Astronomy clicker question: why are white dwarfs small?

Astronomy 10, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q8.5

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the beginning of their learning cycle:

[0.3 points.] Why is a white dwarf star smaller than a main-sequence star that has the same white-hot color?
(A) It is less luminous than the main-sequence star.
(B) It is more luminous than the main-sequence star.
(C) It is cooler than the main-sequence star.
(D) It is hotter than the main-sequence star.

Correct answer: (A).

The fact that both stars have the same white-hot color tells you that they must have the same temperature (Wien's law). From the Stefan-Boltzmann law, luminosity is proportional to size and temperature^4, thus with both stars having the same temperature, the less luminous star is the smaller star.

Student responses
Section 4136
(A) : 9 students
(B) : 4 students
(C) : 7 students
(D) : 11 students

Section 5076
(A) : 2 students
(B) : 1 student
(C) : 10 students
(D) : 3 students