BASS LVI. Connecting X-ray variability with AGN physical properties and a new path to Cosmological distances

Abstract

X-ray variability is a well-established characteristic of active galactic nuclei (AGN), known to correlate inversely with both the supermassive black hole mass and luminosity, although the degree of each remains a topic of debate. The potential of X-ray variability as a proxy for MBH or for intrinsic LX has led to proposals to use AGN as standard candles to test cosmological models. However, the large intrinsic dispersion in these relations has limited their practical applications. In this work, we investigate the dependence of X-ray variability on AGN physical properties using a sample of 134 Seyfert 1 galaxies from the BAT AGN Spectroscopic Survey (BASS), which is the largest sample to date, more than three times larger than those used in previous studies. Contrary to earlier findings, we observe that X-ray variability correlates with luminosity just as strongly as with MBH. Furthermore, we still do not find evidence for the expected anti-correlation between variability and Eddington ratio, even when using refined bolometric luminosities from SED fitting to compute the Eddington ratio. From a cosmological perspective, the increased sample size reduces the scatter in the log(L)-log(exvar) relation to ~0.63 dex - a significant improvement over previous results, but still too large to serve as competitive standard candles, when compared to SNIa (uncertainties on distances of ~5-10%) or the L(X)-L(UV) relation in quasars (uncertainties of 10-12%). We tested including the width of broad emission lines as additional parameters, but found that this does not significantly lower the observed dispersion, contrary to previous studies on smaller samples. Finally, we discuss how future X-ray missions such as AXIS and NewAthena will improve this scenario by enabling precise variability measurements for thousands of AGN up to redshift z~3, thereby enabling it as a new cosmological probe.

Figures (15)

• Figure 1: Left: Relation between the 2-10 keV excess variance ($\sigma_{\rm NXS}^2$) (obtained with time bins of 100 s) and the black hole mass ($M_{BH}$) for the sample of 134 objects. Filled cyan circles show full detections; red down-pointing triangles show upper limits; the grey shaded area shows the confidence interval at 1$\sigma$ for the best fit log-linear relation. Blue stars represent the median value of the $M_{BH}$ and the excess variance in six $M_{BH}$ bins, chosen so that in each bin there are at least 20 objects. Blue error bars indicate the bin width. Blue stars are placed solely to guide the eye, as the fit is performed on the entire sample. The p-value of the relation and the total scatter $\delta_{\rm tot}$ are displayed, together with the best fit result. The best fit is reported on the plot as $y-\bar{y} = a(x -\bar{x}) + b'$, as the fit is performed by centering the variables at their average values $\bar{x}$ and $\bar{y}$. Therefore, the true intercept of the relation is to be recovered as $b=b'+\bar{y}-a\bar{x}$. Right: same but for the Reverberation Mapping sample. The relation is steeper but consistent with what is found for the whole sample.
• Figure 2: Relation between the 2-10 keV excess variance (obtained with time bins of 100 s) and different monochromatic luminosities. The legend is the same as in Figure \ref{['fig:exvar_Mbh']}. Upper plot: 2-10 keV monochromatic luminosity; middle plot: 5100Å monochromatic luminosity; lower plot: 6200Å monochromatic luminosity. Sample size N=134.
• Figure 3: Residual analysis to assess whether black hole mass or luminosity more fundamentally drives X-ray excess variance. Upper left panel: residuals from the best-fit of the $\log(\sigma^2)$--$\log(L_{2-10\,\mathrm{keV}})$ relation plotted against $\log(M_{\rm BH})$. A weak trend is observed ($\alpha = -0.10 \pm 0.06$), but the obtained p-value is 0.88, against the significance of the trend. Upper right panel: residuals from the $\log(\sigma^2)$--$\log(M_{\rm BH})$ relation plotted against $\log(L_{2-10\,\mathrm{keV}})$, showing no significant trend ($\alpha = -0.06 \pm 0.08$); the p-value is 0.75. These findings suggest that for this dataset, neither $M_{\rm BH}$ nor $L$ can be considered the 'main driver' of the variability against the other. Lower left panel: the same as in the Upper left panel, but restricted to the RM-only sample. A 2.3 $\sigma$ significant negative dependence on $M_{BH}$ is observed. Lower right panel: the same as in the Upper right panel, but restricted to the RM-only sample. A 2 $\sigma$ positive dependence on luminosity is observed. This marginally suggests that $M_{BH}$ is more predictive than the luminosity.
• Figure 4: Relation between the X-ray excess variance $\sigma_{\rm NXS}$ and the $\lambda_\mathrm{Edd}$. Blue stars represent averaged bins in Eddington ratio and are shown to guide the eye. Left panel: fit performed for the whole sample, where 102 objects out of 134 have black hole masses estimated using the virial equation, and 32 have Reverberation Mapping estimates. Despite the reduced fraction of upper limits and increased precision of the $\lambda_\mathrm{Edd}$ estimates compared with other studies, we still see no significant relation between X-ray variability and the $\lambda_\mathrm{Edd}$. Right panel: same analysis for the subsample of objects with black hole masses derived from Reverberation Mapping (N=32). We see an anti-correlation, but it is slightly significant.
• Figure 5: Proof-of-concept Hubble Diagram for the BASS sample (gray points) using the relation between X-ray excess variance and the 2-10 keV luminosity. The dark orange points show the mean values obtained by binning the sample into nine equal-sized bins. Cyan points represent the Pantheon+ Supernovae Ia sample Scolnic18, while the black line represents the prediction from a standard flat $\Lambda$CDM model. The redshift range and limited statistics of the BASS sample currently undermine the cosmological implementation of the method, but future probes might open new possibilities (see Section \ref{['sec: future']}).