Physics of star formation history and the luminosity function of
  galaxies therefrom
  We show that the star formation history, the reionization history and the
present luminosity function of galaxies are reproduced in a simple
gravitational collapse model within the $\Lambda$CDM regime to almost a
quantitative accuracy, when the physical conditions, the Jeans criterion and
the cooling process, are taken into account. Taking a reasonable set of the
model parameters, the reionisation takes place sharply at around redshift
$1+z\simeq 7.5$, and the resulting luminosity function turns off at $L\simeq
10^{10.7}L_\odot$, showing the consistency between the star formation history
and the reionisation of the Universe. The model gives the total amount of stars
$\Omega_\mathrm{star}=0.004$ in units of the critical density compared to the
observation $0.0044$ with the recycling factor $1.6$ included. In order to
account for the observed star formation rate and the present luminosity
function, the star formation efficiency is not halo mass independent but
becomes maximum at the halo mass $\simeq 10^{12}M_\odot$ and is suppressed for
both smaller and larger mass haloes.
