Astronomy final exam question: luminosities/colors of an old star cluster?

Astronomy 210 Final Exam 2, fall semester 2016
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:
JG: If you observed a star cluster that was very, very old, what would be the overall luminosities and colors of the stars in this cluster?
rwf: The stars in the cluster would all be dim, and some of them would be red.
Discuss why this answer is correct, and how you know this. Explain using the properties of mass and stellar lifetimes, evolution of stars, and star cluster ages.

[*] answers.yahoo.com/question/index?qid=20100422040137AA35Qc7.

Solution and grading rubric:
  • p:
    Correct. Understands that for stars in an old cluster that were born at the same time, a long time ago:
    1. low-mass stars evolve slowly, and still be in its main-sequence stage as dim red dwarfs;
    2. medium-mass stars evolve relatively quicker, and will have gone through all of its stages to become dim white dwarfs.
    (May also include discussion of how massive stars evolve very quickly, and will have already exploded as type II supernovae.)
  • r:
    Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  • t:
    Contains right ideas, but discussion is unclear/incomplete or contains major errors.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Garbled discussion of properties and evolution of stars.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Discussion other than that of the properties and evolution of stars.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Section 70160
Exam code: finalnwhP
p: 6 students
r: 8 students
t: 2 students
v: 8 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 4135):

A sample "r" response (from student 3575):

A sample "v" response (from student 4431):

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