# What materials can a star produce before dying?

1. Jun 15, 2015

### Ranguna

Is it possible to calculate how much Helium a star can produce when it reaches the end of the main-sequence, right before it starts burning Helium ( given if it has enough mass to do so) ?

And if it is possible then is it also possible to calculate how many materials a star can produce given it's mass ?

I'm kind of starting my journey into physics so forgive me if I write anything that might not be scientifically correct.

2. Jun 15, 2015

### DEvens

Welcome to the forum.

It is possible to model these things. Then, depending on the fate of the star, there are some interesting data points to test those models.

Basically, it requires knowing what interactions are possible, and the cross sections for each possible interaction. If these are known very accurately then what you need to do is, in outline with lots of steps left out, the following.

First, you model the density and temperature of the star. You need to take into account, at a minimum, the gravity of the star, and the reaction rates at each temperature and density. That lets you estimate the energy released, which lets you update the other stuff. You then have to evolve the thing over time to model how much of what kinds of nuclei are produced.

This is by no means an easy task. At this naïve level I have not talked about modeling things like rotation of the star, magnetic fields, and things like motion of star material. Stars are not solid objects and their material can move around in interesting fashion.

Then you can predict the history of the star from a big blob of mostly Hydrogen onward. If your model is accurate enough you can predict how much of various nuclei get produced, and when, and possibly even where these nuclei wind up. For example, in a super nova a large amount of material is blasted away from the star. Some other forms of star will eject material into space in much less violent fashion.

And that gives us some hints as to how to test these models. By looking at super nova fragments, and the other ejected materials, we can get an idea of the relative fractions of various nuclei in actual stars. Or their remnants and ejected matter at any rate.

And that is the interesting thing. By studying the nuclear isotope ratios on Earth, we can get some ideas as to stellar evolution.

http://www.poetryloverspage.com/poets/blake/to_see_world.html

3. Jun 15, 2015

### Ranguna

I don't really want to create a model that accurate, you see, I'm doing this because I'm currently creating a game like Elite: Dangerous or No Man's Sky, and because of that I need to make the algorithms as simple as possible in a way that it delivers the best experience, in a way I don't really need to simulate everything atom by atom, instead I just need to make it look real.

Right now a star is formed by picking a position in space and mass randomly, not by getting hydrogen atoms together, once I know the mass I can calculate the star radius using the mass-radius relation:
R = M0.738

After that I calculate the Luminosity, which is needed to calculate the temperature, with that I determine the color of the star:
T = L☉ ∜(LR⁻²)

(The color of the star is calculated using a little more comples algorithm which outputs color in RGB form)
Now I can effectively draw the star knowing it's radius and color. After that, the time that the star spends in the main-sequence is calculated using this fomula:

The reason I want to know what elements are created by the star is because gradually the star, once it ends the main sequence, will release part of it's core elements to space due to bubbles that mix it's outer layer with the elements on it's core, this combined with the helium flashes will populate the surrounding space with elements which the player can harvest, say if a star can fuse iron then the player will be able to harves iron form around the star, or even uranium or helium (or even denser elements).
All that I need is a simple, very basic and might not even be scientifically accurate,yet it needs to create the illusion of real time star simulation.

Maybe a table that categorises star masses and core composition is available somewhere.

4. Jun 15, 2015

### rootone

Stars with sufficient mass can fuse atoms as far as producing Iron and Nickel and energy is released as a result of the fusion.
More massive stars end their lives as supernova and that is the only known source of heavier elements. Fusion of heavy elements is a process which absorbs energy instead of releasing it, (which hastens the stars core collapse prior to the explosion.)
The majority of stars are only sufficiently massive to fuse elements as far as the lighter elements like oxygen and carbon before ceasing fusion and becoming a white dwarf.
The rare cases of extremely massive stars don't emit much of anything before they collapse to become either a neutron star or black hole.

Last edited: Jun 15, 2015
5. Jun 15, 2015

### Ranguna

I've just read about that too, a giant (or bigger) only produces heavier elements when they blow up to supernovas because that's when the r-process occurres, this process gives energy to the star which will react with the iron core and in the instance of the explosion, the core will have sufficient energy to start iron nuclear fusion and will produce uranium.

Found a nice table that catalogues everything until silicon fusion.

Now that I know, all that's left is to know when the star produces each element given the mass of the star and the time passed since "birth".

6. Jun 15, 2015

### Staff: Mentor

You are aware that stars take millions to billions of years to go through their main sequences, right? What is your time scale for this game? If I play for an hour, will 15 million years pass?

7. Jun 15, 2015

### Ranguna

More or less like that, a sun like star would probably go through it's main sequence in about an year or half a year, so 10 billion years would equal 365 days or half more, a star with 60 times the mass of the sun would go through it's life in a little more than 10 days. That's 3 million years = 10 days, 1 million years = 3 days, 333,333 years = 1 day, 13888 years = 1 hour ( more or less )
Now I need to know the composition of the core given it's mass and time that has passed since the star was created. Basicly I would feed the mass of a star and it's age into a function and that function would output the star's core, this would influence the composition of the surrounding space and the surrounding planets too, if a planet with an atmospher was near the star then that planet's atmoshphere would be influenced by the star's core's composition.

