Energy production of star given mass?

[Lagraaaange]

How would one get the energy production in a star if only given the mass of the star? Something involving mc^2 I suppose?

 

[Orodruin]

There is no direct formula which you can use. The luminosity of a star depends on the rates of its thermonuclear processes, which do depend on the mass of the star. This becomes evident when plotting the temperature vs luminosity of known stars in a Hertzsprung-Russell diagram.

 

[SteamKing]

How would one get the energy production in a star if only given the mass of the star? Something involving mc^2 I suppose?

Stars aren't that simple. Brown dwarfs are different from yellow dwarfs are different from blue giants are different from red supergiants.

As stars age, their internal energy producing mechanisms change as different elements are formed internally by the fusion process. Some of this is well understood, some is not so well understood. That's why things like the H-R diagram were developed. Modelling of the internal dynamics of stellar interiors is one area of active research in stellar astrophysics.

This article describes the different forms of energy production in stars:

https://en.wikipedia.org/wiki/Stellar_nucleosynthesis

Some stars support certain types of fusion reactions based on their initial mass. You pretty much have to know the details of these reactions, coupled with knowledge of the evolution of the individual star to estimate how much energy comes out. Knowledge of a star's mass alone is insufficient for this purpose.

 

[Bandersnatch]

There is no direct formula which you can use.

He could use the mass-luminosity equations?

 

[SteamKing]

He could use the mass-luminosity equations?

Those relations are approximations which apply only to stars on the Main Sequence. They do not cover a variety of other stars falling off the MS.

There are some special mass-luminosity relations for certain stars like white dwarves, but there is no one formula which can be used.

 

[Lagraaaange]

My professor said one can use E=mc^2

 

[SteamKing]

My professor said one can use E=mc^2

You can, but only if you know m, which is the amount of mass being converted to energy by the star at a given instant.

For example, m for the sun is approximately 4.26 million metric tons per second (1 metric ton = 1000 kg) at the present time, but this figure has apparently been lower in the distant past as the sun is thought to have brightened considerably since it was first formed.

BTW, M for the sun is approximately 1.99 × 10³⁰ kg.

https://en.wikipedia.org/wiki/Sun

The relationship between this mass m and the total mass M of a given star is not a direct one.

The density of power production (276.5 watts / m³ ) in the sun's core is surprisingly quite low. It more closely resembles the metabolism of a reptile than an H-bomb detonation.

 

[HomogenousCow]

My professor said one can use E=mc^2

Energy radiated is entirely different from rest mass, don't just blindly use formulas.

 

[Lagraaaange]

So how would one prepare for an exam question like this?

 

[SteamKing]

So how would one prepare for an exam question like this?

Beats me. If your professor knows something of which apparently no other astrophysicist is aware, he should publish a paper.

 

[mfb]

What exactly is the question you got asked? "Estimate the energy release of a star with mass X" is not a proper exam question.
"Calculate the energy released by a star that loses x tons/s of mass due to fusion" is a valid question, but completely different from the one you asked in post 1.

 

[Helios]

Stars with the same mass can have different luminosities. So a function L(m) will fail on this account. Mass-luminosity relationships were certainly investigated a century ago when fusion was not yet understood to be the power source of stars.

 

[Dale]

Several off topic posts have been removed.