Derive an expression for the total number of stars between masses M1 and M2, where M1...

Derive an expression for the total number of stars between masses M1 and M2, where M1 < M2.

Can the Salpeter IMF extend to arbitrarily low mass stars? Justify your answer quantitatively

Derive an expression for the total mass in stars formed with masses between M1 and M2, where M1 < M2.

Solutions

Expert Solution

a) The no of stars can be estimated using Salpeter IMF

In 1955, Salpeter estimated that the mass function for stars in the solar neighborhood is given by

The no of stars between masses M1 and M2 can be estimated using the integral

Evaluating the integral,

b) The no of stars is inversely proportional to the mass of the star.

This means that there will be more low mass stars than high mass stars.

However, the number blows up for very low mass stars.

For example, consider the no of stars between 1 kg and 2 kg.

This number will be very high.

However, we know that it is not possible to have a star of 1 kg.

Thus in the lower limit, the Salpeter IMF can not be used.

c) The mass of stars is given by

Evaluating the integral,

genius_generous answered 1 year ago

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