## 20110611

### Astronomy final exam question: finding age of a star cluster from its colors

Astronomy 210 Final Exam, spring semester 2011
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:
Sng: What is the easiest way to determine the age of a star cluster?
qcp: If a star cluster has a lot of white/blue stars, it's a young cluster. If it contains fewer white stars, but more yellow stars, it's older.
Discuss whether or not if 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.

Solution and grading rubric:
• p:
Correct. Understands that massive stars evolve faster than medium-mass stars, such that massive stars reach the upper left of the main sequence first, (becoming "blue/white stars"), spend the least amount of time there, and leave before medium-mass stars become main-sequence ("yellow") stars would in an older star cluster. May instead interpret statement as incorrect, if "white stars" is taken to mean white dwarfs, which would be in older star clusters than those with medium-mass main sequence stars.
• r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. May instead discuss how the metallicity can be used to find the age of a star cluster (as being "easier" than comparing colors of (main) sequence stars).
• t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least understands how massive and low-mass stars evolve at different rates to get to (and leave) the main sequence.
• v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
Implementation/application of ideas, but credit given for effort rather than merit.
• y:
Irrelevant discussion/effectively blank.
• z:
Blank.
Section 30676
Exam code: finalS45s
p: 8 students
r: 4 students
t: 15 students
v: 14 students
x: 1 student
y: 0 students
z: 1 student

A sample "p" response (from student 8487):

Another sample "p" response (from student 0701), appealing to the "House Party" model of star cluster age and stellar evolution:

A sample "p" response (from student 9936), interpreting "white stars" as white dwarfs instead of white-hot massive main sequence stars: