Question

a) The stellar mass distribution in a young star cluster is seen to follow a Salpeter mass function: phi(M) = AM^{-2.35}, where Phi(M) = dN/dM is the number of stars dN in the mass interval dM, and A is a constant. Assume that the stellar masses in the cluster range from M_min = 0.1M_odot to M_max = 120M_odot. i) Normalise the stellar mass function phi(M) and compute the normalisation constant A. ii) If all the stars with masses above 8M_odot end up as supernova, determine the fraction of all stars in the cluster, by number, that go supernova. iii) The total luminosity of stars in the cluster: L = int_{M_{min}}^{M_{max}} L(M) cdot phi(M) dM. Calculate what fraction of the total luminosity is contributed by stars more massive than 10 M_odot. Assume a simple power-law relation between the luminosity and stellar mass, L(M) propto M^3, for all stars in the cluster.

          a) The stellar mass distribution in a young star cluster is seen to follow a Salpeter mass function:

phi(M) = AM^{-2.35},

where Phi(M) = dN/dM is the number of stars dN in the mass interval dM, and A is a constant.
Assume that the stellar masses in the cluster range from M_min = 0.1M_odot to M_max = 120M_odot.

i) Normalise the stellar mass function phi(M) and compute the normalisation constant A.

ii) If all the stars with masses above 8M_odot end up as supernova, determine the fraction of all stars in the cluster, by number, that go supernova.

iii) The total luminosity of stars in the cluster:

L = int_{M_{min}}^{M_{max}} L(M) cdot phi(M) dM.

Calculate what fraction of the total luminosity is contributed by stars more massive than 10 M_odot.
Assume a simple power-law relation between the luminosity and stellar mass, L(M) propto M^3, for all stars in the cluster.

$a) The stellar mass distribution in a young star cluster is seen to follow a Salpeter mass function: phi(M) = AM^-2.35, where Phi(M) = dN/dM is the number of stars dN in the mass interval dM, and A is a constant. Assume that the stellar masses in the cluster range from Mmin = 0.1Modot to Mmax = 120Modot. i) Normalise the stellar mass function phi(M) and compute the normalisation constant A. ii) If all the stars with masses above 8Modot end up as supernova, determine the fraction of all stars in the cluster, by number, that go supernova. iii) The total luminosity of stars in the cluster: L = intMmin^Mmax L(M) cdot phi(M) dM. Calculate what fraction of the total luminosity is contributed by stars more massive than 10 Modot. Assume a simple power-law relation between the luminosity and stellar mass, L(M) propto M^3, for all stars in the cluster.$

Added by Sherri W.

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