On the Number of Stars in the Sun's Birth Cluster

Abstract

The Sun is thought to be formed within a star cluster. The coexistence of $^{26}{\rm Al}$-rich and $^{26}{\rm Al}$-poor calcium--aluminum-rich inclusions indicates that a direct injection of $^{26}{\rm Al}$-rich materials from a nearby core-collapse supernova should occur in the first $10^5$ years of the solar system. Therefore, at least one core-collapse supernova should occur within the duration of star formation in the Sun's birth cluster. Here we revisit the number of stars in the Sun's birth cluster from the point of view of the probability for acquiring at least one core-collapse supernova within the finite duration of star formation in the birth cluster. We find that the number of stars in the birth cluster can be significantly larger than that previously considered, depending on the duration of star formation.