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We present a model for simulating Carbon Monoxide (CO) rotational lineemission in molecular clouds, taking account of their 3D spatial distributionin galaxies with different geometrical properties. The model implemented isbased on recent results in the literature and has been designed for performingMonte-Carlo simulations of this emission. We compare the simulations producedwith this model and calibrate them, both on the map level and on the powerspectrum level, using the second release of data from the Planck satellite forthe Galactic plane, where the signal-to-noise ratio is highest. We use thecalibrated model to extrapolate the CO power spectrum at low Galactic latitudeswhere no high sensitivity observations are available yet. We then forecast thelevel of unresolved polarized emission from CO molecular clouds which couldcontaminate the power spectrum of Cosmic Microwave Background (CMB)polarization B-modes away from the Galactic plane. Assuming realistic levels ofthe polarization fraction, we show that the level of contamination isequivalent to a cosmological signal with $r \lesssim 0.02$. The Monte-CarloMOlecular Line Emission (MCMole3D) Python package, which implements this model,is being made publicly available.

A 3D model for CO molecular line emission as a potential CMB polarization contaminant