Contributions of extragalactic CO emission lines to ground-based CMB observations

We investigate the potential of CO rotational lines at redshifts $z\ensuremath{\sim}0--6$ being an appreciable source of extragalactic foreground anisotropies in the cosmic microwave background. Motivated by previous investigations, we specifically focus on the frequency bands and small scales probed by ground-based surveys. Using an empirical parametrization for the relation between the infrared luminosity of galaxies and their CO line luminosity, conditioned on sub-mm observations of CO luminosity functions from $J=1$ to $J=7$ at $\ensuremath{\nu}={100,250}\text{ }\text{ }\mathrm{GHz}$, we explore how uncertainty in the CO luminosity function translates into uncertainty in the signature of CO emission in the cosmic microwave background. We find that at $\ensuremath{\ell}=3000$ the amplitude of both CO autocorrelation and cross-correlation with the cosmic infrared background could be detectable in an ACT-like experiment with 90, 150 and 220 GHz bands, even in the scenarios with the lowest amplitude consistent with sub-mm data. We also investigate, for the first time, the amplitude of the $\mathrm{CO}\ifmmode\times\else\texttimes\fi{}$ cosmic infrared background correlation between different frequency bands and find that our model predicts that this signal could be comparable to the amplitude of the cosmic infrared background frequency cross-correlation at certain wavelengths. This implies current observations can potentially be used to constrain the bright end of CO luminosity functions, which are difficult to probe with current sub-mm telescopes due to the small volumes they survey. Our findings corroborate past results and have significant implications in template-based searches for cosmic microwave background secondaries, such as the kinetic Sunyaev Zel'dovich effect, using the frequency-dependent high-$\ensuremath{\ell}$ temperature--temperature power spectrum.