Disk dispersal freezes overstable resonant librations
- 1Institute for Astronomy, School of Physics, Zhejiang University
Abstract
Context. Convergent migration in a gaseous protoplanetary disk can capture a planet pair into mean-motion resonance. Eccentricity damping can subsequently make the resonant libration overstable and drive the pair out of resonance. Most studies of this process, however, assumed a static disk.
Aims. We examine how the decay of disk torques during dispersal changes this outcome and whether it can freeze an overstable libration before the pair escapes.
Methods. We describe disk dispersal by allowing the migration and eccentricity-damping timescales to increase exponentially on a local timescale τ d . Integration of the time-dependent growth rate predicts τ d, crit ∝ τ e , 0 . We tested this scaling with direct N -body integrations and related τ d to the time taken by a photoevaporative cavity edge to cross the local torque-producing region.
Results. The simulations recovered a linear boundary, τ d, crit ≃ Sτ e , 0 , with S ≃ 3 over the explored parameter range. In a fiducial minimum-mass solar nebula, faster propagation of the cavity edge shortened the local dispersal time. The ratio τ d / τ d, crit also decreased with orbital radius, which means that both effects favour resonant survival.
Conclusions. When local disk dispersal is sufficiently rapid, the libration amplitude can freeze and the planet pair can remain in resonance instead of escaping through overstability. Late disk evolution can therefore alter the outcome of resonant overstability.
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BibTeX
@article{lin2026disk,
title = {{Disk dispersal freezes overstable resonant librations}},
author = {Linghong Lin and Beibei Liu},
journal = {Astronomy \& Astrophysics},
year = {2026},
month = oct,
doi = {10.1051/0004-6361/202662886},
url = {https://www.aanda.org/10.1051/0004-6361/202662886},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Disk dispersal freezes overstable resonant librations
AU - Linghong Lin
AU - Beibei Liu
PY - 2026
DA - 2026/10/13
JO - Astronomy & Astrophysics
DO - 10.1051/0004-6361/202662886
UR - https://www.aanda.org/10.1051/0004-6361/202662886
AB - Context. Convergent migration in a gaseous protoplanetary disk can capture a planet pair into mean-motion resonance. Eccentricity damping can subsequently make the resonant libration overstable and drive the pair out of resonance. Most studies of this process, however, assumed a static disk. Aims. We examine how the decay of disk torques during dispersal changes this outcome and whether it can freeze an overstable libration before the pair escapes. Methods. We describe disk dispersal by allowing the migration and eccentricity-damping timescales to increase exponentially on a local timescale τ d . Integration of the time-dependent growth rate predicts τ d, crit ∝ τ e , 0 . We tested this scaling with direct N -body integrations and related τ d to the time taken by a photoevaporative cavity edge to cross the local torque-producing region. Results. The simulations recovered a linear boundary, τ d, crit ≃ Sτ e , 0 , with S ≃ 3 over the explored parameter range. In a fiducial minimum-mass solar nebula, faster propagation of the cavity edge shortened the local dispersal time. The ratio τ d / τ d, crit also decreased with orbital radius, which means that both effects favour resonant survival. Conclusions. When local disk dispersal is sufficiently rapid, the libration amplitude can freeze and the planet pair can remain in resonance instead of escaping through overstability. Late disk evolution can therefore alter the outcome of resonant overstability.
SN - 0004-6361
SN - 1432-0746
ER -