The First Planets: the Critical Metallicity for Planet Formation
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.
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