An empirically-derived formula for the shape of planet-induced gaps in protoplanetary disks

Abstract

This study uses numerical hydrodynamics calculations and a novel method for densely sampling parameter space to measure the precise shape of a gap opened by a planet in a gaseous disk, as a function of planet-to-star mass ratio, disk Mach number, and disk viscosity. Formulas for gap depth and width are determined, which are combined to form a complete formula for surface density as a function of radius in the disk. This new analytical formula is compared with numerically-derived gaps opened by planets ranging from very low masses up to a few times Jupiter's mass, and excellent agreement is found over a wide range of parameter space relevant to planet-disk interactions. A simple-to-use code is presented to rapidly generate synthetic disk profiles.

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Cited by in corpus (25)

• Dust growth and evolution in protoplanetary disks
• Three-dimensional Global Simulations of Type-II Planet-disk Interaction with a Magnetized Disk Wind: I. Magnetic Flux Concentration and Gap Properties
• Pileups and Migration Rates for Planets in Low Mass Disks
• Rapid Formation of Jupiter and Wide-Orbit Exoplanets in Disks with Pressure Bumps
• How Consumption and Repulsion Set Planetary Gap Depths and the Final Masses of Gas Giants
• Accretion of Gas Giants Constrained by the Tidal Barrier
• Retention of Long-Period Gas Giant Planets: Type II Migration Revisited
• Sequential giant planet formation initiated by disc substructure
• Emergence of vortices at the edges of planet-driven gaps in protoplanetary discs
• A gap-sharing planet pair shaping the crescent in HD 163296: a disk sculpted by a resonant chain
• Wide Dust Gaps in Protoplanetary Disks Induced by Eccentric Planets: A Mass-Eccentricity Degeneracy
• Trapping (sub-)Neptunes similar to TOI-216b at the inner disk rim: Implications for the disk viscosity and the Neptunian desert
• TriPoD: Tri-Population size distributions for Dust evolution. Coagulation in vertically integrated hydrodynamic simulations of protoplanetary disks
• Three-dimensional transport of solids in a protoplanetary disk containing a growing giant planet
• Gap-opening Planets Make Dust Rings Wider
• Planetesimal and planet formation in transient dust traps
• The Ophiuchus DIsk Survey Employing ALMA (ODISEA): A Unified Evolutionary Sequence of Planet-Driven Substructures Explaining the Diversity of Disk Morphologies
• Formation of Multiple Dynamical Classes in the Kuiper Belt via Disk Dissipation
• Substructures in protoplanetary disks imprinted by compact planetary systems
• Dust Rings and Cavities in the Protoplanetary Disks around HD 163296 and DoAr 44
• Estimating the depth of gaps opened by planets in eccentric orbit
• Enhanced Pebble Drift Across Planet-Opened Gaps in Windy Protoplanetary Disks
• How two-dimensional are planet-disc interactions? II. Radiation hydrodynamics and suitable cooling prescriptions
• How leaky? A large parameter study of leaky dust traps to quantify the transport of pebbles and ice in protoplanetary discs
• $\alpha \beta q_{\mathrm{th}}$-mapping of planet-induced density wave damping in protoplanetary discs