<p>The Hertzsprung-Russell diagram is an <em>observational</em> tool. The axes are things that can be observed, or at least estimated reasonably well, for most stars (well, those with known distance anyway). We cannot in general measure the masses of stars - only those in 
some binary systems.</p>

<p>The schematic that you show, with an arrow indicating that mass increases with increasing luminosity and temperature is valid <em>for stars on the main sequence</em>. It is not generally true. Whereas the arrow showing increasing size to the top right is always correct, since it merely depends on the other two axes as $L \propto R^2 T^4$.</p>

<p>If one were to add a third axis to the HR diagram - and this is not a bad idea at all - then the possible axes I would choose are: </p>

<p>(i) Something representing photospheric chemical composition, probably overall metallicity [M/H]. This has the advantage of being measurable for large numbers of stars, and increasingly so given the very large spectroscopic surveys now taking place on many telescope (SDSS, Gaia-ESO, RAVE, LAMOST etc.) On the other hand, stars with similar masses but different compositions already separate in the luminosity-temperature plane reasonably well, so another possibility might be:</p>

<p>(ii) Surface gravity. You are correct that stars of different mass but similar radius can end up appearing in more or less the same place in the HR diagram. However, they have different surface gravities. This can be measured from detailed analysis of spectra and would provide an interesting third axis.</p>

CC BY-SA 3.0
2015-01-25T15:25:10.710Z
I understand, but I was talking about evolutionary trends. For what it is, the HRD is a reliable graph. I also like the idea of having replacements for the third axis, but mass does the job. An alternative diagram could, therefore, be considered (or perhaps one may end up with an E4 Lie graph acting as a 2D orthogonal projection of a 4D graph).
Graviton
CC BY-SA 3.0
2015-01-25T16:34:59.230Z
@Graviton I reiterate: you cannot measure the mass for 99.99% of stars. So how would you place these stars on an HR diagram with mass as a third axis?
ProfRob
CC BY-SA 3.0
2015-01-25T18:11:12.110Z
I hadn't thought of that. I have no idea about how to implement that in some other way. So I can say that you are right in most respects. It's just that mass is probably the greatest factor in deciding the fate of a star. You can go to my forum here (http://gravitonsforum.freeforums.net/) and find the topic under "Mainstream" if you want to discuss this further; I am interested.
Graviton
CC BY-SA 3.0
2014-12-20T15:03:07.653Z
2014-12-20T15:03:07.653Z
ProfRob
<p>I am not from astro background. but from what I understood about the diagram, why not try the third axis to be time?. hope u he some data for the time-age for stars in the main sequences and the age for few stars in the giants /WD region. try plotting the available star-age as third axes and try to see what data u get for the other star. I think u will get something like a tilted plane with a wavy pattern near the unstable region.</p>

CC BY-SA 3.0
2015-02-17T16:36:59.340Z
Because you cannot *observe* the age of a star. However the suggestion is not without merit for illustrating the theoretical positions of stars.
ProfRob
CC BY-SA 3.0
2015-02-17T09:01:34.627Z
2015-02-17T09:01:34.627Z
kalai
<p>Yours is a very, very interesting work. If you publish it it may happen that 3D diagrams will be used in the future. Please publish it.</p>

<p>But this does not mean that there is a flaw in the H-R diagram. It is correct as it is: it displays Luminosity Vs. Color and is perfect at that. And then it happens that some extra relations appear: stars are not randomly scattered on the HR diagram, but they group in branches, and these branches are related to stages of their life. The position on each branch is related to each star's mass. This is not a general relation holding for all the diagram. Almost the same happens with size, but this is more tightly related to Luminosity, per definition.</p>

