The Explanation for the Mass-Luminosity Relation

[Ken G]

I'm curious if the readers of this astronomy forum, at this point, have come to understand that the mass-luminosity relation has little to do with the physics of nuclear burning. The reason I ask this is that it is, unfortunately, still common to find textbooks and course websites that say it does rely on fusion physics, despite the clear evidence this is wrong.

The usual story goes, stars with higher mass require hotter cores to support that mass, and that leads to faster fusion, which leads to higher luminosity. Of course this is wrong, because higher mass stars already have higher luminosity even before fusion initiates. It's also clearly wrong because Eddington understood the mass-luminosity relation before he even knew fusion existed.

The real reason has to do with radiative diffusion physics, not fusion physics, and is simple enough to put in an introductory textbook. But I'm just curious if people generally realize this at this point, or if they really have no idea what causes the mass-luminosity relation, or if they are still under the impression that the common textbook explanation involving fusion is correct. I'm trying to see how easy or hard it is to correct misconceptions that have persisted for a long time.

This is kind of an update of a thread from 3 years ago, to see what movement has occurred in that time.

 

[mathman]

You seem to be overlooking the fact that the origin of the energy is the fusion.

 

[Ken G]

I'll take that as being in the camp that doesn't know it's an error to think fusion physics sets the luminosity of a sunlike star. I do appreciate the data point! And you are certainly correct that fusion is the origin of the energy, however you are not correct that I am overlooking that. The simple fact that fusion is the origin in no way argues that fusion physics sets the luminosity. We can think of other examples-- the origin of money is the place that prints it, but the rate money is spent is not set by the rate it is printed, it is set by what is going on in the economy. Similarly, the rate a star emits light is not set by the fusion rate, instead, the fusion rate is set by the rate the star emits light. This is why it is said that stars "self regulate" their fusion rate, rather than exploding like a nuclear bomb.

Just to be clear on this, because I doubt you are the only one who thinks fusion physics sets the luminosity of sunlike stars (it's what the intro textbooks say, but sometimes their arguments are pure nonsense on that score), there are many ways to see that cannot be true. First of all, Eddington understood the mass-luminosity relation of sunlike stars before he even knew fusion existed. Secondly, if you look at the evolutionary track of stars like the Sun, you see the mass-luminosity relation is set long before fusion even initiates, and it continues to hold for a little while after core fusion turns off! So it is evident that we must not look to fusion physics for the mass-luminosity relation, that's going to be wrong. (The correct explanation deals with radiative diffusion, so the way you could change the solar luminosity is by changing its internal opacity, not by changing the fusion physics.)

So although it is important to defeat the misconceptions about the mass-luminosity relation, I'm mostly interested in finding out how widespread those misconceptions continue to be, and that's why it's very helpful to hear people's current opinions on that score.

 

[stefan r]

...We can think of other examples-- the origin of money is the place that prints it, but the rate money is spent is not set by the rate it is printed, it is set by what is going on in the economy...

If you flood an economy with cash then more cash will be spent. Inflation covers the difference between the economic growth and money supply. Restricting or removing the money supply does restrict economic activity.

 

[Ken G]

Your final statement was more or less my point there, though I agree inflation weakens the analogy. Let me give you a better one. In the winter, if you set your thermostat to a given internal temperature, your furnace is going to be the source of your heat. But your furnace is not going to set the rate your house loses heat to the environment-- that's going to be your insulation. In particular, if you throw open a window, your furnace starts pumping out more heat, and you don't need to know anything about the details of how your furnace works. So that's a case where the physics of the source is not relevant to the rate at which it operates.

But the analogy only proves it's possible, we still need to understand why that happens in stars too. It is often said that fusion self-regulates and acts like a thermostat for the stellar core. Sadly, the very books that state that fact rarely (if ever) follow its ramifications! But the ramifications are straightforward-- core fusion self-regulates to equal the rate that light diffuses out of the star. Ironically, the fact that fusion is very sensitive to temperature is often cited as a reason that fusion should control the luminosity, but exactly the opposite is true: the fact that fusion is so T sensitive means that fusion self-regulates with little change in T, so little change in the light content, so little change in the rate the light leaks out, so little change in the luminosity. This directly implies that higher-mass main-sequence stars have slightly higher core temperatures because they are leaking light more rapidly, not the other way around as is invariably claimed. Here we have the evidence the common claim is wrong (along with several even worse elements of the common argument, such as that a higher mass star requires a higher core temperature to balance its gravity-- that's just complete nonsense that is all-too-often quoted).

