<p>It's 7.7 times the absolute temperature of the Sun and if it is 12 times the radius.</p>
<p>The luminosity will therefore be <span class="math-container">$(7.7)^4\times 12^2 = 515000$</span> times that of the Sun.</p>
<p>Close enough, given you haven't cited a source or uncertainty for the temperature or radius.</p>
<p>Your mistake appears to be multiplying by an additional factor of <span class="math-container">$4\pi$</span> when that factor applies to the Sun too.</p>

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2023-09-19T15:53:46.293Z
2023-09-19T15:53:46.293Z
ProfRob
<p>Wikipedia says the Wolf-Rayet star WR124 is 44,700 degrees, and is 562,000 times brighter than our sun. But the Stefan-Boltzmann Law says luminosity per sq meter is proportional to the temperature <span class="math-container">$T^4$</span>. It's about 8 times hotter than Sol, so the luminosity/sq-m should be 4096 times the Sun's.</p>
<p>And, it has a radius 12x bigger than the Sun, so <span class="math-container">$4\pi R^2$</span> (the surface area) times 4096 (luminosity per sq. meter) - which puts the total luminosity at many millions that of the sun.</p>
<p>So why is it only 562,000 times the sun?</p>
<p>Thanks,
Jack</p>

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2023-09-19T21:49:34.163Z
*Welcome to Stack Exchange!* As ProfRob points out in the answer post, in the future always include a link or citation for the information in your question. "Wikipedia says..." needs to link to the place where it actually states the 44,700 degrees and the 562,000 times brighter than the Sun information. *Thanks!*
uhoh
<cosmology>
Why is WR124 not brighter?
Jack
# Why is WR124 not brighter?

(Asked by: username_0 on 2023-09-19)

Wikipedia says the Wolf-Rayet star WR124 is 44,700 degrees, and is 562,000 times brighter than our sun. But the Stefan-Boltzmann Law says luminosity per sq meter is proportional to the temperature $T^4$. It's about 8 times hotter than Sol, so the luminosity/sq-m should be 4096 times the Sun's.

And, it has a radius 12x bigger than the Sun, so $4\pi R^2$ (the surface area) times 4096 (luminosity per sq. meter) - which puts the total luminosity at many millions that of the sun.

So why is it only 562,000 times the sun?

Thanks,
username_0

**Tags:** cosmology

> **Comments:**
> **username_1**: *Welcome to Stack Exchange!* As username_2 points out in the answer post, in the future always include a link or citation for the information in your question. "Wikipedia says..." needs to link to the place where it actually states the 44,700 degrees and the 562,000 times brighter than the Sun information. *Thanks!*  

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## 1 answers

### Answer by username_2 on 2023-09-19. Score: 20

It's 7.7 times the absolute temperature of the Sun and if it is 12 times the radius.

The luminosity will therefore be $(7.7)^4\times 12^2 = 515000$ times that of the Sun.

Close enough, given you haven't cited a source or uncertainty for the temperature or radius.

Your mistake appears to be multiplying by an additional factor of $4\pi$ when that factor applies to the Sun too.


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