Evolution of eccentricity and orbital inclination of migrating planets in 2:1 mean motion resonance
We determine, analytically and numerically, the conditions needed for a system of two migrating planets trapped in a 2:1 mean motion resonance to enter an inclination-type resonance. We provide an expression for the asymptotic equilibrium value that the eccentricity $e_{\rm i}$ of the inner planet r...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
Oxford University Press
2014
|
| _version_ | 1797086167210917888 |
|---|---|
| author | Teyssandier, J Terquem, C |
| author_facet | Teyssandier, J Terquem, C |
| author_sort | Teyssandier, J |
| collection | OXFORD |
| description | We determine, analytically and numerically, the conditions needed for a system of two migrating planets trapped in a 2:1 mean motion resonance to enter an inclination-type resonance. We provide an expression for the asymptotic equilibrium value that the eccentricity $e_{\rm i}$ of the inner planet reaches under the combined effects of migration and eccentricity damping. We also show that, for a ratio $q$ of inner to outer masses below unity, $e_{\rm i}$ has to pass through a value $e_{\rm i,res}$ of order 0.3 for the system to enter an inclination-type resonance. Numerically, we confirm that such a resonance may also be excited at another, larger, value $e_{\rm i, res} \simeq 0.6$, as found by previous authors. A necessary condition for onset of an inclination-type resonance is that the asymptotic equilibrium value of $e_{\rm i}$ is larger than $e_{\rm i,res}$. We find that, for $q \le 1$, the system cannot enter an inclination-type resonance if the ratio of eccentricity to semimajor axis damping timescales $t_e/t_a$ is smaller than 0.2. This result still holds if only the eccentricity of the outer planet is damped and $q \lesssim 1$. As the disc/planet interaction is characterized by $t_e/t_a \sim 10^{-2}$, we conclude that excitation of inclination through the type of resonance described here is very unlikely to happen in a system of two planets migrating in a disc. |
| first_indexed | 2024-03-07T02:18:12Z |
| format | Journal article |
| id | oxford-uuid:a300c4d5-1c5a-472f-b9f5-c1fc92eea52c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:18:12Z |
| publishDate | 2014 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:a300c4d5-1c5a-472f-b9f5-c1fc92eea52c2022-03-27T02:23:48ZEvolution of eccentricity and orbital inclination of migrating planets in 2:1 mean motion resonanceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a300c4d5-1c5a-472f-b9f5-c1fc92eea52cEnglishSymplectic Elements at OxfordOxford University Press2014Teyssandier, JTerquem, CWe determine, analytically and numerically, the conditions needed for a system of two migrating planets trapped in a 2:1 mean motion resonance to enter an inclination-type resonance. We provide an expression for the asymptotic equilibrium value that the eccentricity $e_{\rm i}$ of the inner planet reaches under the combined effects of migration and eccentricity damping. We also show that, for a ratio $q$ of inner to outer masses below unity, $e_{\rm i}$ has to pass through a value $e_{\rm i,res}$ of order 0.3 for the system to enter an inclination-type resonance. Numerically, we confirm that such a resonance may also be excited at another, larger, value $e_{\rm i, res} \simeq 0.6$, as found by previous authors. A necessary condition for onset of an inclination-type resonance is that the asymptotic equilibrium value of $e_{\rm i}$ is larger than $e_{\rm i,res}$. We find that, for $q \le 1$, the system cannot enter an inclination-type resonance if the ratio of eccentricity to semimajor axis damping timescales $t_e/t_a$ is smaller than 0.2. This result still holds if only the eccentricity of the outer planet is damped and $q \lesssim 1$. As the disc/planet interaction is characterized by $t_e/t_a \sim 10^{-2}$, we conclude that excitation of inclination through the type of resonance described here is very unlikely to happen in a system of two planets migrating in a disc. |
| spellingShingle | Teyssandier, J Terquem, C Evolution of eccentricity and orbital inclination of migrating planets in 2:1 mean motion resonance |
| title | Evolution of eccentricity and orbital inclination of migrating planets
in 2:1 mean motion resonance |
| title_full | Evolution of eccentricity and orbital inclination of migrating planets
in 2:1 mean motion resonance |
| title_fullStr | Evolution of eccentricity and orbital inclination of migrating planets
in 2:1 mean motion resonance |
| title_full_unstemmed | Evolution of eccentricity and orbital inclination of migrating planets
in 2:1 mean motion resonance |
| title_short | Evolution of eccentricity and orbital inclination of migrating planets
in 2:1 mean motion resonance |
| title_sort | evolution of eccentricity and orbital inclination of migrating planets in 2 1 mean motion resonance |
| work_keys_str_mv | AT teyssandierj evolutionofeccentricityandorbitalinclinationofmigratingplanetsin21meanmotionresonance AT terquemc evolutionofeccentricityandorbitalinclinationofmigratingplanetsin21meanmotionresonance |