Slowly Rotating Relativistic Stars: VII. Gravitational Radiation from the Quasi-Radial Modes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914025666772992 |
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| author | Hartle, James B. Thorne, Kip S. |
| author_facet | Hartle, James B. Thorne, Kip S. |
| contents | When a relativistic star rotates slowly and rigidly, centrifugal forces flatten it slightly, thereby catalyzing a small admixture of quadrupolar vibration into its radial modes and a damping of the resulting quasi-radial modes. The damping rate $1/τ$ of each quasi-radial mode divided by its frequency $σ^{(0)}$ is given by ${(1/τ) / σ^{(0)} }= β(σ^{(0)})^3 Ω^4 R^8/M \;, $where $Ω$, $R$ and $M$ are the angular velocity, radius and mass of the star, and $β$ is a dimensionless number that depends on the mode, on relativistic corrections, and on the structure of the star, and is typically of order unity for the fundamental quasi-radial mode in the nonrelativistic limit. In this paper we develop equations and an algorithm for computing the emitted waves and the resulting damping factor $β$. The rotation is treated to second-order in the angular velocity and the pulsation amplitudes are assumed small and linearized, but no other approximations are made. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05436 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Slowly Rotating Relativistic Stars: VII. Gravitational Radiation from the Quasi-Radial Modes Hartle, James B. Thorne, Kip S. General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena Solar and Stellar Astrophysics When a relativistic star rotates slowly and rigidly, centrifugal forces flatten it slightly, thereby catalyzing a small admixture of quadrupolar vibration into its radial modes and a damping of the resulting quasi-radial modes. The damping rate $1/τ$ of each quasi-radial mode divided by its frequency $σ^{(0)}$ is given by ${(1/τ) / σ^{(0)} }= β(σ^{(0)})^3 Ω^4 R^8/M \;, $where $Ω$, $R$ and $M$ are the angular velocity, radius and mass of the star, and $β$ is a dimensionless number that depends on the mode, on relativistic corrections, and on the structure of the star, and is typically of order unity for the fundamental quasi-radial mode in the nonrelativistic limit. In this paper we develop equations and an algorithm for computing the emitted waves and the resulting damping factor $β$. The rotation is treated to second-order in the angular velocity and the pulsation amplitudes are assumed small and linearized, but no other approximations are made. |
| title | Slowly Rotating Relativistic Stars: VII. Gravitational Radiation from the Quasi-Radial Modes |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena Solar and Stellar Astrophysics |
| url | https://arxiv.org/abs/2509.05436 |