2025A&A...701A.144C

Context. Active galactic nuclei (AGN) stand as extreme X-ray emitters where disk-corona interplay shapes their spectral energy distribution. The soft X-ray excess, a unique feature of AGN in the 0.5 - 2.0 keV, encodes critical information on the “warm corona” structure bridging the disk and hot corona. However, the systematic evolution of this feature with fundamental accretion parameters in large AGN samples - particularly those studied through the spectral stacking technique - remains observationally unconstrained.
Aims. The eROSITA All-Sky Survey (eRASS:5) provides an unprecedented sample to statistically map AGN spectral properties. We present a multiwavelength investigation of how the average AGN X-ray spectra evolve with accretion parameters (α_ox, L_UV, λ_Edd, M_BH), and we explore the disk-corona connection by further combining stacked UV data.
Methods. We have developed Xstack, a novel X-ray spectral stacking code that consistently stacks rest-frame pulse invariant (PI) spectra and associated responses using optimized response weighting to preserve spectral shapes. With Xstack, we stacked 17 929 AGNs (“spec-z” sample, total exposure ∼23 Ms) with similar X-ray loudness, α_ox, and UV luminosity, L_UV, and 4159 AGNs (“BH-mass” sample, ∼3 Ms) with similar Eddington ratios, λ_Edd, and black hole masses, M_BH. We analyzed the resulting stacked X-ray spectra with a phenomenological model for both samples. We further fit the stacked optical-UV X-ray SED with the physical AGNSED model on a 3 × 3 M_BH - λ_Edd grid.
Results. We observed that the soft excess strength rises strongly with increasing α_ox and λ_Edd binning (by a factor of five), while the hard X-ray spectral shape remains largely unchanged, consistent with the interpretation that soft excess is primarily driven by the warm corona rather than reflection. The trends are weaker with L_UV binning and reversed for M_BH binning. The analysis of the optical-UV X-ray SEDs with AGNSED revealed that the warm corona radius (in units of R_g) generally increases with λ_Edd and decreases with M_BH, or equivalently the disk-to-warm-corona transition consistently occurs near ∼1 × 10⁴ K. The hot corona contracts with λ_Edd, and the radius remains independent of M_BH, aligning with disk evaporation predictions.
Conclusions. The soft excess is likely warm-corona dominated, with the disk-to-warm-corona transition potentially linked to hydrogen ionization instability at ∼1 × 10⁴ K, which is consistent with previous work utilizing eFEDS-HSC stacked data. Our work highlights the power of spectral stacking for revealing the AGN disk-corona connection.