The average soft X-ray spectra of eROSITA active galactic nuclei

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 (αox, LUV, λEdd, MBH), and we explore the disk-corona connection by further combining stacked UV data. Methods. We have developed <ns0:monospace>Xstack</ns0:monospace>, 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 <ns0:monospace>Xstack</ns0:monospace>, we stacked 17 929 AGNs (“spec-z” sample, total exposure ∼23 Ms) with similar X-ray loudness, αox, and UV luminosity, LUV, and 4159 AGNs (“BH-mass” sample, ∼3 Ms) with similar Eddington ratios, λEdd, and black hole masses, MBH. 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 <ns0:monospace>AGNSED</ns0:monospace> model on a 3 × 3 MBH – λEdd grid. Results. We observed that the soft excess strength rises strongly with increasing αox and λEdd 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 LUV binning and reversed for MBH binning. The analysis of the optical-UV X-ray SEDs with <ns0:monospace>AGNSED</ns0:monospace> revealed that the warm corona radius (in units of Rg) generally increases with λEdd and decreases with MBH, or equivalently the disk-to-warm-corona transition consistently occurs near ∼1 × 104 K. The hot corona contracts with λEdd, and the radius remains independent of MBH, 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.