  The average star formation rate (SFR) in galaxies has been declining since
redshift of 2. A fraction of galaxies quench and become quiescent. We constrain
two key properties of the quenching process: the quenching time scale and the
quenching rate among galaxies. We achieve this by analyzing the galaxy number
density profile in NUV-u color space and the distribution in NUV-u v.s. u-i
color-color diagram with a simple toy-model framework. We focus on galaxies in
three mass bins between 10 to 10 and 10 to 10.6 solar mass. In the NUV-u v.s.
u-i color-color diagram, the red u-i galaxies exhibit a different slope from
the slope traced by the star-forming galaxies. This angled distribution and the
number density profile of galaxies in NUV-u space strongly suggest that the
decline of the SFR in galaxies has to accelerate before they turn quiescent. We
model this color-color distribution with a two-phase exponential decline star
formation history. The models with an e-folding time in the second phase (the
quenching phase) of 0.5 Gyr best fit the data. We further use the NUV-u number
density profile to constrain the quenching rate among star-forming galaxies as
a function of mass. Adopting an e-folding time of 0.5 Gyr in the second phase
(or the quenching phase), we found the quenching rate to be 19%/Gyr, 25%/Gyr
and 33%/Gyr for the three mass bins. These are upper limits of quenching rate
as the transition zone could also be populated by rejuvenated red-sequence
galaxies.
