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

¹ Max-Planck-Institut für Extraterrestrische Physik (MPE), Giessenbachstrasse 1, 85748 Garching bei München, Germany
² Department of Astronomy, University of Science and Technology of China, Hefei 230026, People’s Republic of China
³ School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, People’s Republic of China
⁴ Centre for Extragalactic Astronomy, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK
⁵ Department of Physics and McGill Space Institute, McGill University, 3600 University Street, Montreal, QC H3A 2T8, Canada
⁶ Exzellenzcluster ORIGINS, Boltzmannstr. 2, 85748 Garching, Germany
⁷ Department of Astronomy, School of Physics, Peking University, Beijing 100871, China
⁸ Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China
⁹ Institute for Astronomy & Astrophysics, National Observatory of Athens, V. Paulou & I. Metaxa, 11532 Athens, Greece

^⋆ Corresponding author: csj666@mail.ustc.edu.cn

Received: 25 March 2025
Accepted: 24 June 2025

Abstract

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.