B Colliding Gas Cloud to form a Star

[Omega0]

TL;DR Summary

Simple equations to describe the stationary state of a collapsing hydrogen cloud in space

Hello,

I would like to go step by step trough the process of the generation of a star. An AI suggests for a simple model an adiabetic case (an improvement of the isothermal case) with $\gamma=5/3$:

$$

\begin{align}

T &= T_0 \left(\frac{p}{p_0}\right)^{\gamma-1} \\

P &= \rho \frac{k_B T}{\mu m_H} \\

\frac{dP}{dr} &= -\frac{G M(r) \rho(r)}{r^2} \\

\frac{dM}{dr} &= 4\pi r^2 \rho(r)

\end{align}



$$

The solution looks wrong - identical to the iso-thermal case. I am asking myself how $T_0$ and $p_0$ should be assigned. For the temperature the AI takes 10K, okay... but shouldn't $p_0$ be a problem because it is initially almost 0? Also, the setup with both values determines the final result... isn't this wrong? Is a transient approach needed?

Thanks for your ideas!

$\omega_0$

 

[renormalize]

An AI suggests for a simple model an adiabetic case...

Please don't rely on artificial intelligence to develop your model. Find instead a suitable published reference, like a textbook or technical paper.

 

[Nugatory]

TL;DR Summary: Simple equations to describe the stationary state of a collapsing hydrogen cloud in space

Hello,
I would like to go step by step trough the process of the generation of a star. An AI suggests for a simple model an adiabetic case (an improvement of the isothermal case) with $\gamma=5/3$:

We have moved this thread to the astrophysics section where you're more likely to find prople familiar with the physics of stellar-mass gas clouds.

You will want to be very cautious about accepting "help" from any AI - they are notoriously unreliable on complex subjects, often just reflecting the user's own misconceptions back at them. Thus the excellent advice from @renormalize above, and also the forum rules restricting the use of AI. If the formulas in your post are your own work we can sensibly discuss them here; if they came from the AI it will be best to tear them up and start over from your own understanding of the problem.

 

[snorkack]

TL;DR Summary: Simple equations to describe the stationary state of a collapsing hydrogen cloud in space

Hello,

I would like to go step by step trough the process of the generation of a star. An AI suggests for a simple model an adiabetic case (an improvement of the isothermal case) with $\gamma=5/3$:

$$

\begin{align}

T &= T_0 \left(\frac{p}{p_0}\right)^{\gamma-1} \\

P &= \rho \frac{k_B T}{\mu m_H} \\

\frac{dP}{dr} &= -\frac{G M(r) \rho(r)}{r^2} \\

\frac{dM}{dr} &= 4\pi r^2 \rho(r)

\end{align}



$$

The solution looks wrong - identical to the iso-thermal case.

If the formulas in your post are your own work we can sensibly discuss them here; if they came from the AI it will be best to tear them up and start over from your own understanding of the problem.

Another part of the problem is, can the OP usefully critizise and check the AI results?
AI can even hallucinate. Searches cannot hallucinate, but they can quote in wrong context. Then again, so can humans.