A simple model for the evolution of the dust population in protoplanetary disks

Abstract

Context: The global size and spatial distribution of dust is an important ingredient in the structure and evolution of protoplanetary disks and in the formation of larger bodies, such as planetesimals. Aims: We aim to derive simple equations that explain the global evolution of the dust surface density profile and the upper limit of the grain size distribution and which can readily be used for further modeling or for interpreting of observational data. Methods: We have developed a simple model that follows the upper end of the dust size distribution and the evolution of the dust surface density profile. This model is calibrated with state-of-the-art simulations of dust evolution, which treat dust growth, fragmentation, and transport in viscously evolving gas disks. Results: We find very good agreement between the full dust-evolution code and the toy model presented in this paper. We derive analytical profiles that describe the dust-to-gas ratios and the dust surface density profiles well in protoplanetary disks, as well as the radial flux by solid material "rain out", which is crucial for triggering any gravity assisted formation of planetesimals. We show that fragmentation is the dominating effect in the inner regions of the disk leading to a dust surface density exponent of -1.5, while the outer regions at later times can become drift-dominated, yielding a dust surface density exponent of -0.75. Our results show that radial drift is not efficient in fragmenting dust grains. This supports the theory that small dust grains are resupplied by fragmentation due to the turbulent state of the disk.

12 pages, 10 figures, accepted to A&A

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• Dynamical avenues for Mercury's origin II: in-situ formation in the inner terrestrial disk
• The possible formation of Jupiter from supersolar gas
• Global N-body simulations of circumbinary planet formation around Kepler-16 and -34 analogues I: Exploring the pebble accretion scenario
• Determining dispersal mechanisms of protoplanetary disks using accretion and wind mass loss rates
• The effect of luminosity outbursts on the protoplanetary disk dynamics
• The early instability scenario: Mars' mass explained by Jupiter's orbit
• Unveiling the outer dust disc of TW Hya with deep ALMA observations
• Formation of pebbles in (gravito-)viscous protoplanetary disks with various turbulent strengths
• Constraining the turbulence and the dust disk in IM Lup: onset of planetesimal formation
• Revisiting collisional dust growth in Class 0/I protostellar disks: Sweep-up can convert a few $10M_{\oplus }$ of dust into kg pebbles in 0.1 Myr
• Which stars can form planets: Planetesimal formation at low metallicities
• Mineral Snowflakes on Exoplanets and Brown Dwarfs: Coagulation and Fragmentation of Cloud Particles with {\sc HyLandS}
• Pebble-driven migration of low-mass planets in the 2D regime of pebble accretion
• Saving super-Earths: Interplay between pebble accretion and type I migration
• Streaming instabilities in accreting and magnetized laminar protoplanetary disks
• Breakthrough revisited: investigating the requirements for growth of dust beyond the bouncing barrier
• The Roles of Dust Growth in the Temperature Evolution and Snow Line Migration in Magnetically Accreting Protoplanetary Disks
• Resolved imaging of the AR Puppis circumbinary disk
• Primordial Dusty Rings and Episodic Outbursts in Protoplanetary Discs
• Mixing is easy: New insights for cosmochemical evolution from pre-stellar core collapse
• Growing the seeds of pebble accretion through planetesimal accretion
• Dust-vortex instability in the regime of well-coupled grains
• Inside-Out Planet Formation. VII. Astrochemical Models of Protoplanetary Disks and Implications for Planetary Compositions
• Streaming instability in a global patch simulation of protoplanetary disks
• A sub-grid model for the growth of dust particles in hydrodynamical simulations of protoplanetary disks
• Influence of grain sizes and composition on the contraction rates of planetary envelopes and on planetary migration
• The radial structure of planetary bodies formed by the streaming instability
• Imaging the circumstellar environment of the young T Tauri star SU Aurigae
• Gravitoviscous Protoplanetary Discs with a Dust Component. IV. Disc Outer Edges, Spectral Indices, and Opacity Gaps
• The ALMA Survey of Gas Evolution of PROtoplanetary Disks (AGE-PRO): VIII. The impact of external photoevaporation on disk masses and radii in Upper Scorpius
• Mass determination of protoplanetary disks from dust evolution
• Formation of Planetary Populations II: Effects of Initial Disk Size & Radial Dust Drift
• Changing disc compositions via internal photoevaporation I: Solar-mass stars
• Mercury as the relic of Earth and Venus' outward migration
• Dust Coagulation Regulated by Turbulent Clustering in Protoplanetary Disks
• Limits on Protoplanet Growth by Accretion of Small Solids
• Sublimation of refractory minerals in the gas envelopes of accreting rocky planets
• The dimming of RW Auriga. Is dust accretion preceding an outburst?
