X-ray Characterization of Galaxy Groups and Hickson Groups in COSMOS-Web to z~3.8 I. X-ray Luminosity Function Evolution
Galaxy groups are the dominant halo environment in the Universe and a sensitive laboratory for feedback and gas-cycling physics, yet a uniform, intermediate-redshift X-ray characterization of the group population has been limited by the availability of deep, wide-area imaging. We present a uniform X-ray characterization of the COSMOS-Web galaxy group population: 1,678 groups (CW-All) identified with the AMICO algorithm applied to the JWST-selected COSMOS-Web photometric catalog ($0.08 \lesssim z \lesssim 3.7$), and a parallel sample of 993 Hickson compact groups (CW-HCG; $0.08 \lesssim z \lesssim 3.82$) over $0.45~\mathrm{deg}^2$. We apply a uniform aperture-photometry X-ray pipeline to the combined Chandra and XMM-Newton COSMOS mosaic, measuring fluxes, luminosities, temperatures, and halo masses and radii for every group, together with detections, upper limits, and quality flags. We detect X-ray emission from 499 CW-All groups (29.7\%) and 332 CW-HCG groups (33.4\%) at SNR~$\geq 2.0$, and present the X-ray luminosity function in four redshift bins. The characteristic luminosity $L^\star$ rises monotonically by $\sim$1.9--2.1~dex from the lowest to highest redshift bin in both catalogs, a trend that persists under two independent cross-check binning schemes and is not explained by mass or richness selection of the detected population. A targeted search for diffuse X-ray emission from the AmicOne protocluster candidate at $2.50 \lesssim z < 3.09$ finds no statistically significant signal at the current depth. We publicly release the X-ray measurements and derived properties for both catalogs.