Origins of Compact Mean-Motion Resonances: Evidence for Long-Range Migration and the Case of Kepler-36
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912986543685632 |
|---|---|
| author | Batygin, Konstantin Morbidelli, Alessandro |
| author_facet | Batygin, Konstantin Morbidelli, Alessandro |
| contents | The observed census of resonant extrasolar planets spans a tantalizing display of orbital architectures, ranging from familiar 2:1 and 3:2 mean-motion commensurabilities to nearly co-orbital configurations characterized by period ratios close to unity. While mean-motion resonances are widely recognized as signposts of convergent disk-driven migration, the process through which the most compact systems are established remains puzzling, since resonance capture must repeatedly fail at a series of first-order commensurabilities before finally succeeding at a high resonant index. Motivated by this discrepancy, here we develop an analytic theory that fuses the stability-based resonance capture criterion with the conventional paradigm of active accretion disks and the standard model of type-I migration. Within this framework, we derive an expression for the stellocentric radius of resonance capture, $r_{\rm{c}}$, and show that it depends only on the product of the disk viscosity parameter, $α$, and the opacity-contributing small-grain mass fraction, $f_μ$. Applying this formalism to Kepler-36 - the most compact known resonant system with a 7:6 period ratio - we find that resonance locking could not have been established near the disk's inner edge. Instead, capture must have occurred at $r_{\rm{c}}\approx 1-4$ AU, implying orbital decay of the planetary pair by approximately an order of magnitude. Viewed in this light, compact resonant architectures provide the clearest evidence for long-range migration among sub-Jovian planets. Moreover, the emerging picture is fully consistent with formation models in which super-Earths accrete within localized rings of planetesimals at orbital distances comparable to those that gave rise to the terrestrial planets of the Solar System. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27093 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Origins of Compact Mean-Motion Resonances: Evidence for Long-Range Migration and the Case of Kepler-36 Batygin, Konstantin Morbidelli, Alessandro Earth and Planetary Astrophysics The observed census of resonant extrasolar planets spans a tantalizing display of orbital architectures, ranging from familiar 2:1 and 3:2 mean-motion commensurabilities to nearly co-orbital configurations characterized by period ratios close to unity. While mean-motion resonances are widely recognized as signposts of convergent disk-driven migration, the process through which the most compact systems are established remains puzzling, since resonance capture must repeatedly fail at a series of first-order commensurabilities before finally succeeding at a high resonant index. Motivated by this discrepancy, here we develop an analytic theory that fuses the stability-based resonance capture criterion with the conventional paradigm of active accretion disks and the standard model of type-I migration. Within this framework, we derive an expression for the stellocentric radius of resonance capture, $r_{\rm{c}}$, and show that it depends only on the product of the disk viscosity parameter, $α$, and the opacity-contributing small-grain mass fraction, $f_μ$. Applying this formalism to Kepler-36 - the most compact known resonant system with a 7:6 period ratio - we find that resonance locking could not have been established near the disk's inner edge. Instead, capture must have occurred at $r_{\rm{c}}\approx 1-4$ AU, implying orbital decay of the planetary pair by approximately an order of magnitude. Viewed in this light, compact resonant architectures provide the clearest evidence for long-range migration among sub-Jovian planets. Moreover, the emerging picture is fully consistent with formation models in which super-Earths accrete within localized rings of planetesimals at orbital distances comparable to those that gave rise to the terrestrial planets of the Solar System. |
| title | Origins of Compact Mean-Motion Resonances: Evidence for Long-Range Migration and the Case of Kepler-36 |
| topic | Earth and Planetary Astrophysics |
| url | https://arxiv.org/abs/2603.27093 |