Expert: James Gort - 4/16/2007

Question
Hi James,

How are you? Very well I hope!
I have a problem that I really need a little hint on if you don't mind... the
question is:
Suppose a neutron star radiates like a blackbody at the Eddington limit. What
will its temperature be? Explain why you have chosen the mass of the neutron
star used in your calculations.

I know the Eddington Limit = 3.3 x 10^4(M/M.)L.
M = object mass
M. = Solar Mass
L. = Solar Luminosity

and that wien's law will give a temperature:
W = 2.898 x 10-3 / T
W = wavelength (m)
T = temperature (K)

but I'm confused about how the eddington limit actually works and how to
convert from one to the other.

Thanks

Answer
Hi Loz,

Looks like a good problem!  OK, I'll give some hints:

I'm not sure why you mention Wien's Law.  Please DO NOT just look for a formula that will give you a factor you want (such as T).  Instead, look at all the factors - what is the equation telling you?  With Wien's Law, it's telling you the wavelength where radiation intensity is a maximum.  How does this enter into your problem?  I don't think it does.  Look at the Stefan-Boltzmann equation instead.  That has Luminosity, T, and R.  We don't know R, but that has a special relationship to M for neutron stars!

So to solve your problem, you only need to select a value for M and R.  But they're not independent (for neutron stars).  For M, I'd choose the Chandrasekhar Limit.  Explain why that's a good choice.  Then, R is decided for you.  Plug in those values, and you'll get T(effective).

Hope that helps!

Prof. James Gort