OF LOGARITHMS, BINARY ORBITS, AND SELF-REPLICATING DISTRIBUTIONS

Abstract

ABSTRACT 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.