Grain opacity and the bulk composition of extrasolar planets. II. An analytical model for the grain opacity in protoplanetary atmospheres

Abstract

Context. We investigate the grain opacity k_gr in the atmosphere of protoplanets. This is important for the planetary mass-radius relation since k_gr affects the H/He envelope mass of low-mass planets and the critical core mass of giant planets. Aims. The goal of this study is to derive an analytical model for k_gr. Methods. Our model is based on the comparison of the timescales of microphysical processes like grain settling in the Stokes and Epstein regime, growth by Brownian motion coagulation and differential settling, grain evaporation, and grain advection due to envelope contraction. With these timescales we derive the grain size, abundance, and opacity. Results. We find that the main growth process is differential settling. In this regime, k_gr has a simple functional form and is given as 27 Q/8 H rho in the Epstein regime and as 2 Q/H rho for Stokes drag. Grain dynamics lead to a typical radial structure of k_gr with high ISM-like values in the top layers but a strong decrease in the deeper parts where the grain-free molecular opacities take over. Conclusions. In agreement with earlier results we find that k_gr is typically much lower than in the ISM. The equations also show that a higher dust input in the top layer does not strongly increase k_gr with two important implications. First, for a formation of giant planet cores via pebbles, there could be the issue that pebbles increase the grain input high in the atmosphere due to ablation. This could potentially increase k_gr hindering giant planet formation. Our study shows that this adverse effect should not occur. Second, it means that a higher stellar [Fe/H] which presumably leads to a higher surface density of planetesimals only favors giant planet formation without being detrimental to it due to an increased k_gr. This corroborates the result that core accretion explains the increase of the giant planet frequency with [Fe/H].

arXiv comment33 pages, 19 figures. Accepted to A&A. Identical to V1 except for updated references

References in corpus (54)

• Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler
• Planetary Radii across Five Orders of Magnitude in Mass and Stellar Insolation: Application to Transits
• Using FU Orionis Outbursts to Constrain Self-Regulated Protostellar Disk Models
• Rapid growth of gas-giant cores by pebble accretion
• A simple model for the evolution of the dust population in protoplanetary disks
• Understanding the Mass-Radius Relation for Sub-Neptunes: Radius as a Proxy for Composition
• Coagulation, fragmentation and radial motion of solid particles in protoplanetary disks
• Models of Giant Planet formation with migration and disc evolution
• The effect of gas drag on the growth of protoplanets -- Analytical expressions for the accretion of small bodies in laminar disks
• The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier
• The formation and retention of gas giant planets around stars with a range of metallicities
• The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? I. Mapping the zoo of laboratory collision experiments
• Masses, Radii, and Orbits of Small Kepler Planets: The Transition from Gaseous to Rocky Planets
• Line and Mean Opacities for Ultracool Dwarfs and Extrasolar Planets
• The metal-rich nature of stars with planets
• Rapid Coagulation of Porous Dust Aggregates Outside the Snow Line: A Pathway to Successful Icy Planetesimal Formation
• Extrasolar planet population synthesis IV. Correlations with disk metallicity, mass and lifetime
• Planetary population synthesis coupled with atmospheric escape: a statistical view of evaporation
• Atmospheres of protoplanetary cores: critical mass for nucleated instability
• Characterization of exoplanets from their formation I: Models of combined planet formation and evolution
• A Framework for Characterizing the Atmospheres of Low-Mass Low-Density Transiting Planets
• The Mass of KOI-94d and a Relation for Planet Radius, Mass, and Incident Flux
• Models of Jupiter's Growth Incorporating Thermal and Hydrodynamic Constraints
• Formation and Structure of Low Density Exo-Neptunes
• Characterization of exoplanets from their formation II: The planetary mass-radius relationship
• The Heavy Element Masses of Extrasolar Giant Planets, Revealed
• Dust coagulation in protoplanetary disks: porosity matters
• Dynamics of pebbles in the vicinity of a growing planetary embryo: hydro-dynamical simulations
• Planetesimal formation by sweep-up: How the bouncing barrier can be beneficial to growth
• Migration and giant planet formation
• Bulk Composition of GJ 1214b and other sub-Neptune exoplanets
• Formation of Jupiter using opacities based on detailed grain physics
• Theoretical models of planetary system formation: mass vs semi-major axis
• All Six Planets Known to Orbit Kepler-11 Have Low Densities
• Modeling the Formation of Giant Planet Cores I: Evaluating Key Processes
• Planet formation models: the interplay with the planetesimal disc
• Grain sedimentation inside giant planet embryos
• Gas Giant Formation with Small Cores Triggered by Envelope Pollution by Icy Planetesimals
• An Atmospheric Structure Equation for Grain Growth
• The Effect of Composition on the Evolution of Giant and Intermediate-Mass Planets
• Models of Accreting Gas Giant Protoplanets in Protostellar Disks
• The opacity of grains in protoplanetary atmospheres
• Grain opacity and the bulk composition of extrasolar planets. I. Results from scaling the ISM opacity
• The growth and hydrodynamic collapse of a protoplanet envelope
• Critical Core Masses for Gas Giant Formation with Grain-Free Envelopes
• The Effects of Metallicity, and Grain Growth and Settling on the Early Evolution of Gaseous Protoplanets
• Utilitarian Opacity Model for Aggregate Particles in Protoplanetary Nebulae and Exoplanet Atmospheres
• Formation of giant planets in disks with different metallicities
• The steady-state flow pattern past gravitating bodies
• Accretion Rates of Planetesimals by Protoplanets Embedded in Nebular Gas
• Cosmochemical Consequences of Particle Trajectories During FU Orionis Outbursts by the Early Sun
• Growth of Jupiter: Enhancement of Core Accretion by a Voluminous Low-Mass Envelope
• Sungrazing comets: Properties of nuclei and in-situ detectability of cometary ions at 1 AU
• On the Nature of Small Planets around the Coolest Kepler Stars

