Recovering the Dust Mass Budget with PRIMA

Achieving a complete picture of galaxy evolution is a primary goal of extragalactic astrophysics. To accomplish this ambitious task, a wealth of multi-wavelength surveys have been devoted to assess the cosmic evolution of the cold gas and of the stellar mass across cosmic time. In this cosmic census, one elusive component is represented by interstellar dust. In this work, we exploit the IR mission PRIMA (covering wavelengths from 24 $\mu$m to 235 $\mu$m) to perform a deep survey (1000h on 1 deg$^2$) aimed at estimating the still poorly known dust mass function (DMF) at $z \sim 0.5 - 5$. We consider the spectro-photometric realization of the SPRITZ simulation and we compute the dust masses using single temperature Modified Grey Body functions. We show how PRIMA alone, thanks to its unprecedented sensitivities, will constrain the DMF at $z < 1.5$, in terms of mass and faint-end slope. At $z > 1.5$, we stress the key synergy with current or future sub-millimeter facilities, such as the JCMT/SCUBA-2, AtLAST, LMT and ALMA telescopes, that will allow us to probe the R$-$J regime of PRIMA selected galaxies. Finally, PRIMA, thanks to its large photometric coverage, will be able for the first time to constrain strictly the warm dust properties of a two component dust model.