• Effects of pebble accretion on the growth and composition of planetesimals in the inner Solar System
• Solving for the 2D Water Snowline with Hydrodynamic Simulations. Emergence of gas outflow, water cycle and temperature plateau
• Formation of wide-orbit giant planets in protoplanetary disks with a decreasing pebble flux
• Global Modeling of Nebulae With Particle Growth, Drift, and Evaporation Fronts. II. The Influence of Porosity on Solids Evolution
• Circumplanetary disk ices. I. Ice formation vs. viscous evolution and grain drift
• The evolution of circumstellar discs in the Galactic Centre: an application to the G-clouds
• Dense Particle Clouds in Laboratory Experiments in Context of Drafting and Streaming Instability
• Spatial distribution of crystalline silicates in protoplanetary disks: How to interpret mid-infrared observations
• Ring Morphology with Dust Coagulation in Protoplanetary Disks
• Locked In Ice: how Pebble Drift and Volatile Entrapment can Significantly Impact Carbon and Oxygen Ratios in Evolving Protoplanetary Discs
• The observational impact of dust trapping in self-gravitating discs
• Instabilities and Flow Structures in Protoplanetary Disks: Setting the Stage for Planetesimal Formation
• AB Aurigae: Possible evidence of planet formation through the gravitational instability
• Gas-Assisted Growth of Protoplanets in a Turbulent Medium
• 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
• On the suppression of giant planet formation around low-mass stars in clustered environments
• Millimeter Observations of the disk around GW Ori
• Planetary core formation via multi-species pebble accretion
• Toward a Population Synthesis of Disks and Planets I. Evolution of Dust with Entrainment in Winds and Radiation Pressure
• Dust-Gas Coupling in Turbulence- and MHD Wind-Driven Protoplanetary Disks: Implications for Rocky Planet Formation
• A potential site for wide-orbit giant planet formation in the IM Lup disk
• Growth after the streaming instability: The radial distance dependence of the planetary growth
• The growth of super-Earths: the importance of a self-consistent treatment of disc structures and pebble accretion
• Modeling Nitrogen Fractionation in the Protoplanetary Disk around TW Hya: Model Constraints on Grain Population and Carbon-to-Oxygen Elemental Abundance Ratio
• Planet population synthesis: The role of stellar encounters
• Planetesimal formation via the streaming instability with multiple grain sizes
• ExoLyn: a golden mean approach to multi-species cloud modelling in atmospheric retrieval
• Combined Effects of Disk Winds and Turbulence-Driven Accretion on Planet Populations
• A brief overview of planet formation
• MRI-driven angular momentum transport in protoplanetary disks
• Mercury's formation within the Early Instability Scenario
• Extreme Pebble Accretion in Ringed Protoplanetary Discs
• CO isotopolog line fluxes of viscously evolving disks: cold CO conversion insufficient to explain observed low fluxes
• Interstellar planetesimals: potential seeds for planet formation?
• The effect of the streaming instability on protoplanetary disc emission at millimetre wavelengths
• Filling in the Gaps: Can Gravitationally Unstable Discs Form the Seeds of Gas Giant Planets?
• VLA observations of the disk around the young brown dwarf 2MASS J044427+2512
• First MATISSE L-band observations of HD 179218. Is the inner 10 au region rich in carbon dust particles?
