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

Abstract

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 $0.4<z<4.2$ and the luminosity-function measurements and limits at $z\simeq0$ and $4.3\lesssim z\lesssim8$. The four parameters of the double power law are fitted at $z=4.5$ and $5.5$ separately, with no assumption about their evolution, and then jointly across $0<z<7$, and we examine how the uncertainty depends on the modeling assumptions. The shape of the power spectrum is settled by the existing data. The clustering peak stands a factor of $45\,(23$-$93)$ and $64\,(38$-$112)$ above the shot-noise floor at $z=4.5$ and $5.5$, and the two cross at $k_c\simeq0.37$ and $0.44\,h$Mpc$^{-1}$. The amplitude is known less well, the clustering power to $0.5-0.6$ dex and the shot noise to $0.7-0.9$ dex. The results show that the signal comes from halos accessible by current galaxy surveys, those that host the Lyman-break galaxies and Ly$α$ emitters at these redshifts. The luminosity-weighted bias is relatively high, with values of $4-5$.