A Conditional Luminosity Function Model of the Cosmic Far-Infrared Background Anisotropy Power Spectrum

The cosmic far-infrared background (CFIRB) is expected to be generated by faint, dusty star-forming galaxies during the peak epoch of galaxy formation. The anisotropy power spectrum of the CFIRB captures the spatial distribution of these galaxies in dark matter halos and the spatial distribution of dark matter halos in the large-scale structure. Existing halo models of CFIRB anisotropy power spectrum are either incomplete or lead to halo model parameters that are inconsistent with the galaxy distribution selected at other wavelengths. Here we present a conditional luminosity function approach to describe the far-IR bright galaxies. We model the 250 um luminosity function and its evolution with redshift and model-fit the CFIRB power spectrum at 250 um measured by the Herschel Space Observatory. We introduce a redshift dependent duty-cycle parameter so that we are able to estimate the typical duration of the dusty star formation process in the dark matter halos as a function of redshifts. We find the duty cycle of galaxies contributing to the far-IR background is 0.3 to 0.5 with a dusty star-formation phase lasting for \sim0.3-1.6 Gyrs. This result confirms the general expectation that the far-IR background is dominated by star-forming galaxies in an extended phases, not bright starbursts that are driven by galaxy mergers and last \sim10-100 Myrs. The halo occupation number for satellite galaxies has a power-law slope that is close to unity over 0<z<4. We find that the minimum halo mass for dusty, star-forming galaxies with L_250>10^{10} L_Sun is 2\times10^{11}M_Sun and 3\times 10^{10}M_Sun at z=1 and 2, respectively. Integrating over the galaxy population with L_250>10^{9} L_Sun, we find that the cosmic density of dust residing in the dusty, star-forming galaxies responsible for the background anisotropies \Omega_{dust}\sim3\times10^{-6} to 2\times10^{-5}.