High-order Gravity-mode Period Spacing Patterns of Intermediate-mass ($1.5 \, M_\odot < M < 3 \, M_{\odot}$) Main-sequence Stars I. Perturbative Analysis
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911287464689664 |
|---|---|
| author | Hatta, Yoshiki Sekii, Takashi |
| author_facet | Hatta, Yoshiki Sekii, Takashi |
| contents | Theoretical study of high-order gravity-mode period spacing ($ΔP_g$) 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 $ΔP_g$ 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 $ΔP_g$ pattern. The analytical expression shows that the amplitude of the oscillatory $ΔP_g$ 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 ($\sim 2 \, M_\odot$) main-sequence stellar models show that the analytical expression can reproduce the $ΔP_g$ patterns numerically computed reasonably well. The results of our perturbative analysis will be useful for, e.g., improving semi-analytical expressions of the $ΔP_g$ pattern, which would enable us to investigate $ΔP_g$ patterns of SPB stars and $γ$ Dor stars for inferring chemical composition profile and rotation rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-order Gravity-mode Period Spacing Patterns of Intermediate-mass ($1.5 \, M_\odot < M < 3 \, M_{\odot}$) Main-sequence Stars I. Perturbative Analysis Hatta, Yoshiki Sekii, Takashi Solar and Stellar Astrophysics Theoretical study of high-order gravity-mode period spacing ($ΔP_g$) 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 $ΔP_g$ 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 $ΔP_g$ pattern. The analytical expression shows that the amplitude of the oscillatory $ΔP_g$ 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 ($\sim 2 \, M_\odot$) main-sequence stellar models show that the analytical expression can reproduce the $ΔP_g$ patterns numerically computed reasonably well. The results of our perturbative analysis will be useful for, e.g., improving semi-analytical expressions of the $ΔP_g$ pattern, which would enable us to investigate $ΔP_g$ patterns of SPB stars and $γ$ Dor stars for inferring chemical composition profile and rotation rates. |
| title | High-order Gravity-mode Period Spacing Patterns of Intermediate-mass ($1.5 \, M_\odot < M < 3 \, M_{\odot}$) Main-sequence Stars I. Perturbative Analysis |
| topic | Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2511.20948 |