Central galaxies make up the majority of the galaxy population , including the majority of the quiescent population at \mathcal { M } _ { * } > 10 ^ { 10 } \mathrm { M } _ { \odot } .
Thus , the mechanism ( s ) responsible for quenching central galaxies plays a crucial role in galaxy evolution as whole .
We combine a high resolution cosmological N -body simulation with observed evolutionary trends of the “ star formation main sequence , ” quiescent fraction , and stellar mass function at z < 1 to construct a model that statistically tracks the star formation histories and quenching of central galaxies .
Comparing this model to the distribution of central galaxy star formation rates in a group catalog of the SDSS Data Release 7 , we constrain the timescales over which physical processes cease star formation in central galaxies .
Over the stellar mass range 10 ^ { 9.5 } to 10 ^ { 11 } \mathrm { M } _ { \odot } we infer quenching e-folding times that span 1.5 to 0.5 \mathrm { Gyr } with more massive central galaxies quenching faster .
For \mathcal { M } _ { * } = 10 ^ { 10.5 } \mathrm { M } _ { \odot } , this implies a total migration time of \sim 4 ~ { } \mathrm { Gyrs } from the star formation main sequence to quiescence .
Compared to satellites , central galaxies take \sim 2 ~ { } \mathrm { Gyrs } longer to quench their star formation , suggesting that different mechanisms are responsible for quenching centrals versus satellites .
Finally , the central galaxy quenching timescale we infer provides key constraints for proposed star formation quenching mechanisms .
Our timescale is generally consistent with gas depletion timescales predicted by quenching through strangulation .
However , the exact physical mechanism ( s ) responsible for this still remain unclear .