Assume that there was a starburst that produced 1011 solar masses of stars with a minimum...

Assume that there was a starburst that produced 10¹¹ solar masses of stars with a minimum mass of 0.3 solar masses and a maximum mass of 100 solar masses. The number of stars as a function of mass is N(M) = KM^-2.35, where K is a normalization constant. The current turnoff mass of the population is 1 solar mass

Compute the number of stars and the total mass of stars that are still on the main sequence.
Assume that all stars with masses between 1 and 8 solar masses became white dwarfs. Compute the total number of white dwarfs in this population

Solutions

Expert Solution

If N(M) gives the number of stars with mass M then M*N(M) will give the total mass of stars with mass M each

If we sum M*N(M) over all possible masses, we shall get the total mass of the starburst which is 10¹¹ solar masses.

If we do integration, we get inconsistent results. Therefore we will do it numerically.

We assume that N(M) gives the number of stars within the mass range M and M + dM (where dM is small compared to M)

then for a given value of dM, we sum M*N(M) for all possible values of M

It appears that in this way K will depend on dM. It does but we will see that the ratio K/dM approaches a constant value and so do the total number of stars still in the main sequence and total number of white dwarfs

python code:

output:

genius_generous answered 1 year ago

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