<p>It shows that the mass of the (proto)star is the major factor determining bolometric magnitude. </p>

<p>The brightness of the proto-star increases a little as it contracts and becomes significantly hotter (and the radius decreases), The star moves toward the left of the diagram. As fusion in the core becomes significant the star reaches the maximum point on the curve, this stabilises the core and the star settles into the main sequence, it cools slightly and becomes slightly less bright. </p>

CC BY-SA 3.0
2018-04-12T09:55:59.250Z
What determines the luminosity of the star prior to fusion onset?  And since fusion onset does not change the luminosity significantly, should we say that what is determining the luminosity has not changed when fusion begins?
Ken G
CC BY-SA 3.0
2018-04-12T14:38:51.687Z
Luminosity is determined by temperature and size. As a star is forming it is getting smaller and hotter. These two processes balance each other. Fusion stops the star from collapsing further.
James K
CC BY-SA 3.0
2018-04-12T15:03:11.057Z
So you are saying the onset of fusion does not set the luminosity of the star in a first-brush understanding, it only stops further contraction.  I agree.   I'm glad there is at least one other person on here who understands this!
Ken G
CC BY-SA 3.0
2018-04-12T08:02:39.610Z
2018-04-12T08:02:39.610Z
James K
<p>By definition, the luminosity of a <strong>pre-main sequence</strong> (PMS) star cannot possibly depend on fusion physics, since energetically-speaking, there is no significant fusion occurring!</p>
<p>However, the term pre-main sequence refers to hydrogen (protium) burning. if you had plotted some lower mass tracks from sources a bit more modern than 1955 (the tracks you show are out of date and incorrect, not including the Hayashi phase for example), you would see that there is predicted to be a brief plateau in luminosity (for stars/brown dwarfs less than about 0.3 solar masses) caused by deuterium burning. This has yet to be observationally tested. Thus for such stars, fusion physics does have a role to play in determining their luminosities at young ages.</p>
<p>Ignoring that complication, the luminosity of a convective PMS star (which is how they all begin) is determined by its mass and age.
To a very close approximation <span class="math-container">$L\propto t^{-2/3}$</span>, with the constant of proportionality being mass dependent. Higher mass stars are more luminous at the same age, but with <em>a shallower luminosity-mass relationship than on the main sequence</em>.</p>
<p>If the star remains convective, then to first order, stars follow vertical Hayashi tracks, almost independent of their mass. The luminosity is given by the rate of change of gravitational potential energy, which is in turn limited by how fast convection can transfer heat to the surface. The Hayashi track terminates when the star becomes radiative (for higher masses) or when nuclear fusion starts (at lower masses), or never (for brown dwarfs). Thus whilst stars are in the convective phase, their luminosity is dependent on mass and age.</p>
<p><em>If</em> the star becomes largely radiative (say larger than about 0.6 solar masses - so the minority of stars), the luminosity becomes roughly independent of age (very roughly, see diagram below) - that luminosity is fixed by the rate at which radiative diffusion can leak the gravitational potential energy of the contracting star. The star follows the radiative horizontal (actually more diagonal for stars lower than about 4 solar masses) Henyey track in the HR diagram.</p>
<p>A set of more modern tracks is shown below. They are from the Wikipedia page on the Hayashi track, but I believe the tracks are by Palla &amp; Stahler.</p>
<p><a href="https://i.sstatic.net/IEbF4.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/IEbF4.png" alt="PMS tracks." /></a></p>

