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

In this work, we compare the SFRs and SFHs of AGN and non-AGN galaxies. We explore these aspects across different density fields and over three orders of magnitude in LX. For that purpose, we employ X-ray AGN detected in the XMM-XXL field and construct a galaxy control sample, using sources from the VIPERS catalogue. Our final samples consist of 149 X-ray AGN with 42<log, Lₗ, ₂-₁₀₊₄ₕ (ergs^-1) <45 and 3\, 488 non-AGN systems. The sources span a redshift range of 0. 5<z<1. 0 and 10. 5< log\, M_* (M_) <11. 5. For these systems, there are available measurements for their local densities and their spectral lines from the VIPERS catalogue. To compare the SFR of these two populations, we calculate the SFR₍₎ₑ₌ parameter. The latter is defined as the ratio of the SFR of AGN to the SFR of non-AGN galaxies with similar M_* and redshift. Our findings reveal that low and moderate LX AGN that live in low density fields have a nearly flat SFR₍₎ₑ₌-LX relation. In contrast, AGN of similar LX that live in high density environments present an increase of SFR₍₎ₑ₌ with LX. Notably, our results suggest that the most luminous of the AGN exhibit increased SFR relative to non-AGN galaxies, and this trend appears to be independent of the density of the environment. Furthermore, for AGN with similar LX, those in high-density regions tend to have higher SFR₍₎ₑ₌ values compared to their counterparts in low-density areas. Comparison of the Dₙ4000 spectral index, which serves as a proxy for the age of the stellar population, reveals that low-to-moderate LX AGN live in galaxies with comparable stellar populations with non-AGN systems, regardless of the density field they live in. However, the most luminous X-ray sources tend to live in galaxies that have younger stellar populations than non-AGN galaxies, regardless of the galaxy's environment.