Dust Growth and Settling in Protoplanetary Disks and Disk Spectral Energy Distributions. I. Laminar Disks

By Hidekazu Tanaka, Youhei Himeno, Shigeru Ida. 2005

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Dust growth and settling considerably affect the spectral energy distributions (SEDs) of protoplanetary disks. We investigated dust growth and settling in protoplanetary disks through numerical simulations to examine time evolution of the disk optical thickness and SEDs. In this paper we considered laminar disks as the first step in a series of papers. As a result of dust growth and settling, a dust layer forms around the midplane of a gaseous disk. After the formation of the dust layer, small dust grains remain floating above the layer. Although the surface density of the floating small grains is much less than that of the dust layer, they govern the disk optical thickness and the emission. Size distributions of the floating grains obtained from numerical simulations are well described by a universal power-law distribution, which is independent of the disk temperature, the disk surface density, the radial position in the disk, etc. The floating small grains settle onto the dust layer in a long timescale compared with the formation of the dust layer. Typically, it takes 106 yr for micron-sized grains. Rapid grain growth in the inner part of disks makes the radial distribution of the disk optical thickness less steep than that of the disk surface density, Σ. For disks with Σ ∝ R-3/2, the radial distribution of the optical thickness is almost flat for all wavelengths at t ≲ 106 yr. At t > 106 yr, the optical thickness of the inner disk (≲a few AU) almost vanishes, which may correspond to disk inner holes observed by Spitzer Space Telescope. Furthermore, we examined time evolution of disk SEDs, using our numerical results and the two-layer model. The grain growth and settling decrease the magnitude of the SEDs, especially at λ ≥ 100 μm. Our results indicate that grain growth and settling can explain the decrease in observed energy fluxes at millimeter/submillimeter wavelengths with timescales of 106-107 yr without depletion of the disks.

Subfields: Astronomy and Astrophysics, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/24d06a2fe0ad02728e93c4a307d1bde85e11af61

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Citations in the corpus

Dust size distributions in coagulation/fragmentation equilibrium: numerical solutions and analytical fits (2010, background): “Theoretical models of grain growth indicate that particles can grow to sizes much larger than a few μm (see Nakagawa et al. 1981; Weidenschilling 1980, 1984, 1997; Dullemond & Dominik 2005; Tanaka et al. 2005; Brauer et al. 2008a; Birnstiel et al. 2009).”
Numerical Simulation of Dust Aggregate Collisions. II. Compression and Disruption of Three-Dimensional Aggregates in Head-on Collisions (2008, background): “In such growth processes, coupling of dust with disk gas plays an important role in the orbital motion of dust aggregates (e.g., Adachi et al.1976;Weidenschilling1980,1984; Nakagawa et al.1981; Tanaka et al. 2005).”
Chemical enrichment of giant planets and discs due to pebble drift (2017, unknown): “To compute the relative velocity we follow Tanaka et al. (2005), who provide an expression for the dust-gas relative velocity of a distribution of grain sizes when feedback is included.”
RAPID COAGULATION OF POROUS DUST AGGREGATES OUTSIDE THE SNOW LINE: A PATHWAY TO SUCCESSFUL ICY PLANETESIMAL FORMATION (2012, methodology): “The equilibrium velocitiesin the presence of the backreaction are derived by Tanaka et al. (2005) for arbitrary dust size distribution.”
Ring shaped dust accumulation in transition disks (2012, background): “Various mechanisms have been proposed so far to explain the inner disk clearing: photoevaporation winds (e.g. Owen et al. 2011), grain growth (Klahr & Henning 1997; Tanaka et al. 2005) and dynamical interactions with companions (Lin & Papaloizou 1979).”
ELECTRIC CHARGING OF DUST AGGREGATES AND ITS EFFECT ON DUST COAGULATION IN PROTOPLANETARY DISKS (2009, background): “The solar system abundance of condensates including water ice estimated by Pollack et al. (1994) leads to the dust-to-gas ratio fdg = 0.014 as well as the monomer bulk density ρ0 = 1.4 g cm−3 (Tanaka et al. 2005).”
Close-in planetesimal formation by pile-up of drifting pebbles (2016, methodology): “We implement these effects using equations derived by Tanaka et al. (2005), which are also found in Okuzumi et al. (2012).”
Dust properties of protoplanetary disks in the Taurus-Auriga star forming region from millimeter wavelengths (2009, unknown): “Values of q lower than 3.5 have been obtained by, e.g., Tanaka et al. (2005) from simulations of grain growth in stratified protoplanetary disks which give vertically integrated size distributions 8 Note that β-values greater than ≈ 0.85 can be explained by both q <∼ 3.5 and q > ∼ 3.5. with q ≈ 3,…”
EVIDENCE FOR DUST CLEARING THROUGH RESOLVED SUBMILLIMETER IMAGING (2008, background): “Such a steep transition is more consistent with truncations induced by gravitational instabilities than a more gradual process such as dust settling and coagulation (Crida et al. 2006, Dullemond & Dominik 2005, Tanaka et al. 2005).”
Numerical Simulation of Dust Aggregate Collisions. I. Compression and Disruption of Two-Dimensional Aggregates (2007, background): “For example, the structure of dust aggregates determines their cross sections and the gas drag forces on them,which strongly affect theirmotion and collisional growth in a protoplanetary disk (e.g., Weidenschilling 1980, 1984; Nakagawa et al. 1981; Tanaka et al. 2005).”
Multiwavelength analysis for interferometric (sub-)mm observations of protoplanetary disks - Radial constraints on the dust properties and the disk structure (2015, background): “The choice of the dust grain size distribution aims at simply modeling a protoplanetary disk with a surface layer mainly composed of small grains and a midplane layer of larger pebbles (Dullemond & Dominik 2004; Tanaka et al. 2005).”
Planetesimal formation near the snowline: in or out? (2017, background): “These expressions can be generalized to account for a size distribution of particles (Tanaka et al. 2005; Estrada & Cuzzi 2008; Bai & Stone 2010).”
RESOLVED IMAGES OF LARGE CAVITIES IN PROTOPLANETARY TRANSITION DISKS (2011, background): “A variety of dissipation mechanisms have been proposed to explain observations of transition disks, including extensive particle growth (Tanaka et al. 2005; Dullemond & Dominik 2005), photoevaporative massloss in winds (Clarke et al. 2001; Alexander et al. 2006a), and tidal interactions with…”
Cold Disks: Spitzer Spectroscopy of Disks around Young Stars with Large Gaps (2007, background): “An alternative to physically removing the dust is to let it grow beyond the size at which it efficiently radiates as a blackbody so that it no longer emits strongly in the mid-IR (Tanaka et al. 2005).”
TRANSITIONAL AND PRE-TRANSITIONAL DISKS: GAP OPENING BY MULTIPLE PLANETS? (2010, background): “In addition, the large outer disk gap radii (as much as 20-70 AU) pose a challenge for pure coagulation models at an age of ∼ 1 − 2 Myr (Tanaka et al. 2005; Dullemond & Dominik 2005).”