20160114

Astronomy final exam question: comparing metallicities of same-age white dwarf and red dwarf

Astronomy 210 Final Exam, fall semester 2015
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:
??: A white dwarf and a red dwarf are the same age. Which star would contain more metals inside (elements heavier than hydrogen and helium)?
DM: The white dwarf would be considered highly metallic, whereas the red dwarf would have a low metallicity.
Discuss why this answer is correct, and how you know this. Explain using the properties and evolution of stars.

[*] answers.yahoo.com/question/index?qid=20151128104746AAmtupC.

Solution and grading rubric:
  • p:
    Correct. Understands that stars of the same age were born at the same time from the same dust and gas cloud, such that they start with the same metallicity. The white dwarf is the core remnant of a medium-mass star, where all the hydrogen has already been converted to helium, and subsequently to carbon and oxygen "metals." However, a red dwarf only fuses hydrogen to helium, and does not produce more metals.
  • 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. Typically claims that the white dwarf evolved faster and was born more recently than the red dwarf, thus has inherited more metals from the previous generation of stars; while the red dwarf evolves slower and was born earlier than the white dwarf, in a metal-poor, hydrogen-rich universe (despite being told that these two stars are the same age, and thus were born at the same time).
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Garbled discussion of properties and evolution of stars.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Discussion other than that of the properties and evolution of stars.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Section 70158
Exam code: finalS157
p: 6 students
r: 5 students
t: 15 students
v: 6 students
x: 3 students
y: 1 student
z: 2 students

Section 70160
Exam code: finalN157
p: 3 students
r: 2 students
t: 6 students
v: 6 students
x: 5 students
y: 1 student
z: 2 students

A sample "p" response (from student 4338):

A sample "t" response (from student 1795), not recognizing that the white dwarf (end-stage of a more rapidly evolving medium-mass star) and the red dwarf (slowly evolving low-mass star) are stated to be the same age:

A sample "x" response (from student 2306), associating metal production with high temperatures and bright luminosities:

Another sample "x" response (from student 6392), discussing how stars deplete their metals as they get older:

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