A recipe for orbital eccentricity damping in the type-I regime for low viscosity 2D-discs

Abstract

It is known that gap opening depends on the disc's viscosity; however, eccentricity damping formulas have only been derived at high viscosities, ignoring partial gap opening. We aim at obtaining a simple formula to model $e$-damping of the type-I regime in low viscosity discs, where even small planets may start opening partial. We perform high resolution 2D locally isothermal hydrodynamical simulations of planets with varying masses on fixed orbits in discs with varying aspect ratios and viscosities. We determine the torque and power felt by the planet to derive migration and eccentricity damping timescales. We first find a lower limit to the gap depths below which vortices appear; this happens roughly at the transition between type-I and type-II regimes. For the simulations that remain stable, we obtain a fit to the observed gap depth in the limit of vanishing eccentricities that is similar to the one currently used in the literature but is accurate down to $\alpha =3.16\times 10^{-5}$. We record the $e$-damping efficiency as a function of the observed gap depth and $e$: when the planet has opened a deep enough gap, a linear trend is observed independently of $e$; at shallower gaps this linear trend is preserved at low $e$, while it deviates to more efficient damping when $e$ is comparable to the disc's scale height. Both trends can be understood on theoretical grounds and are reproduced by a simple fitting formula. Our combined fits yield a simple recipe to implement type-I $e$-damping in $N$-body for partial gap opening planets that is consistent with high-resolution 2D hydro-simulations. The typical error of the fit is of the order of a few percent, and lower than the error of type-I torque formulas widely used in the literature. This will allow a more self-consistent treatment of planet-disc interactions of the type-I regime for population synthesis models at low viscosities.

Submitted to A&A

References in corpus (34)

• Two accreting protoplanets around the young star PDS 70
• A comparative study of disc-planet interaction
• Ring shaped dust accumulation in transition disks
• Toward a Deterministic Model of Planetary Formation V. Accumulation Near the Ice Line
• Halting Type I planet migration in non-isothermal disks
• Molecules with ALMA at Planet-forming Scales (MAPS) I: Program Overview and Highlights
• A Three-Dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk using DCO${}^{+}$
• Three-dimensional simulations of multiple protoplanets embedded in a protostellar disc
• Multiple Disk Gaps and Rings Generated by a Single Super-Earth
• The New Generation Planetary Population Synthesis (NGPPS). I. Bern global model of planet formation and evolution, model tests, and emerging planetary systems
• Formation of planetary systems by pebble accretion and migration: Growth of gas giants
• The newborn planet population emerging from ring-like structures in discs
• Treating gravity in thin disk simulations
• Molecules with ALMA at Planet-forming Scales (MAPS) XIV: Revealing disk substructures in multi-wavelength continuum emission
• Improved torque formula for low and intermediate mass planetary migration
• Planet population synthesis driven by pebble accretion in cluster environments
• Gas and dust dynamics in starlight-heated protoplanetary disks
• Protoplanetary Disks as (Possibly) Viscous Disks
• Building Giant-Planet Cores at a Planet Trap
• Planet-disk interaction in disks with cooling: basic theory
• The effects of disk self-gravity and radiative cooling on the formation of gaps and spirals by young planets
• On the planetary interpretation of multiple gaps and rings in protoplanetary disks seen by ALMA
• Thermal torque effects on the migration of growing low-mass planets
• The Sandwich Mode for Vertical Shear Instability in Protoplanetary Disks
• Influence of planetary gas accretion on the shape and depth of gaps in protoplanetary discs
• The onset of instability in resonant chains
• Pushing planets into an inner cavity by a resonant chain
• Are the observed gaps in protoplanetary discs caused by growing planets?
• A Criterion for the Stability of Planets in Chains of Resonances
• Unified simulations of planetary formation and atmospheric evolution: Effects of pebble accretion, giant impacts, and stellar irradiations on super-Earth formation
• Properties of Density and Velocity Gaps Induced by a Planet in a Protoplanetary Disk
• The Kepler-223 resonance holds information on turbulence during the gas disk phase
• Multiplanet systems in inviscid discs can avoid forming resonant chains
• Emerging population of gap-opening planets around type-A stars -- Long-term evolution of the forming planets around HD 163296

Cited by in corpus (11)

• When, where, and how many planets end up in first-order resonances?
• Forming the Trappist-1 system in two steps during the recession of the disc inner edge
• Dissipative Capture of Planets Into First-Order Mean-Motion Resonances
• Resonance Capture and Stability Analysis for Planet Pairs under Type I Disk Migration
• Overstability of the 2:1 mean motion resonance: Exploring disc parameters with hydrodynamic simulations
• Diversity of disc viscosities can explain the period ratios of resonant and non-resonant systems of hot super-Earths and mini-Neptunes
• Pushing the limits of eccentricity in planet-disc interactions
• Long-term evolution of the temperature structure in magnetized protoplanetary disks and its implication for the dichotomy of planetary composition
• Timescales diagnostics for saving viscous and MHD-driven dusty discs from external photoevaporation
• Callisto's Nonresonant Orbit as an Outcome of Circum-Jovian Disk Substructure
• How to measure tidal dissipation in long resonant chains