8. Jun 15, 2015

### Staff: Mentor

The planet's atmosphere should be composed solely of elements that existed at the time the star formed, minus any material lost over time (like how the Earth lost all of its helium billions of years ago). The only time the core composition is going to have an effect is at the very end of the star's life, and even then not all stars will eject material from their cores into space.

9. Jun 15, 2015

### Ranguna

Planets will not be effected then, but when a star goes supernova it does release a whole bunch of elements into space in a form of a nebula, this will be available for harvest if the player feels like it. The outer layer of the star will be hydrogen mixed with all the core's elements due to the bubbles that are formed when the stars' shape gets all convective, once the layer is released then the surrounding space will be populated with materials from hydrogen to iron and maybe even a little bit or uranium.

Last edited: Jun 15, 2015
10. Jun 16, 2015

### Chronos

Iron is the heaviest element a star can create. Elements heavier [with more protons] than iron can only be created by supernova, to the best of our knowledge.

11. Jun 16, 2015

### e.bar.goum

The s-process is thought to occur in massive AGB stars. http://iopscience.iop.org/0954-3899/35/1/014007

ETA: In fact, it's thought to mostly occur in AGB stars, not supernovae.

Last edited: Jun 16, 2015
12. Jun 16, 2015

### Ranguna

r-process, s-process.. It all depends on the mass of the star, the s-process occures in stars from 0.6-10 solar masses and the r-process occurres in supernove explosion in stars that have mass ~>= 8 solar masses.
So a star that has ~>= 8 solar masses will be able to fuse iron into uranium once the star "blows up" and then the surrounding space will contain little bits of uranium, and the s-process will only work in the inert carbon core and will only produce elements up to bismuth, any higher then that will produce unstable nuclei which have a very fast decay time. (source, the last two paragraphs of the page)

All stars begin with 70-75% hydrogen and 25-30% helium (with other small percentages of heavier elements) and then they go through the main sequence which will consist of the fusion of four hydrogen atoms (~1*4 atomic weight) to create one helium atom (~4 atomic weight), this will happen until the core of the star reaches a point where it is mainly composed of hydrogen burning in a thin shell around a helium core; once this happens, the outer layer of a star will star to grow outward due to the high temperature of the core caused by the electron degeneracy, this will cause the core to ignite helium which will cause the star to flash, marking the end of the main sequence. This will happen to stars with a minimum weigh of 0.4 solar masses, if the star is not massive enough then it will never reach the degenerate point to fuse helium and we don't really know what happens after that because the universe isn't old enought to have stars this small that have evolved out of their main sequence, for the sake of the game let's just assume that the helium core will get so big that the star will not be able to fuse hydrogen anymore and it will turn into a black dwarf.. probably..
After that, it all depends on the mass of the star, here's the table of elements that a star can fuse ( see the last tables ).

As the star's core gets hotter it grows bigger, until it doesn't have enought mass to generate gravity to compress itself to electron degeberacy or it reaches a dense iron core, it's impossible to fuse iron while the star is "alive" because the only way fuse iron is to use energy and all the other elements before iron created energy instead.
Once a star reached either of these points it will "blow up" as a planetary nebula, supernova or the infamous balck hole, depending on it's mass:

Stars with [0.4, 8[ times the mass of the sun will turn into planetary nebula due to the fast gas and energy emissions that originate solar winds that leave the surrounding space rich with the elements that the star has fused, this will happen repeatidly originating nebulas like the cat's eye nebula, and a white dwarf will also be left behind, this white dwarf was the core the star, so it's probably made out of a shell burning hydrogen, a shell burning helium and a core with carbon and/or oxygen, this white dwarf will follow the steps described before.

Stars with [8, 20[ times the mass of the sun will collapse on themselfs because they can no longer produce energy to balance the gravity and so they can no longer achieve hydrostatic equilibrium; when the star was healthy, it pushed it's outer layer outward which balanced with the gravity that pushed all mass inward, but once it stops its production of energy, gravity gets the upper hand and pushes everything inward, this causes the layer to hit the dense core with such a speed that it will bounce back and it'll completely destroy the core in the process, just like when you throw a rock agains a wall, the rock bounces back and if you throw it with enough speed, the wall breaks ( or the rock does, either way you get the point )
What's left is just a nebula composed of all the elements that the star was made of, from hydrogen to uranium, iron is usually more present in this nebula due to the dense iron core that all stars which are this massive have. Iron marks the end of all stars, this has already been explained but uranium is created from fusing iron, this is possible because once the r-process occurres in the moment of the supernova, there's enough energy to fuse the iron and so we get uranium ash.
Sometime there might be an absence of hydrogen and helium in the nebula, this is because the star was so hot that it had completly burned all the hydrogen and helium it had, this happens in blue stars.

