[Paper Review] CAIXA: a catalogue of AGN in the XMM-Newton archive III. Excess Variance Analysis

G. Ponti, I. E. Papadakis+6 more|UvA-DARE (University of Amsterdam)|Dec 12, 2011

Astrophysical Phenomena and ObservationsPhysics and Astronomy93 references113 citations

TL;DR

This study presents the largest systematic excess variance analysis of 161 radio-quiet, X-ray unobscured AGN in the XMM-Newton archive, demonstrating that X-ray variability tightly correlates with black hole mass (M_BH) and can be used as a precise M_BH estimator—more accurate than single-epoch optical methods. The results confirm that AGN variability is universal when rescaled by M_BH and accretion rate, with the power spectral density amplitude decreasing as ṁ^−0.8, indicating a common physical engine across all accreting black holes.

ABSTRACT

We report on the results of the first XMM systematic "excess variance" study of all the radio quiet, X-ray un-obscured AGN. The entire sample consist of 161 sources observed by XMM for more than 10 ks in pointed observations which is the largest sample used so far to study AGN X-ray variability on time scales less than a day. We compute the excess variance for all AGN, on different time-scales (10, 20, 40 and 80 ks) and in different energy bands (0.3-0.7, 0.7-2 and 2-10 keV). We observe a highly significant and tight (~0.7 dex) correlation between excess variance and MBH. The subsample of reverberation mapped AGN shows an even smaller scatter (~0.45 dex) comparable to the one induced by the MBH uncertainties. This implies that X-ray variability can be used as an accurate tool to measure MBH and this method is more accurate than the ones based on single epoch optical spectra. The excess variance vs. accretion rate dependence is weaker than expected based on the PSD break frequency scaling, suggesting that both the PSD high frequency break and the normalisation depend on accretion rate in such a way that they almost completely counterbalance each other. A highly significant correlation between excess variance and 2-10 keV spectral index is observed. Both the variability vs. LBol and FWHM_Hbeta correlations are consistent with being just by-products of the correlation with MBH. The soft and medium variability is very well correlated with the hard variability, suggesting that the additional soft components (i.e. soft excess, warm absorber) add a minor contribution to the total variability. Once the variability is rescaled for MBH and mdot, no significant difference between narrow-line and broad-line Seyfert 1 is observed. The results are in agreement with a picture where, to first approximation, all local AGN have the same variability properties once rescaled for MBH and accretion rate.

Motivation & Objective

• To investigate the universal scaling of X-ray variability in AGN across a large sample, testing the hypothesis that all accreting black holes share the same underlying variability engine.
• To determine whether excess variance correlates with black hole mass (M_BH) and accretion rate (ṁ), and whether these correlations can be used to estimate M_BH more accurately than existing optical methods.
• To examine the role of spectral components (e.g. soft excess, warm absorber) in contributing to total variability, and assess differences between narrow-line and broad-line Seyfert 1 galaxies.
• To test the robustness of the M_BH–variability relation by comparing with reverberation-mapped AGN and analyzing the dependence on spectral index and luminosity.

Proposed method

• Systematically computed excess variance (σ²_rms) for 161 AGN across multiple timescales (10, 20, 40, 80 ks) and energy bands (0.3–0.7, 0.7–2, 2–10 keV).
• Used the excess variance as a proxy for power spectral density (PSD) normalization to infer scaling with M_BH and accretion rate (ṁ), leveraging the relation σ²_rms ∝ PSD_amp.
• Applied corrections for M_BH and ṁ to test for residual dependencies, identifying whether variability is truly universal when properly rescaled.
• Correlated σ²_rms with spectral index (Γ), bolometric luminosity (L_Bol), and FWHM of Hβ to assess whether these are independent drivers or by-products of M_BH scaling.
• Compared results between narrow-line and broad-line Seyfert 1 AGN to test for intrinsic differences in variability behavior.
• Used reverberation-mapped AGN subsample to validate the M_BH–σ²_rms relation and assess its scatter and reliability.

Experimental results

Research questions

• RQ1 Does excess variance in X-ray light curves of AGN correlate tightly with black hole mass (M_BH), and can this be used as a reliable M_BH estimator?
• RQ2 How does the dependence of variability on accretion rate (ṁ) compare to theoretical expectations from PSD break frequency scaling?
• RQ3 Are correlations between σ²_rms and spectral index, L_Bol, or FWHM Hβ independent of the M_BH dependence, or are they indirect consequences of the M_BH–variability relation?
• RQ4 Do narrow-line and broad-line Seyfert 1 AGN show different variability properties after accounting for M_BH and ṁ?
• RQ5 What is the contribution of soft X-ray components (e.g. soft excess, warm absorber) to total X-ray variability, and is it significant?

Key findings

• A highly significant and tight correlation (scatter ~0.7 dex) exists between excess variance (σ²_rms) and black hole mass (M_BH), with the scatter in the reverberation-mapped subsample reduced to only a factor of 2–3, indicating high precision for M_BH estimation.
• The power spectral density (PSD) amplitude scales with accretion rate as PSD_amp ∝ ṁ^−0.8, which nearly cancels the dependence of the break frequency on ṁ, resulting in weak net dependence of σ²_rms on ṁ when normalized by M_BH.
• A highly significant correlation (>99.99% confidence) was detected between σ²_rms and the 2–10 keV spectral index, supporting the hypothesis that spectral index depends on accretion rate (Γ ∝ ṁ^0.1).
• Correlations between σ²_rms and both bolometric luminosity (L_Bol) and FWHM of Hβ are fully explained by their dependence on M_BH, indicating they are not independent drivers of variability.
• The soft and medium energy band excess variances are tightly correlated with the hard band (2–10 keV) excess variance, with no significant deviation from a one-to-one linear relation, implying minor contributions from soft components to total variability.
• After rescaling for M_BH and ṁ, no significant difference in variability properties is observed between narrow-line and broad-line Seyfert 1 AGN, supporting a universal variability engine across AGN types.