  A rapidly growing body of observational results suggests that planet
formation takes place preferentially at high metallicity. In the core accretion
model of planet formation this is expected because heavy elements are needed to
form the dust grains which settle into the midplane of the protoplanetary disk
and coagulate to form the planetesimals from which planetary cores are
assembled. As well, there is observational evidence that the lifetimes of
circumstellar disks are shorter at lower metallicities, likely due to greater
susceptibility to photoevaporation. Here we estimate the minimum metallicity
for planet formation, by comparing the timescale for dust grain growth and
settling to that for disk photoevaporation. For a wide range of circumstellar
disk models and dust grain properties, we find that the critical metallicity
above which planets can form is a function of the distance r at which the
planet orbits its host star. With the iron abundance relative to that of the
Sun [Fe/H] as a proxy for the metallicity, we estimate a lower limit for the
critical abundance for planet formation of [Fe/H]_crit ~ -1.5 + log(r/1 AU),
where an astronomical unit (AU) is the distance between the Earth and the Sun.
This prediction is in agreement with the available observational data, and
carries implications for the properties of the first planets and for the
emergence of life in the early Universe. In particular, it implies that the
first Earth-like planets likely formed from circumstellar disks with
metallicities Z > 0.1 Z_Sun. If planets are found to orbit stars with
metallicities below the critical metallicity, this may be a strong challenge to
the core accretion model.
