tokens: probability distributions are shown in the right-hand panel of Fig. 2 , and lead to a strong bias towards Solar and super-Solar metallicity systems as potential terrestrial planet hosts, while substantial tails of potentially habitable terrestrial planet systems remain down to low metallicities. Given the flat evolution in the mean gas phase metallicity of the Universe over cosmic time, this probability distribution has relatively little effect on the evolution of habitabilities at any lookback time 10 Gyr, but instead acts primarily as a scaling factor, truncating the maximum habitable fraction at any redshift at ∼50 per cent. It will, however, tend to suppress the habitable fraction in low-mass galaxies (log(M/M ⊙ ) 8.5), since these have lower typical metallicities as shown in Fig. 3 . We note that since Lineweaver ( 2001 ) defined this probability distribution, the number of exoplanetary systems known has grown exponentially (see e.g. Winn Fabrycky 2015 , for a recent review). None the less, the metallicity dependence of planet hosting remains a complex subject, with relatively poor observational constraints, particularly at the low end of the planetary and stellar-mass functions where observational selection effects are significant. None the less, the distribution above remains broadly consistent with current observations. Wang Fischer ( 2015 ) examined the distribution of planets selected by the Kepler telescope. They lacked the sample size to determine the detailed metallicity distribution of the planet hosts, but found that the median metallicity for terrestrial planet hosts is log( Z /Z ⊙ ) = 0.04 (with Z ⊙ = 0.018), which matches the peak of the Lineweaver ( 2001 ) distribution in P HE ( Z ). By contrast, other studies such as that of Adams Kane ( 2016 ) and Buchhave et al. ( 2012 ) have found no statistically significant difference in metallicity between stars hosting terrestrial planet candidates and the whole Kepler sample, even when only planets in their habitable zones are considered. Hobson et al. ( 2017 ) also suggest that, while M-dwarf stars hosting massive planets are biased towards high metallicities, no such bias is seen for the hosts of low-mass planets. At the lowest metallicities, Zackrisson et al. ( 2016 ) have studied the history of metallicity enhancement in the Universe and its effect on terrestrial planet formation. They apply a gradual iron enrichment cut-off between 10 per cent and 1 per cent of Solar metallicity, extending well below the Lineweaver ( 2001 ) cut-off we apply, although, as Fig. 2 demonstrates, the vast bulk of galaxies have a mean gas phase metallicity above 10 per cent Solar for the entire lookback interval being considered. It is likely that future exoplanet telescope missions such as TESS and PLATO , together with extensive ground-based follow-up, will be required to clarify this issue. However, as noted above, given the relatively slow evolution of mean metallicities in cosmic time, we
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