Fooled by mass? Recovering the Γ−λEdd relation of quasars from their X-ray variability
Abstract
We measure the relation between the X-ray photon index Γ and the Eddington ratio λEdd in unobscured type-1 quasars, using as parent sample the cross-match of the SDSS DR16Q catalogue with the 4XMM-DR14 serendipitous catalogue. After cleaning the sample of potential observational biases, we obtain 7835 objects, one order of magnitude larger than most previous analyses in the literature. A single regression of Γ against logλEdd, with single-epoch virial black-hole masses, returns slopes that depend on the mass indicator (Hβ, MgII, CIV) and on the bolometric correction, and that are generally flat. We interpret this as regression dilution: the systematic uncertainty on virial masses is much larger than the intrinsic spread of λEdd in SDSS quasars. We therefore introduce a different approach, which removes the black-hole mass from the problem. For quasars observed by XMM-Newton at multiple epochs, the mass of each object is fixed, and changes in its X-ray luminosity trace changes in its accretion state. We fit the Γ-log(L2keV) relation of each object (for a sample of N=893) and combine the per-object posteriors. This recovers the mean response of the population aX = 0.35±0.03, which steepens to ≈0.43 when only epochs with precisely measured photon indices are used. Translated to the Eddington ratio, this corresponds to aλ≈0.20-0.25, depending on the choice of bolometric correction and on the LX-LUV slope. The Γ--λEdd relation therefore exists, but it can be uncovered only by exploiting the variability of individual sources, which removes the black-hole mass from the problem. Moreover, its shallowness implies that the differences in Eddington ratio, as currently measured, cannot by themselves account for the variety of photon indices observed among unobscured quasars.
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BibTeX
@misc{signorini2026fooled,
title = {{Fooled by mass? Recovering the $Γ-λ_Edd$ relation of quasars from their X-ray variability}},
author = {Matilde Signorini and Andrea Sacchi and Bartolomeo Trefoloni and Matteo Guainazzi and Elisabeta Lusso and Emanuele Nardini and Chiara Niccolai and Federica Ricci and Anastasia Shlentsova and Mateusz Rałowski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37607},
eprint = {2609.37607},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37607},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Fooled by mass? Recovering the Γ−λ_Edd relation of quasars from their X-ray variability
AU - Matilde Signorini
AU - Andrea Sacchi
AU - Bartolomeo Trefoloni
AU - Matteo Guainazzi
AU - Elisabeta Lusso
AU - Emanuele Nardini
AU - Chiara Niccolai
AU - Federica Ricci
AU - Anastasia Shlentsova
AU - Mateusz Rałowski
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37607
UR - https://arxiv.org/abs/2609.37607
AB - We measure the relation between the X-ray photon index Γ and the Eddington ratio λ_Edd in unobscured type-1 quasars, using as parent sample the cross-match of the SDSS DR16Q catalogue with the 4XMM-DR14 serendipitous catalogue. After cleaning the sample of potential observational biases, we obtain 7835 objects, one order of magnitude larger than most previous analyses in the literature. A single regression of Γ against logλ_Edd, with single-epoch virial black-hole masses, returns slopes that depend on the mass indicator (Hβ, MgII, CIV) and on the bolometric correction, and that are generally flat. We interpret this as regression dilution: the systematic uncertainty on virial masses is much larger than the intrinsic spread of λ_Edd in SDSS quasars. We therefore introduce a different approach, which removes the black-hole mass from the problem. For quasars observed by XMM-Newton at multiple epochs, the mass of each object is fixed, and changes in its X-ray luminosity trace changes in its accretion state. We fit the Γ-log(L_2keV) relation of each object (for a sample of N=893) and combine the per-object posteriors. This recovers the mean response of the population a_X = 0.35±0.03, which steepens to ≈0.43 when only epochs with precisely measured photon indices are used. Translated to the Eddington ratio, this corresponds to a_λ≈0.20-0.25, depending on the choice of bolometric correction and on the LX-LUV slope. The Γ--λ_Edd relation therefore exists, but it can be uncovered only by exploiting the variability of individual sources, which removes the black-hole mass from the problem. Moreover, its shallowness implies that the differences in Eddington ratio, as currently measured, cannot by themselves account for the variety of photon indices observed among unobscured quasars.
ER -