Benchmarking the calculation of stochastic heating and emissivity of dust grains in the context of radiative transfer simulations

Context. Thermal emission by stochastically heated dust grains (SHGs) plays an important role in the radiative transfer (RT) problem for a dusty medium. It is therefore essential to verify that RT codes properly calculate the dust emission before studying the effects of spatial distribution and other model parameters on the simulated observables. Aims. We define an appropriate problem for benchmarking dust emissivity calculations in the context of RT simulations, specifically including the emission from SHGs. Our aim is to provide a self-contained guide for implementors of such functionality and to offer insight into the effects of the various approximations and heuristics implemented by the participating codes to accelerate the calculations. Methods. The benchmark problem definition includes the optical and calorimetric material properties and the grain size distributions for a typical astronomical dust mixture with silicate, graphite, and PAH components. It also includes a series of analytically defined radiation fields to which the dust population is to be exposed and instructions for the desired output. We processed this problem using six RT codes participating in this benchmark effort and compared the results to a reference solution computed with the publicly available dust emission code DustEM. Results. The participating codes implement different heuristics to keep the calculation time at an acceptable level. We study the effects of these mechanisms on the calculated solutions and report on the level of (dis) agreement between the participating codes. For all but the most extreme input fields, we find agreement within 10% across the important wavelength range 3 mu m <= lambda <= 1000 mu m. Conclusions. We conclude that the relevant modules in RT codes can and do produce fairly consistent results for the emissivity spectra of SHGs. This work can serve as a reference for implementors of dust RT codes, and it will pave the way for a more extensive benchmark effort focusing on the RT aspects of the various codes