Prospects of Detecting a Jet in Sagittarius A* with VLBI

Event Horizon Telescope (EHT) images of the horizon-scale emission around the Galactic Center supermassive black hole Sagittarius A* (Sgr A*) favor accretion flow models with a jet component. However, this jet has not been conclusively detected. Using the "best-bet" models of Sgr A* from the EHT collaboration, we assess whether this non-detection is expected for current facilities and explore the prospects of detecting a jet with VLBI at four frequencies: 86, 115, 230, and 345 GHz. We produce synthetic image reconstructions for current and next-generation VLBI arrays at these frequencies that include the effects of interstellar scattering, optical depth, and time variability. We find that no existing VLBI arrays are expected to detect the jet in these best-bet models, consistent with observations to-date. We show that next-generation VLBI arrays at 86 and 115 GHz -- in particular, the EHT after upgrades through the ngEHT program and the ngVLA -- successfully capture the jet in our tests due to improvements in instrument sensitivity and (u,v) coverage at spatial scales critical to jet detection. These results highlight the potential of enhanced VLBI capabilities in the coming decade to reveal the crucial properties of Sgr A* and its interaction with the Galactic Center environment.