<p>When calculating luminosity/radius/temperature for several stars, I've noticed that while the majority of stars conform to the luminosity relationship <span class="math-container">$L=4\pi R^{2}\sigma T^{4}$</span>, there are a few that don't. Take 8 Ursae Minoris. As far as I can tell it has a luminosity 56 times that of the sun, a radius of 8.5 solar radii and an effective temperature of about 5000 K. When I substitute those numbers in they don't match. The math isn't wrong so I can only assume either the data isn't reliable, or maybe there is a certain class of stars that don't conform to that relation. I don't know enough astronomy to determine which is correct, but I suspect obtaining a reliable luminosity value for some stars could be the problem.</p>

<p>Does anyone know the answer to this riddle? </p>

CC BY-SA 4.0
2019-06-26T23:03:31.913Z
Using the Stefan-Boltzmann law, I get $L\approx64L_{\odot}$, which isn't bad - only about a 15% difference from the measured value. Is that around what you got? Keep in mind that the Stefan-Boltzmann law only holds for black bodies, and while stars are close to black bodies, they aren't perfect black bodies - hence the deviations in various cases.
HDE 226868
CC BY-SA 4.0
2019-06-26T23:09:49.127Z
@HDE226868 oops, I wrote 5600 K for the surface temperature rather than 5000 K, which is what my data says. I only get about $L\approx 40 L_{⊙}$ in that case.
TeeJay
CC BY-SA 4.0
2019-06-27T04:41:05.460Z
Ah, I see. Would you mind listing the sources of those values, just for completeness? Thanks.
HDE 226868
CC BY-SA 4.0
2019-06-27T14:37:34.943Z
Well, there's always the simple "star thermal behavior isn't a pure black-body" but I suspect that only applies to real oddballs like neutron stars.
Carl Witthoft
CC BY-SA 4.0
2019-06-27T14:38:42.470Z
Any chance you're looking at stars which are masked by significant dust clouds which are not pure black-body absorbers?
Carl Witthoft
CC BY-SA 4.0
2020-09-10T07:58:15.043Z
Although not the case for 8 Ursae Minoris, be wary of red giants, and very cool stars because they have very large amounts of absorption in visible near-ir spectrum, making them nowhere near blackbody.
TazAstroSpacial
<star><temperature><luminosity>
Stars that don't fit $L=4\pi R^{2}\sigma T^{4}$?
TeeJay
# Stars that don't fit $L=4\pi R^{2}\sigma T^{4}$?

(Asked by: username_0 on 2019-06-26)

When calculating luminosity/radius/temperature for several stars, I've noticed that while the majority of stars conform to the luminosity relationship $L=4\pi R^{2}\sigma T^{4}$, there are a few that don't. Take 8 Ursae Minoris. As far as I can tell it has a luminosity 56 times that of the sun, a radius of 8.5 solar radii and an effective temperature of about 5000 K. When I substitute those numbers in they don't match. The math isn't wrong so I can only assume either the data isn't reliable, or maybe there is a certain class of stars that don't conform to that relation. I don't know enough astronomy to determine which is correct, but I suspect obtaining a reliable luminosity value for some stars could be the problem.

Does anyone know the answer to this riddle?

**Tags:** star, temperature, luminosity

> **Comments:**
> **username_1**: Using the Stefan-Boltzmann law, I get $L\approx64L_{\odot}$, which isn't bad - only about a 15% difference from the measured value. Is that around what you got? Keep in mind that the Stefan-Boltzmann law only holds for black bodies, and while stars are close to black bodies, they aren't perfect black bodies - hence the deviations in various cases.  
> **username_0**: @HDE226868 oops, I wrote 5600 K for the surface temperature rather than 5000 K, which is what my data says. I only get about $L\approx 40 L_{⊙}$ in that case.  
> **username_1**: Ah, I see. Would you mind listing the sources of those values, just for completeness? Thanks.  
> **username_2**: Well, there's always the simple "star thermal behavior isn't a pure black-body" but I suspect that only applies to real oddballs like neutron stars.  
> **username_2**: Any chance you're looking at stars which are masked by significant dust clouds which are not pure black-body absorbers?  
> **username_3**: Although not the case for 8 Ursae Minoris, be wary of red giants, and very cool stars because they have very large amounts of absorption in visible near-ir spectrum, making them nowhere near blackbody.  

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## 0 answers

