An Estimate of the Age Distribution of Terrestrial Planets in the Universe: Quantifying Metallicity as a Selection Effect

Planets such as the Earth cannot form unless elements heavier than helium are available. These heavy elements, or "metals," were not produced in the Big Bang. They result from fusion inside stars and have been gradually building up over the lifetime of the Universe. Recent observations indicate that the presence of giant extra-solar planets at small distances from their host stars is strongly correlated with high metallicity of the host stars. The presence of these close-orbiting giants is incompatible with the existence of Earth-like planets. Thus, there may be a Goldilocks selection effect: with too little metallicity, Earths are unable to form for lack of material; with too much metallicity, giant planets destroy Earths. Here I quantify these effects and obtain the probability, as a function of metallicity, for a stellar system to harbor an Earth-like planet. I combine this probability with current estimates of the star formation rate and of the gradual buildup of metals in the Universe to obtain an estimate of the age distribution of Earth-like planets in the Universe. The analysis done here indicates that three-quarters of the Earth-like planets in the Universe are older than the Earth and that their average age is 1.8 ± 0.9 billion years older than the Earth. If life forms readily on Earth-like planets - as suggested by the rapid appearance of life on Earth - this analysis gives us an age distribution for life on such planets and a rare clue about how we compare to other life which may inhabit the Universe.