<p>This is an answer that I am writing up based on comments by <a href="https://astronomy.stackexchange.com/users/2531/profrob">ProfRob</a> and <a href="https://astronomy.stackexchange.com/users/616/mike-g">Mike G</a>.</p>
<p>The meaning of 'beta' in these plots is the slope of the line.  The figure itself is from <a href="https://ui.adsabs.harvard.edu/abs/2021MNRAS.507.2643A/abstract" rel="nofollow noreferrer">Radio spectral properties of star-forming galaxies in the MIGHTEE-COSMOS field and their impact on the far-infrared-radio correlation</a> (<a href="https://arxiv.org/abs/2108.02778" rel="nofollow noreferrer">arXiv link</a>).</p>
<p>From the caption of the figure in the above question:</p>
<p>&quot;The linear fit is performed by minimizing the <span class="math-container">$\chi^{2}$</span> and using the uncertainties of <span class="math-container">$\alpha^{3.0GHz}_{1.3GHz}$</span> as the inverse weights. The slopes of these linear fits, <span class="math-container">$\beta$</span>, are given on the right-bottom corner of each panel.&quot;</p>

CC BY-SA 4.0
2022-01-02T17:18:54.463Z
Which for me, raises another question: what's the point of performing a linear fit, when there's no clear correlation between the x and y variables? What am I missing?
Jim421616
CC BY-SA 4.0
2022-01-02T13:48:11.887Z
2022-01-02T13:48:11.887Z
GrapefruitIsAwesome
<p><img src="https://i.sstatic.net/emMXL.jpg" alt="X-Y plot from article" /></p>
<blockquote>
<p>Correlation between the mass of the galaxies (X-axis) and the difference of their radio emissions at different radio frequencies (Y-axis). Each symbol represents an individual galaxy. The image of an example galaxy is from NASA/ESA Hubble Space Telescope T means the time for light to travel from these galaxies to us.</p>
<p>Credit: Fangxia An (IDIA/UWC)</p>
</blockquote>
<p>From <a href="https://phys.org/news/2021-08-analysis-galaxies-meerkat-radio-telescope.html" rel="nofollow noreferrer">Phys.org</a>
and <a href="https://theconversation.com/analysis-of-2-000-galaxies-using-the-meerkat-radio-telescope-reveals-fresh-insights-166353" rel="nofollow noreferrer">The Conversation</a>,</p>
<blockquote>
<p>Using the Meerkat Telescope on over 2,000 radio galaxies...</p>
</blockquote>

CC BY-SA 4.0
2021-08-29T06:45:52.450Z
It would help if you posted the actual url to the webpage in question.
Rob
CC BY-SA 4.0
2021-08-29T07:56:20.320Z
Surely it's the slope of the line?
ProfRob
CC BY-SA 4.0
2021-08-29T13:09:53.827Z
In the article, "our new study" links to [this MNRAS paper](https://ui.adsabs.harvard.edu/abs/2021MNRAS.tmp.2057A/abstract).
Mike G
CC BY-SA 4.0
2021-08-29T13:47:15.600Z
The abstract of that paper confirms @ProfRob’s suggestion — it’s the slope of the relation.
Peter Erwin
<observational-astronomy><astrophysics><cosmology><radio-astronomy>
What does lowercase 'beta' mean in this graph of radio-emitting galaxies?
Kurt Hikes
# What does lowercase 'beta' mean in this graph of radio-emitting galaxies?

(Asked by: username_0 on 2021-08-29)

![X-Y plot from article](https://i.sstatic.net/emMXL.jpg)

> Correlation between the mass of the galaxies (X-axis) and the difference of their radio emissions at different radio frequencies (Y-axis). Each symbol represents an individual galaxy. The image of an example galaxy is from NASA/ESA Hubble Space Telescope T means the time for light to travel from these galaxies to us.
>
> Credit: Fangxia An (IDIA/UWC)

From [Phys.org](https://phys.org/news/2021-08-analysis-galaxies-meerkat-radio-telescope.html)
and [The Conversation](https://theconversation.com/analysis-of-2-000-galaxies-using-the-meerkat-radio-telescope-reveals-fresh-insights-166353),

> Using the Meerkat Telescope on over 2,000 radio galaxies...

**Tags:** observational-astronomy, astrophysics, cosmology, radio-astronomy
> **Comments:**
> **username_1**: It would help if you posted the actual url to the webpage in question.  
> **username_2**: Surely it's the slope of the line?  
> **username_3**: In the article, "our new study" links to [this MNRAS paper](https://ui.adsabs.harvard.edu/abs/2021MNRAS.tmp.2057A/abstract).  
> **username_4**: The abstract of that paper confirms @ProfRob’s suggestion — it’s the slope of the relation.  

---

## 1 answers

### Answer by username_5 on 2022-01-02. Score: 3

This is an answer that I am writing up based on comments by [ProfRob](https://astronomy.stackexchange.com/users/2531/profrob) and [Mike G](https://astronomy.stackexchange.com/users/616/mike-g).

The meaning of 'beta' in these plots is the slope of the line. The figure itself is from [Radio spectral properties of star-forming galaxies in the MIGHTEE-COSMOS field and their impact on the far-infrared-radio correlation](https://ui.adsabs.harvard.edu/abs/2021MNRAS.507.2643A/abstract) ([arXiv link](https://arxiv.org/abs/2108.02778)).

From the caption of the figure in the above question:

"The linear fit is performed by minimizing the $\chi^{2}$ and using the uncertainties of $\alpha^{3.0GHz}\_{1.3GHz}$ as the inverse weights. The slopes of these linear fits, $\beta$, are given on the right-bottom corner of each panel."

> **Comments:**
> **username_6**: Which for me, raises another question: what's the point of performing a linear fit, when there's no clear correlation between the x and y variables? What am I missing?  

---

