A stochastic propagation model to the energy dependent rapid temporal behaviour of Cygnus X-1 as observed by AstroSat in the hard state

Abstract

We report the results from analysis of six observations of Cygnus X-1 by Large Area X-ray Proportional Counters (LAXPC) and Soft X-ray Telescope (SXT) on-board AstroSat, when the source was in the hard spectral state as revealed by the broad band spectra. The spectra obtained from all the observations can be described by a single temperature Comptonizing region with disk and reflection components. The event mode data from LAXPC provides unprecedented energy dependent fractional root mean square (rms) and time-lag at different frequencies which we fit with empirical functions. We invoke a fluctuation propagation model for a simple geometry of a truncated disk with a hot inner region. Unlike other propagation models, the hard X-ray emission (> 4 keV) is assumed to be from the hot inner disk by a single temperature thermal Comptonization process. The fluctuations first cause a variation in the temperature of the truncated disk and then the temperature of the inner disk after a frequency dependent time delay. We find that the model can explain the energy dependent rms and time-lag at different frequencies.

Spectral and Timing Properties of the Galactic X-Ray Transient Swift J1658.2–4242 Using Astrosat Observations

“…For a QPO frequency of 1.56 Hz, the time lag between the δT in and δT e is about −1.5 ms, implying that the variation δT e occurs first. For Cygnus X-1, the time lag is similar for the same frequency, but is positive, implying that the variation δT in occurs first (Maqbool et al 2019). Thus, while for Cygnus X-1, the corona responds to a stochastic perturbation that occurs in the disk, for Swift J1658.2-4242 it is opposite, such that the QPO originates in the corona and the fluctuation propagates outwards towards the disk.…”

Unveiling the Temporal Properties of MAXI J1820+070 through AstroSat Observations

“…Although Figure 3 (Top panel) gives an idea about temporal behavior of the system in frequency and energy realm, they neither provide an interpretation of physical behavior of the system nor its association to the time-averaged PDS. Hence to make such an association, we have modeled the observed fractional rms and timelag using the stochastic propagation model developed by Maqbool et al (2019). We present this result along with a comparison of the results of Cygnus X-1 in the following sections.…”

“…Recent works carried out by Cowperthwaite & Reynolds (2014), Hogg & Reynolds (2016) and Ahmad et al (2018) have shown that for standard optically thick and geometrically thin disks the propagation time-scales are frequency dependent and are different from the viscous ones. Maqbool et al (2019) quantified this behavior for hot, optically thin, geometrically thick flows considering the propagation time from the transition region onwards. They also considered the Comptonized spectrum to arise from a single Comptonizing zone as opposed to multi Comptonizing zones assumed in previous works.…”

“…The primary goal here is to quantify fractional rms and time-lag measured by LAXPC as described in §2.3 in terms of the model discussed in Maqbool et al (2019). The model is characterized by three parameters photon index (Γ), electron temperature (T e ) and blackbody temperature (T bb ), which are obtained from the spectral fitting described in §2.2.…”

“…The motivation being that such efforts could provide the necessary tools to probe the geometry of the system within this regime and possibly explain the exact mechanism of origin of QPOs (Böttcher & Liang 1999;Misra 2000;Kotov et al 2001). arXiv:2001.00755v3 [astro-ph.HE] 8 Jan 2020 Maqbool et al (2019) proposed and validated one such model by comparing its predictions with observed data of Cygnus X-1 from AstroSat. The model invokes a simple geometry of standard truncated disk with a hot inner region (Esin et al 1997) and assumes that hard X-ray component originates from this hot inner region by a single temperature thermal Comptonization process.…”