CBA Center for Backyard Astrophysics

The Evolution of Cataclysmic and Low-Mass X-Ray Binaries

Joseph Patterson

Astrophysical Journal, Supplement Series

April 1984, Volume 54, Page 443

We present an observational study of the structure and evolution of cataclysmic and low-mass X-ray binaries, concentrating on the 124 systems for which orbital periods are known. The eruptive properties and mass transfer rates of these stars are found to be highly correlated with their orbital periods, suggesting that both the eruptive activity and the long-term evolution are determined by the properties of the lobe-filling secondaries. The secondaries do not satisfy the commonly used theoretical models of low-mass zero-age main-sequence (ZAMS) stars, but are, in general, consistent with the empirically derived properties of the lower main sequence. We show that R / Rsol = ( M / Msol ) 0.88 for low-mass ZAMS stars in the field, in wide binaries, and in cataclysmic binaries. For masses above 0.8 Msol, the empirical ZAMS is in reasonable agreement with the models. But in this regime (corresponding to orbital periods > 9 hr), the secondaries in cataclysmic binaries are found to be slightly evolved from the ZAMS.

Distance and absolute magnitude estimates are made for 83 systems, using a variety of techniques: expansion parallax, interstellar absorption, photometric parallax of the secondary, and an empirical absolute magnitude-equivalent width relation. These distances, coupled with an analysis of sky surveys at high and low galactic latitude, lead to estimates of the local space density of each kind of eruptive variable: 8 × 10-7 pc-3 for high-M-dot dwarf novae, 4 ×l 10-6 pc-3 for low-M-dot dwarf novae, 4 × 1O-7 pc-3 for classical novae, 5 × 10-7 pc-3 for AM Her stars, and 5 × 10-10 pc-3 for low-mass X-ray binaries.

Various methods for deducing the mass transfer rate M-dot are reviewed; the most generally useful method yields M-dot by comparing the observed magnitudes to models of accretion disks. There is a good correlation with orbital period (M-dot proportional to Porb3.2) The observed values of M-dot suggest that there are two important regimes of evolution: (1) 0.7 hr < Porb <~ 3.3 hr, in which M-dot is always low ( 10-11 - 10-10 Msol yr-1) and the evolution is driven by gravitational radiation; (2) 3.3 hr < Porb <~ 1 day, in which M-dot is, in general, high ( 10-9 - 10-8 Msol yr-1) and the evolution is driven by some mechanism which removes angular momentum from the binary with far greater efficiency.

We believe that this mechanism can be identified as magnetic braking in a stellar wind emanating from the secondary. Observed orbital period changes and observed correlations of rotational velocity with age and spectral type indicate that this mechanism appears to operate efficiently wherever rapidly rotating stars with convective envelopes are found: in solitary dwarfs, in solitary giants, and in every type of binary (detached, semidetached, and contact). We show in detail that the rate of angular momentum loss inferred from these observations suffices to drive the observed rates of mass transfer in cataclysmic binaries. Surprisingly, the theoretical time scale for mass transfer through magnetic braking is found to be always very near the thermal time scale of the lobe-filling secondary, independent of the secondary's mass.

An evolutionary model is constructed which is capable of reproducing most of the characteristics of observed systems: the M-dot ( Porb ) relation; the period distribution and the period "gap"; the restriction of secondaries to spectral types later than GO; and most of the observed lifetimes and space densities. But we are still unable to identify the descendants of classical novae, which are produced in enormous numbers since novae are fairly common and have short lifetimes. The most likely explanation is that some unknown mechanism manages to destroy many systems in a time short compared to the age of the Galaxy. In order to produce a period gap, the secondaries probably turn off the magnetic braking rather suddenly at an orbital period of ~ 3 - 4 hr. This could arise from the inability of completely convective, low-mass secondaries ( ~ 0.3 Msol ) to drive significant magnetic winds.

Finally, we note that magnetic braking should shorten the lifetimes of all close binaries with cool main-sequence components, whether or not an accreting compact star is present. Available data on the frequency of spectroscopic and eclipsing binaries are consistent with this possibility. It seems likely that magnetic braking controls the evolution of all low-mass binaries with orbital periods <~ 10 days.


Copyright © 1984 American Astronomical Society.