Bayes-based orbital elements estimation in triple hierarchical stellar
  systems
  Under certain rather prevalent conditions (driven by dynamical orbital
evolution), a hierarchical triple stellar system can be well approximated, from
the standpoint of orbital parameter estimation, as two binary star systems
combined. Even under this simplifying approximation, the inference of orbital
elements is a challenging technical problem because of the high dimensionality
of the parameter space, and the complex relationships between those parameters
and the observations (astrometry and radial velocity). In this work we propose
a new methodology for the study of triple hierarchical systems using a Bayesian
Markov-Chain Monte Carlo-based framework. In particular, graphical models are
introduced to describe the probabilistic relationship between parameters and
observations in a dynamically self-consistent way. As information sources we
consider the cases of isolated astrometry, isolated radial velocity, as well as
the joint case with both types of measurements. Graphical models provide a
novel way of performing a factorization of the joint distribution (of parameter
and observations) in terms of conditional independent components (factors), so
that the estimation can be performed in a two-stage process that combines
different observations sequentially. Our framework is tested against three
well-studied benchmark cases of triple systems, where we determine the inner
and outer orbital elements, coupled with the mutual inclination of the orbits,
and the individual stellar masses, along with posterior probability (density)
distributions for all these parameters. Our results are found to be consistent
with previous studies. We also provide a mathematical formalism to reduce the
dimensionality in the parameter space for triple hierarchical stellar systems
in general.
