Question

A quasar has a brightness that corresponds to apparent magnitude 14.6 (Unit 55.4). a. If it is 1.29 billion pc away, how many times brighter than the Sun is it? The quasar is × 1011 times brighter than the Sun. b. How does this compare to the brightness of the Milky Way? Assume that the Milky Way contains about 1011 stars. The quasar is times brighter than the Milky Way.

Answer 1

Absolute magnitude is related to apparent magnitude by the relation:

M = m - 5log(d/10)

where d is in pc.

=> M = 14.6 - 5log(10⁹/10) = - 25.4

Absolute magnitude of Sun = M' = 4.83

Use the relation: M - M' = - 2.5log(B/B')

=> B/B' = 10^{-(-25.4 - 4.83)/2.5}

=> B/B' = 12.359 x 10¹¹

this is how much brighter the quasar is as compared to the Sun.

Absolute magnitude of the Milky way is M'' = - 21.

=> B/B'' = 10^{-(-25.4 + 21)/2.5} = 57.544

this is how much brighter the quasar is as compared to the Milky Way.