Astronomy midterm question: star cluster age

Astronomy 10 Midterm 3, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q9.5

[15 points.] Shown at right is an H-R diagram of a star cluster, where all of these stars have the same age. Discuss whether this star cluster is very young or is very old, and explain why.

Solution and grading rubric:

• p = 15/15:
  Correct. Understands that low mass stars evolve slower than massive stars, and that since they have reached the main sequence line, after the massive stars have come and left, this must be a very old star cluster. May use the turnoff point on main sequence line.
  
• r = 12/15:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Understands that the two stars must have the same temperature, but typically misapplies the Stefan-Boltzmann law.
  
• t = 9/15:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least understands evolutionary stages of stars, but determines cluster to be very young.
  
• v = 6/15:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Argument based on temperature or luminosity of stars.
  
• x = 3/15:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 1.5/15:
  Irrelevant discussion/effectively blank.
  
• z = 0/15:
  Blank.
  

Grading distributions:
Section 0135
p: 19 students
r: 4 students
t: 6 students
v: 5 students
x: 1 student
y: 0 students
z: 0 students

A sample of a "p" response (from student 1338) is shown below:

Another "p" response (from student 4136):