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

By T. Birnstiel, H. Klahr, Barbara Ercolano. 2012

535 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/0ad443a19349ff7b0ca3e64891a9df9215e38756

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Citations in the corpus

The Gemini Planet Imager Exoplanet Survey: Giant Planet and Brown Dwarf Demographics from 10 to 100 au (2019, background): “Pascucci et al. (2016)support St M1 1 2*µ for fragmentation-limited particle growth (Birnstiel et al.2012); this relation steepens to 1/M* if particle sizes are fixed and gas disk masses scale linearly with stellar mass. 47 This is not to say that there are not outstanding problems intrinsic to the…”
DUST FILTRATION BY PLANET-INDUCED GAP EDGES: IMPLICATIONS FOR TRANSITIONAL DISKS (2012, background): “But we note that dust growth and fragmentation can potentially change this relationship (e.g. Birnstiel et al. 2012).”
Dust Evolution and the Formation of Planetesimals (2016, background): “Birnstiel et al. (2012b) found that fragmentation tends to dominate in the inner regions of the disk, while outer regions, or regions of lowered dustto-gas ratio are limited by radial drift.”
Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants (2018, methodology): “Typically, the pebbles accreted by planets in our model have Stokes numbers in the range of 0.05 < τf < 0.4, as those are the Stokes numbers of the pebbles dominated by radial drift (Birnstiel et al. 2012; Lambrechts & Johansen 2014).”
Planetesimal formation starts at the snow line (2017, methodology): “The dry aggregates inside of the snow line only grow to sub-millimeter sizes, corresponding to St < αv/2, which means that they are well-coupled to the gas and follow its viscous evolution, or are in so-called mixing regime, as discussed by Birnstiel et al. (2012).”
ALMA continuum observations of the protoplanetary disk AS 209. Evidence of multiple gaps opened by a single planet (2017, methodology): “Given a measure of the local dust density, the timescale for dust growth to a given size is readily obtained from grain growth models (e.g., Birnstiel et al. 2012).”
THE MASS DEPENDENCE BETWEEN PROTOPLANETARY DISKS AND THEIR STELLAR HOSTS (2013, background): “Models of this material evolution predict that growth timescales increase like 1/ζ √ M∗ up to grain sizes (a) that are limited by fragmentation (amax ∝ Md; Birnstiel et al. 2011) or drift (amax ∝ M∗Md ζ; Birnstiel et al. 2012).”
A Kinematical Detection of Two Embedded Jupiter-mass Planets in HD 163296 (2018, background): “…gas-to-dust ratios, radially varying grain opacities, complex grain evolution dictated by a coupling of the solid particles to the gas (Birnstiel et al. 2012) and local chemical and excitation effects (Öberg et al. 2015; Cleeves 2016) all conspire to limit the accuracy of the…”
Planck 2013 results. XI. All-sky model of thermal dust emission (2013, background): “Interstellar dust grains are thought to be the seeds from which larger particles form in the ISM, up to planetesimals in circumstellar environments (Brauer et al. 2008; Beckwith et al. 2000; Birnstiel et al. 2012).”
CONSTRAINTS ON THE RADIAL VARIATION OF GRAIN GROWTH IN THE AS 209 CIRCUMSTELLAR DISK (2012, methodology): “We compare our observational constraints with theoretical models of grain growth, employing the approximations presented in Birnstiel et al. (2012) for the evolution of amax with radius.”
The great dichotomy of the Solar System: Small terrestrial embryos and massive giant planet cores (2015, methodology): “where r ice is the location of the snowline). Beyond the snowline there is a ow of icy pebbles. Lambrechts and Johansen (2014) have developed a pebble coagulation and drift model based on the work of Birnstiel et al. (2012). They found that, at t= 105{106 y of the disk’s evolution, icy pebbles at ˘4”
Close-in planetesimal formation by pile-up of drifting pebbles (2016, methodology): “Even for compact grains, interplay between the radial drift and dust growth can lead to a pile-up A105, page 2 of 12 of solids in the inner regions of the disc (Birnstiel et al. 2012; Laibe et al. 2012; Pinte & Laibe 2014).”
Survival of molecular gas in cavities of transition disks - I. CO (2013, methodology): “Pure graingrowth on the other hand (e.g. Dullemond & Dominik 2005; Birnstiel et al. 2012a) should not alter the gas structure much (δgas ∼ 1).”
Forming the cores of giant planets from the radial pebble flux in protoplanetary discs (2014, methodology): “(19) We now obtain, by setting tg,p = tr, the dominant particle size of τf ≈ √ 3 8 p η Σp Σg (20) (Brauer et al. 2008; Birnstiel et al. 2012).”
Separating gas-giant and ice-giant planets by halting pebble accretion (2014, methodology): “…scenario, as outlined in Lambrechts & Johansen (2012), starts with the growth of pebbles from the initial grains embedded in the protoplanetary disc (with sizes ≈µm) by collisions (Birnstiel et al. 2012) or through sublimation and condensation cycles around ice lines (Ros & Johansen 2013).”
Multiwavelength analysis for interferometric (sub-)mm observations of protoplanetary disks - Radial constraints on the dust properties and the disk structure (2015, methodology): “…amax(R) profiles, we compute the dust spectral index β(R) profiles (shown in the right 6 This choice is justified by the outer disk maximum grain size distribution derived by other authors and by simple fits to the predictions of global dust evolution models, e.g., Birnstiel et al. (2012).”
The nature of the TRAPPIST-1 exoplanets. (2018, background): “First, as dust coagulates and drifts through the disk (Güttler et al. 2010; Birnstiel et al. 2012), 10-100 km-scale planetesimals form by a hydrodynamical instability (such as the streaming instability; (Youdin & Goodman 2005; Johansen et al. 2014)) in regions where the local solids-to-gas ratio is…”