and gamma Doradus stars
• Asteroseismic measurement of surface-to-core rotation in a main sequence A star, KIC 11145123
• Asteroseismic measurement of slow, nearly-uniform surface-to-core rotation in the main sequence F star KIC 9244992
• A new asteroseismic diagnostic for internal rotation in $\gamma$ Doradus stars
• Structural glitches near the cores of red giants revealed by oscillations in g-mode period spacings from stellar models
• KIC 10526294: a slowly rotating B star with rotationally split, quasi-equally spaced gravity modes
• Period spacings of $\gamma$ Doradus pulsators in the \textit{Kepler} field: Rossby and gravity modes in 82 stars
• Rotation of the convective core in $\gamma$ Dor stars measured by dips in period spacings of g modes coupled with inertial modes
• First evidence of inertial modes in $\gamma$ Doradus stars: The core rotation revealed
• Probing the temperature gradient in the core boundary layer of stars with gravito-inertial modes: the case of KIC7760680
• Impact of rotation on stochastic excitation of gravity and gravito-inertial waves in stars
• Internal rotation and inclinations of slowly pulsating B stars: Evidence of interior angular momentum transport
• Detection of period-spacing patterns due to the gravity modes of rotating dwarfs in the TESS southern continuous viewing zone
• Rotating Convective Core Excites Non-Radial Pulsations to Cause Rotational Modulations in Early-Type Stars
• Internal rotation and buoyancy travel time of 60 gamma Doradus stars from uninterrupted TESS light curves spanning 352 days
• Asteroseismology of the dip structure in period-spacings of rapidly rotating gamma Doradus stars caused by the coupling between core and envelope oscillations
• Spectroscopic and asteroseismic analysis of the remarkable main-sequence A star KIC 11145123
• Non-standard modeling of a possible blue straggler star, KIC 11145123

Cited by in corpus (5)

• The Asteroseismic Imprints of Mass Transfer: A Case Study of a Binary Mass Gainer in the SPB Instability Strip
• Buoyancy glitches in pulsating stars revisited
• Parametric models of core-helium-burning stars: structural glitches near the core
• Asteroseismology and Buoyancy Glitch Inversion with Fourier Spectra of Gravity Mode Period Spacings
• Asteroseismic Imprints of Mass Transfer in Binary Stars: Probing the Interiors of Donors and Accretors with Gravity and Acoustic Modes