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We explore the dependence of the incidence of moderate-luminosity ($L_{X} =10^{41.9-43.7}$ erg s$^{-1}$) AGNs and the distribution of their accretionrates on host color at 0.5 < z < 2.5, using deep X-ray data in GOODS fields. Weuse extinction-corrected rest-frame U-V colors to divide both AGN hosts andnon-AGN galaxies into red sequence (quiescent), green valley (transition), andblue cloud (star-forming) populations. We find that both the AGN fraction atfixed stellar mass and its evolution with redshift are dependent on hostcolors. Most notably, red galaxies have the lowest AGN fraction (~5\%) at z~1yet with most rapid redshift evolution, increasing by a factor of 5 (~24\%) atz~2. Green galaxies exhibit the highest AGN fraction across all redshifts,which is most pronounced at z~2 with more than half of them hosting an AGN at$M_{*} > 10^{10.6} M_{\odot}$. Together with the high AGN fraction in redgalaxies at z~2, this indicates that X-ray AGNs could be important in bothtransforming blue galaxies into red ones and subsequently maintaining theirquiescence at high redshift. Furthermore, consistent with low-redshift studies,we find that the probability of hosting an AGN in the total galaxy populationcan be characterized by a universal Eddington ratio ($p(\lambda_{Edd}) \sim\lambda_{Edd}^{-0.4}$) and a moderate redshift evolution. Yet consistent withtheir different AGN fractions, different populations appear to also havedifferent $p(\lambda_{Edd})$ with red galaxies exhibiting more rapid redshiftevolution than green and blue ones. Evidence for a steeper power law of$p(\lambda_{Edd})$ in red galaxies is also presented, though larger samples areneeded to confirm. These results suggest that the AGN accretion or the growthof supermassive black holes is related to their host properties, and may alsoinfluence their hosts in a different mode dependent on the host color.

AGN-Host Connection at 0.5 < z < 2.5: A rapid evolution of AGN fraction in red galaxies during the last 10 Gyr