CC BY-SA 3.0
2018-04-12T22:18:48.430Z
I agree, the pre-main-sequence mass-luminosity relation cannot depend on fusion physics for just the reason you said.  You might find it interesting, therefore, to cogitate on the fact that it is *essentially the same* as the main-sequence mass-luminosity relation.  What do you conclude from that?  Your other comments are false, the paper is from 1995 and intentionally does not use the Hayashi track because it is interested in radiative diffusion physics, not convection physics.  (The paper is by Henyey, originator of the "Henyey track" concept that the paper focuses on.)
Ken G
CC BY-SA 3.0
2018-04-12T22:21:22.467Z
Check your sources on the deuterium burning, I think you are wrong there.  But above all, notice when the mass-luminosity relation first starts to hold.  Really, really notice that.
Ken G
CC BY-SA 3.0
2018-04-12T22:25:40.223Z
Yes the paper is from 1955,I misspoke, but the tracks are not so different today-- Henyey simply started them after the Hayashi track.  Another thing to notice from the plots you kindly supplied is where the mass-luminosity relation does not hold-- on the lower main sequence where the plateau, where the mass-luminosity relation starts to hold for all the higher masses, does not appear.  You should see that's because the radiative diffusion physics that the mass-luminosity relation relies on has not set in for those low masses.
Ken G
CC BY-SA 3.0
2018-04-12T22:29:51.173Z
It's explained in https://astro.uni-bonn.de/~nlanger/siu_web/ssescript/new/chapter8.pdf.  Notice Langer does not invoke fusion physics in the explanation of the mass-luminosity relation.  I'm not allowed to tell you what you should conclude from that, but I think it's already obvious.
Ken G
CC BY-SA 3.0
2018-04-12T22:55:16.203Z
Figure 8.4 from the paper I just cited does not find any kind of plateau when deuterium burning begins, so that's why I think you should check your sources on that.   It's the dashed curves in Figure 8.5 to which I referred when I pointed out those curves contain zero fusion physics.  Anyway, it should be very clear the role of radiative diffusion in the mass-luminosity relation, but I'll leave you to draw your own conclusions.
Ken G
CC BY-SA 3.0
2018-04-12T23:18:28.473Z
@KenG Hardly surprising that a *1955* paper (got around to checking your own sources yet?) on radiative stars had nothing to say about D burning. The brief plateau shows up in low mass stars. Pictures and references in https://astronomy.stackexchange.com/questions/22355/turn-on-point-for-fusion
ProfRob
CC BY-SA 3.0
2018-04-13T02:01:10.703Z
I'm talking about the Langer reference I gave.  It shows D burning.  No plateau in the stars we're talking about (those that obey the simple mass-luminosity relation).  But it's not the issue anyway, the issue is, do you agree that the mass-luminosity relation applies (it's an approximate law) to pre-main-sequence stars, or don't you?
Ken G
CC BY-SA 3.0
2018-04-13T07:11:15.923Z
Langer specifically says (p.110) that D burning causes a plateau in the luminosity for a few hundred thousand years (sounds about right for a solar mass. It's longer in lower mass stars).
ProfRob
CC BY-SA 3.0
2018-04-13T10:09:30.877Z
You are talking about L vs time, not L vs. mass.  This is about L vs. mass.  Obviously a new heat source will pause the contraction.  D burning happens on the Hayashi track, well before there is a mass-luminosity relation.  It's not relevant.
Ken G
CC BY-SA 3.0
2018-04-13T10:15:45.137Z
What is relevant is the question that you have not addressed: what do you conclude from the fact that most of the figure you kindly posted shows stars achieving the mass-luminosity relation prior to undergoing fusion?
Ken G
CC BY-SA 4.0
2018-04-12T22:09:50.853Z
2024-08-16T10:35:58.973Z
2024-08-16T10:35:58.973Z
ProfRob
<p>Check out Figure 1 in <a href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1955PASP...67..154H&amp;data_type=PDF_HIGH&amp;whole_paper=YES&amp;type=PRINTER&amp;filetype=.pdf" rel="nofollow noreferrer">http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1955PASP...67..154H&amp;data_type=PDF_HIGH&amp;whole_paper=YES&amp;type=PRINTER&amp;filetype=.pdf</a> .</p>

<p><a href="https://i.sstatic.net/wg48U.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/wg48U.png" alt="enter image description here"></a></p>

