Questions about nuclear physics inside a star

[aeonflux]

Hi! I am currently interested in working on a simulator that emulates the creation of a star in c++. Basically, I'm thinking of generating a large number of particles (protons) fairly close to each other and apply gravitational and electro-magnetic force to them, and then see what happens. It goes without saying that my simulation will use a rather simple model (for now), but I still need to understand what happens at the nuclear level when two protons collide. So far I have Newton's law of gravitation, and Faraday's law for the electro-magnetic field, which are nearly the same.

So my question is, at what proximity particles enter nuclear fusion ? And what would be the equation (or equations) that would describe the nuclear force that will hold the particles together (or break them appart, if fission occurs instead of fusion) ? Is fission possible when two protons collide together ?

Also, more generally, do you think that this basic model is a good enough approximation of what goes on in a star when it is born ?

Thank you in advance for your answer!

Aeonflux

 

[mathman]

http://en.wikipedia.org/wiki/Star_formation
http://en.wikipedia.org/wiki/Nuclear_fusion

The above sites should answer your questions.

When protons collide, fusion is possible. Fission is completely different - it refers to processes involving heavy nuclei, such as U235.

 

[aeonflux]

ok thanks a lot! :-)

 

[Drakkith]

Have you ever done any simulations involving extremely large numbers of particles before? The process is...daunting, to say the least. The sheer number of particles for even very small simulations increases the number of calculations for each time step to astronomical amounts.

 

[aeonflux]

yeah you're probabaly right... my interest in it is also in "theoretical" phase...

 

[Vanadium 50]

This is not going to work.

Even if you have it modeled correctly, what you will have is a giant explosion from electrostatic repulsion.

 

[aeonflux]

That depends on the number of particles that are initially crammed together, no? If there's enough, the ones in the middle will get enough velocity to enter fusion, and the whole of the "star" will hold together because of the gravitationnal force ? that's what I think, anyway, though I don't know how many billions of billions of particles that would take...

 

[Drakkith]

That depends on the number of particles that are initially crammed together, no? If there's enough, the ones in the middle will get enough velocity to enter fusion, and the whole of the "star" will hold together because of the gravitationnal force ? that's what I think, anyway, though I don't know how many billions of billions of particles that would take...

For one thing, the core of a star isn't just protons. It's full of electrons as well, with a smattering of nuclei from other elements. And about 25% helium by mass if I'm not mistaken. At least at the time of "birth" where the core starts to fuse hydrogen. The amount of helium increases as the life of the star goes on. If it were purely protons stars would never form, as the gas cloud from which they are born would never have been able to start collapsing.

As for how many particles it would take, the Sun's mass is approximately 2x10³⁰ kg's. There are approximately 5.975x10²⁶ hydrogen atoms in 1 kg. I leave the rest of the math to you.

 

[aeonflux]

For one thing, the core of a star isn't just protons. It's full of electrons as well, with a smattering of nuclei from other elements. And about 25% helium by mass if I'm not mistaken. At least at the time of "birth" where the core starts to fuse hydrogen. The amount of helium increases as the life of the star goes on. If it were purely protons stars would never form, as the gas cloud from which they are born would never have been able to start collapsing.

As for how many particles it would take, the Sun's mass is approximately 2x10³⁰ kg's. There are approximately 5.975x10²⁶ hydrogen atoms in 1 kg. I leave the rest of the math to you.

interesting... that's the kind of conclusions I was interested to observe in the simulation... but if the numbers are that big I guess it would take around 6.49x10¹⁰⁴ seconds per time step to simulate, which is a bit too big... I'd probably have to simplify the model and update my physics' facts for it to work... thanks for the input guys...

 

[Drakkith]

Look up "Particle-in-cell" for methods of calculating large numbers of particles if you are interested.

 

[Chronos]

This is a numerical, not analytical exercise. No computer on Earth can yet run a numerical analysis involving googles of particles. It is only useful as a tool to test various assumptions. It fails to offer any solutions.

 

[Astronuc]

interesting... that's the kind of conclusions I was interested to observe in the simulation... but if the numbers are that big I guess it would take around 6.49x10¹⁰⁴ seconds per time step to simulate, which is a bit too big... I'd probably have to simplify the model and update my physics' facts for it to work... thanks for the input guys...

When one is doing multi-scale multiphysics, one has to consider the physics at the scales. There's the cloud of hydrogen and other elements distributed of a few billion km, which coalesces over sometime like 100 k years. The particle interactions would be scattering.

See this simulation page - http://www.astro.ex.ac.uk/people/mbate/Cluster/cluster3d.html

As one simulaties the proto-star then star, if one is interested in particle simulations, then one would simulate small volumes at different locations in the protostar/star, and the physics from those volumes would drive the physics of the larger system.