CC BY-SA 3.0
2014-06-24T10:00:36.520Z
Ah, I didn't word it right... The HR diagram fits it purpose, but extra purposes have been attributed to it and some of these purposes don't fit it. But thanks; I appreciate it. (I can't upvote this right now; I wish I could but I don't have enough reputation).
Graviton
CC BY-SA 3.0
2014-06-24T12:39:36.343Z
Oh yeah, almost forgot - how should I publish this? I've already been in touch with the Institute of Physics and they know about it - but where else can I go? (BTW I upvoted your answer. :))
Graviton
CC BY-SA 3.0
2014-06-24T14:02:24.390Z
You need to write an article about the 3D diagram, its advantages, some use cases, fancy images, and send it to some academic magazine.
Envite
CC BY-SA 3.0
2014-06-24T14:55:46.023Z
BTW don't be confused - I have changed my name. Will try to submit my work to New Scientist!
Graviton
CC BY-SA 3.0
2014-06-25T01:58:58.817Z
@DeathHammer000, you should ask to some professional scientists for help: publishing serious stuff is not an easy work at all, that any "profane" can do :) I suggest you to get in connection to some universities or research institutes, and ask them.
Py-ser
CC BY-SA 3.0
2014-06-24T07:46:32.667Z
2014-06-24T07:46:32.667Z
Envite
<p>When I was younger, I was looking at HR diagrams, and began to experiment with the HR diagram. </p>

<p>I was looking at plotting different groups of stars on the HR diagram when I found RV Tauri stars.</p>

<p>These are stars between 0.4 and 9 solar masses; they have reached the end of their "life" and the fusion shell of such a swollen star is advancing towards its surface (when it hits, the planetary nebula starts to form), thus its heats up and swells further. This phase occurs after the Asymptotic Giant Branch/Red Clump phases (AGB for high-metallicity stars, RC for low-metallicity stars).</p>

<p>Taking into account the above information, RV Tauri stars are BOTH more luminous and hotter at the surface than red giants (and AGB/RC stars), they should appear to the upper-left of the latter of the aforementioned groups (given the inversion of the temperature axis). All seemed well.</p>

<p>But then I saw this:</p>

<p><img src="https://i.sstatic.net/AsJVE.jpg" alt="Additional correlations"></p>

<p>My knowledge of astrophysics tells me that due to stellar winds and the equation E=MC^2, a star's mass (after "birth") will usually decrease over time (unless receiving matter from another star). But if RV Tauri stars are above and to the left of red giants, it means that according to the graph, an increase in mass occurs every time a star migrates to the RV Tauri stage.</p>

<p>I know that all graphs have their limitations, but in my mind it was wrong to claim that these correlations were set in stone. Only axes could ever display data in a perfect way (they treat different units of data as separate simple measures, not "more unstable" compound measures). So I added a third axis of mass (as this is whole problem is to do with plotting the evolutionary "tracks" of stars); this is what is known to affect stellar evolution to the greatest extent. Here is what I came up with:</p>

<p><img src="https://i.sstatic.net/GSrH1.png" alt="3DHRD"></p>

<p>I did this in order to show that the HR diagram shows general trends of stars (not the evolutionary ones that scientists claim).</p>

<p><strong>My question:</strong></p>

<p>Was this a valid flaw with the HR diagram - and if so, is mass the best axis to add to it?</p>

<p>--EDIT--</p>

<p>The HR diagram is not flawed, I respect that. I also know that there will always be outliers. But the extra correlation of mass seems to be too flawed for that (as detailed above). My new question: is the attribution of these extra correlations wrong?</p>

CC BY-SA 3.0
2014-06-24T03:24:39.877Z
It is my impression that the luminosity-mass relation only holds for main sequence stars.
Py-ser
CC BY-SA 3.0
2014-06-24T06:12:45.000Z
You are totally right @Py-ser , that's actually the definition for Main Sequence Star.
Joan.bdm
CC BY-SA 3.0
2014-06-24T07:12:19.217Z
But then if it is only true of the main sequence, then what about other stars like red giants, supergiants and the aforementioned RV Tauri stars?
Graviton
CC BY-SA 3.0
2014-06-24T07:52:14.953Z
A star being in a Giant phase doesn't mean it is more massive than other stars, it only makes reference to it's **Radius and Surface Temp**. That is why Red Giants, Supergiants and Tauri stars are not in the MS. HR diagram makes no reference to Mass unless for MS. http://astro.unl.edu/naap/hr/animations/hrExplorer.html
Joan.bdm
CC BY-SA 3.0
2014-06-24T10:01:01.640Z
Edited post for below reason.
Graviton
CC BY-SA 3.0
2014-06-24T10:10:47.973Z
I don't understand your edit, could you please reword it ? As a general tip, in Astronomy and Physics in general, ALWAYS consider that what is used is CORRECT, and what we can't see is because of *our lack of knowledge*. This is generally speaking, of course, but it is really really really hard to find "wrong" things in physics, especially in so much used tools, like the HR diagram.
Py-ser
CC BY-SA 3.0
2014-06-24T14:48:31.527Z
What I mean is that the HR diagram - and indeed, any heavily revised work - fits its ORIGINAL purpose. But additional purposes were added. These new purposes were not compatible, but this does not mean that the original diagram is not vaild.
Graviton
<star><mass><hr-diagram>
Is there a flaw with the newer purposes and correlations attributed to the HR diagram? (And would a third axis of mass correct the enclosed flaw?)
Graviton
# Is there a flaw with the newer purposes and correlations attributed to the HR diagram? (And would a third axis of mass correct the enclosed flaw?)