<p>It seems to show that the luminosity of a pre-main-sequence star depends primarily on the mass of the star, and that this basic relation continues to hold, to reasonable accuracy, into the main sequence.  Since there is no fusion in a pre-main-sequence star, is it correct to conclude that the relationship between the mass and luminosity of a pre-main-sequence star does not hinge on fusion physics?</p>

CC BY-SA 3.0
2018-04-12T09:14:32.227Z
Deuterium and Lithium can be burned in PMS stars, but the luminosity is still mainly determined by Kelvin-Helmholtz contraction.
AtmosphericPrisonEscape
CC BY-SA 3.0
2018-04-12T09:54:22.603Z
I agree the source of the energy must be gravitational contraction, but what do you mean that the luminosity is "determined by" contraction?  Being the source of is not the same thing as determining.  For example, one might rather say that the rate of contraction is determined by the luminosty.
Ken G
CC BY-SA 3.0
2018-04-12T09:56:38.060Z
(By the way, thanks to StephenG for including the figure so nicely.)
Ken G
CC BY-SA 3.0
2018-04-12T09:56:43.983Z
"mainly determined" means "is the main source of". Are you worried about semantics or physics here?
AtmosphericPrisonEscape
CC BY-SA 3.0
2018-04-12T09:59:47.263Z
I care not about semantics, there is a great deal of physical content in the concept of "determination."   Thus, "mainly determined by" is not necessarily the same things as "is the main source of."  I'll give you an example: your furnace is the main source of heat leaking out of a cracked window in winter.  Does your furnace determine the rate that heat leaks out through a cracked window?  The isssue is not semantic, it speaks to why you insulate your house, not change your furnace, when your heating bill is high.
Ken G
CC BY-SA 3.0
2018-04-12T10:59:04.400Z
You're making a good point, but you will find that KH-contraction is a framework that corresponds to "house+furnace" instead of only "furnace". The KH-timescale is often simply determined by dividing energy content over energy loss. The energy loss is then in turn also modeled through 'house walls'.
AtmosphericPrisonEscape
CC BY-SA 3.0
2018-04-12T13:46:48.290Z
OK, so now we are in agreement.  KH contraction is occuring, gravity is the source of the energy that is appearing in the luminosity, but it does not follow from those facts that contraction is determining the luminosity, as I could equally (and more correctly) argue that the luminosity is determining the contraction rate.  For example, I could look at the structure of the star in a snapshot, derive its luminosity, and then derive the contraction rate.  The contraction rate would introduce a time parameter I did not need for the rest of the calculation.
Ken G
CC BY-SA 3.0
2018-04-12T23:21:38.720Z
The last sentence of this "question" is an absurd truism.
ProfRob
CC BY-SA 4.0
2024-08-16T12:26:56.187Z
The question would make more sense if it asked whether the luminosiity of a main sequence star depends on fusion physics.
ProfRob
<star><luminosity>
What does this figure imply about the luminosity of pre-main-sequence stars?
Ken G
# What does this figure imply about the luminosity of pre-main-sequence stars?

(Asked by: username_0 on 2018-04-12)

Check out Figure 1 in <http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1955PASP...67..154H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf> .

[![enter image description here](https://i.sstatic.net/wg48U.png)](https://i.sstatic.net/wg48U.png)

It seems to show that the luminosity of a pre-main-sequence star depends primarily on the mass of the star, and that this basic relation continues to hold, to reasonable accuracy, into the main sequence. Since there is no fusion in a pre-main-sequence star, is it correct to conclude that the relationship between the mass and luminosity of a pre-main-sequence star does not hinge on fusion physics?

