The interstellar dust emission spectrum

François-Xavier Désert

doi:10.1051/0004-6361/202142617

Abstract

Context. Most of the modelling of the interstellar dust infrared emission spectrum is done by assuming some variations around a single-temperature grey-body approximation. For example, the foreground modelling of Planck mission maps involves a single dust temperature, T, along a given line-of-sight with a single emissivity index, β. The two parameters are then fitted and therefore variable from one line-of-sight to the other. Aims. Our aim is to go beyond that modelling in an economical way. Methods. We model the dust spectrum with a temperature distribution around the mean value and show that only the second temperature moment matters. We advocate the use of the temperature logarithm as the proper variable. Results. If the interstellar medium is not too heterogeneous, there is a universal analytical spectrum, which is derived here, that goes beyond the grey-body assumption. We show how the cosmic microwave background radiatively interacts with the dust spectrum (a non-negligible corrective term at millimetre wavelengths). Finally, we construct a universal ladder of discrete temperatures, which gives a minimal and fast description of dust emission spectra as measured by photometric mapping instruments that lends itself to an almost linear fitting. This data modelling can include contributions from the cosmic infrared background fluctuations.

Highlights

When modelling the interstellar dust emission it is usually assumed that its spectrum is close to that produced by a grey body
The model has been sufficient to explain the dust spectral energy distribution (SED) along a given line-of-sight, be it in the diffuse interstellar medium (ISM; e.g. Hensley & Draine 2021), in molecular clouds, in star-forming regions, or in galaxies (Galliano et al 2018). This SED is determined by a few broadband photometric measurements with rather large uncertainties, so to the first order a single temperature is enough for the fits to be satisfactory
We have shown an analytical development around the Planck function

Summary

Introduction

When modelling the interstellar dust emission it is usually assumed that its spectrum is close to that produced by a grey body. This assumption has been used over the last 50 years. Hensley & Draine 2021), in molecular clouds, in star-forming regions, or in galaxies (Galliano et al 2018). This SED is determined by a few broadband photometric measurements with rather large uncertainties (statistical and systematic), so to the first order a single temperature is enough for the fits to be satisfactory.

Objectives

Discussion

Conclusion