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.

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The phenomenon of clustering of galaxies on the basis of correlation functions in an expanding Universe is studied by using equation of state, taking gravitational interaction between galaxies of extended nature into consideration. The partial differential equation for the extended mass structures of a two-point correlation function developed earlier by Iqbal, Ahmad and Khan is studied on the basis of assigned boundary conditions. The solution for the correlation function for extended structures satisfies the basic boundary conditions, which seem to be sufficient for understanding the phenomena, and provides a new insight into the gravitational clustering problem for extended mass structures.Comment: 3 pages, no figure

The UV emission from X-ray binaries, is more likely to be produced by reprocessing of X-rays by the outer regions of an accretion disk. The structure of the outer disk may be altered due to the presence of X-ray irradiation and we discuss the physical regimes where this may occur and point out certain X-ray binaries where this effect may be important. The long term X-ray variability of these sources is believed to be due to stochastic fluctuations in the outer disk, which propagate inwards giving rise to accretion rate variation in the X-ray producing inner regions. The X-ray variability will induce structural variations in the outer disk which in turn may affect the inner accretion rate. To understand the qualitative behaviour of the disk in such a scenario, we adopt simplistic assumptions that the disk is fully ionised and is not warped. We develop and use a time dependent global hydrodynamical code to study the effect of a sinusoidal accretion rate perturbation introduced at a specific radius. The response of the disk, especially the inner accretion rate, to such perturbations at different radii and with different time periods is shown. While we didn't find any oscillatory or limit cycle behaviour, our results show that irradiation enhances the X-ray variability at time-scales corresponding to the viscous time-scales of the irradiated disk.

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