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 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) ∝ṁ β (t − τ d ). The fluctuating accretion rate drives the oscillations of the inner radius after a time delay τ 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.

Study of Timing Evolution from Nonvariable to Structured Large-amplitude Variability Transition in GRS 1915 + 105 Using AstroSat

“…The energy-dependent lag spectra at the mHz QPO frequency shown in the upper middle left panel of Figure 10 also exhibits a peculiar trend of hard lag of the order of few seconds up to 6 keV and then a soft lag of the order of few tens of seconds at harder X-ray bands. Similar behaviour has also been observed from the RXTE/PCA time lag spectra of ρ class in GRS 1915+105 at the heartbeat frequency (Mir et al 2016). The rms spectra for the HS show different behaviour in comparison to that observed by (Mir et al 2016) for ρ class.…”

“…However, the rms spectra show opposite behaviour. During the HS, the fractional rms strictly decreases with energy while the energy-dependent fractional rms during the ρ class either increases with energy or initially increases up to ∼10 keV and then decreases (Mir et al 2016). The time lag versus frequency plot shows the same behaviour at QPO (∼5.0 Hz) and harmonic frequency as observed in χ class and IMS.…”

A timing view of the heartbeat state of GRS 1915+105

“…Uttley et al 2011;Tripathi et al 2011;Wilkins & Fabian 2013). The hard and soft lags of the order of a second could be caused by the differential responses of the inner disk radius and the corona to the mass accretion rate (Mir et al 2016) or by the differential QPO frequency in the soft and hard energy bands (van den Eijnden et al 2016). The hard lag of the order of a second could also be produced by the inward propagation of mass accretion fluctuations through the disk (e.g.…”

“…The model of Mir et al (2016) is used to interpret the phase lag of a QPO resulted by the oscillation of the inner disk radius, and thus cannot directly explain the QPOs studied here which are highly correlated with the corona (Yan et al 2013b). Nevertheless, its concept deserves consideration.…”

“…We use the model of van den Eijnden et al (2016) and the model of Mir et al (2016) to discuss the lag of the QPO since these two models can explain both hard and soft lags of the order of few tens of milliseconds (which is the case here).…”