Impact of X-rays on CO emission from high-z galaxies

We study the impact of active galactic nuclei (AGN) on the CO Spectral Line Energy Distribution (SLED) of high-$z$ galaxies. In particular, we want to assess if the CO SLED can be used as a probe of AGN activity. To this purpose, we develop a semi-analytical model that takes into account the radiative transfer and the clumpy structure of giant molecular clouds where the CO lines are excited, their distribution in the galaxy disk, and the torus obscuration of the AGN radiation. We study the joint effect on the CO SLED excitation of (i) the X-ray luminosity from the AGN ($L_{X}$), (ii) the size of the molecular disk, (iii) the inclination angle ($\Omega$) of the torus with respect to the molecular disk, and (iv) the GMC mean density. We also discuss the possibility of an enhanced Cosmic Ray Ionization Rate (CRIR). We find that the X-ray Dominated Region (XDR) generated by the AGN in every case enhances the CO SLED for $J>5$, with increasing excitation of high-$J$ CO lines for increasing X-ray luminosity. Because high-$z$ galaxies are compact, the XDR region typically encloses the whole disk, thus its effect can be more important with respect to lower redshift objects. The impact of the XDR can be disentangled from an enhanced CRIR either if $L_X>10^{44} \rm \,erg\, s^{-1}$, or if $\Omega \geq 60^{\circ}$. We finally provide predictions on the CO(7-6)/[CII] and CO(17-16)/[CII] ratios as a function of $L_X$, which can be relevant for ALMA follow up of galaxies and quasars previously detected in [CII].