The dust emissivity index β in infrared-bright galaxies at 1.5 < z < 4.2

We have measured the dust emissivity index $\beta$ for 21 infrared-bright sources (including several gravitationally lensed galaxies) at $1.5 < z < 4.2$ using Atacama Large Millimetre/submillimetre Array 101–199 GHz data sampling the Rayleigh–Jeans side of the spectral energy distribution. These data are largely insensitive to temperature variations and therefore should provide robust measurements of $\beta$. We obtain a mean $\beta$ of 2.2 with a standard deviation of 0.6 that is at the high end of the range of values that had previously been measured in many galactic and extragalactic sources. We find no systematic variation in $\beta$ versus redshift. We also demonstrate with a subset of our sources that these higher $\beta$ values have significant implications for modelling dust emission and in particular for calculating dust masses or the wavelength at which dust becomes optically thick.