20160114

Astronomy final exam question: no mid-main-sequence line star cluster?

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

The following claim was made on an online discussion board[*]:
eta: When a star cluster is very young, or when it is very old, there will be very few 
stars on the middle of the main-sequence line.
Discuss why this statement is correct (for both a very young and a very old cluster), 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=20090427201220AA1weW2.

Solution and grading rubric:
  • p:
    Correct. Understands that:
    1. stars in the same cluster are all born at the same time, but massive stars evolve faster than medium-mass stars, which evolve faster than low-mass stars;
    2. for a very young star cluster, massive stars reach the main-sequence line before medium-mass stars (which are in the "middle" of the main-sequence line);
    3. for a very old star cluster, by the time low-mass stars reach the main-sequence line, medium-mass stars will have already ended their main-sequence lifetime and left the main-sequence line.
  • 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. Discusses only one out of three concepts in (p) correctly, typically at least understands correlation between mass and main-sequence lifetimes.
  • 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 70158
Exam code: finalS157
p: 11 students
r: 5 students
t: 11 students
v: 4 students
x: 3 students
y: 1 student
z: 3 students

Section 70160
Exam code: finalN157
p: 1 student
r: 4 students
t: 5 students
v: 4 students
x: 5 students
y: 2 students
z: 4 students

A sample "p" response (from student 3695), referring to the "House Party model" of stellar evolution in determining a star cluster's age:

A sample "y" response (from student 2456), who is apparently more interested on seeing the new Star Wars movie than discussing star evolution rates:

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