Is There Mathematical Proof That Stars Are Still Being Formed?

[Max.Planck]

Hello,

I have a question from the Dutch Astrophysics Olympiad, which I can't solve.

" Is there mathematical proof that stars are still being formed? "

In previous questions, i had to derive the following equations, which i need to use in my answer for the question above:

L = σ * T⁴ * 4πR²

(Luminosity-Temperature relation of a star, where σ is the Boltzmann constant, T is temperature and R is the radius of the star)

t = life time of sun * (M/Msun)^-2,6

(where t equals the life time of a type V star and M equals mass)

Can anyone help me with this?

Thanks,

Max.Planck

 

[Matterwave]

Observational evidence? yes. Mathematical proof? don't think so...

I don't see how you can get a mathematical proof for star formation...

Perhaps they are asking you to show that the life-time of some stars is less than that of the age of the universe and therefore if there was no star formation after the BB, we wouldn't see any of those stars...? This still relies on observation (of the massive stars), and it doesn't preclude the possibility that star formation has stopped this instant (rather than billions of years in the past).

I honestly can't think of any proof that would both not rely on observational evidence, and preclude the possibility of star formation stopping this instant.

Maybe I'm missing something here haha...

 

[silentbob14]

Yeah it's a very interesting question ;] And a hard one indeed. It will be interesting to find out the answer.

 

[amarante]

Hello,

I have a question from the Dutch Astrophysics Olympiad, which I can't solve.

" Is there mathematical proof that stars are still being formed? "

In previous questions, i had to derive the following equations, which i need to use in my answer for the question above:

L = σ * T⁴ * 4πR²

(Luminosity-Temperature relation of a star, where σ is the Boltzmann constant, T is temperature and R is the radius of the star)

t = life time of sun * (M/Msun)^-2,6

(where t equals the life time of a type V star and M equals mass)

Can anyone help me with this?

Thanks,

Max.Planck

lets think about it...
Luminosity is the amount of energy released by time...
and that life time you found I suppose is the time that the star spend in the Main Sequence, right? so actually if you find some stars, that you measure its luminosity and with this you would calculate that it would actually spend some Myears in the MS, so it means that they are younger than the Sun and actually stars are being created. So maybe, yes you can proove it mathematically, but I don't have here a paper and a pencil to write down things, but I think it is possible, with this 2 relations

 

[sardar]

Dear Max.Planck,

Thank you for your question. The answer to whether stars are still being formed can be found in the equations you have provided. The first equation, L = σ * T4 * 4πR2, relates the luminosity of a star to its temperature and radius. This equation is derived from the Stefan-Boltzmann law, which states that the total energy radiated by a blackbody is proportional to the fourth power of its temperature. This means that as a star's temperature increases, its luminosity also increases.

The second equation, t = life time of sun * (M/Msun)-2,6, gives the lifetime of a type V star in terms of its mass. This equation is derived from the mass-luminosity relation, which states that a star's luminosity is proportional to its mass raised to a certain power. In this case, the power is -2.6, which means that as a star's mass increases, its lifetime decreases.

Combining these two equations, we can see that as a star's temperature increases (as it is forming), its luminosity also increases. However, as its mass increases (as it is forming), its lifetime decreases. This means that a star can only continue to form if its temperature increases at a faster rate than its mass. Otherwise, it will reach a point where its lifetime is too short to continue forming.

In conclusion, the mathematical proof that stars are still being formed lies in the relationship between temperature, luminosity, and mass. As long as the temperature of a star is increasing at a faster rate than its mass, it can continue to form. I hope this helps with your question.

Best regards,