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Abstract: We study mass flow rate through a disc resulting from a varying mass supplyrate. Variable mass supply rate occurs, e.g., during disc state transitions,and in interacting eccentric binaries. It is, however, damped by the viscosityof the disc. Here, we calculate this damping in detail. We derive an analyticaldescription of the propagation of the flow rate using the solution ofLynden-Bell and Pringle, in which the disc is assumed to extend to infinity. Inparticular, we derive the accretion-rate Green-s function, and its Fouriertransform, which gives the fractional damping at a given variability frequency.We then compare this model to that of a finite disc with the mass supply at itsouter edge. We find significant differences with respect to the infinite discsolution, which we find to overestimate the viscous damping. In particular, theasymptotic form of the Green-s function is power-law for the infinite disc andexponential for the finite one. We then find a simple fitting form for thelatter, and also calculate its Fourier transform. In general, the dampingbecomes very strong when the viscous time at the outer edge of the disc becomeslonger than the modulation time scale. We apply our results to a number ofastrophysical systems. We find the effect is much stronger in low-mass X-raybinaries, where the disc size is comparable to that of the Roche lobe, than inhigh-mass binaries, where the wind-fed disc can have a much smaller size.



Author: A. A. Zdziarski, R. Kawabata, S. Mineshige

Source: https://arxiv.org/







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