The main sequence lifetimes of stars follow a particular relationship. A consequ

Question

The main sequence lifetimes of stars follow a particular relationship. A consequence of this relationship is that whenever you double the mass of a star, its main sequence lifetime increases by a fixed amount. Let us test this simulation against that relationship.

Set the mass of the star to 1.0 solar masses.

a) What is the total main sequence lifetime of a 1 solar mass star? (Recall that the main sequence lifetime is the age that the star has at the left-most point on its curve on the HR diagram.)
b) What is the total main sequence lifetime of a 2 solar mass star?
c) What is the total main sequence lifetime of a star that is 4 solar masses?
d) What is the ratio of the main sequence lifetime of a 1 solar-mass star to that of a 2 solar-mass star? (Show your work for full credit.)
e) What is the ratio of the main sequence lifetime of a 2 solar-mass star to that of a 4 solar mass star?
f) Did you get the approximately the same number? (What does approximately mean in this context? It turns out that when analyzed as a whole that the simulation does even better.)

Please explain each question.

Explanation / Answer

a) Lifetime = 10 billion years /M^2.5 (M=no of solar masses)

= 10x109/1^2.5 = 10x10^9 years

b) Lifetime = 10 billion years /2^2.5 = 1.8 x 10^9 years

c) Lifetime = 10 billion years /4^2.5 = 312500000 years

d) ratio = Ans(a)/ Ans(b) = 5.56

e) ratio = Ans(b)/Ans(c) = 5.76

f) Yes,

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