An X-ray reverberation mass measurement of Cygnus X-1

Abstract

We present the first X-ray reverberation mass measurement of a stellar-mass black hole. Accreting stellar-mass and supermassive black holes display characteristic spectral features resulting from reprocessing of hard X-rays by the accretion disc, such as an Fe Kα line and a Compton hump. This emission probes of the innermost region of the accretion disc through general relativistic distortions to the line profile. However, these spectral distortions are insensitive to black hole mass, since they depend on disc geometry in units of gravitational radii. Measuring the reverberation lag resulting from the difference in path length between direct and reflected emission calibrates the absolute length of the gravitational radius. We use a relativistic model able to reproduce the behaviour of the lags as a function of energy for a wide range of variability timescales, addressing both the reverberation lags on short timescales and the intrinsic hard lags on longer timescales. We jointly fit the time-averaged spectrum and the real and imaginary parts of the cross-spectrum as a function of energy for a range of Fourier frequencies to Rossi X-ray Timing Exporer data from the X-ray binary Cygnus X-1. We also show that introducing a self-consistently calculated radial ionisation profile in the disc improves the fit, but requires us to impose an upper limit on ionisation profile peak to allow a plausible value of the accretion disc density. This limit leads to a mass value more consistent with the existing dynamical measurement.

Exploring the radial disc ionization profile of the black hole X-ray binary GRS 1915+105

“…We have modelled the X-ray reflection spectrum of GRS 1915+105 by including a self-consistently calculated radial profile of the disc ionization parameter. Our best fit is achieved by assuming the disc to be in the radiation pressure dominated zone A regime of the Shakura & Sunyaev (1973) disc model, similar to the results of Mastroserio et al (2019) for Cygnus X-1. Since the accretion rate during this observation was high, we expect at least the inner ∼ 300 r g of the disc to be in the zone A regime.…”

Multi-timescale reverberation mapping of Mrk 335

“…These approximations are good for the low frequencies (in terms of c/R g ) probed by fits to X-ray binary data (e.g. Mastroserio et al 2019), but break down for the higher frequencies (again in terms of c/R g ) probed by fits to AGN data. We therefore first address the inaccuracies in the old model (Section 3) before fitting to the Mrk 335 data (Section 4).…”

“…not just the strength but also the shape of the reflection spectrum fluctuates) that are taken into account in the model. RELTRANS has been successfully tested on Cygnus X-1 (Mastroserio et al 2019) and previously used for a proof of principle of the method (fitting only the reverberation lags) in Mrk 335 (Ingram et al 2019).…”

Relativistic Reflection and Reverberation in GX 339–4 with NICER and NuSTAR

“…This is one specific geometry of the disk corona, which makes PROPFLUC a bottom-up approach. On the other hand, the phenomenological hard lag treatment with the pivoting power law in the newly public model reltrans (Ingram et al 2019;Mastroserio et al 2019) is a top-down approach, using which different theoretical predictions could be tested.…”

“…With reltrans, we could jointly fit the time-averaged spectrum and the real and imaginary parts of the energydependent cross-spectrum for a range of Fourier frequencies. The first X-ray reverberation mass measurement of a stellarmass black hole is obtained with reltrans for CygnusX-1 (Mastroserio et al 2019). The fitted disk truncation radius is < R 10 g at ∼1.6%L Edd .…”