Soft x ray source, find radius, suggest object

[ghosts_cloak]

Hi guys!
Question:
A soft x ray source has an observed luminosity of 10^30W. The spectral shape indicates black body radiation with a peak in the emmision at 4KeV. Estimate the radius of the object. Suggest what source this might be.

So, using L=sigma*A*T^4 and the peak energy is approx kT and taking surface area to be 4*Pi*r^2 I get a radius of 550 metres, hmm low!

I then tried using Weins law and get a radius of 13.5 Km, which would be reasonable for a neutron star?

Any suggestions for the 550m radius, and which method is correct?

Thanks,

~Gaz

 

[SpaceTiger]

Any suggestions for the 550m radius, and which method is correct?

The second method will be more accurate and yes, 13.5 km is a reasonable size for a neutron star. For comparison, a solar mass black hole has a Schwarzschild radius of ~3 km.

 

[ghosts_cloak]

Hi :-)
Thanks for the reply. Yup, I thought the second method gave a better result!
I wouldn't normally have bothered about posting it on here but the lecture notes kind of hint towards the first method, and we haven't covered Weins law in this course (although we have in previous courses).
Cheers,
~Gaz

 

[SpaceTiger]

I wouldn't normally have bothered about posting it on here but the lecture notes kind of hint towards the first method, and we haven't covered Weins law in this course (although we have in previous courses).

If it's a perfect blackbody, the peak is given exactly by Wein's Law. The other method is usually just for order of magnitude calculations (that is, to get an equivalent temperature from an energy, just divide by Boltzmann's constant).