Relating grain size distributions in circumstellar discs to the spectral index at millimetre wavelengths

TL;DR

This paper examines how spectral index measurements at millimetre wavelengths relate to dust grain size distributions in circumstellar discs, revealing that traditional assumptions underestimate the sensitivity of size distribution indexes to observed spectral slopes.

Contribution

It challenges common approximations by showing that inferred size distribution indexes are more sensitive and generally larger, influenced by the transition from small to large grains and their optical properties.

Findings

Inferred size distribution indexes are greater than previously thought.

Spectral indexes are more sensitive to grain size distributions than earlier models suggested.

Material composition and optical properties introduce significant uncertainties.

Abstract

The excess emission seen in spectral energy distributions (SEDs) is commonly used to infer the properties of the emitting circumstellar dust in protoplanetary and debris discs. Most notably, dust size distributions and details of the collision physics are derived from SED slopes at long wavelengths. This paper reviews the approximations that are commonly used and contrasts them with numerical results for the thermal emission. The inferred size distribution indexes are shown to be greater and more sensitive to the observed sub(mm) spectral indexes than previously considered. This effect results from aspects of the transition from small grains with volumetric absorption to bigger grains that absorb and emit near to their surface, controlled by both the real and the imaginary part of the refractive index. The steeper size distributions indicate stronger size-dependence of material strengths or impact velocities or, otherwise, less efficient transport or erosion processes. Strong uncertainties remain because of insufficient knowledge of the material composition, porosity, and optical properties at long wavelengths.