Homework 4

Due: 2017/11/13

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20. 12.2
21. 12.6
22. 12.11
23. 12.14
24. 12.18
25. A newly formed cluster of stars has total mass 10⁶ M_sun and initial mass function

dN/dM = aM^-2.35

over the mass range 0.1 to 20 M_sun.

a. Find a.
b. Find the total luminosity of the cluster if L ∝ M⁴. What fraction of the luminosity is produced by stars with mass M > 8M_sun.
c. Find the mean mass of a star in the cluster.
d. Assume that the lifetime of a 1 solar mass star is 10 billion years. What is the mass of the most massive Main Sequence star after 1 billion years? What is the total luminosity of the remaining Main Sequence stars at this time?

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