Dynamical Stability of Polar Circumbinary Orbits and Planet Formation in the Planetary Disk of 99 Herculis
A possible polar-ring debris disk, the dynamics of which can be described by the outer hierarchical restricted three-body problem, has been detected in 99 Herculis. An empirical formula for the minimum radius beyond which test particles in polar orbits can keep stable within 10 ^7 binary periods is...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | The Astronomical Journal |
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| Online Access: | https://doi.org/10.3847/1538-3881/ace039 |
| _version_ | 1797699385378734080 |
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| author | Ying Wang Wei Sun Ji-lin Zhou Ming Yang Fu-yao Liu |
| author_facet | Ying Wang Wei Sun Ji-lin Zhou Ming Yang Fu-yao Liu |
| author_sort | Ying Wang |
| collection | DOAJ |
| description | A possible polar-ring debris disk, the dynamics of which can be described by the outer hierarchical restricted three-body problem, has been detected in 99 Herculis. An empirical formula for the minimum radius beyond which test particles in polar orbits can keep stable within 10 ^7 binary periods is provided through numerical fitting, applying to the binary eccentricity ${e}_{1}\in \left[0,0.8\right)$ and the mass ratio of the binary $\lambda \in \left[0.1,1\right]$ , where λ = m _0 / m _1 ( m _0 and m _1 represent the masses of the two binary stars). The polar planetary disk has the lowest statistical accretion efficiency and a moderate impact frequency of collisions among planetesimals (with radii of 1–10 km) compared to those in a circumbinary coplanar disk and a standard disk around the single host star. The collision timescale in the circumbinary disk (both polar and coplanar configurations) is longer than 10 ^7 yr, exceeding the dissipation timescale of the gas disk. Stochastic simulations show that successive collisions cannot make planetesimals grow, which may explain the formation of the debris disk observed in 99 Herculis. |
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| id | doaj.art-e9fa9d770d5e497ab07ee4d7f1f306b5 |
| institution | Directory Open Access Journal |
| issn | 1538-3881 |
| language | English |
| last_indexed | 2024-03-12T04:07:15Z |
| publishDate | 2023-01-01 |
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| spelling | doaj.art-e9fa9d770d5e497ab07ee4d7f1f306b52023-09-03T11:14:42ZengIOP PublishingThe Astronomical Journal1538-38812023-01-0116625210.3847/1538-3881/ace039Dynamical Stability of Polar Circumbinary Orbits and Planet Formation in the Planetary Disk of 99 HerculisYing Wang0https://orcid.org/0000-0003-0506-054XWei Sun1https://orcid.org/0000-0003-2620-6835Ji-lin Zhou2https://orcid.org/0000-0003-1680-2940Ming Yang3https://orcid.org/0000-0002-6926-2872Fu-yao Liu4School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science , Shanghai 201620, People's Republic of ChinaSchool of Mathematics, Physics and Statistics, Shanghai University of Engineering Science , Shanghai 201620, People's Republic of ChinaSchool of Astronomy and Space Science and Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University , Nanjing 210093, People's Republic of ChinaCollege of Surveying and Geo-Informatics, Tongji University , Shanghai 200092, People's Republic of ChinaSchool of Mathematics, Physics and Statistics, Shanghai University of Engineering Science , Shanghai 201620, People's Republic of ChinaA possible polar-ring debris disk, the dynamics of which can be described by the outer hierarchical restricted three-body problem, has been detected in 99 Herculis. An empirical formula for the minimum radius beyond which test particles in polar orbits can keep stable within 10 ^7 binary periods is provided through numerical fitting, applying to the binary eccentricity ${e}_{1}\in \left[0,0.8\right)$ and the mass ratio of the binary $\lambda \in \left[0.1,1\right]$ , where λ = m _0 / m _1 ( m _0 and m _1 represent the masses of the two binary stars). The polar planetary disk has the lowest statistical accretion efficiency and a moderate impact frequency of collisions among planetesimals (with radii of 1–10 km) compared to those in a circumbinary coplanar disk and a standard disk around the single host star. The collision timescale in the circumbinary disk (both polar and coplanar configurations) is longer than 10 ^7 yr, exceeding the dissipation timescale of the gas disk. Stochastic simulations show that successive collisions cannot make planetesimals grow, which may explain the formation of the debris disk observed in 99 Herculis.https://doi.org/10.3847/1538-3881/ace039Exoplanet formationExoplanet dynamicsDebris disksProtoplanetary disksPlanetesimalsThree-body problem |
| spellingShingle | Ying Wang Wei Sun Ji-lin Zhou Ming Yang Fu-yao Liu Dynamical Stability of Polar Circumbinary Orbits and Planet Formation in the Planetary Disk of 99 Herculis The Astronomical Journal Exoplanet formation Exoplanet dynamics Debris disks Protoplanetary disks Planetesimals Three-body problem |
| title | Dynamical Stability of Polar Circumbinary Orbits and Planet Formation in the Planetary Disk of 99 Herculis |
| title_full | Dynamical Stability of Polar Circumbinary Orbits and Planet Formation in the Planetary Disk of 99 Herculis |
| title_fullStr | Dynamical Stability of Polar Circumbinary Orbits and Planet Formation in the Planetary Disk of 99 Herculis |
| title_full_unstemmed | Dynamical Stability of Polar Circumbinary Orbits and Planet Formation in the Planetary Disk of 99 Herculis |
| title_short | Dynamical Stability of Polar Circumbinary Orbits and Planet Formation in the Planetary Disk of 99 Herculis |
| title_sort | dynamical stability of polar circumbinary orbits and planet formation in the planetary disk of 99 herculis |
| topic | Exoplanet formation Exoplanet dynamics Debris disks Protoplanetary disks Planetesimals Three-body problem |
| url | https://doi.org/10.3847/1538-3881/ace039 |
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