VLBI studies of FLASH H I 21-cm absorbers -- I

We have conducted VLBA 1.4 GHz (L-band) continuum observations towards twelve sources with HI 21-cm absorption detections at redshift $0.4<z<0.7$ in the pilot surveys of FLASH, an ongoing survey with the ASKAP radio telescope. 11 of the 12 targets are resolved in the VLBA observations. Using the parsec scale radio images, we have classified the source morphology and identified the radio core. Six of the twelve targets have core-jet morphology, four have two-sided jet morphology, one has a complex morphology, and one is unresolved. We describe a methodology to test whether the emission from the core or the total emission detected in the VLBA image has sufficient flux density to cause the entire HI 21-cm absorption, and we estimate limits on the gas covering factor and velocity-integrated optical depth (VOD). We find that for seven of the twelve sources, the core has sufficient flux density to cause all the HI 21-cm absorption detected in the ASKAP spectrum. For three other targets, with projected sizes in the range $\rm 305-409 \ pc$, a large fraction of the entire emission in the VLBA map could be occulted by the gas. For 0903+010 (NVSS J090331+010846), we estimate that at least $\approx 73\%$ of the peak absorption detected in the ASKAP spectrum could arise against the emission detected in the VLBA image. For the target 0023+010 (NVSS J002331+010114), we estimate an upper limit on the VOD of $\rm 169 \ km \ s^{-1}$, the highest in our sample. For 0903+010 (NVSS J090331+010846) we estimate a lower limit of $\rm 104 \ km \ s^{-1}$ on the VOD. We find that the distribution of HI 21-cm VODs at $0.4<z<1.0$ could increase by up to a factor of three after correction for the covering factors using our VLBA measurements.