Characterizing dynamical states of Galactic open clusters with Gaia DR2
  In this work, we investigate the dynamical properties of 38 Galactic open
clusters: 34 of them are located at low Galactic latitudes (|b| < 10$^{\circ}$)
and are projected against dense stellar fields; the other 4 comparison objects
present clearer contrasts with the field population. We determine structural
and time-related parameters that are associated with the clusters' dynamical
evolution: core ($r_c$), tidal ($r_t$) and half-mass ($r_{hm}$) radii, ages
($t$) and crossing times ($t_{cr}$). We have also incorporated results for 27
previously studied clusters, creating a sample of 65, spanning the age and
Galactocentric distance ($R_G$) ranges: 7.0 < log ($t$) < 9.7 and 6 < $R_G$
(kpc) < 13. We employ a uniform analysis method which incorporates photometric
and astrometric data from the Gaia DR2 catalogue. Member stars are identified
by employing a decontamination algorithm which operates on the 3D astrometric
space of parallax and proper motion and attributes membership likelihoods for
stars in the cluster region. Our results show that the internal relaxation
causes $r_c$ to correlate negatively with the dynamical ratio $\tau_{dyn}$ =
$t/t_{cr}$. This implies that dynamically older systems tend to be more
centrally concentrated. The more concentrated ones tend to present smaller
$r_{hm}/r_t$ ratios, which means that they are less subject to tidal
disruption. The analysis of coeval groups at compatible $R_G$ suggests that the
inner structure of clusters is reasonably insensitive to variations in the
external tidal field. Additionally, our results confirm, on average, an
increase in $r_t$ for regions with less intense Galactic gravitational field.
