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 binaries (LMXBs), the correlation between most observable X-ray spectral and timing parameters on the one hand, and X-ray luminosity on the other, while generally good in a given source on a timescale of hours, is absent both on longer 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 independent parameters, such as accretion rate through the disk and through a more radial inflow, just one independent variable is in fact sufficient, provided 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 depends on the total accretion rate). This provides a way in which parameters can be uncorrelated with accretion rate, yet vary in response to variations in accretion rate. Numerical simulations are presented of such a model, describing the relation between kHz QPO frequency and X-ray luminosity, which observationally is characterized by a striking pattern of parallel tracks in the frequency versus luminosity plane, both in individual sources and across sources. The model turns out to reproduce the observations remarkably well. Physical interpretations are suggested that would produce such a scenario; particularly promising seems an 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. 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.