(Asked by: username_0 on 2014-06-23)

When I was younger, I was looking at HR diagrams, and began to experiment with the HR diagram.

I was looking at plotting different groups of stars on the HR diagram when I found RV Tauri stars.

These are stars between 0.4 and 9 solar masses; they have reached the end of their "life" and the fusion shell of such a swollen star is advancing towards its surface (when it hits, the planetary nebula starts to form), thus its heats up and swells further. This phase occurs after the Asymptotic Giant Branch/Red Clump phases (AGB for high-metallicity stars, RC for low-metallicity stars).

Taking into account the above information, RV Tauri stars are BOTH more luminous and hotter at the surface than red giants (and AGB/RC stars), they should appear to the upper-left of the latter of the aforementioned groups (given the inversion of the temperature axis). All seemed well.

But then I saw this:

![Additional correlations](https://i.sstatic.net/AsJVE.jpg)

My knowledge of astrophysics tells me that due to stellar winds and the equation E=MC^2, a star's mass (after "birth") will usually decrease over time (unless receiving matter from another star). But if RV Tauri stars are above and to the left of red giants, it means that according to the graph, an increase in mass occurs every time a star migrates to the RV Tauri stage.

I know that all graphs have their limitations, but in my mind it was wrong to claim that these correlations were set in stone. Only axes could ever display data in a perfect way (they treat different units of data as separate simple measures, not "more unstable" compound measures). So I added a third axis of mass (as this is whole problem is to do with plotting the evolutionary "tracks" of stars); this is what is known to affect stellar evolution to the greatest extent. Here is what I came up with:

![3DHRD](https://i.sstatic.net/GSrH1.png)

I did this in order to show that the HR diagram shows general trends of stars (not the evolutionary ones that scientists claim).

**My question:**

Was this a valid flaw with the HR diagram - and if so, is mass the best axis to add to it?

--EDIT--

The HR diagram is not flawed, I respect that. I also know that there will always be outliers. But the extra correlation of mass seems to be too flawed for that (as detailed above). My new question: is the attribution of these extra correlations wrong?

**Tags:** star, mass, hr-diagram
> **Comments:**
> **username_1**: It is my impression that the luminosity-mass relation only holds for main sequence stars.  
> **username_2**: You are totally right @Py-ser , that's actually the definition for Main Sequence Star.  
> **username_0**: But then if it is only true of the main sequence, then what about other stars like red giants, supergiants and the aforementioned RV Tauri stars?  
> **username_2**: A star being in a Giant phase doesn't mean it is more massive than other stars, it only makes reference to it's **Radius and Surface Temp**. That is why Red Giants, Supergiants and Tauri stars are not in the MS. HR diagram makes no reference to Mass unless for MS. http://astro.unl.edu/naap/hr/animations/hrExplorer.html  
> **username_0**: Edited post for below reason.  
> **username_1**: I don't understand your edit, could you please reword it ? As a general tip, in Astronomy and Physics in general, ALWAYS consider that what is used is CORRECT, and what we can't see is because of *our lack of knowledge*. This is generally speaking, of course, but it is really really really hard to find "wrong" things in physics, especially in so much used tools, like the HR diagram.  
> **username_0**: What I mean is that the HR diagram - and indeed, any heavily revised work - fits its ORIGINAL purpose. But additional purposes were added. These new purposes were not compatible, but this does not mean that the original diagram is not vaild.  

