Probing the turbulent mixing strength in protoplanetary disks across the stellar mass range: no significant variations

¹ Astronomical Institute “Anton Pannekoek”, University of Amsterdam, PO Box 94249, 1090 GE Amsterdam, The Netherlands
e-mail: mulders@uva.nl
² SRON Netherlands Institute for Space Research, PO Box 800, 9700 AV Groningen, The Netherlands
³ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands

Received: 20 September 2011
Accepted: 18 December 2011

Abstract

Context. Dust settling and grain growth are the first steps in the planet-formation process in protoplanetary disks. These disks are observed around stars with different spectral types, and there are indications that the disks around lower mass stars are significantly flatter, which could indicate that they settle and evolve faster, or in a different way.

Aims. We aim to test this hypothesis by modeling the median spectral energy distributions (SEDs) of three samples of protoplanetary disks: around Herbig stars, T Tauri stars and brown dwarfs. We focus on the turbulent mixing strength to avoid a strong observational bias from disk and stellar properties that depend on stellar mass.

Methods. We generated SEDs with the radiative transfer code MCMax, using a hydrostatic disk structure and settling the dust in a self-consistent way with the α-prescription to probe the turbulent mixing strength.

Results. We are able to fit all three samples with a disk with the same input parameters, scaling the inner edge to the dust evaporation radius and disk mass to millimeter photometry. The Herbig stars require a special treatment for the inner rim regions, while the T Tauri stars require viscous heating, and the brown dwarfs lack a good estimate of the disk mass because only few millimeter detections exist.

Conclusions. We find that the turbulent mixing strength does not vary across the stellar mass range for a fixed grain size distribution and gas-to-dust ratio. Regions with the same temperature have a self-similar vertical structure independent of stellar mass, but regions at the same distance from the central star appear more settled in disks around lower mass stars. We find a relatively low turbulent mixing strength of α = 10^-4 for a standard grain size distribution, but our results are also consistent with α = 10^-2 for a grain size distribution with fewer small grains or a lower gas-to-dust ratio.