Validation of Gaia DR3 orbital and acceleration solutions with hierarchical triples

Using data from Gaia DR3, we construct a sample of 14,791 gravitationally bound wide pairs in which one of the components is an unresolved binary with an astrometric orbital or acceleration solution. These systems are hierarchical triples, with inner binary separations of order $1$ au, and outer separations of $100$-$100,000$ au. Leveraging the fact that the inner binary and outer tertiary should have nearly identical parallaxes, we use the sample to calibrate the parallax uncertainties for orbital and acceleration binary solutions. We find that the parallax uncertainties of orbital solutions are typically underestimated by a factor of $1.3$ at $G>14$, and by a factor of $1.7$ at $G = 8$-$14$. The true parallax uncertainties are nevertheless a factor of $\sim 10$ smaller than those of the single-star astrometric solutions for the same sources. The parallax uncertainties of acceleration solutions are underestimated by larger factors of $2$-$3$ but still represent a significant improvement compared to the sources' single-star solutions. We provide tabulated uncertainty inflation factors for astrometric binary solutions and make the catalog of hierarchical triples publicly available.