$texttt{Chronostar}$: a novel Bayesian method for kinematic age determination. I. Derivation and application to the $beta$ Pictoris Moving Group. (arXiv:1902.07732v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Crundall_T/0/1/0/all/0/1">Timothy D. Crundall</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Ireland_M/0/1/0/all/0/1">Michael J. Ireland</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Krumholz_M/0/1/0/all/0/1">Mark R. Krumholz</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Federrath_C/0/1/0/all/0/1">Christoph Federrath</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Zerjal_M/0/1/0/all/0/1">Maruša Žerjal</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hansen_J/0/1/0/all/0/1">Jonah T. Hansen</a>
$textit{Gaia}$ DR2 provides an unprecedented sample of stars with full 6D
phase-space measurements, creating the need for a self-consistent means of
discovering and characterising the phase-space overdensities known as
$textit{moving groups}$ or $textit{associations}$. Here we present
$texttt{Chronostar}$, a new Bayesian analysis tool that meets this need.
$texttt{Chronostar}$ uses the Expectation-Maximisation algorithm to remove the
circular dependency between association membership lists and fits to their
phase-space distributions, making it possible to discover unknown associations
within a kinematic data set. It uses forward-modelling of orbits through the
Galactic potential to overcome the problem of tracing backward stars whose
kinematics have significant observational errors, thereby providing reliable
ages. In tests using synthetic data sets with realistic measurement errors and
complex initial distributions, $texttt{Chronsotar}$ successfully recovers
membership assignments and kinematic ages up to $approx 100$ Myr. In tests on
real stellar kinematic data in the phase-space vicinity of the $beta$ Pictoris
Moving Group, $texttt{Chronostar}$ successfully rediscovers the association
without any human intervention, identifies 15 new likely members, corroborates
43 candidate members, and returns a kinematic age of $18.3^{+1.3}_{-1.2},$Myr.
In the process we also rediscover the Tucana-Horologium Moving Group, for which
we obtain a kinematic age of $36.0^{+1.2}_{-1.3},$Myr.
$textit{Gaia}$ DR2 provides an unprecedented sample of stars with full 6D
phase-space measurements, creating the need for a self-consistent means of
discovering and characterising the phase-space overdensities known as
$textit{moving groups}$ or $textit{associations}$. Here we present
$texttt{Chronostar}$, a new Bayesian analysis tool that meets this need.
$texttt{Chronostar}$ uses the Expectation-Maximisation algorithm to remove the
circular dependency between association membership lists and fits to their
phase-space distributions, making it possible to discover unknown associations
within a kinematic data set. It uses forward-modelling of orbits through the
Galactic potential to overcome the problem of tracing backward stars whose
kinematics have significant observational errors, thereby providing reliable
ages. In tests using synthetic data sets with realistic measurement errors and
complex initial distributions, $texttt{Chronsotar}$ successfully recovers
membership assignments and kinematic ages up to $approx 100$ Myr. In tests on
real stellar kinematic data in the phase-space vicinity of the $beta$ Pictoris
Moving Group, $texttt{Chronostar}$ successfully rediscovers the association
without any human intervention, identifies 15 new likely members, corroborates
43 candidate members, and returns a kinematic age of $18.3^{+1.3}_{-1.2},$Myr.
In the process we also rediscover the Tucana-Horologium Moving Group, for which
we obtain a kinematic age of $36.0^{+1.2}_{-1.3},$Myr.
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