Name: ________________________ DUE 11/01 ID number: ________________________

Homework 10. Main-Sequence Stars


The table below lists key properties -- mass M, luminosity L, and surface temperature T -- for a small sample of main-sequence stars. In this table, M is given in units of the Sun's mass (M), and L is given in units of the Sun's luminosity (L), while T is given in degrees Kelvin.

star M L T star M L T
a 40 500000 40000 g 1.1 1.3 6000
b 18 20000 28000 h 0.8 0.4 4900
c 6.4 800 15000 i 0.7 0.2 4100
d 3.2 80 9900 j 0.5 0.1 3500
e 2.1 20 8500 k 0.2 0.01 2800
f 1.7 6.3 7400 l 0.1 0.001 2400

Using the temperatures and luminosities listed above, plot each star on the HR diagram below. Write the letter for each star next to its point as you plot it, using small letters.

As usual, this diagram uses geometric spacing along both axes. Each step leftward is factor of 2 increase in T, and each step upward is a factor of 10 increase in L. Use care when plotting values between the labeled marks. For example, a star with T = 14142°K would be plotted exactly halfway between the 20000°K and 10000°K marks, because a half-step to the left is a factor of 2 = 1.4142 increase from 10000°K.

The next part of this assignment asks you to calculate the main-sequence lifetime of each star. This can be a bit tricky, so I've broken it down into two seperate steps. In the first step, assume that each star, regardless of its actual mass, has exactly the same amount of fuel available as the Sun. In this case, the lifetime of a star is just inversely proportional to its luminosity L. For example, star e, with L = 20 L, would live 1/20 times as long as the Sun. The Sun's main-sequence lifetime is 1010 yr, so star e lives for 1010 yr ÷ 20 = 5 × 108 yr.

star lifetime (1st step) star lifetime (1st step) star lifetime (1st step)
a ________________ e 5 × 108 yr i ________________
b ________________ f ________________ j ________________
c ________________ g ________________ k ________________
d ________________ h ________________ l ________________

In the second step, correct the lifetimes you computed above to take into account the fact that the amount of fuel a star actually has is proportional to its mass. For example, star e has mass M = 2.1 M, so its corrected lifetime is 2.1 × (5 × 108 yr) = 1.05 × 109 yr.

star lifetime (2nd step) star lifetime (2nd step) star lifetime (2nd step)
a ________________ e 1.05 × 109 yr i ________________
b ________________ f ________________ j ________________
c ________________ g ________________ k ________________
d ________________ h ________________ l ________________

Finally, assume that all the stars formed at the same time. Using the lifetimes from the 2nd step, sketch which part of the main sequence is still present after 108 yr (left) and 1010 yr (right).


Joshua E. Barnes (barnes@ifa.hawaii.edu)
Last modified: October 26, 1999
http://www.ifa.hawaii.edu/~barnes/ast110_99/homework/hw10.html