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

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/ρ state show peculiar behaviour at the fundamental and harmonic frequencies where the lags at the fundamental show a turn around at ~10 keV, while the lags at the harmonic do not show any turn around at least till ~20 keV. The magnitude of lags is 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 disc blackbody and a hard X-ray power-lawcomponent and from phase-resolved spectroscopy, it has been shown that the inner disc radius varies during the oscillation. Here, we propose that there is a delayed response of the inner disc radius to the accretion rate such that rin(t ) ∝ mß (t - τd). The fluctuating accretion rate drives the oscillations of the inner radius after a time delay τd 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.