Cited by in corpus (76)

• The imprint of exoplanet formation history on observable present-day spectra of hot Jupiters
• To Cool is to Accrete: Analytic Scalings for Nebular Accretion of Planetary Atmospheres
• The New Generation Planetary Population Synthesis (NGPPS). IV. Planetary systems around low-mass stars
• Hydrodynamics of Embedded Planets' First Atmospheres. II. A Rapid Recycling of Atmospheric Gas
• 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
• Reduced gas accretion on super-Earths and ice giants
• Planet formation with envelope enrichment: new insights on planetary diversity
• Constraining the Nature of the PDS 70 Protoplanets with VLTI/GRAVITY
• Planetary evolution with atmospheric photoevaporation I. Analytical derivation and numerical study of the evaporation valley and transition from super-Earths to sub-Neptunes
• Characterization of exoplanets from their formation III: The statistics of planetary luminosities
• Super-Earth masses sculpted by pebble isolation around stars of different masses
• Hydrodynamics of embedded planets' first atmospheres - III. The role of radiation transport for super-Earth planets
• How planetary growth outperforms migration
• The formation of Jupiter by hybrid pebble-planetesimal accretion
• Minimum Core Masses for Giant Planet Formation With Realistic Equations of State and Opacities
• Critical core mass for enriched envelopes: the role of H2O condensation
• How cores grow by pebble accretion I. Direct core growth
• WASP-107b's density is even lower: a case study for the physics of planetary gas envelope accretion and orbital migration
• Planetary population synthesis
• Formation, Orbital and Internal Evolutions of Young Planetary Systems
• Keck/NIRC2 $L$'-Band Imaging of Jovian-Mass Accreting Protoplanets around PDS 70
• The ARCiS framework for Exoplanet Atmospheres: The Cloud Transport Model
• The Exoplanet Radius Valley from Gas-driven Planet Migration and Breaking of Resonant Chains
• The origin of the high metallicity of close-in giant exoplanets: Combined effect of the resonant and aerodynamic shepherding
• Evolution of Gas Giant Entropy During Formation by Runaway Accretion
• The formation of mini-Neptunes
• How planets grow by pebble accretion. III. Emergence of an interior composition gradient
• Connecting planet formation and astrochemistry: Refractory carbon depletion leading to super-stellar C/O in giant planetary atmospheres
• Tables of phase functions, opacities, albedos, equilibrium temperatures, and radiative accelerations of dust grains in exoplanets
• How planets grow by pebble accretion II: Analytical calculations on the evolution of polluted envelopes
• Do Metal-Rich Stars Make Metal-Rich Planets? New Insights on Giant Planet Formation from Host Star Abundances
• Most super-Earths formed by dry pebble accretion are less massive than 5 Earth masses
• Tidal Downsizing model. I. Numerical methods: saving giant planets from tidal disruptions
• The maximum mass of planetary embryos formed in core-accretion models
• Theoretical vs. observational uncertainties: composition of giant exoplanets
• Giant planet formation models with a self-consistent treatment of the heavy elements
