<p>Here is another plot of a Hertzsprung Russell diagram (luminosity versus temperature), but this time based on theoretical models. (The plot is from D. Prialnik 2000, An Introduction to the theory of stellar structure and evolution). Note that the zero age main sequence <em>is</em> well behaved in this plot. Luminosity and temperature are related by smoothly changing power laws that are largely due to the varying temperature dependence of energy generation and modes of energy transport within stars of different mass.</p>

<p><a href="https://i.sstatic.net/wvqeW.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/wvqeW.png" alt="A Hertzsprung Russell diagram"></a></p>

<p>Your diagram is actually an absolute magnitude versus colour diagram. This is not the same thing. The transformation between absolute magnitude and luminosity and especially between colour and temperature are distinctly non-linear and dependent on what particular spectral features happen to be present in the photometric bands that are used to construct the plot. For example, there is a knee for cool M-dwarfs because the B-V colour "saturates" at a value of about 1.6 because there is hardly any flux in the B and V bands and their ratio doesn't change very much with temperature because of the characteristics of the opacity sources in the atmospheres of these stars at those wavelengths.</p>

<p>To demonstrate that the plot is not necessarily "wiggly", the plot below shows the colour-magnitude for the Hyades and Praesepe clusters (basically at the ZAMS) in the Gaia filter system (from <a href="https://arxiv.org/abs/1804.09378" rel="nofollow noreferrer">Babusiaux et al. 2018</a>). Nice and smooth - though it doesn't cover as big a luminosity range as the Hipparcos plot in your question; the main wiggle at B-V~0.3 is still in the Gaia data (off the top of the plot), but the M-dwarf "knee" is smoothed out by the redder filter response.</p>

<p><a href="https://i.sstatic.net/iOCH9.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/iOCH9.png" alt="enter image description here"></a></p>

CC BY-SA 4.0
2019-05-18T18:15:56.423Z
But is the empirical data for ZAMS that neat? That the Hz diagram is a bit messy due to mixed ages and nonlinear colour scaling, fine, but there is plenty of temperature dependent opacity, convection and other nonlinearities that could make the ZAMS curve messy too.
Anders Sandberg
CC BY-SA 4.0
2019-05-18T20:26:06.810Z
@AndersSandberg There are (almost) no "empirical" measurements of luminosity and Teff, they are derived from observational quantities and it is plots of these observational quantities that show the wiggles. The effects you talk about are included in modern evolutionary models. Choice of filters is important. I've included a ZAMS CMD which doesn't have the knee in the M-dwarfs because it doesn't use B-V.
ProfRob
CC BY-SA 4.0
2019-05-18T20:39:17.920Z
That is a compelling plot. I am now entirely convinced.
Anders Sandberg
CC BY-SA 4.0
2019-05-16T21:22:48.597Z
2019-05-18T20:27:17.987Z
2019-05-18T20:27:17.987Z
ProfRob
<p>When I look at a <a href="https://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram" rel="noreferrer">Hertzsprung-Russell diagram</a>, I'm able to see a main-sequence line from the most luminous main-sequence stars at the top left to the dimmest main-sequence stars at the bottom right. However, this line isn't straight - it's quite squiggly. Why is the line squiggly, and not defined by a polynomial or rational function?</p>

<p><a href="https://i.sstatic.net/JlYXq.png" rel="noreferrer"><img src="https://i.sstatic.net/JlYXq.png" alt="The Hertzsprung-Russell diagram, courtesy of Wikipedia. Shows the main-sequence line as &quot;V: Main Sequence&quot;."></a></p>

CC BY-SA 4.0
2019-05-16T20:38:15.790Z
Can you say where the diagram is from and what data it uses/plots. Luminosity and temperature cannot be measured directly. So is the graph actually of absolute (visual?) magnitude vs B-V?
ProfRob
CC BY-SA 4.0
2019-05-16T20:43:34.530Z
The image description on Wikipedia Commons states that the image uses 23,000 stars from both the Hipparcos catalogue (HIP) and the Gliese catalogue (GJ). Specifically, 22,000 are from Hipparcos and 1,000 are from Gliese.
Cloudy7
CC BY-SA 4.0
2019-05-16T21:06:37.453Z
Ok so its actually a colour-magnitude diagram and would look different using different bands and colours.
ProfRob
CC BY-SA 4.0
2019-05-17T05:30:10.820Z
FWIW, that image is originally from [The Atlas of the Universe](http://www.atlasoftheuniverse.com/hr.html), and it was created by Richard Powell.
PM 2Ring
<star><main-sequence>
On a Hertzsprung-Russell diagram, why is the main-sequence line squiggly?
Cloudy7
# On a Hertzsprung-Russell diagram, why is the main-sequence line squiggly?

