20170519

Astronomy final exam question: star cluster more likely to have white dwarfs?

Astronomy 210 Final Exam, spring semester 2017
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:
Curi: Star cluster A is 12 billion years old, while star cluster B is one million years old. Which star cluster will have more white dwarfs?
arsl: Star cluster A.
Discuss whether this answer is correct or incorrect, 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=20110402021909AA2fbXz.

Solution and grading rubric:
• p:
Correct. Understands that star cluster A will have more white dwarfs (while star cluster B would not have any) because:
1. medium-mass stars become white dwarfs well after the end of their main-sequence lifetimes (approximately 10 billion years, much longer than one million years); and
2. medium-mass stars in the younger star cluster B will not have had enough time to become white dwarf, while the medium-mass stars in the older star cluster A will have had enough time to become white dwarfs.
• r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. At least discusses white dwarfs as end-stages of medium-mass main sequence stars, but does not explicitly discuss that a million years is not enough time for that to happen.
• t: Contains right ideas, but discussion is unclear/incomplete or contains major errors. Argues that an older star cluster would be more likely to have end-stage stars than a younger cluster.
• 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 30676
Exam code: finalSBr6
p: 5 students
r: 9 students
t: 14 students
v: 5 students
x: 2 students
y: 0 students
z: 2 students

A sample "p" response (from student):