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## The angular momentum-vs-mass relation and the distribution of mass ratios for visual binary systems

- Author(s): Trimble, V
- Walker, D
- et al.

## Abstract

The investigation of the angular momentum vs mass relation for binary stars is completed with a study of the 847 systems contained in the Fourth Catalog of Orbits of Visual Binary Stars. Because both J and M of a visual binary depend steeply on the distance to the system (5th and 3rd powers, respectively), and many of the distances are not well known, the study makes use of an auxiliary parameter R which is independent of distance and proportional to JM-5/3. R appears to be uncorrelated with M for the 789 systems for which both can be determined. The non-correlation implies that J ∝M5/3, expected from Kepler's third law, provides a better fit to the visual binaries than does J ∝M2, predicted by some more complex considerations. The distribution function f(q=M2/M1) of mass ratios for the visual binaries results as a byproduct of the investigation. It peaks extremely sharply toward q=1.0 (much more so than for spectroscopic binaries). Because most visual binaries are wide enough to consist of stars that condensed independently (and so that can be thought of as chosen at random from an initial mass function), one expects the real f(q) to rise toward low ratios. Observational selection against the discovery and study of systems with large magnitude differences between the components must be very large indeed to account for the discrepancy between expectation and observation. The alternative is a mechanism for formation of wide binaries that favours equal components. The distribution of mass ratios for eclipsing binaries is given in an appendix. It peaks strongly at q=0.6-0.75 and largely reflects processes of angular momentum, mass, and energy exchange between the stars in contact systems. © 1986 D. Reidel Publishing Company.

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