Constraining the orbits of substellar companions imaged over short orbital arcs
Abstract
Imaging a star's companion at multiple epochs over a short orbital arc provides only four of the six coordinates required for a unique orbital solution. Probability distributions of possible solutions are commonly generated by Monte Carlo (MCMC) analysis, but these are biased by priors and may not probe the full parameter space. We suggest alternative methods to characterize possible orbits, which complement the MCMC technique. First, the allowed ranges of orbital elements are priorindependent, and we provide means to calculate these ranges without numerical analyses. Hence several interesting constraints (including whether a companion even can be bound, its minimum possible semimajor axis and its minimum eccentricity) may be quickly computed using our relations as soon as orbital motion is detected. We also suggest an alternative to posterior probability distributions as a means to present possible orbital elements, namely contour plots of elements as functions of lineofsight coordinates. These plots are priorindependent, readily show degeneracies between elements and allow readers to extract orbital solutions themselves. This approach is particularly useful when there are other constraints on the geometry, for example if a companion's orbit is assumed to be aligned with a disc. As examples we apply our methods to several imaged substellar companions including Fomalhaut b, and for the latter object we show how different origin hypotheses affect its possible orbital solutions. We also examine visual companions of A and Gtype mainsequence stars in the Washington Double Star Catalogue, and show that ≳ 50 per cent must be unbound.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 April 2015
 DOI:
 10.1093/mnras/stv252
 arXiv:
 arXiv:1502.01834
 Bibcode:
 2015MNRAS.448.3679P
 Keywords:

 astrometry;
 planets and satellites: fundamental parameters;
 planets and satellites: individual: Fomalhaut b;
 binaries: visual;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 Accepted for publication in MNRAS