- #1
Piano man
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Homework Statement
In a particular star forming cloud the initial mass function (IMF) is given by
[tex] N(M_{*})=Cexp(-M_*^2) [/tex]
where C is a normalisation constant. (The IMF describes the initial relative number of stars of different masses). Assuming that the number of hydrogen Lyman continuum photons created by stars of different mass, [tex] N_{Lyc}=10^{34}M_*^{32}[/tex] which mass stars dominate the volume of ionized natal star forming material?
Homework Equations
I've found this equation while I was searching for a lead:
[tex]N=\int_{m_1}^{m_2} dN=\int_{m_1}^{m_2} \frac{dN}{dm}dm[/tex]
but I'm not sure what values to use as integration limits.
Also, the problem sheet gives the following formula (including gamma and Riemann zeta functions) which is probably useful at some point, though I don't know where or how.
[tex] \int_0^\infty x^n\frac{1}{exp(x)-1}dx=\zeta(n+1)\Gamma(n+1)[/tex]
The Attempt at a Solution
My first step was differentiating the expression I was given to get
[tex]\frac{dN}{dM}=-2M_*Cexp(-M_*^2)[/tex]
which looks like something similar to the first equation, and also hints at the formula given in the problem sheet.
But I'm really not sure where to go from here, and how to incorporate the value given for [tex]N_{Lyc}[/tex].
Any help/pointers would be greatly appreciated.