Astronomy clicker question: main sequence lifetimes

Astronomy 10, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal M1.4

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

[0.3 points.] The main sequence lifetime of a star is how long it will be able to release energy from hydrogen fusion in its core. Which type of main sequence star will have the longest lifetime?
(A) A massive main sequence star.
(B) A medium-mass main sequence star.
(C) A low-mass main sequence star.
(D) The lifetime of a main sequence star does not depend on its mass.

Correct answer: (C)

Student responses
Section 4160
(A) : 11 students
(B) : 2 students
(C) : 17 students
(D) : 1 student

Section 5166
(A) : 19 students
(B) : 4 students
(C) : 18 students
(D) : 1 student

Explanations for typical student responses are elicited in a whole-class discussion after results have been posted.

Some students offer that they chose response (A) because the massive stars have more hydrogen to fuse, and thus will last the longest. Other students remark that they chose response (B) because low-mass stars have much slower fusion rates, and thus will be the most frugal and have the longest main sequence lifetime. (If both effects are important, perhaps the medium-mass star would live the longest?)

"Wasteful!" or "Live Fast, Die Young"
Due to their rapid fusion rates, massive stars have the shortest main sequence lifetimes, after the hydrogen in their cores has been depleted in hundreds of thousands to a few million years. They are the "wasteful" stars in the sense that there is still plenty of hydrogen in their outer layers, but this is unavailable to the core of the massive star to maintain its main sequence lifetime.

"Churn and Burn" or "Be Mellow, Live Forever"
However, low mass stars ("red dwarfs") have such slow fusion rates that they are cool and opaque enough for convection to stir up the entire star, such that fresh hydrogen is continuously cycled between the core and the rest of the star. Due to these two effects (slow fusion and a disproportionally larger amount of available hydrogen to fuse), low mass stars have extremely long main sequence lifetimes, measured in tens of billions of years. As the currently accepted age of the universe is 13-14 billion years, no low-mass stars are expected to have ever reached the end of their main sequence lifetimes yet!