• ALMA constraints on assembly of Core Accretion planets
• Positive Feedback: How a Synergy Between the Streaming Instability and Dust Coagulation Forms Planetesimals
• Magnetic disk winds in protoplanetary disks: Description of the model and impact on global disk evolution
• Chemical transformation of CO in evolving protoplanetary discs across stellar masses: a route to C-rich inner regions
• Migration of gap-opening planets in 3D stellar-irradiated accretion disks
• Planetesimal and planet formation in transient dust traps
• There is no disk mass budget problem of planet formation
• Chemical evolution in planet-forming regions with growing grains
• Chemical enrichment of the planet forming region as probed by accretion
• Refractory carbon depletion by photolysis through dust collisions and vertical mixing
• Migration traps as the root cause of the Kepler dichotomy
• Self-Sustaining Vortices in Protoplanetary Disks: Setting the Stage for Planetary System Formation
• A Tale of Two Grains: impact of grain size on ring formation via nonideal MHD processes
• Millimeter emission in photoevaporating disks is determined by early substructures
• Formation of Planetary Populations III: Core Composition & Atmospheric Evaporation
• Massive Protostellar Disks as a Hot Laboratory of Silicate Grain Evolution
• Size and density sorting of dust grains in SPH simulations of protoplanetary disc II: Fragmentation
• Dust dynamics in planet-driven spirals
• Rapid grain growth in post-AGB disc systems from far-infrared and sub-millimetre photometry
• Planetesimal formation via the streaming instability in simulations of infall dominated young disks
• The solar abundance problem and eMSTOs in clusters
• Illuminating a tadpole's metamorphosis II: observing the on-going transformation with ALMA
• The role of density perturbation on planet formation by pebble accretion
• Vertical shear instability with dust evolution and consistent cooling times. On the importance of the initial dust distribution
• Constraining giant planet formation with synthetic ALMA images of the Solar System's natal protoplanetary disk
• Nonlinear Outcome of Coagulation Instability in Protoplanetary Disks II: Dust Ring Formation Mediated by Backreaction and Fragmentation
• How external photo-evaporation changes the chemical composition of the inner disc
• Accretion bursts in young intermediate-mass stars make planet formation challenging
• Effects from different grades of stickiness between icy and silicate particles on carbon depletion in protoplanetary disks
• Primordial dust rings, hidden dust mass, and the first generation of planetesimals in gravitationally unstable protoplanetary disks
• Super-Earth formation in systems with cold giants
• How Flow Isolation May Set the Mass Scale for Super-Earth Planets
• Formation of super-Earths and mini-Neptunes from rings of planetesimals
• Multi-frequency analysis of the ALMA and VLA high resolution continuum observations of the substructured disc around CI Tau. Preference for sub-mm-sized low-porosity amorphous carbon grains
• Iceline Variations Driven by Protoplanetary Disc Gaps
• Modelling thermochemical processes in protoplanetary disks I: numerical methods
• The Ophiuchus DIsk Survey Employing ALMA (ODISEA): A Unified Evolutionary Sequence of Planet-Driven Substructures Explaining the Diversity of Disk Morphologies
• Using planet migration and dust drift to weigh protoplanetary discs
• Selective Aggregation Experiments on Planetesimal Formation and Mercury-Like Planets
• Shaping the CO snowline in protoplanetary disks
• Composition constraints of the TRAPPIST-1 planets from their formation
• Mid-infrared blends and continuum signatures of dust drift and accretion in protoplanetary disks
• Dust Rings and Cavities in the Protoplanetary Disks around HD 163296 and DoAr 44
• Connecting planet formation and astrochemistry: C/O and N/O of warm giant planets and Jupiter-analogs
• On the evolution of pebble-accreting planets in evolving protoplanetary discs
• A formation pathway for terrestrial planets with moderate water content involving atmospheric-volatile recycling
• Binary planet formation by gas-assisted encounters of planetary embryos
• On the origin of transition disk cavities: Pebble-accreting protoplanets vs Super-Jupiters
• Radio multiwavelength analysis of the compact disk CX Tau: Presence of strong free-free variability or anomalous microwave emission
• The paradox of youth for ALMA planet candidates
• Changing disc compositions via internal photoevaporation II: M dwarf systems
• Dust Dynamics in Transitional Disks: Clumping and Disk Recession
• A "no-drift" runaway pile-up of pebbles in protoplanetary disks II. Characteristics of the resulting planetesimal belt
• The late formation of chondrites as a consequence of Jupiter-induced gaps and rings
• How does the chemical composition of solids influence the formation of planetesimals?
