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We determine the fraction of G-dwarf stars that could host stable planetarysystems based on the observed properties of binaries in the Galactic field, andin various postulated primordial binary populations, which assume that theprimordial binary fraction is higher than that in the field. We first considerthe frequency of Solar System analogues - planetary systems that form eitheraround a single G-dwarf star, or a binary containing a G-dwarf where the binaryseparation exceeds 100-300au. If the primordial binary fraction and perioddistribution is similar to that in the field, then up to 63 per cent of G-dwarfsystems could potentially host a Solar System analogue. However, if theprimordial binary fraction is higher, the fraction of G-dwarf systems thatcould host a planetary system like our own is lowered to 38 per cent.  We extend our analysis to consider the fraction of G-dwarf systems (bothsingle and binary) that can host either circumprimary planets (orbiting theprimary star of the binary) or circumbinary planets (orbiting both stars in thebinary) for fiducial planetary separations between 1 - 100au. Depending on theassumed binary population, in the circumprimary case between 65 and 95 per centof systems can host a planet at 1au, decreasing to between 20 and 65 per centof systems that can host a planet at 100au. In the circumbinary case, between 5and 59 per cent of systems can host a planet at 1au, increasing to between 34and 75 per cent of systems that can host a planet at 100au.  Our results suggest that the assumed binary fraction is the key parameter indetermining the fraction of potentially stable planetary systems in G-dwarfsystems and that using the present-day value may lead to significantoverestimates if the binary fraction was initially higher.

On the frequency of planetary systems around G-dwarfs