GMOSS: All-sky model of spectral radio brightness based on physical components and associated radiative processes

We present Global MOdel for the radio Sky Spectrum (GMOSS) -- a novel, physically motivated model of the low-frequency radio sky from 22 MHz to 23 GHz. GMOSS invokes different physical components and associated radiative processes to describe the sky spectrum over 3072 pixels of $5^{\circ}$ resolution. The spectra are allowed to be convex, concave or of more complex form with contributions from synchrotron emission, thermal emission and free-free absorption included. Physical parameters that describe the model are optimized to best fit four all-sky maps at 150 MHz, 408 MHz, 1420 MHz and 23 GHz and two maps at 22 MHz and 45 MHz generated using the Global Sky Model of de Oliveira-Costa et al. (2008). The fractional deviation of model to data has a median value of $6\%$ and is less than $17\%$ for $99\%$ of the pixels. Though aimed at modeling of foregrounds for the global signal arising from the redshifted 21-cm line of Hydrogen during Cosmic Dawn and Epoch of Reionization (EoR) - over redshifts $150\lesssim z \lesssim 6$, GMOSS is well suited for any application that requires simulating spectra of the low-frequency radio sky as would be observed by the beam of any instrument. The complexity in spectral structure that naturally arises from the underlying physics of the model provides a useful expectation for departures from smoothness in EoR foreground spectra and hence may guide the development of algorithms for EoR signal detection. This aspect is further explored in a subsequent paper.