# Spread of the dust temperature distribution in circumstellar disks

## TL;DR

This study examines how subdividing dust grain sizes in circumstellar disks affects temperature distribution and spectral energy output, revealing significant differences from average-property models especially in optically thin regions.

## Contribution

It introduces a method to account for grain size distribution effects on temperature and spectral energy distribution in circumstellar disks, improving upon models using average optical properties.

## Key findings

- Temperature spread can reach ~63% in optically thin regions.
- Differences between detailed and average models decrease with increasing optical depth.
- Multiple grain sizes lead to stronger thermal emission at short wavelengths.

## Abstract

Accurate temperature calculations for circumstellar disks are particularly important for their chemical evolution. Their temperature distribution is determined by the optical properties of the dust grains, which, among other parameters, depend on their radius. However, in most disk studies, only average optical properties and thus an average temperature is assumed to account for an ensemble of grains with different radii. We investigate the impact of subdividing the grain radius distribution into multiple sub-intervals on the resulting dust temperature distribution and spectral energy distribution (SED). These quantities were computed for two different scenarios: (1) Radius distribution represented by 16 logarithmically distributed radius intervals, and (2) radius distribution represented by a single grain species with averaged optical properties (reference). Within the considered parameter range, i.e., of grain radii between 5 nm and 1 mm and an optically thin and thick disk with a parameterized density distribution, we obtain the following results: In optically thin disk regions, the temperature spread can be as large as ~63% and the relative grain surface below a certain temperature is lower than in the reference disk. With increasing optical depth, the difference in the midplane temperature and the relative grain surface below a certain temperature decreases. Furthermore, below ~20K, this fraction is higher for the reference disk than for the case of multiple grain radii, while it shows the opposite behavior for temperatures above this threshold. The thermal emission in the case of multiple grain radii at short wavelengths is stronger than for the reference disk. The freeze-out radius is a function of grain radius, spanning a radial range between the coldest and warmest grain species of ~30AU.