Soft x ray source, find radius, suggest object

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Homework Help Overview

The discussion revolves around estimating the radius of a soft x-ray source based on its observed luminosity and spectral characteristics, specifically using black body radiation principles. The original poster presents two methods for calculation, leading to significantly different radius estimates.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use the Stefan-Boltzmann law and Wien's law to estimate the radius, questioning the validity of the results from both methods. Participants discuss the accuracy of the second method and its relevance to the context of neutron stars.

Discussion Status

Participants are engaging in a productive discussion about the methods used for calculation, with some suggesting that the second method is more accurate. There is acknowledgment of the lecture notes hinting towards the first method, which raises questions about the appropriateness of the methods covered in the course.

Contextual Notes

There is mention of the course content, indicating that Wien's law has not been covered in the current course, although it has been addressed in previous ones. This context may influence the participants' understanding and application of the methods discussed.

ghosts_cloak
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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
 
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ghosts_cloak said:
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.
 
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
 
ghosts_cloak said:
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).