The effect of dust settling on the appearance of protoplanetary disks

By C. Dullemond, C. Dominik. 2004

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We analyze how the process of dust settling affects the spectral energy distribution and optical appearance of pro- toplanetary disks. Using simple analytic estimates on the one hand, and detailed 1+1-D models on the other hand, we show that, while the time scale for settling down to the equator may exceed the life time of the disk, it takes much less time for even small grains of 0.1 µm to settle down to a few pressure scale heights. This is often well below the original location of the disk's photosphere, and the disk therefore becomes effectively "flatter". If turbulent stirring is included, a steady state solution can be found, which is typically reached after a few ×10 5 years. In this state, the downward settling motion of the dust is balanced by vertical stirring. Dependent on the strength of the turbulence, the shape of the disk in such a steady state can be either fully flaring, or flaring only up to a certain radius and self-shadowed beyond that radius. These geometries are similar to the geometries that were found for disks around Herbig Ae/Be stars in our previous papers (Dullemond 2002, AA Dullemond & Dominik 2004, A&A, 417, 159, henceforth DD04). In those papers, however, the reason for a disk to turn self-shadowed was by loss of optical depth through dust grain growth. Here we show that dust settling can achieve a similar effect without loss of vertical optical depth, although the self-shadowing in this case only affects the outer regions of the disk, while in DD04 the entire disk outside of the puffed-up inner rim was shadowed. In reality it is likely that both grain growth and grain settling act simultaneously. The spectral energy distributions of such self-shadowed - or partly self-shadowed - disks have a relatively weak far-infrared excess (in comparison to flaring disks). We show here that, when dust settling is the cause of self-shadowing, these self-shadowed regions of the disk are also very weak in resolved images of scattered light. A reduc- tion in the brightness was already predicted in DD04, but we find that dust settling is far more efficient than grain growth at dimming the scattered light image of the disk. Settling is also efficient in steepening the spectral energy distribution at mid- to far-infrared wavelengths. From the calculations with compact grains it follows that, after about 10 6 years, most disks should be self-shadowed. The fact that some older disks are still observed with the characteristics of flaring disks therefore seems somewhat inconsistent with the time scales predicted by the settling model based on compact grains. This suggests that perhaps even the small grains (<0.1 µm) have a porous or fractal structure, slowing down the settling. Alternatively, it could mean that the different geometries of observed disks is merely a reflection of the turbulent state of these disks.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/8bc3b34a9cd8221436d200459e1cfc18585b1771

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Citations in the corpus

RESOLVED IMAGES OF LARGE CAVITIES IN PROTOPLANETARY TRANSITION DISKS (2011, methodology): “Simulations of the stellar irradiation of that model density grid were conducted to determine the dust temperature structure, using the two-dimensional axisymmetric Monte Carlo radiative transfer code RADMC (see Dullemond & Dominik 2004a).”
The Gas Temperature in the Surface Layers of Protoplanetary Disks (2004, neutral): “This puts great pressure on theoretical modeling efforts of the structure and appearance of these disks (e.g., D’Alessio et al. 1998; Chiang & Goldreich 1997; Bell et al. 1997; Lachaume et al. 2003; Dullemond & Dominik 2004a).”
Three Radial Gaps in the Disk of TW Hydrae Imaged with SPHERE (2016, methodology): “Concerning assumption 3: size-dependent dust settling is incorporated using the formalism of Dullemond & Dominik (2004) which was implemented in MCMax by Mulders & Dominik (2012).”
THE MASS DEPENDENCE BETWEEN PROTOPLANETARY DISKS AND THEIR STELLAR HOSTS (2013, background): “Unfortunately, the processes that control dust sedimentation and their impact on midplane temperatures are quite complicated (e.g., Dullemond & Dominik 2004; D’Alessio et al. 2006).”
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).”
PROTOPLANETARY DISK STRUCTURES IN OPHIUCHUS (2009, methodology): “For many disks, there is compelling evidence that dust grains have settled toward the disk midplane (Chiang et al. 2001; Dullemond & Dominik 2004b; D’Alessio et al. 2006).”
A Three-dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk Using DCO+ (2017, background): “In the vertical direction, dust grain motion is subject to the competing effects of settling toward the midplane and turbulence lifting them back up into the disk atmosphere (Dullemond & Dominik 2004).”
Dust size distributions in coagulation/fragmentation equilibrium: numerical solutions and analytical fits (2010, background): “We focus on the Epstein regime where the Stokes number can be approximated by St = Ωk · τst a ρs Σg π 2 (26) with Σg being the gas surface density and ρs being the internal density of the particles which relates mass and size via m = 4π/3ρs a3, Settling starts to play a role as soon as the Stokes nu”
Probing dust grain evolution in IM Lupi's circumstellar disc. Multi-wavelength observations and mo (2008, background): “The stratified structure resulting from grain growth and settling has direct consequences on disc observables like their spectral energy distributions (SEDs) and scattered light images (e.g. Dullemond & Dominik 2004, hereafter D04).”
A Survey and Analysis of Spitzer Infrared Spectrograph Spectra of T Tauri Stars in Taurus (2006, background): “…(Weidenschilling 1997; Dullemond & Dominik 2004); the upper disk layers close to the star (within a few AU) are depleted on a very short timescale, much less than the 10 Myr lifetime of a protoplanetary disk (Dullemond & Dominik 2004), with larger grains settling faster than the small grains.”
Complex organic molecules in protoplanetary disks (2013, background): “…gravitational settling and grain Article number, page 3 of 34 A&A proofs:manuscript no. complex_chemistry_astroph coagulation (grain growth) will perturb the dust size and density distribution from that observed in dense clouds (see, e.g., Dullemond & Dominik 2004, 2005; D’Alessio et al. 2006).”
On the diversity and statistical properties of protostellar discs (2018, background): “This effect is expected due to dust growth (Goldreich & Ward 1973; Weidenschilling 1980; Cuzzi et al. 1993; Dullemond & Dominik 2004) and inward radial migration of large grains (Whipple 1972; Weidenschilling 1977).”
Theory of Star Formation (2007, background): “Quite sophisticated radial-vertical radiative models (including grain growth and settling) have been developed that agree well with observed spectral energy distributions from µm to mm wavelengths (see e.g. Dullemond & Dominik, 2004, D’Alessio et al., 2006 and references therein).”