Astronomy midterm question: live fast, die young

Astronomy 210 Midterm 2, Spring Semester 2009
Cuesta College, San Luis Obispo, CA

[20 points.] Massive stars have much more hydrogen in their cores than do less massive stars. Why, then, do they run out of hydrogen in their cores faster than the cores of stars of low mass? Explain using the properties and evolution of stars.

(Adapted from a test bank question from Karl F. Kuhn, Theo Koupelis, In Quest of the Universe.)

Solution and grading rubric:

• p = 20/20:
  Correct. Higher temperatures and pressures in the cores of massive main sequence stars cause them to fuse hydrogen into helium much faster than in the cores of low mass stars (the pressure-temperature thermostat). (Also, low mass stars are cool enough for convection to occur throughout, such that hydrogen from all parts of the star (and not just in the core) can undergo fusion, extending the lifetime for these stars much longer than for massive stars.)
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Some attempt at explaning how the pressure-temperature thermostat sets a faster fusion rate for massive stars.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least recognizes that the rate of fusion for massive stars is greater than for low mass star, but does not explain how the pressure-temperature thermostat sets a faster fusion rate for massive stars.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 30674
p: 14 students
r: 4 students
t: 14 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

An artistic sample "p" response (from student 0528) with a graphical representation of hydrostatic equilibrium:

Another sample "p" response (from student 2048) displaying the convection cells inside of massive and low-mass main sequence stars:

And one last sample "p" response (from student 2902) discussing the "higher thermostat setting" for massive stars: