Radial Flow of Dust Particles in Accretion Disks

By T. Takeuchi, D. Lin. 2002

320 citations recorded by the source corpus.

We study the radial migration of dust particles in accreting protostellar disks analogous to the primordial solar nebula. Our main objective is to determine the retention efficiency of dust particles, which are the building blocks of the much larger planetesimals. This study takes account of the two-dimensional (radial and normal) structure of the disk gas, including the effects of the variation in the gas velocity as a function of distance from the midplane. It is shown that the dust component of disks accretes slower than the gas component. At high altitude from the disk midplane (higher than a few disk scale heights), the gas rotates faster than the particles because of the inward pressure gradient force, and its drag force causes particles to move outward in the radial direction. Viscous torque induces the gas within a scale height from the disk midplane to flow outward, carrying small (size ≲ 100 μm at 10 AU) particles with it. Only particles at intermediate altitude or with sufficiently large sizes (≳1 mm at 10 AU) move inward. When the particles' radial velocities are averaged over the entire vertical direction, the particles have a net inward flux. The magnitude of their radial motion depends on their distance from the central star. At large distances, particles migrate inward with a velocity much faster than the gas accretion velocity. However, their inward velocity is reduced below that of the gas in the inner regions of the disk. The rate of velocity decrease is a function of the particles' size. While larger particles retain fast accretion velocity until they approach closer to the star, 10 μm particles have slower velocity than the gas in the majority of the disk (r ≲ 100 AU). This differential migration of particles causes size fractionation. Dust disks composed mostly of small particles (size ≲ 10 μm) accrete slower than gas disks, resulting in an increase in the dust-gas ratio during the gas accretion phase. If the gas disk has a steep radial density gradient or if dust particles sediment effectively to the disk midplane, the net vertically averaged flux of particles can be outward. In this case, the accretion of the dust component is prevented, leading to the formation of residual dust disks after their gas component is severely depleted.

Subfields: Astronomy and Astrophysics, Biomedical Engineering, Fluid Flow and Transfer Processes

View Paper: https://www.semanticscholar.org/paper/0393bf96eb2b8be3baa01f15e549a899111e2dbe

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Citations in the corpus

RINGED SUBSTRUCTURE AND A GAP AT 1 au IN THE NEAREST PROTOPLANETARY DISK (2016, background): “The millimeter-sized particles needed to assemble larger planetesimals (Ormel & Klahr 2010; Lambrechts & Johansen 2012) experience aerodynamic drag with the gas that results in their rapid migration toward the host star (Weidenschilling 1977; Takeuchi & Lin 2002).”
Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants (2018, methodology): “The radial speed of the gas vr,gas in an α disc is estimated by Takeuchi & Lin (2002) as vr,gas = −3α c2s vK ( 3 2 − αΣ ) .”
DUST FILTRATION BY PLANET-INDUCED GAP EDGES: IMPLICATIONS FOR TRANSITIONAL DISKS (2012, background): “…with radii smaller than 1 mm5, these particles are in the Epstein regime (Whipple 1972, Weidenschilling 1977), so that the dust stopping time (Takeuchi & Lin, 2002) is ts = sρp ρgvT , (3) 5 With our disk parameters, the mean free path of the molecule is 0.1 mm at 0.1 AU and 5 m at 10 AU,…”
Fossilized condensation lines in the Solar System protoplanetary disk (2015, background): “Because the radial migration speed of embryos is proportional to their mass (Tanaka et al., 2002), the innermost embryos are lost into the star and are not replaced at the same rate by embryos migrating inward from farther out.”
Dust dynamics during protoplanetary disc clearing (2007, methodology): “The form of this velocity was studied in depth by Takeuchi & Lin (2002), and we adopt their prescription for u d : u d = T −1 s u g − ηu K T s + T −1 s .”
The effect of dust settling on the appearance of protoplanetary disks (2004, background): “While there are many studies into the effects of settling onto the dust distribution relevant for planet formation (see e.g., Takeuchi & Lin 2002, 2003), there are curiously few studies which discuss the observational consequences of dust settling in a quantitative way.”
Dust flow in gas disks in the presence of embedded planets (2006, background): “…of gas and dust is much smaller than the local sound speed, the drag force is written as: fd = −Σ ΩK Ts ∆v, (11) whereΩK is the Keplerian angular velocity,∆v is the velocity difference between gas and dust, andTs is the dimensionless stopping time (Takeuchi & Lin 2002): Ts = √ π 8 ρpsvK ρgrcs .”
THE TW Hya DISK AT 870 μm: COMPARISON OF CO AND DUST RADIAL STRUCTURES (2011, background): “In the outer disk, the drift rates are expected to be largest for millimeter-sized particles (e.g., Takeuchi & Lin 2002).”
THE MASS DEPENDENCE BETWEEN PROTOPLANETARY DISKS AND THEIR STELLAR HOSTS (2013, background): “Particle growth promotes a net decrease in the disk-averaged κν , while particle migration (dominated by radial drift; Weidenschilling 1977) effectively decreases ζ over most of the disk volume (e.g., Takeuchi & Lin 2002; Brauer et al. 2008; Birnstiel et al. 2010).”
The Disk Substructures at High Angular Resolution Project (DSHARP). I. Motivation, Sample, Calibration, and Overview (2018, background): “The predicted drift rates for mm/cm solids located tens of au from the host star are fast enough to severely limit planetesimal growth (Takeuchi & Lin 2002, 2005; Brauer et al. 2007, 2008) and are in conflict with routine observations of emission from those particles at r ≈ 10–100 au (e.g.,…”
A SPATIALLY RESOLVED VERTICAL TEMPERATURE GRADIENT IN THE HD 163296 DISK (2013, background): “This phenomenon is thought to play an important role in the radial migration and growth of solids in these disks (Weidenschilling 1977b; Takeuchi & Lin 2002; Birnstiel et al. 2010), but is a subtle effect that slows down the gas from the fiducial Keplerian velocities by a rough factor of (1 − c2s…”
Accelerated planetesimal growth in self-gravitating protoplanetary discs (2004, background): “The dust, which is not affected by the gas pressure gradient, and the gas therefore orbit with different velocities and the resulting drag force causes the dust grains to drift inwards at a rate that depends on their size (Weidenschilling 1977; Takeuchi & Lin 2002).”
A simple model for the evolution of the dust population in protoplanetary disks (2012, unknown): “The gas radial velocity can be written as (see Takeuchi & Lin 2002) ug = −3αt c 2 s Vk (2 − p − q) , (29) where p is defined as Σg ∝ r−p and q as T ∝ r−q, and αtis taken to be constant.”
Planets opening dust gaps in gas disks (2004, background): “However, they assumed a constant dust-to-gas mass ratio of 1:100, whereas in the presence of large pressure gradients the gas and the dust evolution will decouple to some extent (Takeuchi & Lin 2002).”
Dust Evolution and the Formation of Planetesimals (2016, background): “Takeuchi & Lin (2002) derived this component of the dust radial velocity to be ur,dust = 1 1 + St2 ur,gas.”