We investigate the potential of CO rotational lines at redshifts $z\sim 0-6$ 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 parameterization 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 $\nu = \{100,250\}$ GHz, we explore how uncertainty in the CO luminosity function translates into uncertainty in the signature of CO emission in the CMB. We find that at $\ell = 3000$ the amplitude of both CO autocorrelation and cross-correlation with the CIB 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 CO$\times$CIB 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 CMB secondaries, such as the kinetic Sunyaev Zel'dovich effect, using the frequency-dependent high-$\ell$ TT power spectrum.
Eclipse mapping uses the shape of the eclipse of an exoplanet to measure its two-dimensional structure. Light curves are mostly composed of longitudinal information, with the latitudinal information only contained in the brief ingress and egress of the eclipse. This imbalance can lead to a spuriously confident map, where the longitudinal structure is constrained by out-of-eclipse data and the latitudinal structure is wrongly determined by the priors on the map. We present a new method to address this issue. The method tests for the presence of an eclipse mapping signal by using k-fold cross-validation to compare the performance of a simple mapping model to the null hypothesis of a uniform disk. If a signal is found, the method fits a map with more degrees of freedom, optimising its information content. The information content is varied by penalising the model likelihood by a factor proportional to the spatial entropy of the map, optimised by cross-validation. We demonstrate this method for simulated datasets then apply it to three observational datasets. The method identifies an eclipse mapping signal for JWST MIRI/LRS observations of WASP-43b but does not identify a signal for JWST NIRISS/SOSS observations of WASP-18b or Spitzer Space Telescope observations of HD 189733b. It is possible to fit eclipse maps to these datasets, but we suggest that these maps are overfitting the eclipse shape. We fit a new map with more spatial freedom to the WASP-43b dataset and show a flatter east-west structure than previously derived.