Is the Mass-Luminosity Relationship for Main-Sequence Stars Linear?

[Agasthiyaraj L]

when we draw a mass-time graph of a star in x-axis as time and y-axis as mass whether it will be linear or not?

 

[Bandersnatch]

No it wouldn't and it isn't. More massive stars burn their fuel much, much faster than the less massive ones. It's a power function.
The most massive, brightest stars(0-class stars; ~200 solar masses) have lifetimes in the vicinity of millions of years, while the least massive brown dwarfs(0.1 solar masses) can slowly burn for trillions of years before running out of fuel.

Have a look at this page for more information:
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/startime.html

If you google "mass lifetime relation for stars" you'll get plenty more pages with good overview of the subject.

 

[Ken G]

And if you want to know why the luminosity scales as such a high power of the mass, there's actually a pretty simple approximate explanation. A star is essentially a big leaky bucket of light-- it contains a lot of light because it is very hot in its interior, and it's very hot in its interior because gravity makes it that way. This means it obeys the "virial theorem", which allows you to estimate the average temperature, and you find it is proportional to M/R. If the star is a main-sequence star, then its average temperature has to be something like 10 million K, as that is roughly the temperature where hydrogen fusion occurs. So if you know M, you know R.

Now that you know how hot it is and how big it is, given M, you know its light energy content (the Stefan-Boltzmann law simply connects temperature to radiation), so you then only need to know how long it takes for that bucket of light to empty, i.e., the timescale for the light to escape. That requires some diffusion physics of light bouncing around inside the density of the star, but a fairly straightforward estimate indicates that the escape time is pretty similar for all main-sequence stars (this glosses over some details like there can be convection, etc., but of course we cannot obtain a simple understanding by including everything).

So we now have that the T and the M/R are roughly the same, and the diffusion time is roughly the same, so the luminosity must depend mostly on the volume of the star (the size of the bucket). That all gives you a high power of dependence of L on M, something like the power 3 (and of course more detailed analyses are needed to yield 3.5, which it itself only a global approximation to much more varying dependences).

Incidentally, I only mentioned nuclear fusion once, when I said it requires the average T be something like 10 million K. Indeed that is pretty much all you need to know about fusion to understand the luminosities of main-sequence stars, until you want to get into finer details. If it has not been stressed, please note this whole thread is about main-sequence stars, they are the ones that obey a mass-luminosity relation, and that is the long-lived stage of a star's life, before it reaches its end stage.

 

[TumblingDice]

If it has not been stressed, please note this whole thread is about main-sequence stars...

This "whole thread" consists of a straight-forward question and a helpful answer, followed by your truckload of extraneous information. Did a mentor remove more messages from this thread?

Edit: Could all of this be useful to the OP question? Forgive me if I got lost - it wasn't for lack of trying.

 

[Ken G]

Well, personally I think if someone asks what the mass-luminosity relationship is for main-sequence stars, they might also want to know why it is that. Maybe that's just me.