  The power spectrum of cosmic infrared background (CIB) anisotropies is
sensitive to the connection between star formation and dark matter halos over
the entire cosmic star formation history. Here we develop a model that
associates star-forming galaxies with dark matter halos and their subhalos. The
model is based on a parameterized relation between the dust-processed infrared
luminosity and (sub)halo mass. By adjusting 3 free parameters, we attempt to
simultaneously fit the 4 frequency bands of the Planck measurement of the CIB
anisotropy power spectrum. To fit the data, we find that the star-formation
efficiency must peak on a halo mass scale of ~ 5x10^12 solar mass and the
infrared luminosity per unit mass must increase rapidly with redshift. By
comparing our predictions with a well-calibrated phenomenological model for
shot noise, and with a direct observation of source counts, we show that the
mean duty cycle of the underlying infrared sources must be near unity,
indicating that the CIB is dominated by long-lived quiescent star formation,
rather than intermittent short "star bursts". Despite the improved flexibility
of our model, the best simultaneous fit to all four Planck channels remains
relatively poor. We discuss possible further extensions to alleviate the
remaining tension with the data. Our model presents a theoretical framework for
a future joint analysis of both background anisotropy and source count
measurements.
