20130103

Astronomy final exam question: stars on versus off the main-sequence

Astronomy 210 Final Exam, fall semester 2012
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board(*) was asked and answered:
Jayden: While looking at the H-R diagram I noticed the brighter, hotter stars were bigger, and the dimmer, cooler stars were smaller. Is this always the case [for] stars on the main sequence?
DLM: For main sequence stars, that's essentially an accurate statement...
Discuss why this statement would be incorrect for stars not on the main sequence, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

*Adapted from: http://answers.yahoo.com/question/index?qid=20090920095747AAfgLH2.

Solution and grading rubric:
  • p = 20/20:
    Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to give a concrete example of two stars off the main sequence (or one star off the main sequence, compared to a main sequence star) that are not consistent with the brighter/hotter/bigger and dimmer/cooler/smaller trend on the main sequence.
  • r = 16/20:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. As (p), but typically discusses the Stefan-Boltzmann law for two stars with arbitrary parameters inconsistent with the brighter/hotter/bigger and dimmer/cooler/smaller trend on the main sequence, but not a concrete example of stars found on an H-R diagram.
  • t = 12/20:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors.
  • v = 8/20:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, the Stefan-Boltzman law, and/or the H-R diagram.
  • x = 4/20:
    Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, the Stefan-Boltzman law, and/or the H-R diagram.
  • y = 2/20:
    Irrelevant discussion/effectively blank.
  • z = 0/20:
    Blank.
Grading distribution:
Section 70158
Exam code: finalSor3
p: 9 students
r: 9 students
t: 1 student
v: 5 students
x: 4 students
y: 0 students
z: 1 student

A sample "p" response (from student 0640):

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