(Asked by: username_0 on 2019-05-16)

When I look at a [Hertzsprung-Russell diagram](https://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram), I'm able to see a main-sequence line from the most luminous main-sequence stars at the top left to the dimmest main-sequence stars at the bottom right. However, this line isn't straight - it's quite squiggly. Why is the line squiggly, and not defined by a polynomial or rational function?

[![The Hertzsprung-Russell diagram, courtesy of Wikipedia. Shows the main-sequence line as ](https://i.sstatic.net/JlYXq.png)](https://i.sstatic.net/JlYXq.png)

**Tags:** star, main-sequence
> **Comments:**
> **username_1**: Can you say where the diagram is from and what data it uses/plots. Luminosity and temperature cannot be measured directly. So is the graph actually of absolute (visual?) magnitude vs B-V?  
> **username_0**: The image description on Wikipedia Commons states that the image uses 23,000 stars from both the Hipparcos catalogue (HIP) and the Gliese catalogue (GJ). Specifically, 22,000 are from Hipparcos and 1,000 are from Gliese.  
> **username_1**: Ok so its actually a colour-magnitude diagram and would look different using different bands and colours.  
> **username_2**: FWIW, that image is originally from [The Atlas of the Universe](http://www.atlasoftheuniverse.com/hr.html), and it was created by Richard Powell.  

---

## 1 answers

### Answer by username_1 on 2019-05-16. Score: 7 | Accepted answer

Here is another plot of a Hertzsprung Russell diagram (luminosity versus temperature), but this time based on theoretical models. (The plot is from D. Prialnik 2000, An Introduction to the theory of stellar structure and evolution). Note that the zero age main sequence *is* well behaved in this plot. Luminosity and temperature are related by smoothly changing power laws that are largely due to the varying temperature dependence of energy generation and modes of energy transport within stars of different mass.

[![A Hertzsprung Russell diagram](https://i.sstatic.net/wvqeW.png)](https://i.sstatic.net/wvqeW.png)

Your diagram is actually an absolute magnitude versus colour diagram. This is not the same thing. The transformation between absolute magnitude and luminosity and especially between colour and temperature are distinctly non-linear and dependent on what particular spectral features happen to be present in the photometric bands that are used to construct the plot. For example, there is a knee for cool M-dwarfs because the B-V colour "saturates" at a value of about 1.6 because there is hardly any flux in the B and V bands and their ratio doesn't change very much with temperature because of the characteristics of the opacity sources in the atmospheres of these stars at those wavelengths.

To demonstrate that the plot is not necessarily "wiggly", the plot below shows the colour-magnitude for the Hyades and Praesepe clusters (basically at the ZAMS) in the Gaia filter system (from [Babusiaux et al. 2018](https://arxiv.org/abs/1804.09378)). Nice and smooth - though it doesn't cover as big a luminosity range as the Hipparcos plot in your question; the main wiggle at B-V~0.3 is still in the Gaia data (off the top of the plot), but the M-dwarf "knee" is smoothed out by the redder filter response.

[![enter image description here](https://i.sstatic.net/iOCH9.png)](https://i.sstatic.net/iOCH9.png)

> **Comments:**
> **username_3**: But is the empirical data for ZAMS that neat? That the Hz diagram is a bit messy due to mixed ages and nonlinear colour scaling, fine, but there is plenty of temperature dependent opacity, convection and other nonlinearities that could make the ZAMS curve messy too.  
> **username_1**: @AndersSandberg There are (almost) no "empirical" measurements of luminosity and Teff, they are derived from observational quantities and it is plots of these observational quantities that show the wiggles. The effects you talk about are included in modern evolutionary models. Choice of filters is important. I've included a ZAMS CMD which doesn't have the knee in the M-dwarfs because it doesn't use B-V.  
> **username_3**: That is a compelling plot. I am now entirely convinced.  

---

