A VLBA Survey of radio stars in the Orion Nebula Cluster: II. Astrometry
  From Very Long Baseline Array (VLBA) observations we previously identified a
population of 123 young stellar systems with nonthermal radio emission toward
the core of the Orion Nebula Cluster (ONC). We find optical sources in the Gaia
DR2 catalog for 34 of them within 0.2" of the radio positions. Most of the
radio sources are likely companions of Gaia detections. However, there are 11
stars whose VLBA position differs from Gaia by $<1.6$ mas, and some of these
radio sources probably are the direct counterparts of the optical stars. We are
able to obtain radio proper motions for 23 stars. Combining the stellar proper
motions derived from the VLBA and Gaia data we find the global motion and
velocity dispersion of the ONC to be
($\mu_\alpha*,\mu_\delta$)=($1.20\pm0.09,0.18\pm0.09$) mas yr$^{-1}$ and
($\sigma_{\mu_\alpha*},\sigma_{\mu_\delta}$)=($0.84\pm0.09,1.30\pm0.09$) mas
yr$^{-1}$. Finally, we looked for ordered motions by estimating the means of
scalar and vectorial products, which results in
$\mathbf{\overline{v\cdot\hat{r}}}=-0.61\pm1.00$ km s$^{-1}$ and
$\mathbf{\overline{v\times\hat{r}}}=0.57\pm0.95$ km s$^{-1}$. These do not show
indications that the young stellar cluster is in expansion, contraction, or
rotation.
