The physical properties of massive green valley galaxies as a function of environments at $0.5<z<2.5$ in 3D-\textit{HST}/CANDELS fields

To investigate the effects of environment in the quenching phase, we study the empirical relations for green valley (GV) galaxies between overdensity and other physical properties (i.e., effective radius $r_{\rm e}$, Sérsic indices $n$, and specific star formation rate sSFR). Based on five 3D-{\it HST}/CANDELS fields, we construct a large sample of 2126 massive ($M_{\star} > 10^{10} M_{\sun}$) GV galaxies at $0.5<z<2.5$ and split it into the higher overdensity quarter and the lower overdensity quarter. The results shows that GV galaxies in denser environment have higher $n$ values and lower sSFR at $0.5< z <1$, while there is no discernible distinction at $1 < z < 2.5$. No significant enlarging or shrinking is found for GV galaxies in different environments within the same redshift bin. It suggests that a dense environment would promote the growth of bulge and suppress star formation activity of GV galaxies at $0.5< z <1.5$, but would not affect the galaxy size. We also study the dependence of the fraction of three populations (Blue Cloud, Green Valley, and Red Sequence) on both environments and $M_{\star}$. At a given $M_{\star}$, blue cloud fraction goes down with increasing environment density, while red sequence fraction is opposite. For the most massive GV galaxies, a sharp drop appears in the denser environment. Coupled with the mass dependence of three fractions in different redshift bins, our result implies that stellar mass and environments jointly promote the quenching process. Such dual effect is also confirmed by re-calculating the new effective GV fraction as the number of GV galaxies over the number of non-quiescent galaxies.