Question

Assume that a star’s luminosity is given by L ∝ M^3.5 for all masses. After a burst of star formation, does most of the stellar luminosity come from low-mass stars or high-mass stars? Justify your answer quantitatively.

What is the average stellar luminosity?

What is the mass of a star with the average luminosity?

Answer 1

1) Stars shown their relationship between mass and their luminosity,the more massive main sequence stars are hotter and more luminous than the low mass main sequence stars. And the luminosity depends on the mass raised to a power that is between 3and 4 ,that's even a slight difference in the mass among star produces a large difference in their luminosity. Take an example of O type stars 20times more massive than sun and luminosity is 10,000times much as sun. The massive stars have greater gravitational compression in their cores because of the larger weight of the overlying layers of than that found in low mass stars .It also need greater thermal and radiation pressure pushing outward to balance the greater gravitational compression.

2),

Luminosity is the total amount of electromagnetic energy emitted per unit of time bya star. A star luminosity can be determined by two stellar characteristics one is size and effective temperature.To measure a stellar luminosity is to measure the stars apparent brightness and distance. If the stellar medium have gas and dust present ,in that case one more term is needed to determine luminosity that is interstellar extinction.

The value of luminosity for a black body can be determined

Where A is the surface area

is the Stefan - Boltzmann constant.

3) Consider a point source of light of luminosity L that radiates equally all directions.As a hollow sphere centered on the point would have its entire interior surface illuminated. A s the radius increase surface area also increase. So the flux density F is

F=L/A

Surface area of the sphere with radius r

For stars on the main sequence luminosity also related to mass

L/Lo=(M/Mo)^3.5