## 20101023

### Astronomy quiz question: Procyon B vs. Barnard's Star, Rigel B vs. Arcturus

Astronomy 210 Quiz 4, Fall Semester 2010
Cuesta College, San Luis Obispo, CA

[Version 1]

Procyon B, a white dwarf, has the same luminosity as Barnard's Star, a red dwarf. Procyon B is ___________ compared to Barnard's Star.
(A) smaller and cooler.
(B) smaller and hotter.
(C) larger and cooler.
(D) larger and hotter.

From Wien's law and/or using an H-R diagram, Procyon B (white dwarf) must be hotter than Barnard's Star (red dwarf). In order to have the same luminosity, from the Stefan-Boltzmann law, Procyon B must be smaller in size to compensate for its higher temperature, compared to Barnard's Star, which must be larger in size to compensate for its lower temperature.

Section 70158
(A) : 1 student
(B) : 35 students
(C) : 3 students
(D) : 6 students

"Success level": 79% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.42

[Version 2]

Rigel B, a blue-hot star, has the same luminosity as Arcturus, a yellow-hot star. Rigel B is ___________ compared to Arcturus.
(A) cooler and smaller.
(B) cooler and larger.
(C) hotter and smaller.
(D) hotter and larger.

From Wien's law, Rigel B (blue-hot) must be hotter than Arcturus (yellow-hot). In order to have the same luminosity, from the Stefan-Boltzmann law, Rigel B must be smaller in size to compensate for its higher temperature, compared to Arcturus, which must be larger in size to compensate for its lower temperature.

Section 70160
(A) : 0 students
(B) : 1 student
(C) : 34 students
(D) : 6 students

"Success level": 85% (including partial credit for multiple-choice)
Discrimination index (Aubrecht & Aubrecht, 1983): 0.18