Astronomy midterm question: absolute magnitude of "Scholz's star?"

Astronomy 210 Midterm 2, spring semester 2018
Cuesta College, San Luis Obispo, CA

"A Star Disturbed"
José A. Peñas, Servicio de Información y Noticias Científicas

"Scholz's star" (official name WISE J072003.20-084651.2) is a red dwarf that passed very close to our solar system 70,000 years ago[*]. At its closest distance of 0.25 parsecs, if "Scholz's star" had an apparent magnitude of +6 (just barely visible to the naked eye), would its absolute magnitude be a positive number that is smaller or bigger than +6? Explain using the relationships between apparent magnitude, absolute magnitude, and distance.

[*] E.E. Mamajek, S.A. Barenfeld, V.D. Ivanov, A.Y. Kniazev, P. Vaisanen, Y. Beletsky, and H.M.J. Boffin, "The Closest Known Flyby of a Star to the Solar System," Astrophysical Journal Letters, vol. 800 no. 1 (2015), iopscience.iop.org/article/10.1088/2041-8205/800/1/L17/pdf.

Solution and grading rubric:
  • p:
    Correct. Understands difference between apparent magnitude m (brightness as seen from Earth, while at its actual distance from Earth) and absolute magnitude M (brightness as seen from Earth, when placed at the "fair comparison distance" of 10 parsecs away). Discusses how this star with an apparent magnitude value of +6 (measured at 0.25 parsecs) will seem to get dimmer when placed farther away at 10 parsecs, such that its absolute magnitude will be dimmer than its apparent magnitude, and thus a positive number bigger than +6.
  • 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 relationships between apparent magnitudes, absolute magnitudes, and distances.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use relationships between apparent magnitudes, absolute magnitudes, and distances.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Discussion based on garbled definitions of, or not based on proper relationships between apparent magnitudes, absolute magnitudes, and distances.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Section 30674
Exam code: midterm02nVd4
p: 17 students
r: 1 student
t: 1 student
v: 4 students
x: 1 student
y: 0 students
z: 0 students

Section 30676
Exam code: midterm02StWr
p: 30 students
r: 4 students
t: 1 student
v: 7 student
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 1313):

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