Constraints on planet formation via gravitational instability across cosmic time

We estimate the maximum temperature at which planets can form via gravitational instability (GI) in the outskirts of early circumstellar disks. We show that due to the temperature floor set by the cosmic microwave background, there is a maximum distance from their host stars beyond which gas giants cannot form via GI, which decreases with their present-day age. Furthermore, we show that planet formation via GI is not possible at metallicities < 10^-4 Z_Sun, due to the reduced cooling efficiency of low-metallicity gas. This critical metallicity for planet formation via GI implies a minimum distance from their host stars of ~ 6 AU within which planets cannot form via GI; at higher metallicity, this minimum distance can be significantly greater, out to several tens of AU. We show that these maximum and minimum distances significantly constrain the number of observed planets to date that are likely to have formed via GI at their present locations. That said, the critical metallicity we find for GI is well below that for core accretion to operate; thus, the first planets may have formed via GI, although only within a narrow region of their host circumstellar disks.