  Quenching is a key topic in exploring the formation and evolution of
galaxies. In this work, we study the quenching rate, i.e., the variation in the
fraction of quenched galaxies per unit time, of the Illustris-1 simulation. By
building the quenched fraction function $f(m,\rho, t)$ of each snapshot in the
simulation, we derive an accurate form of quenching rate as
$\Re_q=df(m,\rho,t)/dt$. According to the analytic expression of the quenching
rate $\Re_q$, we split it into four components: mass quenching, environmental
quenching, intrinsic mass quenching and intrinsic environmental quenching. The
precise value and evolutions can be given via the formula of $\Re_q$. With this
method, we analyze the Illustris-1 simulation. We find that quenched galaxies
concentrate around $M_*\simeq10^{11}h^{-1}M_\odot$ and $\delta+1\simeq10^{3.5}$
at earlier times, and that the quenching galaxy population slowly shifts to
lower stellar mass and lower overdensity regions with time. We also find that
mass quenching dominates the quenching process in this simulation, in agreement
with some previous analytical models. Intrinsic quenching is the second most
important component. Environmental quenching is very weak, because it is
possible that the pre- or postprocessing of environments disguises
environmental quenching as intrinsic quenching. We find that our method roughly
predict the actual quenching rate. It could well predict the actual amount of
galaxies quenched by intrinsic quenching. However, it overestimates the amount
of mass quenching galaxies and underestimates the amount of environmental
quenching. We suggest that the reason is the nonlinearity of the environmental
overdensity change and mass growth of the galaxy.
