A model of spectral line broadening in signal forecasts for line-intensity mapping experiments

Line-intensity mapping observations will find fluctuations of integrated line emission are attenuated by varying degrees at small scales due to the width of the line emission profiles. This attenuation may significantly impact estimates of astrophysical or cosmological quantities derived from measurements. We consider a theoretical treatment of the effect of line broadening on both the clustering and shot-noise components of the power spectrum of a generic line-intensity power spectrum using a halo model. We then consider possible simplifications to allow easier application in analysis, particularly in the context of inferences that require numerous, repeated, fast computations of model line-intensity signals across a large parameter space. For the CO Mapping Array Project (COMAP) and the CO(1-0) line-intensity field at $z\sim3$ serving as our primary case study, we expect a $\sim10\%$ attenuation of the spherically averaged power spectrum on average at relevant scales of $k\approx0.2$-$0.3$ Mpc$^{-1}$, compared to $\sim25\%$ for the interferometric Millimetre-wave Intensity Mapping Experiment (mmIME) targeting shot noise from CO lines at $z\sim1$-$5$ at scales of $k\gtrsim1$ Mpc$^{-1}$. We also consider the nature and amplitude of errors introduced by simplified treatments of line broadening, and find that while an approximation using a single effective velocity scale is sufficient for spherically-averaged power spectra, a more careful treatment is necessary when considering other statistics such as higher multipoles of the anisotropic power spectrum or the voxel intensity distribution.