Of logarithms, binary orbits, and self-replicating distributions

Stellar binary orbital periods and semimajor axes both appear to be distributed in much the same smooth and nearly scale-free form: the probability density functions of both are monotonically decreasing with increasing period (semimajor 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 logarithmic data transforms, which typically introduce spurious structure into otherwise structureless distributions; distributions of binary periods themselves show no significant peaks. The form of distribution of semimajor axes (proportional to a(-1)) is mathematically self-replicating, allowing inference 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.