But although these theoretical considerations are insightful, the real reason that we know fusion physics is not a central aspect of the mass-luminosity relation comes from the observational agreement that the theories produce, so let's look at what is known from observations: the mass-luminosity relation is already established prior to the onset of fusion, and continues to hold for some time after core fusion has ended. Also, the observed mass-luminosity relation was well understood by Eddington, without any knowledge of fusion whatsoever. So these facts make it very clear that no good explanation of the mass-luminosity relation should hinge on fusion physics, it should hinge on what the light is doing (the Wiki on that topic gives such a good explanation), not what the fusion is doing. It's how open the windows are in winter, not the physics of the heater.

 

[Dale]

@Ken G please provide professional scientific references that make this claim

 

[Ken G]

Graduate level textbooks like Kippenhahn and Wiegert generally try to do better than a basic explanation, so they will include more details, but in an introductory explanation, we should stick to the basics. They are provided well in http://www.mikepeel.net/physics/mphys/pc3692/8. Mass, Radius and Luminosity Relations.pdf leading up to equation (190). It is clearly a simplified argument (it uses only free electron opacity, best for massive stars) but shows the point quite nicely. The very fact that it comes after 189 other equations demonstrates that it is intended at an advanced level, but this particular argument is really quite simple. Please note that fusion is never mentioned. The physics is hydrostatic equilibrium and radiative energy diffusion. No doubt including fusion physics produces a more accurate answer, as would more accurate opacities. But we seek a simple answer, and it should not claim the pressure in high mass stars is high, as a very basic requirement of stellar structure is that more massive stars don't contract as much, and don't reach as high pressures, to reach the main sequence. Also, the fact that fusion self-regulates is also quite well understood, but not its immediate corollaries. The history of the mass-luminosity relation is that it was understood before it was known what physics is responsible for the energy, which is a lot like understanding how the insulation of a house affects the rate it loses heat-- without knowing how its furnace works.

 

[Dale]

They are provided well in http://www.mikepeel.net/physics/mphys/pc3692/8. Mass, Radius and Luminosity Relations.pdf

This is an exceptionally weak reference for supporting your argument. None of the formulas are explained, few of the variables are even identified, and most importantly none of your specific claims are echoed. At least it doesn’t explicitly contradict you, but it also certainly doesn’t explicitly claim that the common textbook explanation involving fusion is incorrect as you do.

In other fields, when undergraduate textbooks are wrong or even merely poorly written, there is a plethora of clear discussion in the literature. See the many discourses on relativistic mass for example. If such is not the case here then it is an indication that the scientific community does not consider those common explanations to be wrong.

 

[Ken G]

It's hard for me to know what you would prefer, when the equations of physics don't satisfy in comparison to quotes from non-science major introductory astronomy textbooks. But I could just site some random research papers that calculate pre-main-sequence evolution, so people can see where the mass-luminosity relation actually comes from. Try http://articles.adsabs.harvard.edu/..._paper=YES&type=PRINTER&filetype=.pdf, where you can peruse figure 1. Notice that fusion is absent over most of those tracks, and the luminosity generally varies by less than 50% over a period where the surface temperature varies by about a factor of 2. I trust I'm allowed to mention the Stefan-Boltzmann law without a reference, which makes it clear that when luminosity rises by 50% as the surface temperature rises by a factor of about 2, the radius is falling by about a factor of 3. Given that, it should not be surprising that the core temperature is also rising considerably. No fusion is occurring, yet the luminosity is already set by the mass to a good approximation. This is the mass-luminosity relation. Then when fusion does begin, the luminosity drops a little, certainly too little to care about in an elementary explanation of the mass-luminosity relation. Basic logic then requires us to recognize that fusion physics does not determine the mass-luminosity relation, unless you are a believer in incredible coincidences. Basic logic then also requires us to recognize that the elementary textbooks are quite wrong, even without mentioning the ones that claim the pressure is higher in high mass stars.

 

[Ken G]

So far it looks like I have one person who came into the thread thinking fusion physics is essential to the mass-luminosity relation, and another who did not come in with understanding of the relation but has a duty to enforce the ways sources are used. Do we have others who understand the mass-luminosity relation, and do they think fusion physics is important or not? It's interesting to track how these misconceptions propagate, and this is a pretty important one because it relates to the lifetime of stars and is the centerpiece of stellar evolution.

 

[Dale]

Try http://articles.adsabs.harvard.edu/..._paper=YES&type=PRINTER&filetype=.pdf, where you can peruse figure 1.

Excellent! From now on, whenever this topic arises, please simply cite this source. There is no need for all of the histrionics.

This thread is closed. A poll of the opinions of the membership is not necessary. The claim is covered in the literature. That is sufficient