Astronomy midterm question: more luminous star redder than same-size less luminous star?

Astronomy 210 Midterm 2, fall semester 2017
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

RC: Star X is more luminous than star Y, but they are the same size. Is star X redder or bluer than star Y?
BrT: Since they have the same size, because star X is more luminous it will be redder.

Discuss why this answer is incorrect, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

[*] answers.yahoo.com/question/index?qid=20110203173510AAHqejO.

Solution and grading rubric:

• p:
  Correct. Uses the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate that in order for two stars to have the same size, the more luminous star X must be hotter than the less luminous star Y, and from Wien's law "redder" corresponds to cooler temperatures, and thus star X cannot be redder than star Y.
• 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. At least attempts to use Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 70158
Exam code: midterm02Sm5n
p: 29 students
r: 5 students
t: 9 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02nJv3
p: 24 students
r: 2 students
t: 5 students
v: 0 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 8622), using a graphical "box method" to indicate relative quantities in the Stefan-Boltzmann law:
A sample "p" response (from student 1881), using an H-R diagram:
A sample "p" response (from student 1072), using both an H-R diagram and the "box method":