Gaia-EDR3 Parallax Distances to the Great Carina Nebula and its Star
  Clusters (Trumpler 14, 15, 16)
  Using offset-corrected Gaia-EDR3 parallax measurements and spectrophotometric
methods, we have determined distances for 69 massive stars in the Carina OB1
association and associated clusters: Trumpler 16 (21 stars), Trumpler 14 (20
stars), Trumpler 15 (3 stars), Bochum 11 (5 stars), and South Pillars region
(20 stars). Past distance estimates to the Carina Nebula range from 2.2 to 3.6
kpc, with uncertainties arising from photometry and anomalous dust extinction.
The EDR3 parallax solutions show considerable improvement over DR2, with
typical errors $\sigma_{\varpi}/\varpi \approx$~3-5%. The O-type stars in the
Great Carina Nebula lie at essentially the same distance ($2.35\pm0.08$ kpc),
quoting mean and rms variance. The clusters have distances of $2.32\pm0.12$ kpc
(Tr 16), $2.37\pm0.15$ kpc (Tr 14), $2.36\pm0.09$ kpc (Tr 15), and
$2.33\pm0.12$ kpc (Bochum 11) in good agreement with the $\eta$ Car distance of
around 2.3 kpc. O-star proper motions suggest internal (2D) velocity
dispersions $\sim4$ km/s for Tr 14 and Tr 16. Reliable distances allow
estimates of cluster sizes, stellar dynamics, luminosities, and fluxes of
photoionizing radiation incident on photodissociation regions in the region. We
estimate that Tr 14 and Tr 16 have half-mass radii $r_h = 1.5-1.8$ pc, stellar
crossing times $t_{\rm cr} = r_h/v_m \approx 0.7-0.8$ Myr, and two-body
relaxation times $t_{rh} \approx 40-80$ Myr. The underlying velocity dispersion
for Tr 14, if a bound cluster, would be $v_m \approx 2.1^{+0.7}_{-0.4}$ km/s
for $N = 7600^{+5800}_{-2600}$ stars. With the higher dispersions of the
O-stars, mass segregation might occur slowly, on times scales of 3-6~Myr.
