Stellar Mass Function of Active and Quiescent Galaxies via the
  Continuity Equation
  The continuity equation is developed for the stellar mass content of
galaxies, and exploited to derive the stellar mass function of active and
quiescent galaxies over the redshift range $z\sim 0-8$. The continuity equation
requires two specific inputs gauged on observations: (i) the star formation
rate functions determined on the basis of the latest UV+far-IR/sub-mm/radio
measurements; (ii) average star-formation histories for individual galaxies,
with different prescriptions for discs and spheroids. The continuity equation
also includes a source term taking into account (dry) mergers, based on recent
numerical simulations and consistent with observations. The stellar mass
function derived from the continuity equation is coupled with the halo mass
function and with the SFR functions to derive the star formation efficiency and
the main sequence of star-forming galaxies via the abundance matching
technique. A remarkable agreement of the resulting stellar mass function for
active and quiescent galaxies, of the galaxy main sequence and of the
star-formation efficiency with current observations is found; the comparison
with data also allows to robustly constrain the characteristic timescales for
star formation and quiescence of massive galaxies, the star formation history
of their progenitors, and the amount of stellar mass added by in-situ star
formation vs. that contributed by external merger events. The continuity
equation is shown to yield quantitative outcomes that must be complied by
detailed physical models, that can provide a basis to improve the (sub-grid)
physical recipes implemented in theoretical approaches and numerical
simulations, and that can offer a benchmark for forecasts on future
observations with multi-band coverage, as it will become routinely achievable
in the era of JWST.