**Tags:** star, luminosity
> **Comments:**
> **username_1**: Deuterium and Lithium can be burned in PMS stars, but the luminosity is still mainly determined by Kelvin-Helmholtz contraction.  
> **username_0**: I agree the source of the energy must be gravitational contraction, but what do you mean that the luminosity is "determined by" contraction?  Being the source of is not the same thing as determining.  For example, one might rather say that the rate of contraction is determined by the luminosty.  
> **username_0**: (By the way, thanks to StephenG for including the figure so nicely.)  
> **username_1**: "mainly determined" means "is the main source of". Are you worried about semantics or physics here?  
> **username_0**: I care not about semantics, there is a great deal of physical content in the concept of "determination."   Thus, "mainly determined by" is not necessarily the same things as "is the main source of."  I'll give you an example: your furnace is the main source of heat leaking out of a cracked window in winter.  Does your furnace determine the rate that heat leaks out through a cracked window?  The isssue is not semantic, it speaks to why you insulate your house, not change your furnace, when your heating bill is high.  
> **username_1**: You're making a good point, but you will find that KH-contraction is a framework that corresponds to "house+furnace" instead of only "furnace". The KH-timescale is often simply determined by dividing energy content over energy loss. The energy loss is then in turn also modeled through 'house walls'.  
> **username_0**: OK, so now we are in agreement.  KH contraction is occuring, gravity is the source of the energy that is appearing in the luminosity, but it does not follow from those facts that contraction is determining the luminosity, as I could equally (and more correctly) argue that the luminosity is determining the contraction rate.  For example, I could look at the structure of the star in a snapshot, derive its luminosity, and then derive the contraction rate.  The contraction rate would introduce a time parameter I did not need for the rest of the calculation.  
> **username_2**: The last sentence of this "question" is an absurd truism.  
> **username_2**: The question would make more sense if it asked whether the luminosiity of a main sequence star depends on fusion physics.  

---

## 2 answers

### Answer by username_3 on 2018-04-12. Score: 1

It shows that the mass of the (proto)star is the major factor determining bolometric magnitude.

The brightness of the proto-star increases a little as it contracts and becomes significantly hotter (and the radius decreases), The star moves toward the left of the diagram. As fusion in the core becomes significant the star reaches the maximum point on the curve, this stabilises the core and the star settles into the main sequence, it cools slightly and becomes slightly less bright.

> **Comments:**
> **username_0**: What determines the luminosity of the star prior to fusion onset?  And since fusion onset does not change the luminosity significantly, should we say that what is determining the luminosity has not changed when fusion begins?  
> **username_3**: Luminosity is determined by temperature and size. As a star is forming it is getting smaller and hotter. These two processes balance each other. Fusion stops the star from collapsing further.  
> **username_0**: So you are saying the onset of fusion does not set the luminosity of the star in a first-brush understanding, it only stops further contraction.  I agree.   I'm glad there is at least one other person on here who understands this!  

---

### Answer by username_2 on 2018-04-12. Score: 1

By definition, the luminosity of a **pre-main sequence** (PMS) star cannot possibly depend on fusion physics, since energetically-speaking, there is no significant fusion occurring!

However, the term pre-main sequence refers to hydrogen (protium) burning. if you had plotted some lower mass tracks from sources a bit more modern than 1955 (the tracks you show are out of date and incorrect, not including the Hayashi phase for example), you would see that there is predicted to be a brief plateau in luminosity (for stars/brown dwarfs less than about 0.3 solar masses) caused by deuterium burning. This has yet to be observationally tested. Thus for such stars, fusion physics does have a role to play in determining their luminosities at young ages.

Ignoring that complication, the luminosity of a convective PMS star (which is how they all begin) is determined by its mass and age.
To a very close approximation $L\propto t^{-2/3}$, with the constant of proportionality being mass dependent. Higher mass stars are more luminous at the same age, but with *a shallower luminosity-mass relationship than on the main sequence*.

If the star remains convective, then to first order, stars follow vertical Hayashi tracks, almost independent of their mass. The luminosity is given by the rate of change of gravitational potential energy, which is in turn limited by how fast convection can transfer heat to the surface. The Hayashi track terminates when the star becomes radiative (for higher masses) or when nuclear fusion starts (at lower masses), or never (for brown dwarfs). Thus whilst stars are in the convective phase, their luminosity is dependent on mass and age.

