The most common type of star is a main sequence star. The Sun is a main...

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The most common type of star is a "main sequence star". The Sun is a main sequence star. Main sequence stars are born with a wide range of masses. Considering only main sequence stars more massive than the Sun, Edwin Salpeter showed in 1955 that the probability density function characterizing the distribution of stellar masses in the disk of the Milky Way is approximately given by N(m) dm = C m-2.35 dm where m is the stellar mass divided by the mass of the Sun, and C is a constant. Your textbook gives the following expression for the luminosity of a main sequence star more massive than the Sun: 1 = m3.92 where I is the stellar luminosity divided by the luminosity of the Sun. (Note that I have rounded the formula very slightly to simplify the computation.) (a) Find C. (10 pts.) (b) Determine the probability density function f(l) for stellar luminosity for main sequence stars having m> 1. (10 pts.) (c) Show that your answer to part (b) gives the expected result when integrated over all l. (10 pts.) The most common type of star is a "main sequence star". The Sun is a main sequence star. Main sequence stars are born with a wide range of masses. Considering only main sequence stars more massive than the Sun, Edwin Salpeter showed in 1955 that the probability density function characterizing the distribution of stellar masses in the disk of the Milky Way is approximately given by N(m) dm = C m-2.35 dm where m is the stellar mass divided by the mass of the Sun, and C is a constant. Your textbook gives the following expression for the luminosity of a main sequence star more massive than the Sun: 1 = m3.92 where I is the stellar luminosity divided by the luminosity of the Sun. (Note that I have rounded the formula very slightly to simplify the computation.) (a) Find C. (10 pts.) (b) Determine the probability density function f(l) for stellar luminosity for main sequence stars having m> 1. (10 pts.) (c) Show that your answer to part (b) gives the expected result when integrated over all l. (10 pts.)

Answer rating: 100% (QA)

a To find C we need to integrate the probability density function Nm dm We can do this as ... View the full answer