• Planet Formation: An Optimized Population-Synthesis Approach
• Accreting protoplanets: Spectral signatures and magnitude of gas and dust extinction at H alpha
• Steady State by Recycling prevents Premature Collapse of Protoplanetary Atmospheres
• Giants are bullies: how their growth influences systems of inner sub-Neptunes and super-Earths
• The distribution of heavy-elements in giant protoplanetary atmospheres: the importance of planetesimal-envelope interactions
• On the structure and mass delivery towards circumplanetary discs
• The Primordial Entropy of Jupiter
• The mass-radius relation of intermediate-mass planets outlined by hydrodynamic escape and thermal evolution
• Recycling of the first atmospheres of embedded planets: Dependence on core mass and optical depth
• Formation of Planetary Populations I: Metallicity & Envelope Opacity Effects
• Towards a new era in giant exoplanet characterisation
• How planets grow by pebble accretion IV: Envelope opacity trends from sedimenting dust and pebbles
• The Endgame of Gas Giant Formation: Accretion Luminosity and Contraction Post-Runaway
• Using Deep Neural Networks to compute the mass of forming planets
• Inner rocky super-Earth formation: distinguishing the formation pathways in viscously heated and passive discs
• The Formation of Uranus and Neptune: Fine Tuning in Core Accretion
• Tidal Downsizing Model. IV. Destructive feedback in planets
• Steamworlds: atmospheric structure and critical mass of planets accreting icy pebbles
• Influence of grain sizes and composition on the contraction rates of planetary envelopes and on planetary migration
• Sub-Neptunes Are Drier Than They Seem: Rethinking the Origins of Water-Rich Worlds
• Limits on Protoplanet Growth by Accretion of Small Solids
• Sublimation of refractory minerals in the gas envelopes of accreting rocky planets
• How planets form by pebble accretion V. Silicate rainout delays contraction of sub-Neptunes
• HATS-50b through HATS-53b: four transiting hot Jupiters orbiting G-type stars discovered by the HATSouth survey
• The bulk metallicity of giant planets around M stars
• Planet population synthesis: The role of stellar encounters
• Migrating Jupiter up to the habitable zone: Earth-like planet formation and water delivery
• Rocky sub-Neptunes formed by pebble accretion: Rain of rocks from polluted envelopes
• Turbulent Disk Viscosity and the Bifurcation of Planet Formation Histories
• A formation pathway for terrestrial planets with moderate water content involving atmospheric-volatile recycling
• The New Generation Planetary Population Synthesis (NGPPS). VII. Statistical comparison with the HARPS/Coralie survey
• Giant planet formation via pebble accretion across different stellar masses
• Constraining the formation history of the HAT-P-11 system by atmospheric abundances
• Dust processing in protoplanetary envelopes as the origin of hot minerals in comets
• Solid accretion onto planetary cores in radiative disks
• Compositional Turbulence and Layering in the Gaseous Envelopes of Forming Planets
• Ohmic dissipation during the formation of super-Earth
• Interior dynamics of envelopes around disk-embedded planets
• Evolution and Observable Properties of Rocky Planet Atmospheres