  In the previous work of Xu & Peng (2021), we investigated the structural and
environmental dependence on quenching in the nearby universe. In this work we
extend our investigations to higher redshifts by combining galaxies from SDSS
and ZFOURGE surveys. In low density, we find a characteristic $\Sigma_{1\ kpc}$
above which the quenching is initiated as indicated by their
population-averaged color. $\Sigma^{crit}_{1\ kpc}$ shows only weakly
mass-dependency at all redshifts, which suggests that the internal quenching
process is more related to the physics that acts in the central region of
galaxies. In high density, $\Sigma^{crit}_{1\ kpc}$ for galaxies at $z > 1$ is
almost indistinguishable with their low-density counterparts. At $z < 1$,
$\Sigma^{crit}_{1\ kpc}$ for low-mass galaxies becomes progressively strongly
mass-dependent, which is due to the increasingly stronger environmental effects
at lower redshifts. $\Sigma^{crit}_{1\ kpc}$ in low density shows strong
redshift evolution with $\sim 1$ dex decrement from $z = 2.5$ to $z = 0$. It is
likely due to that at a given stellar mass, the host halo is on average more
massive and gas-rich at higher redshifts, hence a higher level of integrated
energy from more massive black hole is required to quench. As the halo evolves
from cold to hot accretion phase at lower redshifts, the gas is shock-heated
and becomes more vulnerable to AGN feedback processes, as predicted by theory.
Meanwhile, angular momentum quenching also becomes more effective at low
redshifts, which complements a lower level of integrated energy from black hole
to quench.
