Constraints on Planetesimal Collision Models in Debris Disks

TL;DR

This study uses new and archival millimeter observations of debris disks to constrain grain size distributions, comparing results with theoretical collisional models and revealing variability in stellar emission for AU Mic.

Contribution

It provides the first comprehensive analysis combining multi-wavelength data to tightly constrain grain size distributions in debris disks and tests collisional cascade models against observations.

Findings

Average grain size distribution slope q = 3.36±0.02

Possible trend of decreasing q with later spectral types

Stellar activity affects millimeter emission in AU Mic

Abstract

Observations of debris disks offer a window into the physical and dynamical properties of planetesimals in extrasolar systems through the size distribution of dust grains. In particular, the millimeter spectral index of thermal dust emission encodes information on the grain size distribution. We have made new VLA observations of a sample of seven nearby debris disks at 9 mm, with 3" resolution and $\sim5$ $\mu$Jy/beam rms. We combine these with archival ATCA observations of eight additional debris disks observed at 7 mm, together with up-to-date observations of all disks at (sub)millimeter wavelengths from the literature to place tight constraints on the millimeter spectral indices and thus grain size distributions. The analysis gives a weighted mean for the slope of the power law grain size distribution, $n(a)\propto a^{-q}$, of $\langle q \rangle = 3.36\pm0.02$, with a possible trend of decreasing $q$ for later spectral type stars. We compare our results to a range of theoretical models of collisional cascades, from the standard self-similar, steady-state size distribution ($q=3.5$) to solutions that incorporate more realistic physics such as alternative velocity distributions and material strengths, the possibility of a cutoff at small dust sizes from radiation pressure, as well as results from detailed dynamical calculations of specific disks. Such effects can lead to size distributions consistent with the data, and plausibly the observed scatter in spectral indices. For the AU Mic system, the VLA observations show clear evidence of a highly variable stellar emission component; this stellar activity obviates the need to invoke the presence of an asteroid belt to explain the previously reported compact millimeter source in this system.