20080430

Astronomy midterm question: cool star brighter than a hot star?

Astronomy 10 Midterm 3, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q8.5

[15 points.] How is it possible that a cool star can be more luminous than a hot star? Using an H-R diagram, explain your reasoning with Wien's law and/or the Stefan-Boltzmann law

Solution and grading rubric:
  • p = 15/15:
    Correct. The Stefan-Boltzmann law states that luminosity depends on both the size (surface area) of the star, and its temperature. Thus a merely warm star can still be more luminous than a hotter star if the warm star is much bigger in size than the hotter star.
  • r = 12/15:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Stefan-Boltzmann law is garbled, but at least understands how size can be independent from temperature in determining the luminosity of a star.
  • t = 9/15:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. Discussion based somehow on Wien's law and/or the Stefan-Boltzmann law.
  • v = 6/15:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Typically confuses luminosity with apparent magnitude by saying that the warm star could be closer to the Earth than the hotter star, when in fact luminosity (and absolute magnitude) are unaffected by distance.
  • x = 3/15:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y = 1.5/15:
    Irrelevant discussion/effectively blank.
  • z = 0/15:
    Blank.
Grading distribution:
Section 4160
p: 19 students
r: 10 students
t: 7 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1231):
Another "p" response (from student 4607), using what appears to be a luminosity versus wavelength graph (due to the Planck curves) rather than a luminosity versus temperature (H-R digram) graph:

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