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 \mu m luminosity function and its evolution with redshift and model-fit the CFIRB power spectrum at 250 \mu m 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 \sim 0.3 - 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 \sim 10 - 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 \times 10 ^ { 11 } M _ { \odot } and 3 \times 10 ^ { 10 } M _ { \odot } 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 } \sim 3 \times 10 ^ { -6 } to 2 \times 10 ^ { -5 } , relative to the critical density of the Universe .