The Formation of Solar System Analogs in Young Star Clusters

The Solar system was once rich in the short-lived radionuclide (SLR) $^{26}$Al\, but deprived in $^{60}$Fe. Several models have been proposed to explain these anomalous abundances in SLRs, but none has been set within a self-consistent framework of the evolution of the Solar system and its birth environment. The anomalous abundance in $^{26}$Al may have originated from the accreted material in the wind of a massive $\apgt 20$\,$M_\odot$ Wolf-Rayet star, but the star could also have been a member of the parental star-cluster instead of an interloper or an older generation that enriched the proto-solar nebula. The protoplanetary disk at that time was already truncated around the Kuiper-cliff (at $45$ au) by encounters with another cluster members before it was enriched by the wind of the nearby Wolf-Rayet star. The supernova explosion of a nearby star, possibly but not necessarily the exploding Wolf-Rayet star, heated the disk to $\apgt 1500$K, melting small dust grains and causing the encapsulation and preservation of $^{26}$Al into vitreous droplets. This supernova, and possibly several others, caused a further abrasion of the disk and led to its observed tilt of $5.6\pm1.2^\circ$ with respect to the Sun's equatorial plane. The abundance of $^{60}$Fe originates from a supernova shell, but its preservation results from a subsequent supernova. At least two supernovae are needed (one to deliver $^{60}$Fe\, and one to preserve it in the disk) to explain the observed characteristics of the Solar system. The most probable birth cluster then has $N = 2500\pm300$ stars and a radius of $r_{\rm vir} = 0.75\pm0.25$ pc. We conclude that Solar systems equivalent systems form in the Milky Way Galaxy at a rate of about 30 per Myr, in which case approximately 36,000 Solar system analogues roam the Milky Way.