20150525

Astronomy final exam question: less-massive star bigger than more-massive star?

Astronomy 210 Final Exam, spring semester 2015
Cuesta College, San Luis Obispo, CA

"Wikipedia says NML Cygni (33 Msun, 1,700 Rsun) is the largest star in size, but it is less massive than R136a1 (256 Msun, 29 Rsun). How is this possible?" This question was asked on an online discussion board and a possible answer was given[*]:
zei: A less-massive star near the end of its life could be much larger than a younger, more massive main-sequence star.
Discuss why this answer is correct, and how you know this. Explain using the properties and evolution of stars.

[*] answers.yahoo.com/question/index?qid=20120827061217AAtzkXA.

Solution and grading rubric:
  • p:
    Correct. Massive stars will expand to become supergiants after their main-sequence lifetimes end. A less-massive star that is older, and at the end of its main-sequence lifetime will have expanded (increasing its size, but not affecting its mass), becoming bigger than a more-massive star that is younger, and still in its main-sequence phase. May also discuss how they may have both ended their main-sequence phases, but the older less-massive star would have had more time to expand and be a supergiant (or an impending type II supernova) bigger in size than the newer more-massive star.
  • 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:
    Blank.
Grading distribution:
Section 30674
Exam code: finaln1N3
p: 5 students
r: 3 students
t: 9 students
v: 10 students
x: 1 student
y: 1 student
z: 0 students

Section 30676
Exam code: finals3nG
p: 12 students
r: 5 students
t: 5 students
v: 19 students
x: 3 students
y: 1 student
z: 0 students

A sample "p" response (from student 4676, a self-proclaimed "H-R diagram homeboi"):

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