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

## TL;DR

This study analyzes AstroSat observations of Cygnus X-1 in the hard state, using a stochastic propagation model to explain energy-dependent variability and time-lags based on a truncated disk with a hot inner region.

## Contribution

It introduces a novel stochastic propagation model with a simple geometry to explain energy-dependent timing features in Cygnus X-1.

## Key findings

- Model successfully explains energy-dependent rms and time-lags.
- Fluctuations propagate from the truncated disk to the inner hot region.
- Hard X-ray emission originates from the hot inner disk via thermal Comptonization.

## 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.