*If* the star becomes largely radiative (say larger than about 0.6 solar masses - so the minority of stars), the luminosity becomes roughly independent of age (very roughly, see diagram below) - that luminosity is fixed by the rate at which radiative diffusion can leak the gravitational potential energy of the contracting star. The star follows the radiative horizontal (actually more diagonal for stars lower than about 4 solar masses) Henyey track in the HR diagram.

A set of more modern tracks is shown below. They are from the Wikipedia page on the Hayashi track, but I believe the tracks are by Palla & Stahler.

[![PMS tracks.](https://i.sstatic.net/IEbF4.png)](https://i.sstatic.net/IEbF4.png)

> **Comments:**
> **username_0**: I agree, the pre-main-sequence mass-luminosity relation cannot depend on fusion physics for just the reason you said.  You might find it interesting, therefore, to cogitate on the fact that it is *essentially the same* as the main-sequence mass-luminosity relation.  What do you conclude from that?  Your other comments are false, the paper is from 1995 and intentionally does not use the Hayashi track because it is interested in radiative diffusion physics, not convection physics.  (The paper is by Henyey, originator of the "Henyey track" concept that the paper focuses on.)  
> **username_0**: Check your sources on the deuterium burning, I think you are wrong there.  But above all, notice when the mass-luminosity relation first starts to hold.  Really, really notice that.  
> **username_0**: Yes the paper is from 1955,I misspoke, but the tracks are not so different today-- Henyey simply started them after the Hayashi track.  Another thing to notice from the plots you kindly supplied is where the mass-luminosity relation does not hold-- on the lower main sequence where the plateau, where the mass-luminosity relation starts to hold for all the higher masses, does not appear.  You should see that's because the radiative diffusion physics that the mass-luminosity relation relies on has not set in for those low masses.  
> **username_0**: It's explained in https://astro.uni-bonn.de/~nlanger/siu_web/ssescript/new/chapter8.pdf.  Notice Langer does not invoke fusion physics in the explanation of the mass-luminosity relation.  I'm not allowed to tell you what you should conclude from that, but I think it's already obvious.  
> **username_0**: Figure 8.4 from the paper I just cited does not find any kind of plateau when deuterium burning begins, so that's why I think you should check your sources on that.   It's the dashed curves in Figure 8.5 to which I referred when I pointed out those curves contain zero fusion physics.  Anyway, it should be very clear the role of radiative diffusion in the mass-luminosity relation, but I'll leave you to draw your own conclusions.  
> **username_2**: @KenG Hardly surprising that a *1955* paper (got around to checking your own sources yet?) on radiative stars had nothing to say about D burning. The brief plateau shows up in low mass stars. Pictures and references in https://astronomy.stackexchange.com/questions/22355/turn-on-point-for-fusion  
> **username_0**: I'm talking about the Langer reference I gave.  It shows D burning.  No plateau in the stars we're talking about (those that obey the simple mass-luminosity relation).  But it's not the issue anyway, the issue is, do you agree that the mass-luminosity relation applies (it's an approximate law) to pre-main-sequence stars, or don't you?  
> **username_2**: Langer specifically says (p.110) that D burning causes a plateau in the luminosity for a few hundred thousand years (sounds about right for a solar mass. It's longer in lower mass stars).  
> **username_0**: You are talking about L vs time, not L vs. mass.  This is about L vs. mass.  Obviously a new heat source will pause the contraction.  D burning happens on the Hayashi track, well before there is a mass-luminosity relation.  It's not relevant.  
> **username_0**: What is relevant is the question that you have not addressed: what do you conclude from the fact that most of the figure you kindly posted shows stars achieving the mass-luminosity relation prior to undergoing fusion?  

---

