An Empirically Calibrated [C II] Luminosity-Halo Mass Relation for Line Intensity Mapping

Millimeter-wave line intensity mapping aims to observe the high-redshift universe through the 158 $μ$m fine-structure line of [C II], the brightest far-infrared line of star-forming galaxies. Whether a [C II] experiment at $z>4$ measures the clustering of large-scale structure, which carries rich cosmological information, rather than the shot noise of the emitters depends on the amplitude and the shape of the [C II] power spectrum. Forecasts often build the power spectrum from a halo mass--luminosity relation, $L(M_h)$, chained from scaling relations measured in other regimes or read off simulations, without a quantified uncertainty. We instead calibrate a double power-law $L(M_h,z)$ on [C II] data alone: the mean [C II] intensity from tomographic cross-correlation at $0.4