Of Logarithms, Binary Orbits, and Self-Replicating Distributions

Details Of Logarithms, Binary Orbits, and Self-Replicating Distributions Of Logarithms, Binary Orbits, and Self-Replicating Distributions

Jul 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996pasp..108..591h&link_type=abstract

Publications of the Astronomical Society of the Pacific, v.108, p.591

Mathematics

Probability

7

Scientific paper

Stellar binary orbital periods and semi-major axes appear to both be distributed in much the same smooth and nearly scale-free form: the probability density funcations of both are monotonically decreasing with increasing period (semi-major axis) and approximately proportional to P^-1 (a^-1). The impression that the binary period distribution has a single maximum is an artifact of the use of the use of logarithmic data transofmrs, which typically introduce spurious structure into otherwise structureless distributions; distributions of binary periods themselves show no significant peaks. The form of distribution of semi-major axes (proportional to a^-1) is mathematically self-replicating, allowing interference of a similar form of distributions of orbital angular momentum and binding energy without specific knowledge of the joint distributions of component masses and orbital eccentricities. (SECTION: Stars)

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