Probing star formation rates and histories in AGN and non-AGN galaxies across diverse cosmic environments and X-ray luminosity ranges

In this work, we compare the star formation rates (SFRs) and star formation histories (SFHs) of active galactic nucleus (AGN) and non-AGN galaxies. We explore these aspects across different density fields and over three orders of magnitude in X-ray luminosity (L_X). For that purpose, we employed X-ray AGNs detected in the XMM-XXL field and constructed a galaxy control sample, using sources from the VIPERS catalogue. We applied strict photometric and quality selection criteria to ensure that only sources with robust (host) galaxy measurements were included in the analysis. Our final samples consist of 149 X-ray AGNs with 42 < log,[L_{X,2#x2212;10 keV} (erg s⁻¹)] < 45 and 3488 non-AGN systems. The sources span a redshift range of 0.5 < z < 1.0 and have stellar masses within, 10.5 < log [M_*(M_⊙)] < 11.5. For these systems, we adopted the available measurements for their local densities and their spectral lines (D_n4000) from the VIPERS catalogue. To compare the SFRs of these two populations, we calculated the SFR_norm parameter. The latter is defined as the ratio of the SFRs of AGNs to the SFRs of non-AGN galaxies with similar M_* and redshift. Our findings reveal that low- and moderate-L_X AGNs (42 < log,[L_{X,2#x2212;10 keV} (erg s⁻¹)] < 44) that reside in low-density fields have a nearly flat SFR_norm-L_X relation. In contrast, the AGNs of similar L_X values that reside in high-density environments present an increase in SFR_norm with L_X. These results are in line with previous studies. Notably, our results suggest that the most luminous of the AGNs (log,[L_{X,2#x2212;10 keV} (erg s⁻¹)] > 44) exhibit an increased SFR in comparison to non-AGN galaxies. This trend appears to be independent of the density of the environment. Furthermore, for AGNs with similar L_X, those in high-density regions tend to have higher SFR_norm values compared to their counterparts in low-density areas. Comparisons of the D_n4000 spectral index, which serves as a proxy for the age of the stellar population, reveals that low- and moderate-L_X AGNs reside in galaxies with comparable stellar populations with non-AGN systems, regardless of the density field they are situated in. However, the most luminous X-ray sources tend to reside in galaxies that have younger stellar populations, as compared to non-AGN galaxies, regardless of the galaxy's environment.