As discussed in class and in the text, more massive stars are more luminous than

Question

As discussed in class and in the text, more massive stars are more luminous than less massive stars and, as a result, live for a shorter period of time despite their larger size. Assume that more massive stars have an equal fraction of their mass available to burn as 'fuel' (this isn't exactly true, but is good enough for the estimates we are about to make). Use the following expression for the mass-luminosity relationship in stars with masses roughly from 1-20 x the mass of the Sun: L/Lsun = 1.5 x (M/Msun) 3.5. Take the lifetime of a Sun-like star to be 1x1010 years. In the following calculations, be sure to consider the differing luminosity of each star as well as its differing amount of available fuel.

a) Calculate the expected lifetimes of the stars Betelgeuse (8 Msun) and Rigel (18 Msun) in the constellation Orion. Assuming these stars are close to the end of their lives (and they are), roughly when did they appear in our sky?

b) On the other hand, stars less than about 1 Msun follow a relation which is closer to L/Lsun = (M/Msun) 4.0. The star Epsilon Eridani is an 0.8 Msun star which is visible to the naked eye (in the constellation Eridanus (roughly overhead in our Caribbean sky). What is the expected lifetime of this star?

Explanation / Answer

A) given for stars heavier than sun;

L/L sun = 1.5×(M/Msun)^(-3.5)

So,for Betelgeuse ; L= Lsun ×(1.5× 8^(-3.5))= 1.03×10^7 years.

For Revel; L= Lsun×(1.5×16^(-3.5))= 10^6 years.

B) for light stars L= Lsun(M/Msun)^4

For Eridani; L = Lsun( 0.8)^(-4) = 2× 10^10 years.

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