Predicting the intensity mapping signal for multi-$J$ CO lines

Abstract: We present a novel approach to estimating the intensity mapping signal of any CO rotational line emitted during the Epoch of Reionization (EoR). Our approach is based on large velocity gradient (LVG) modeling, a radiative transfer modeling technique that generates the full CO spectral line energy distribution (SLED) for a specified gas kinetic temperature, volume density, velocity gradient, molecular abundance, and column density. These parameters, which drive the physics of CO transitions and ultimately dictate the shape and amplitude of the CO SLED, can be linked to the global properties of the host galaxy, mainly the star formation rate (SFR) and the SFR surface density. By further employing an empirically derived SFR-M relation for high redshift galaxies, we can express the LVG parameters, and thus the specific intensity of any CO rotational transition, as functions of the host halo mass M and redshift z. Integrating over the range of halo masses expected to host CO-luminous galaxies, i.e. M >= 10^8 M{_\odot}, we predict a mean CO(1-0) brightness temperature ranging from ~1 {\mu}K at z = 6 to ~ 0.2 {\mu}K at z = 10 in the case where the duty cycles of star formation and CO luminous activity are assumed to be 0.1 (f_{UV} = f_{duty} = 0.1). In this model, the CO emission signal remains strong for higher rotational levels, with < T_{CO} > ~ 0.3 and 0.1 {\mu}K for the CO J = 10->9 transition at z = 6 and 10 respectively. If instead we adopt duty cycles of unity, the estimated CO(1-0) brightness temperature declines to < T_{CO}>~ 0.6 {\mu}K at z = 6 and ~0.03 {\mu}K at z =10 respectively; the correspondingly reduced signal strengths of the higher J lines make detection of these transitions at high significance less likely in the f_{UV} = f_{duty} = 1 model.