X-ray reverberation black hole mass and distance estimates of Cygnus X-1

TL;DR

This study applies distance‑sensitive X‑ray reverberation modelling to RXTE data for Cygnus X‑1 in the hard state to estimate the black hole mass and system distance. By updating cross‑spectral uncertainty treatment and employing density‑dependent reflection grids, the authors compare three models (Model A reproducing M19, Model B with free disc density, and Model C with distance as an input) and identify disc variability driven by inward propagating fluctuations. The preferred Model B yields $M = 15 \pm 4$ M$_\odot$ and $D = 3.4_{-1.2}^{+1.6}$ kpc, consistent with independent measurements, and reveals disc variability that leads the coronal flux; a self‑consistent, highly compact lamppost (Model C) is disfavoured by a significantly worse fit. The results validate X‑ray reverberation mapping as a viable, independent probe of BHXBs and motivate future work with extended corona geometries and broader energy coverage to further constrain the innermost accretion flow and distance estimates.

Abstract

We fit X-ray reverberation models to Rossi X-ray Timing Explorer data from the X-ray binary Cygnus X-1 in its hard state to yield estimates for the black hole mass and the distance to the system. The rapid variability observed in the X-ray signal from accreting black holes provides a powerful diagnostic to indirectly map the ultra-compact region in the vicinity of the black hole horizon. X-ray reverberation mapping exploits the light crossing delay between X-rays that reach us directly from the hard X-ray emitting 'corona', and those that first reflect off the accretion disc. Here we build upon a previous reverberation mass measurement of Cygnus X-1 that used the RELTRANS software package. Our new analysis enhances signal to noise with an improved treatment of the statistics, and implements new RELTRANS models that are sensitive to distance. The reduced uncertainties uncover evidence of mass accretion rate variability in the inner region of the disc that propagates towards the corona, which we approximate as a point-like 'lamppost' source. Our best fitting model returns a mass of $M=15\pm 4 ~M_\odot$ and a distance of $D=3.4_{-1.2}^{+1.6}$ kpc (90 per cent uncertainties), which are consistent with the most recent dynamical and parallax measurements respectively.

Figures (12)

• Figure 1: Top Panel: Unfolded time-average spectrum using the reltransDCp (blue and orange) and rtdist (green) reflection models. Bottom panel: residuals of the time averaged spectrum. These models were obtained via fitting the time-averaged and cross spectra simultaneously.
• Figure 2: Comparison of the $3\sigma$ mass, $M$, interval obtained in M19 (red) and our Model A (blue). The $3\sigma$ confidence interval obtained in M19 constrains $M\sim10-50$ M$_{\odot}$; while the same confidence interval obtained here constrains $M\sim15-40$ M$_{\odot}$. Both contours are in agreement with dynamical mass measurements indicated by the grey and purple shaded regions.
• Figure 3: Unfolded cross spectrum (top) and contributions to the overall $\chi^2$ (bottom) in a single frequency band ($0.001 - 0.005$ Hz), with uncertainties calculated using BP:2000 formulae (Model A). Real and imaginary parts are plotted on the left and right respectively. We see that the error bars are overestimated.
• Figure 4: Contributions to $\chi^2$ obtained by two models for the time-averaged spectrum (top) and the real part of the cross spectrum in a single frequency band (bottom). Orange points are for our Model B, whereas purple points are for TBabs$\times$reltransDCp only (i.e. with no disk or calibration components). Although we only show the real part of the cross spectrum for a single frequency band ($\nu \sim 0.001 - 0.005$ Hz), similarly structured residuals at low energies are present at all frequencies.
• Figure 5: Model B: Unfolded real (top panels) and imaginary (bottom panels) parts of the cross spectrum in all 10 frequency bands. The bottom axis of each panel show the contributions to $\chi^2$.