How to account for the effect of Star Formation History on the inferred Stellar Initial Mass Function?

I am studying a paper The effect of star formation history on the inferred stellar initial mass function and trying to reproduce the given results.

According equation (1) in the paper, the inferred IMF f(M) can be determined if the PDMF phi(M) and the star formation history S(t) is known. I am trying to calculate S(t) as per the description given in that paper in vain. Roughly, by what amount will the slope of f(M) change from phi(M) if S(t) is calculated? Example: If phi(M) = M^(-2.5), then by what amount will the index change in f(M) if S(t) is calculated and inserted into equation (1)?

• It seems that you have not asked any specific questions, and thus it sounds like a "do my work for me" kind of question. Please provide details for the concepts you are confused about. If you don't understand the basics, describe what concepts are confusing. The more detailed your question, the better answers it will attract. May 12, 2021 at 14:50
• My intention was sincerely not to make my question sound like what you felt. According equation (1) in the paper, the inferred IMF f(M) can be determined if the PDMF phi(M) and the star formation history S(t) is known. I am trying to calculate S(t) as per the description given in that paper in vain. Roughly, by what amount will the slope of f(M) change from phi(M) if S(t) is calculated? Example: If phi(M) = M^(-2.5), then by what amount will the index change in f(M) if S(t) is calculated and inserted into equation (1)? May 13, 2021 at 5:17
• @KrishnaKumarKowshik - Put that clarification into the question. That would improve it a lot. May 13, 2021 at 7:48
• No worries! :) Thank you for clarifying. This will probably attract more people now. I've added +1 May 13, 2021 at 13:10