Gaia-based Isochronal, Kinematic, and Spatial Analysis of the $\epsilon$
  Cha Association
  The precise parallax, proper motion, and photometric measurements contained
in Gaia Data Release 2 (DR2) offer the opportunity to re-examine the membership
and ages of Nearby Young Moving Groups (NYMGs), i.e., loose groups of stars of
age $\lesssim100$ Myr in the solar vicinity. Here, we analyze the available DR2
data for members and candidate members of the $\epsilon$ Cha Association
($\epsilon$CA) which, at an estimated age of $\sim$3--5 Myr, has previously
been identified as among the youngest NYMGs. The several dozen confirmed
members of $\epsilon$CA include MP Mus and T Cha, two of the nearest stars of
roughly solar mass that are known to host primordial protoplanetary disks, and
the Herbig Ae/Be star HD 104237A. We have used Gaia DR2 data to ascertain the
Galactic positions and kinematics and color-magnitude diagram positions of
$\epsilon$CA members and candidates, so as to reassess their membership status
and thereby refine estimates of the distance, age, multiplicity, and disk
fraction of the group. Our analysis yields 36 \textit{bona fide} $\epsilon$CA
members, as well as 20 provisional members, including 3 new members identified
here as comoving companions to previously known $\epsilon$CA stars. We
determine a mean distance to $\epsilon$CA of 101.0$\pm$4.6 pc and confirm that,
at an age of $5^{+3}_{-2}$ Myr, $\epsilon$CA represents the youngest stellar
group within $\sim$100 pc of Earth. We identify several new photometric binary
candidates, bringing the overall multiplicity fraction (MF) of $\epsilon$CA to
40\%, intermediate between the MFs of young T associations and the field.
