Estimating Milky Way Absolute Magnitude

[tristan3214]

Important: All Logs are base 10 and not the natural log.

Homework Statement

This question is from Foundations of Astrophysics from chapter 19

Suppose the Milky Way consisted of 2.7x10^11 stars, each of solar luminosity M_B=4.7. What would be the absolute magnitude of the whole galaxy?

To clarify that is absolute magnitude in the B band rather than the V band.

Homework Equations

Some equations I have been using:
M=m-5Log(d)+5 Distance Modulus
m₂-m₁=2.5Log(Flux₁/Flux₂) for finding flux
F=L/(4∏d^2) for finding luminosity
n=number density=#of stars/volume of cylinder for the galaxy.
average distance=1/n^1/3, this is for a sphere though so it is very hand wavy
M_bol=M_bol,sun-2.5Log[L/L_sun]

The Attempt at a Solution

So when I first saw this problem I wanted to go from absolute magnitude of one star and find the luminosity. With that I would find the total luminosity of the galaxy by multiplying by the number of stars then find absolute magnitude of the galaxy from there.

The ideal way would be to use bolometric magnitudes to get luminosity comparatively to the sun. However, my biggest problem here is that I have absolute magnitude of the stars in B band making things harder. As well as with going a bolometric route there is a lot of looking up of values that aren't easy to find.

I tried finding apparent magnitude of the star by using the average distance between the stars but when I try to find the flux of one of the stars to find the luminosity I don't have the flux of the sun in the B band.

Overall I come here because I feel like maybe there is an easier way than having to search around for things like the luminosity or flux of the sun in the B band.

 

[dshyles]

They tell you "solar luminosity" in the problem, implying L=3.84e26W. I take the fact that they give you the absolute magnitude in the B-band as unnecessary information. But it's a reinforcement that they're truly talking of "sun-like" stars. Then you can just find bolometric magnitude.