Stellar evolution path and Regression line

[hongseok]

TL;DR Summary

I analyzed the relationship between the surface temperature and luminosity of stars of similar mass using a regression model. Through this, I was able to obtain a regression line. Since stars of similar mass show similar evolutionary paths, I believe this regression line can be viewed as a rough evolutionary path for stars of a certain mass. Is this right?

I analyzed the relationship between the surface temperature and luminosity of stars of similar mass using a regression model. Through this, I was able to obtain a regression line. Since stars of similar mass show similar evolutionary paths, I believe this regression line can be viewed as a rough evolutionary path for stars of a certain mass. Is this right?

 

[davenn]

hi

are you not aware of the hertzsprung-russell diagram ?

 

[Vanadium 50]

I believe this regression line can be viewed as a rough evolutionary path for stars of a certain mass. Is this right?

Luminosity should go as r²rT⁴ so I don't understand what this line you fit is.

Both r and T change over the lifetime of a star, but it is not as simple as going up or down a line.

 

[hongseok]

Luminosity should go as r²rT⁴ so I don't understand what this line you fit is.

Both r and T change over the lifetime of a star, but it is not as simple as going up or down a line.

In the case of stars with a mass of 0.43 to 2 times that of the Sun, the relationship is known to be (luminosity/luminosity of the Sun) = (mass/mass of the Sun)^4. Through this, the mass of the star was obtained.
I plotted stars of similar mass on Hertzsprung–Russell diagram, and confirmed the tendency of the distribution. It was similar to the stellar evolution path in my textbook.
Is this a coincidence? I really don't know.

 

[Vanadium 50]

I don't think you are plotting what you think you are plotting, This is L vs. T:

Do you see things on a line? I sure don't. I see a complicated curve. Further, such stars spend most of their lives at the bottom of this curve.

 

[Nik_2213]

And then you have the complex results of binary / tertiary interactions, including eg 'Blue Stragglers'...

 

[hongseok]

I don't think you are plotting what you think you are plotting, This is L vs. T:
View attachment 338654

Do you see things on a line? I sure don't. I see a complicated curve. Further, such stars spend most of their lives at the bottom of this curve.

The post-AGB phase is short-lived, and the mass changes after the supernova explosion. Therefore, doesn't the scatter plot mainly consist of the process from main sequence stars to supergiants, and can appear in a form close to a straight line?

 

[hongseok]

And then you have the complex results of binary / tertiary interactions, including eg 'Blue Stragglers'...

Yes.. thank you

 

[Vanadium 50]

Every curve, when looking at a small enough restricted region, can be approximated by a straight line. This is not a new discovery; it's the basis of calculus.

 

[Ken G]

In the case of stars with a mass of 0.43 to 2 times that of the Sun, the relationship is known to be (luminosity/luminosity of the Sun) = (mass/mass of the Sun)^4. Through this, the mass of the star was obtained.

It sounds to me like you are just talking about "main sequence stars", the core hydrogen burning phase that most stars are in. If you restrict to most stars, therefore, you get a simpler relation than the evolutionary paths of stars as they reach the late phases of their lives, and it looks a lot like your expression. But that is how L depends on m for main sequence stars of different m, and since stars don't really change their m on the main sequence, that's not at all an "evolutionary" path, it is just the difference between stars of different mass that are not evolving much at all.

I plotted stars of similar mass on Hertzsprung–Russell diagram, and confirmed the tendency of the distribution. It was similar to the stellar evolution path in my textbook.

Here I think you are imagining that stars "evolve along the main sequence line", which is a common misconception. The line of the main sequence in an HR diagram is not an evolutionary path, and the "sequence" is not a time sequence, it is a mass sequence. You are seeing how L depends on m for stars of different m, that does not relate to the evolution of those stars.

Is this a coincidence? I really don't know.

No, it's not a coincidence, it has to do with the fact that radiation diffuses out from the interiors of stars in a way that depends mostly on their mass. Hence, stars that are mostly transporting energy by radiative diffusion (which includes most stars before, during, and slightly after the main sequence phase) have a close connection between their mass and luminosity, called the "mass luminosity relation." You have rediscovered this relation, which is very important for most stars, it is indeed a useful way of estimating the mass of a star based on its luminosity, but the star cannot be in a late stage of evolution.

 

[hongseok]

It sounds to me like you are just talking about "main sequence stars", the core hydrogen burning phase that most stars are in. If you restrict to most stars, therefore, you get a simpler relation than the evolutionary paths of stars as they reach the late phases of their lives, and it looks a lot like your expression. But that is how L depends on m for main sequence stars of different m, and since stars don't really change their m on the main sequence, that's not at all an "evolutionary" path, it is just the difference between stars of different mass that are not evolving much at all.

I'm not claiming that mass changes. Rather, it was taken advantage of. Because the mass of a star does not change, it was thought that when stars of the same mass were plotted on the H-R diagram, it would correspond to their evolutionary path.

Here I think you are imagining that stars "evolve along the main sequence line", which is a common misconception. The line of the main sequence in an HR diagram is not an evolutionary path, and the "sequence" is not a time sequence, it is a mass sequence. You are seeing how L depends on m for stars of different m, that does not relate to the evolution of those stars.

No. I had no such Imagination. I think you misunderstood what I said.

I admit that my initial claim was somewhat wrong, but I am replying because I think there is some misunderstanding in your reply.

 

[Ken G]

Do you still have any unresolved questions?

 

[hongseok]

Do you still have any unresolved questions?

no. Most of it has been resolved. thank you