Constraining the C II luminosity function from the power spectrum of line-intensity maps at redshift 3.6

Context. Forthcoming measurements of the line-intensity mapping (LIM) power spectrum (PS) are expected to provide valuable constraints on several quantities of astrophysical and cosmological interest. Aims. We focus on the C II luminosity function (LF) at high redshift, which remains poorly constrained, especially at the faint end. As an example of future opportunities, we present forecasts for the Deep Spectroscopic Survey (DSS) that is to be conducted with the Fred Young Submillimeter Telescope (FYST) at z ≃ 3.6. We also make predictions for hypothetical surveys with a ten times larger sky coverage and/or a sensitivity that is higher by a factor of √10. We account for the Lorentzian spectral profile of Fabry-Pérot interferometers and investigate the effect of their increased resolving power R on the constraints. Methods. Motivated by the halo-occupation properties of C II emitters in the M ARIGOLD simulations, we used an abundance-matching approach to connect two versions of the ALPINE LF to the halo mass function. The resulting luminosity–mass relation was used in a halo-model framework to predict the PS signal and its uncertainty. Bayesian inference on mock PS data allowed us to forecast constraints on the first two LF moments and Schechter function parameters. Results. Depending on the true LF, the DSS is expected to be able to detect clustering and shot-noise components with signal-to-noise ratios of ≳2. At R = 100, spectral smoothing overwhelms the signal from redshift-space distortions, rendering the associated damping scale σ unmeasurable. For R ≳ 500, σ can be distinguished from instrumental effects, although the degeneracies with amplitude parameters increase. Joint fits to the PS and LF yield precise constraints on the Schechter normalisation and cutoff luminosity, while the faint-end slope remains uncertain (unless the true value approaches −2). Conclusions. An increased survey sensitivity offers greater gains than a wider area. A higher spectral resolution improves the access to physical parameters, but intensifies degeneracies. This highlights key design trade-offs in LIM surveys.