# Relationship between IMF and time spent during an evolutionary phase

I was reading a little about stellar evolution and was wondering whether there was any relationship between the lifetime of an evolutionary phase and the IMF, I searched on google but all I found were claims that there is a relationship, but I couldn't find any numerical formula which explains this. Does there exist such a formula that relates the lifetime of an evolutionary phase with the IMF and other properties?

For example, given the luminosities, IMF, number of stars, can we determine the lifetime in,say the RGB or the subgiant branch?

I know that main sequence lifetime is proportional to $$M/L$$, was hoping to get such a relation for other branches

• How can the lifetime be related to a distribution of masses? What do you understand the IMF to mean? – Rob Jeffries Dec 8 '19 at 15:35
• @RobJeffries The IMF as in the function that dictates the initial mass distribution,example: Kroupa(2001), Salpeter,etc. As for how can it be related, that's exactly my question. Can it or can it not? – Hrsht Dec 8 '19 at 16:15
• It is related to a distribution of lifetimes of course. The lifetime of a star is determined by iits mass. Not the IMF. – Rob Jeffries Dec 8 '19 at 16:28