<p>There is no simple answer to these questions - although I could be brief and say
(i) No it doesn't and (ii) no they won't.</p>
<p>If you make a simple two component atmosphere then the observed spectrum will be the flux-weighted combination of two spectra.
<span class="math-container">$$ S_{\rm obs} = \frac{A_1 T_1^4 S_1 + A_2 T_2^4 S_2}{A_1 T_1^4 + A_2 T_2^4}\ , $$</span>
where <span class="math-container">$A_1, T_1, S_1$</span> are the area, temperature and spectrum of material at <span class="math-container">$T_1$</span> and the quantities with subscript 2 are for the regions at temperature <span class="math-container">$T_2$</span>.</p>
<p>Now, depending on the response of any spectral feature to a change in temperature this could make the equivalent width of that feature become stronger or weaker in the flux-weighted average spectrum. If you then analyse that spectrum assuming that there is a single temperature then what you derive for an abundance based on that feature could get bigger or smaller.</p>
<p>For example most lines of neutral species (e.g. Fe I, Li I) get stronger in cooler atmospheres. If you put cool starspots on a star then the equivalent widths of these lines will become stronger. The average temperature of the star will decline very slightly. The net effect would be to estimate that the abundance of iron or lithium in that star was larger.</p>
<p>On the other hand if the line was very strong such that it was in the saturated part of the curve of growth, then it wouldn't get much stronger in a cooler atmosphere and it could even be that by adopting a lower average temperature, the lack of a significant increase in line equivalent wdth would lead one to infer a reduced abundance.</p>
<p>A more clear-cut case might be lines of ionised Fe II. These would become weaker in a cooler atmosphere, so you would end up inferring a lower iron abundance from the flux-weighted average spectrum.</p>
<p>Then there is the issue of the over-simplification that a simple two-temperature model imposes. Real granulation also involves the movement of plasma with consequent implications for micro- and macro-turbulence and how those affect the line formation and assumption of local thermodynamic equilibrium. These can only be addressed using expensive 3D stellar atmosphere models. Such models do exist and they offer grids of 3D NLTE corrections to abundances determined using 1D LTE atmospheric analyses. The corrections can go in either direction depending on the strengths of the lines and the intrinsic parameters of the star. As an example, <a href="https://arxiv.org/abs/2010.15248" rel="nofollow noreferrer">Wang et al. (2021)</a> present a grid of corrections for the Li I optical/NIR lines that I have a particular interest in.</p>

CC BY-SA 4.0
2021-05-08T15:18:11.723Z
@uhoh very generous. It was a good question (the ones without easy answers normally are).
ProfRob
CC BY-SA 4.0
2021-05-08T15:23:13.200Z
This is great, thanks for the thorough answer, it's very different than what I expected so I can now learn a lot. Yes the question is really interested, I sometimes wish I could grant "good question!" bounties also.
uhoh
CC BY-SA 4.0
2021-05-08T13:59:33.893Z
2021-05-08T14:14:52.220Z
2021-05-08T14:14:52.220Z
ProfRob
<p>The spectrum from <a href="https://en.wikipedia.org/wiki/Granule_(solar_physics)" rel="nofollow noreferrer">stellar granules</a> will obviously be for hotter gas, while the spectrum from the lanes between them will be for cooler gas.</p>
<ul>
<li>Does this &quot;average out&quot; so that an average temperature distribution can be used for a <a href="https://en.wikipedia.org/wiki/Metallicity#Photometric_colors" rel="nofollow noreferrer">metallicity analysis</a>?</li>
<li>Will the spectroscopic effects be the same for all lines?</li>
</ul>

CC BY-SA 4.0
2021-04-30T00:53:22.247Z
`+1` I've made a small edit is all that's necessary here. The question makes perfect sense; the surface of a star may be seen as a mosaic of two separate spectral sources, while spectral analysis would be made from a combination of both. I don't think any details need to be added here, the question is complete. Nonetheless I've added some links for those unfamiliar with the topics.
uhoh
<star><spectroscopy><stellar-astrophysics><stellar-atmospheres><photosphere>
What effect does stellar granulation to have on a chemical analysis of a star's spectrum?
Jay D
# What effect does stellar granulation to have on a chemical analysis of a star's spectrum?

(Asked by: username_0 on 2021-04-27)

The spectrum from [stellar granules](https://en.wikipedia.org/wiki/Granule_(solar_physics)) will obviously be for hotter gas, while the spectrum from the lanes between them will be for cooler gas.

* Does this "average out" so that an average temperature distribution can be used for a [metallicity analysis](https://en.wikipedia.org/wiki/Metallicity#Photometric_colors)?
* Will the spectroscopic effects be the same for all lines?

**Tags:** star, spectroscopy, stellar-astrophysics, stellar-atmospheres, photosphere

> **Comments:**
> **username_1**: `+1` I've made a small edit is all that's necessary here. The question makes perfect sense; the surface of a star may be seen as a mosaic of two separate spectral sources, while spectral analysis would be made from a combination of both. I don't think any details need to be added here, the question is complete. Nonetheless I've added some links for those unfamiliar with the topics.  

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## 1 answers

### Answer by username_2 on 2021-05-08. Score: 2

There is no simple answer to these questions - although I could be brief and say
(i) No it doesn't and (ii) no they won't.

If you make a simple two component atmosphere then the observed spectrum will be the flux-weighted combination of two spectra.
$$ S\_{\rm obs} = \frac{A\_1 T\_1^4 S\_1 + A\_2 T\_2^4 S\_2}{A\_1 T\_1^4 + A\_2 T\_2^4}\ , $$
where $A\_1, T\_1, S\_1$ are the area, temperature and spectrum of material at $T\_1$ and the quantities with subscript 2 are for the regions at temperature $T\_2$.

Now, depending on the response of any spectral feature to a change in temperature this could make the equivalent width of that feature become stronger or weaker in the flux-weighted average spectrum. If you then analyse that spectrum assuming that there is a single temperature then what you derive for an abundance based on that feature could get bigger or smaller.

For example most lines of neutral species (e.g. Fe I, Li I) get stronger in cooler atmospheres. If you put cool starspots on a star then the equivalent widths of these lines will become stronger. The average temperature of the star will decline very slightly. The net effect would be to estimate that the abundance of iron or lithium in that star was larger.

On the other hand if the line was very strong such that it was in the saturated part of the curve of growth, then it wouldn't get much stronger in a cooler atmosphere and it could even be that by adopting a lower average temperature, the lack of a significant increase in line equivalent wdth would lead one to infer a reduced abundance.

A more clear-cut case might be lines of ionised Fe II. These would become weaker in a cooler atmosphere, so you would end up inferring a lower iron abundance from the flux-weighted average spectrum.

Then there is the issue of the over-simplification that a simple two-temperature model imposes. Real granulation also involves the movement of plasma with consequent implications for micro- and macro-turbulence and how those affect the line formation and assumption of local thermodynamic equilibrium. These can only be addressed using expensive 3D stellar atmosphere models. Such models do exist and they offer grids of 3D NLTE corrections to abundances determined using 1D LTE atmospheric analyses. The corrections can go in either direction depending on the strengths of the lines and the intrinsic parameters of the star. As an example, [Wang et al. (2021)](https://arxiv.org/abs/2010.15248) present a grid of corrections for the Li I optical/NIR lines that I have a particular interest in.

> **Comments:**
> **username_2**: @username_1 very generous. It was a good question (the ones without easy answers normally are).  
> **username_1**: This is great, thanks for the thorough answer, it's very different than what I expected so I can now learn a lot. Yes the question is really interested, I sometimes wish I could grant "good question!" bounties also.  

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