Astronomy final exam question: seeing Betelgeuse explode already?

Astronomy 210 Final Exam, spring semester 2016
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked:

I've heard the star Betelgeuse is a supergiant [640 light years away], and could explode as a type II supernova any moment now. If that were true, wouldn't we have seen it already?

Discuss whether or not it is possible for us to have seen Betelgeuse explode if it is a supergiant right now. Explain using the properties of mass and stellar lifetimes, and light.

[*] answers.yahoo.com/question/index?qid=20160504225623AAy0q47.

Solution and grading rubric:

• p:
  Correct. Discusses how it is not possible to have already seen Betelgeuse explode as a type II supernova if it is a supergiant right now, due to the finite speed of light (where it takes one year of time to travel a distance of one light-year), it will take 640 years for the light from Betelgeuse to travel to Earth, and applies this to one of the following arguments:
  1. if Betelgeuse were still a supergiant, it would take 640 years after it undergoes a type II supernova for this light to travel to Earth, and this explosion would only be visible 640 years from that moment; or
  2. if this explosion were visible now, it had to have happened 640 years in the past, and Betelgeuse would not still be a supergiant; or
  3. if Betelgeuse had already undergone a type II supernova less than 640 years ago, it would not be a supergiant right now, but we would not have yet seen this explosion.
• 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.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Garbled discussion of mass, stellar lifetimes, and light.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on mass, stellar lifetimes, and light.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 30674
Exam code: finalNKPd
p: 8 students
r: 3 students
t: 0 students
v: 1 student
x: 2 students
y: 0 students
z: 0 students

Section 30676
Exam code: finalSre6
p: 18 students
r: 6 students
t: 0 students
v: 2 students
x: 9 students
y: 6 students
z: 1 student

A sample "p" response (from student 1503):
Another sample "p" response (from student 0716):