A possible explanation for the "parallel tracks" phenomenon in low-mass X-ray binaries

An explanation is proposed for the observation that in low-mass X-ray binar ies (LMXBs), the correlation between most observable X-ray spectral and tim ing parameters on the one hand, and X-ray luminosity on the other, while ge nerally good in a given source on a timescale of hours, is absent both on l onger timescales and between sources. This phenomenon, particularly evident in kHz quasi-periodic oscillation (QPO) sources, leads to parallel tracks in plots of such parameters versus luminosity. It is pointed out that where previously proposed explanations require at least two time-variable indepe ndent parameters, such as accretion rate through the disk and through a mor e radial inflow, just one independent variable is in fact sufficient, provi ded that the systemic response to time variations in this variable has both a prompt and a time-averaged component. A specific scenario is explored in which most observable spectral and timing parameters to first order depend on the disk accretion rate normalized by its own long-term average, rather than on any individual accretion rate (luminosity, on the contrary, just d epends on the total accretion rate). This provides a way in which parameter s can be uncorrelated with accretion rate, yet vary in response to variatio ns in accretion rate. Numerical simulations are presented of such a model, describing the relation between kHz QPO frequency and X-ray luminosity, whi ch observationally is characterized by a striking pattern of parallel track s in the frequency versus luminosity plane, both in individual sources and across sources. The model turns out to reproduce the observations remarkabl y well. Physical interpretations are suggested that would produce such a sc enario; particularly promising seems an interpretation involving a radial i nflow with a rate that derives through a time-averaging process from the di sk accretion rate, and an inner disk radius that depends on the balance bet ween the accretion through the disk and the total luminosity. The consequen ces of this idea for our understanding of states and tracks in LMXBs are di scussed, and the applicability of the idea to black hole candidates, where the observational situation is more complex, is briefly addressed.