A Possible Explanation for the "Parallel Tracks" Phenomenon in Low-Mass X-Ray Binaries

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Abstract
An explanation is proposed for the fact that in LMXBs the correlation between most observable X-ray spectral and timing parameters (such as kHz QPO frequency) on the one hand, and Lx on the other, while generally good in a given source on a time scale of hours, is absent both on longer time scales and between sources. This leads to parallel tracks in plots of such parameters vs. Lx. Where previous explanations require at least two time-variable independent parameters, e.g. Mdot through the disk and through a radial inflow, one is in fact sufficient if the systemic response to time variations in this variable has both a prompt and a time-averaged component. I explore a scenario in which most observable spectral and timing parameters to first order depend on disk accretion rate normalized by its own long-term average rather than on any individual Mdot; Lx just depends on total Mdot. Thus, parameters can be uncorrelated to Mdot, yet vary in response to Mdot variations. Numerical simulations of the model describing the dependence of kHz QPO frequency on Lx, which observationally is characterized by a striking pattern of parallel tracks both in individual sources and between sources, reproduce the observations remarkably well. A physical interpretation involving a radial inflow with a rate that derives through a time averaging process from the disk accretion rate, and an inner disk radius that depends on the balance between the accretion through the disk and the total luminosity seems particularly promising. The consequences of this idea for our understanding of states and tracks in LMXBs are discussed, and the applicability of the idea to black-hole candidates, where the observational situation is more complex, is briefly addressed.

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