Dust Growth and Dynamics in Protoplanetary Nebulae: Implications for Opacity, Thermal Profile and Gravitational Instability

Abstract

In spite of making a small contribution to total protoplanetary disk mass, dust affects the disk temperature by controlling absorption of starlight. As grains grow from their initial ISM-like size distribution, settling depletes the disk's upper layers of dust and decreases the optical depth, cooling the interior. Here we investigate the effect of collisional growth of dust grains and their dynamics on the thermal and optical profile of the disk, and explore the possibility that cooling induced by grain growth and settling could lead to gravitational instability. We develop a Monte Carlo dust collision model with a weighting technique and allow particles to collisionally evolve through sticking and fragmentation, along with vertical settling and turbulent mixing. We explore two disk models, the MMEN (minimum-mass extrasolar nebula), and a "heavy" disk with higher surface density than the MMEN, and perform simulations for both constant and spatially variable turbulence efficiency profile \(\alpha(R,z)\). We then calculate mean wavelength-dependent opacities for the evolving disks and perform radiative transfer to calculate the temperature profile \(T(R,z)\). Finally, we calculate the Toomre Q parameter, a measure of the disk's stability against self-gravity, for each disk model after it reaches a steady state dust-size distribution. We find that even weak turbulence can keep sub-micron sized particles stirred in the disk's upper layer, affecting its optical and thermal profiles, and the growth of large particles in the midplane can make a massive disk optically thick at millimeter wavelengths, making it difficult to calculate the surface density of dust available for planet formation in the inner disk. Also, for an initially massive disk, grain settling and growth can produce a drop in the Toomre Q parameter, driving the disk to \(Q < 1.4\) and possibly triggering spiral instabilities.