• The evolution of the $M_{\mathrm{d}}-M_{\star }$ and $\dot{M}-M_{\star }$ correlations traces protoplanetary disc dispersal
• How disc initial conditions sculpt the atmospheric composition of giant planets
• The evolution of the flux-size relationship in protoplanetary discs by viscous evolution and radial pebble drift
• Non-equilibrium condensation of the first Solar System solids
• Molecules with ALMA at Planet-forming Scales (MAPS) VIII: CO Gap in AS 209--Gas Depletion or Chemical Processing?
• Architecture of planetary systems predicted from protoplanetary disks observed with ALMA II: evolution outcomes and dynamical stability
• The Influence of Magnetic Field Geometry on the Formation of Close-in Exoplanets
• SHAMPOO: A stochastic model for tracking dust particles under the influence of non-local disk processes
• Constraining the formation history of the HAT-P-11 system by atmospheric abundances
• Filament formation due to diffusive instabilities in dusty protoplanetary disks
• Dust enrichment and growth in the earliest stages of protoplanetary disk formation
• The PAIRS project: a global formation model for planets in binaries. I. Effect of disc truncation on the growth of S-type planets
• Long-term evolution of the temperature structure in magnetized protoplanetary disks and its implication for the dichotomy of planetary composition
• Early Solar System Turbulence Constrained by High Oxidation States of the Oldest Non-Carbonaceous Planetesimals
• Planetary nurseries: vortices formed at smooth viscosity transition
• A pebble accretion model for the formation of the terrestrial planets in the Solar System
• Enhanced Pebble Drift Across Planet-Opened Gaps in Windy Protoplanetary Disks
• Probing dust and grain growth in the optically thick circumbinary ring of V892 Tau
• Dynamics and Origin of Comets: New Problems Appeared after the Rosetta Space Mission
• The extremely truncated circumstellar disc of V410 X-ray 1: a precursor to TRAPPIST-1?
• Positive Feedback II: How Dust Coagulation inside Vortices Can Form Planetesimals at Low Metallicity
• The Prospects for Hurricane-like Vortices in Protoplanetary Disks
• Dust in the wind of outbursting young stars
• Interpreting the atmospheric composition of exoplanets: sensitivity to planet formation assumptions
• Journey of complex organic molecules: Formation and transport in protoplanetary disks
• Effects of Stellar X-ray Photoevaporation on Planetesimal Formation via the Streaming Instability
• Timescales diagnostics for saving viscous and MHD-driven dusty discs from external photoevaporation
• A tension between dust and gas radii: the role of substructures and external photoevaporation in protoplanetary disks
• Gaps and Rings: A Near-Universal Trait of Extended Protoplanetary Discs
• A Pathway for Collisional Planetesimal Growth in the Ice-Dominant Regions of Protoplanetary Disks
• Icy Volatile Enhancements in Evolving Protoplanetary Disks
• How leaky? A large parameter study of leaky dust traps to quantify the transport of pebbles and ice in protoplanetary discs
• How two-dimensional are planet-disc interactions? II. Radiation hydrodynamics and suitable cooling prescriptions
• Hydrodynamical simulations of the vertical shear instability with dynamic dust and cooling rates in protoplanetary disks
• A fast tree algorithm for multi-component coagulation equation
• The Dispersal of Planet-forming discs: Theory confronts Observations
• Architectures of planetary systems formed by pebble accretion
• Explosive ejections generated by gravitational interactions
• Linking Outer Disk Pebble Dynamics and Gaps to Inner Disk Water Enrichment
• Planet formation in intermediate-separation binary systems
• Optical constants of Ih, Ic, and amorphous H${}_2$O ices in the THz and IR ranges
• The Influence of the Fractal Dimension on Dust Evolution in Protoplanetary Disks
• A close-encounter method for simulating the dynamics of planetesimals
• Rapid Formation of Super-Earths Around Low-Mass Stars
• Protoplanetary disk formation from the collapse of a prestellar core
• Formation of Water-rich Giant Planet Satellites at Decretion Disk Ice Lines
• Delivery of complex organic molecules to the system of Jupiter
• Dust-driven vortex cascades originating at water snow regions: A pathway to planetesimal formation
• Dispersal of protoplanetary discs: How stellar properties and the local environment determine the pathway of evolution
• Modelling the secular evolution of proto-planetary disc dust sizes -- A comparison between the viscous and magnetic wind case