---

## 3 answers

### Answer by username_5 on 2014-06-24. Score: 6 | Accepted answer

Yours is a very, very interesting work. If you publish it it may happen that 3D diagrams will be used in the future. Please publish it.

But this does not mean that there is a flaw in the H-R diagram. It is correct as it is: it displays Luminosity Vs. Color and is perfect at that. And then it happens that some extra relations appear: stars are not randomly scattered on the HR diagram, but they group in branches, and these branches are related to stages of their life. The position on each branch is related to each star's mass. This is not a general relation holding for all the diagram. Almost the same happens with size, but this is more tightly related to Luminosity, per definition.

> **Comments:**
> **username_0**: Ah, I didn't word it right... The HR diagram fits it purpose, but extra purposes have been attributed to it and some of these purposes don't fit it. But thanks; I appreciate it. (I can't upvote this right now; I wish I could but I don't have enough reputation).  
> **username_0**: Oh yeah, almost forgot - how should I publish this? I've already been in touch with the Institute of Physics and they know about it - but where else can I go? (BTW I upvoted your answer. :))  
> **username_5**: You need to write an article about the 3D diagram, its advantages, some use cases, fancy images, and send it to some academic magazine.  
> **username_0**: BTW don't be confused - I have changed my name. Will try to submit my work to New Scientist!  
> **username_1**: @DeathHammer000, you should ask to some professional scientists for help: publishing serious stuff is not an easy work at all, that any "profane" can do :) I suggest you to get in connection to some universities or research institutes, and ask them.  

---

### Answer by username_3 on 2014-12-20. Score: 4

The Hertzsprung-Russell diagram is an *observational* tool. The axes are things that can be observed, or at least estimated reasonably well, for most stars (well, those with known distance anyway). We cannot in general measure the masses of stars - only those in
some binary systems.

The schematic that you show, with an arrow indicating that mass increases with increasing luminosity and temperature is valid *for stars on the main sequence*. It is not generally true. Whereas the arrow showing increasing size to the top right is always correct, since it merely depends on the other two axes as $L \propto R^2 T^4$.

If one were to add a third axis to the HR diagram - and this is not a bad idea at all - then the possible axes I would choose are:

(i) Something representing photospheric chemical composition, probably overall metallicity [M/H]. This has the advantage of being measurable for large numbers of stars, and increasingly so given the very large spectroscopic surveys now taking place on many telescope (SDSS, Gaia-ESO, RAVE, LAMOST etc.) On the other hand, stars with similar masses but different compositions already separate in the luminosity-temperature plane reasonably well, so another possibility might be:

(ii) Surface gravity. You are correct that stars of different mass but similar radius can end up appearing in more or less the same place in the HR diagram. However, they have different surface gravities. This can be measured from detailed analysis of spectra and would provide an interesting third axis.

> **Comments:**
> **username_0**: I understand, but I was talking about evolutionary trends. For what it is, the HRD is a reliable graph. I also like the idea of having replacements for the third axis, but mass does the job. An alternative diagram could, therefore, be considered (or perhaps one may end up with an E4 Lie graph acting as a 2D orthogonal projection of a 4D graph).  
> **username_3**: @Graviton I reiterate: you cannot measure the mass for 99.99% of stars. So how would you place these stars on an HR diagram with mass as a third axis?  
> **username_0**: I hadn't thought of that. I have no idea about how to implement that in some other way. So I can say that you are right in most respects. It's just that mass is probably the greatest factor in deciding the fate of a star. You can go to my forum here (http://gravitonsforum.freeforums.net/) and find the topic under "Mainstream" if you want to discuss this further; I am interested.  

---

### Answer by username_4 on 2015-02-17. Score: 0

I am not from astro background. but from what I understood about the diagram, why not try the third axis to be time?. hope u he some data for the time-age for stars in the main sequences and the age for few stars in the giants /WD region. try plotting the available star-age as third axes and try to see what data u get for the other star. I think u will get something like a tilted plane with a wavy pattern near the unstable region.

> **Comments:**
> **username_3**: Because you cannot *observe* the age of a star. However the suggestion is not without merit for illustrating the theoretical positions of stars.  

---

