Radial velocity data sets hold information about the direct observability (e.g., separation and flux) of inferred companions. They also contain information about the types of Keplerian solution compatible with the data. ``Monte Carlo projection'' and ``χ2 portrayal'' are two techniques for discovering and pursuing the implications of this information. The first (projection) involves random solutions consistent with the data set, from which we can estimate (1) the probability distribution of the true solution in the six-dimensional space of the Keplerian parameters and (2) the probability distribution of the companion's position in space at future times, in order to predict observability. The second technique (portrayal) involves the distribution in parameter space of values of the numerical χ2 function, from which we can estimate the regions that contain the true solution at various levels of confidence. We study the case of HD 72659, a Sun-like star at 51 pc with a radial velocity companion inferred from 16 data points. We find at least two types of Keplerian solutions present in the data set: (1) periods 2500-25,000 days and eccentricity 0-0.8 (type A1), (2) periods 25,000-250,000 days and eccentricity 0.8-0.95 (type A2), and (3) periods 2000-2500 days and eccentricity 0-0.5 (type B). (Types A1 and A2 may not be distinct.) Pursuing direct observability, we randomize the inclination angle and compute the apparent separation, true separation, and phase angle of the companion. We compute a minimum flux ratio to the star assuming no self-luminosity and that the companion is Jupiter sized and has Jupiter's albedo and the phase function of a Lambert sphere. We plot the probability distribution of direct observability at specific epochs.
Stars: Binaries: Spectroscopic - Instrumentation: High Angular Resolution - Stars: Planetary Systems - Stars: Individual: Henry Draper Number: HD 72659 - Techniques: Radial Velocities