And one would have modules on different scales, e.g., modeling sunspots, or granules, would be intermediate scale compared to the core or the star itself.


Particle-particle interactions would only be practical on millions of particles.

One may wish to find examples of Birdsall and Langdon's work on Plasma Physics Simulation Codes.

https://www.amazon.com/dp/0750310251/?tag=pfamazon01-20

https://www.amazon.com/dp/0852743920/?tag=pfamazon01-20

https://www.amazon.com/dp/1439810214/?tag=pfamazon01-20

 

[julcab12]

Hi! I am currently interested in working on a simulator that emulates the creation of a star in c++. Basically, I'm thinking of generating a large number of particles (protons) fairly close to each other and apply gravitational and electro-magnetic force to them, and then see what happens. It goes without saying that my simulation will use a rather simple model (for now), but I still need to understand what happens at the nuclear level when two protons collide. So far I have Newton's law of gravitation, and Faraday's law for the electro-magnetic field, which are nearly the same.

So my question is, at what proximity particles enter nuclear fusion ? And what would be the equation (or equations) that would describe the nuclear force that will hold the particles together (or break them appart, if fission occurs instead of fusion) ? Is fission possible when two protons collide together ?

Also, more generally, do you think that this basic model is a good enough approximation of what goes on in a star when it is born ?



Thank you in advance for your answer!

Aeonflux

Wow! Very neat.

Have you ever done any simulations involving extremely large numbers of particles before? The process is...daunting, to say the least. The sheer number of particles for even very small simulations increases the number of calculations for each time step to astronomical amounts.

It will took million of cores to simulate a simple dynamic fluid problem(local ocean waves Or local tornadoes). Human history, we can use ~10^33 – 10^36 operations as a rough estimate. In principle it is achievable to simulate a complete highly near accurate model of our solar system exclusion of (HUP) but it will took a HUGE amount of computing power and time(millions or billions) even if we have (latest)20 petaflops of computing power equivalent of thousand trillion floating point operations per second considering the approximate number of particle in our universe(We have an approximation of 1 × 10^80-85 of fundamental particles in the observable universe/5.1 × 10^96 Planck density) which is near limitless and unlikely to get a value on such.

But we can assume a simplier version as a backdrop like instead of particle. We derived value from observed density let's say 1h atom m3. The universe is about 13.+ billion years old, and using the fact that there are pi times 10[7] (10 to the 7) seconds in a year, you can calculate the total energy that's available in the whole universe. Remembering that there's a certain amount of energy, you then divide by Planck's Constant — which tells you how many ops per second can be performed — and multiply by the age of the universe, and you get the total number of elementary logical operations that could have been performed since the universe began. You get a number that's around 10[120] (10 to the 120) and so on. For more details check on THE COMPUTATIONAL UNIVERSE: SETH LLYOD".

http://www.physicsoftheuniverse.com/numbers.html


Unfortunately, a home computer has lowly 8 cores (the fastest in the market) and heavily relies on "adaptive" measurement, compressed equal derivations and scripting to get the job done. In my field we've use adaptive ray tracing and quasi monte carlo method to compute light illuminations that is 50% faster than photon raytracing method and give near equal result of 5% compared to other method.

 

[Raghnar]

You need weak force driven nuclear fusion, since the start of the nuclear reactions inside a star are p+p fusing into a deuteron (so a proton goes into a neutron + antielectron + neutrino). The gravitational pressure you will need must have temperature of the order of the energy difference of proton and neutron (so, huge) and a lot lot of particles (even if not 10^56 at least 10^54 for sparkling a brown star, but you need impurities), and you need also strong-force to counterfeit the coulomb repulsion at short distances, that will be otherwise the same order of magnitude as the gravitational pressure and a star cannot form.

In other words you need a computer big as a planet at least to do the math without approximating even if you're clever and adopt all the nice shortcuts.

Depending on what you want you have to adopt approximation.

If you want just a nice movie you can define an effective interaction that goes to zero at infinite range, have a maximum at about 10fm, and a relative minimum (higher than zero) at 1 fm and goes to + infinity at zero.
Then do Hartree Fock to have a mean field and then compute the orbits with the shroedinger equation. Then add the gravitational 1/r^2 with some kind of gauss based approximation, and whatch the evolution every time-step.
The graphical evolution that should be more or less a condensation, since a certain self-consistent "breathing-like" point (not sure, in any casee you can compute the temperature and stop where it reaches the proton-neutron mass difference) where you need to include the proton proton fusion to start the reaction and have an outer pressure that outbalance the gravitational pressure.

Good job.