Bayesian inference methodology to characterize the dust emissivity at far-infrared and submillimeter frequencies

We present a Bayesian inference method to characterise the dust emission properties using the well-known dust-HI correlation in the diffuse interstellar medium at Planck frequencies $\nu \ge 217$ GHz. We use the Galactic HI map from the Galactic All-Sky Survey (GASS) as a template to trace the Galactic dust emission. We jointly infer the pixel-dependent dust emissivity and the zero level present in the Planck intensity maps. We use the Hamiltonian Monte Carlo technique to sample the high dimensional parameter space ($D \sim 10^3$). We demonstrate that the methodology leads to unbiased recovery of dust emissivity per pixel and the zero level when applied to realistic Planck sky simulations over a 6300 deg$^2$ area around the Southern Galactic pole. As an application on data, we analyse the Planck intensity map at 353 GHz to jointly infer the pixel-dependent dust emissivity at Nside=32 resolution (1.8\deg\ pixel size) and the global offset. We find that the spatially varying dust emissivity has a mean of 0.031 MJysr$^{-1} (10^{20} \mathrm{cm^{-2}})^{-1}$ and $1\sigma$ standard deviation of 0.007 MJysr$^{-1} (10^{20} \mathrm{cm^{-2}})^{-1}$. The mean dust emissivity increases monotonically with increasing mean HI column density. We find that the inferred global offset is consistent with the expected level of Cosmic Infrared Background (CIB) monopole added to the Planck data at 353 GHz. This method is useful in studying the line-of-sight variations of dust spectral energy distribution in the multi-phase interstellar medium.