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 { \raise - 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } } 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 { \raise - 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } } 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 \pm 1.2 ^ { \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 \pm 300 stars and a radius of r _ { vir } = 0.75 \pm 0.25 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 .