On the formation of a $33\,M_{\odot}$ black hole in a low-metallicity binary

A $33\,M_\odot$ black hole (BH) was recently discovered in an 11.6-year binary only 590 pc from the Sun. The system, Gaia BH3, contains a $0.8\,M_\odot$ low-metallicity giant ($\rm [M/H]=-2.2$) that is a member of the ED-2 stellar stream. This paper investigates whether the system could have formed via isolated binary evolution. I construct evolutionary models for metal-poor massive stars with initial masses ranging from $35-55\,M_{\odot}$, which reach maximum radii of $1150-1800\,R_{\odot}$ as red supergiants. I then explore what combinations of initial orbit, mass loss, and natal kick can produce the period and eccentricity of Gaia BH3. Initial orbits wide enough to accommodate the BH progenitor as a red supergiant can match the observed period and eccentricity, but only if the BH formed with a significant natal kick ($v_{\rm kick}\gtrsim 20\, {\rm km\,s^{-1}}$). These models are disfavored because such a kick would have ejected the binary from the ED-2 progenitor cluster. I conclude that Gaia BH3 likely formed through dynamical interactions, unless the BH progenitor did not expand to become a red supergiant. Only about 1 in 10,000 stars in the solar neighborhood have metallicities as low as Gaia BH3. This suggests that BH companions are dramatically over-represented at low-metallicity, though caveats related to small number statistics apply. The fact that the luminous star in Gaia BH3 has been a giant -- greatly boosting its detectability -- only for $\sim$1% of the time since the system's formation implies that additional massive BHs remain to be discovered with only moderately fainter companions. Both isolated and dynamically-formed BH binaries with orbits similar to Gaia BH3 are likely to be discovered in Gaia DR4.