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

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, we predict a mean CO(1-0) brightness temperature ranging from ~0.6 {mu}K at z= 6 to ~0.03 {mu} at z= 10 with brightness temperature fluctuations of $Delta_{CO}^2$ ~ 0.1 and 0.005 {mu}K respectively, at k = 0.1 Mpc$^{-1}$. In this model, the CO emission signal remains strong for higher rotational levels at z = 6, with <T$_{CO}$>~ 0.3 and 0.05 {mu}K for the CO J = 6->5 and CO J = 10->9 transitions respectively. Including the effects of CO photodissociation in these molecular clouds, especially at low metallicities, results in the overall reduction in the amplitude of the CO signal, with the low- and high-J lines weakening by 2-20% and 10-45%, respectively, over the redshift range 4 < z < 10.