Constraining the Star Formation Histories in Dark Matter Halos: I.
  Central Galaxies
  Using the self-consistent modeling of the conditional stellar mass functions
across cosmic time by Yang et al. (2012), we make model predictions for the
star formation histories (SFHs) of {\it central} galaxies in halos of different
masses. The model requires the following two key ingredients: (i) mass assembly
histories of central and satellite galaxies, and (ii) local observational
constraints of the star formation rates of central galaxies as function of halo
mass. We obtain a universal fitting formula that describes the (median) SFH of
central galaxies as function of halo mass, galaxy stellar mass and redshift. We
use this model to make predictions for various aspects of the star formation
rates of central galaxies across cosmic time. Our main findings are the
following. (1) The specific star formation rate (SSFR) at high $z$ increases
rapidly with increasing redshift [$\propto (1+z)^{2.5}$] for halos of a given
mass and only slowly with halo mass ($\propto M_h^{0.12}$) at a given $z$, in
almost perfect agreement with the specific mass accretion rate of dark matter
halos. (2) The ratio between the star formation rate (SFR) in the main-branch
progenitor and the final stellar mass of a galaxy peaks roughly at a constant
value, $\sim 10^{-9.3} h^2 {\rm yr}^{-1}$, independent of halo mass or the
final stellar mass of the galaxy. However, the redshift at which the SFR peaks
increases rapidly with halo mass. (3) More than half of the stars in the
present-day Universe were formed in halos with $10^{11.1}\msunh < M_h <
10^{12.3}\msunh$ in the redshift range $0.4 < z < 1.9$. (4) ... [abridged]
