Astronomy midterm question: red dwarf and white dwarf with same luminosity

Astronomy 10 Midterm 3, Summer Session 2007
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q8.3

[15 points.] How is it possible that a red dwarf and a white dwarf can have different colors, yet have the same luminosity? 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. Wien's law: white dwarf is hotter, red dwarf is cooler (can also read this information off of the H-R diagram). The Stefan-Boltzmann law: luminosity proportional to size * (Temperature)^4, such that a tiny, hot white dwarf can have the same luminosity as a (slightly) larger, warm red dwarf.
  • r = 12/15:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  • t = 9/15:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least uses an H-R diagram and/or Wien's law to determine that the white dwarf is hotter than the red dwarf.
  • v = 6/15:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  • 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:
Grading distribution:
Section 8027
p: 4 students
r: 0 students
t: 3 students
v: 6 students
x: 0 students
y: 0 students
z: 0 students

A sample of a "p" response (from O. G.):

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