Insights from Analytical Theory of Eccentric Circumbinary Disks
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916037423792128 |
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| author | Grcic, Marcela D'Orazio, Daniel J. Pessah, Martin E. |
| author_facet | Grcic, Marcela D'Orazio, Daniel J. Pessah, Martin E. |
| contents | Eccentric cavities in circumbinary disks precess on timescales much longer than the binary orbital period. These long-lived steady states can be understood as trapped modes in an effective potential primarily determined by the binary quadrupole and the inner-disk pressure support, with associated frequencies $ω_Q$ and $ω_P$. Within this framework, we show that the ratio $ω_P/ω_Q$ is the main parameter determining the mode spectrum, and obtain a thorough understanding of it by systematically solving this problem with various degrees of sophistication. We first find analytical solutions for truncated power-law disks and use this insight in disks with smooth central cavities. Our main findings are: (i) The number of modes increases for thinner disks and more-equal-mass binaries. (ii) For 2D disks, the normalized ground-mode frequency, $ω_0/(ω_Q+ω_P)$, decreases monotonically with the ratio $ω_P/ω_Q$. (iii) For thin disks, $ω_P\llω_Q$, the ground-mode frequency coincides with the maximum of the effective potential, which tracks the gravitational quadrupole frequency inside the inner-disk cavity, and is thus rather sensitive to the density profile of the cavity, where these modes are localized. (iv) For thick disks, $ω_P\ggω_Q$, increasing pressure support anchors the peak of the effective potential at the inner cavity radius as the ground-mode extends farther out and its frequency decreases. (v) In agreement with numerical simulations, with $ω_P/ω_Q \simeq 0.1$, we find that disk precession is rather insensitive to the density profile and ground-mode frequencies for 3D disks are about half the value for 2D disks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_17658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Insights from Analytical Theory of Eccentric Circumbinary Disks Grcic, Marcela D'Orazio, Daniel J. Pessah, Martin E. Solar and Stellar Astrophysics Earth and Planetary Astrophysics Eccentric cavities in circumbinary disks precess on timescales much longer than the binary orbital period. These long-lived steady states can be understood as trapped modes in an effective potential primarily determined by the binary quadrupole and the inner-disk pressure support, with associated frequencies $ω_Q$ and $ω_P$. Within this framework, we show that the ratio $ω_P/ω_Q$ is the main parameter determining the mode spectrum, and obtain a thorough understanding of it by systematically solving this problem with various degrees of sophistication. We first find analytical solutions for truncated power-law disks and use this insight in disks with smooth central cavities. Our main findings are: (i) The number of modes increases for thinner disks and more-equal-mass binaries. (ii) For 2D disks, the normalized ground-mode frequency, $ω_0/(ω_Q+ω_P)$, decreases monotonically with the ratio $ω_P/ω_Q$. (iii) For thin disks, $ω_P\llω_Q$, the ground-mode frequency coincides with the maximum of the effective potential, which tracks the gravitational quadrupole frequency inside the inner-disk cavity, and is thus rather sensitive to the density profile of the cavity, where these modes are localized. (iv) For thick disks, $ω_P\ggω_Q$, increasing pressure support anchors the peak of the effective potential at the inner cavity radius as the ground-mode extends farther out and its frequency decreases. (v) In agreement with numerical simulations, with $ω_P/ω_Q \simeq 0.1$, we find that disk precession is rather insensitive to the density profile and ground-mode frequencies for 3D disks are about half the value for 2D disks. |
| title | Insights from Analytical Theory of Eccentric Circumbinary Disks |
| topic | Solar and Stellar Astrophysics Earth and Planetary Astrophysics |
| url | https://arxiv.org/abs/2504.17658 |