A model for the energy-dependent time-lag and rms of the heartbeat oscillations in GRS 1915+105

TL;DR

This paper presents a model explaining energy-dependent time-lags and rms in GRS 1915+105's heartbeat oscillations by proposing a delayed inner disk response to accretion rate changes, accounting for observed spectral features.

Contribution

It introduces a delayed response model of the inner disk radius to accretion rate variations, explaining complex timing features with minimal parameters.

Findings

The model reproduces the shape and magnitude of energy-dependent rms and time-lag spectra.

It explains the differences in lag behaviour at fundamental and harmonic frequencies.

The proposed scenario accounts for observed spectral timing features with a sinusoidal accretion rate oscillation.

Abstract

Energy dependent phase lags reveal crucial information about the causal relation between various spectral components and about the nature of the accretion geometry around the compact objects. The time-lag and the fractional root mean square (rms) spectra of GRS 1915+105 in its heartbeat oscillation class/$\rho$ state show peculiar behaviour at the fundamental and harmonic frequencies where the lags at the fundamental show a turn around at $\sim$ 10 keV while the lags at the harmonic do not show any turn around at least till $\sim$ 20 keV. The magnitude of lags are of the order of few seconds and hence cannot be attributed to the light travel time effects or Comptonization delays. The continuum X-ray spectra can roughly be described by a disk blackbody and a hard X-ray power-law component and from phase resolved spectroscopy it has been shown that the inner disk radius varies during the oscillation. Here, we propose that there is a delayed response of the inner disk radius (DROID) to the accretion rate such that $r_{in}(t)\propto \dot{m}^\beta (t-\tau_d)$. The fluctuating accretion rate drives the oscillations of the inner radius after a time delay $\tau_d$ while the power-law component responds immediately. We show that in such a scenario a pure sinusoidal oscillation of the accretion rate can explain not only the shape and magnitude of energy dependent rms and time-lag spectra at the fundamental but also the next harmonic with just four free parameters.