Astronomy midterm question: red dwarf same size as white dwarf?

Astronomy 210 Midterm 2, spring semester 2016
Cuesta College, San Luis Obispo, CA

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

??: Can a red dwarf have the same size as a white dwarf?
Bpt: They can have the same size if the red dwarf was dimmer than the white dwarf.

Discuss why this answer is correct, 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=20160402083607AA27vRN.

Solution and grading rubric:

• p:
  Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how a red dwarf can be the same size as a white dwarf by recognizing that:
  1. from Wien's law, the red dwarf is cooler than the white dwarf;
  2. from the Stefan-Boltzmann law (or interpreting an H-R diagram), the lower temperature red dwarf must have a lower luminosity than a white dwarf of the same size.
• 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. At least discussion demonstrates understanding of Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
• 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, H-R diagram and/or the Stefan-Boltzmann law.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 30676
Exam code: midterm02sLoX
p: 37 students
r: 8 students
t: 4 students
v: 3 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 0796), using the "box method" to fill in relative Stefan-Boltzmann law parameters:
A sample "p" response (from student 5713), using the diagonal lines on an H-R diagram to compare size:
A sample "p" response (from student 8041):