Stars with [20,+inf(or 150)[ times the mass of the sun will live the shortest, because their core is so hot that they burn through hydrogen in just a few thousands of years, once they stop producing energy, their mass will collapse on itself but since these stars are so massive they never really blow into supernovas but instead thire mass collapses into this point with infinite density that we call a black hole.

(I got all this from searching on the web, so please correct everything that might not be scientifically correct)

Now, with all that information, I can build a table of elements that a star creates through it's life time, the problem is to know how much of each element the star has in a given point in time.
All that's left is an algorithm that calculates the percentage of each element present in the core of a star knowing that every star stars with 70-75% hydrogen and 25-30% helium, and H + H + H + H = He; He + He + He = C; C + He = O; O + He = Ne; C + C = Mg; O + O = S, and I don't really know how the iron is formed. With all that information I think it's possible to create an equation that outputs how much of each element is present in the core of a star in a given time.

Last edited: Jun 16, 2015
13. Jun 16, 2015

### Staff: Mentor

The problem is that there are multiple reactions going on in the core of a star during any point in its life. For example, the Sun gets most of its energy through the Proton-Proton chain, which is:
H + H = Deuterium (D)
D + H = 3He
3He + P = 4He

But it also gets a non-trivial amount of energy from the CNO cycle. The CNO cycle starts at higher temperatures than the PP chain, but the reaction rate rises much faster. Stars a bit more massive than the Sun generate most of their energy from this cycle.

Each time the core starts a new burning process (IE helium burning, oxygen burning, silicon burning, etc) there are new sets of side reactions going on in addition to the 'main' one. This is compounded by the fact that most online sources don't go into depth about all of these processes and typically only give the initial reactants and final products, skipping many of the intermediate stages. Another example is the Silicon burning process, which has at least 8 reaction steps.

At some point you're probably either going to have to 'fudge' the numbers, or become an astrophysicist.

14. Jun 16, 2015

### Ranguna

I'd love to become an astrophysicist but if I became one then I wouldn't be programming a game anymore, I'd be programming a stellar evolution model and that's no fun for the average guy that just wants to play a nice sci-fi game

As for the fuging the numbers part, there are two types of variables in my algorithms: the intermediate variables and the terminal variables, terminal variables are the variables that have visible impact on the game and intermediate variables are the ones that don't and they are subdivided into two subtypes: essential and nonessential, the essential subtype is the kind of variable that is needed to calculate a terminal variable and the nonessential subtypes isn't needed or addes little accuracy to calculate a terminal value, these can be excluded from the equations as a means to optimize the code and to make user experience more enjoyable by allowing higher FPS to be achieved. The intermediate reactions of the fusion of atoms are intermediate nonessential variables because every time a reaction occurres, the same intermediate reaction happens, so calculating what you've said:
H + H = Deuterium (D)
D + H = 3He
3He + P = 4He
Is the same thing as:
H + H + H + H = He
In tearms of visuals there's no need for anything else and since there are less procedures involved then the code is able to run faster.

In conclusion, yes, I'm going to to 'fudge' the numbers together but the problem is to get the right numbers and to come up with the "right" equation.
For exemple, imagine that a star was randomly generated and it had the following propriaties:
Position = {0,0} (Don't mind this variable, terminal)
Mass = 8 (in solar units, intermediate essential)
Radius = 80.738 (in solar units, terminal)
Luminosity = 1887.78317097 (in solar units I think, intermediate essential)
Temperature = 17684.8148276 (in kelvin, intermediate essential)
Color = Blue (simple algorithm that turns kelvin into RGB color code, terminal)
Lifetime = 8/1887.78317097 (in solar units, terminal)
Composition = { hydrogen = 75, helium = 25 } (in percentage, intermediate essential)
Age = 0
As time goes on, the 'Age' variable will go up, once the player comes closer to this star, the game will calculate the core's composition and then it destributes the surrounding space with elements.
To calculate this, all I need to do is to calculate how much hydrogen the star transformes to helium per year, multiply that by 'Age'(=hydBurned, how much hydrogen was used since it was born),
Do (8*0.75 - hyd)/8 (how much hydrogen is still present in the core in percentages)
And then 1 - (8*0.75 - hyd)/8 ( how much helium is present in the core in precentages)
The space around the star will be "filled" with energy and some kg? of helium and hydrogen (due to gas emission)?.
As you can see, I didn't need to calculate intermediate reaction to come up with this conclusion, it might not be accurate but it's good enough for a game
The question now is how to calculate how much hydrogen a star fuses to helium per year. Maybe this can be solved by using E = mc2 ? We know the stars luminosity, that's E.. now what ?

Last edited: Jun 16, 2015
15. Jun 16, 2015

### Bandersnatch

Here's a quick, roughly approximate way to do it:

Find on the wiki the total energy production in a single instance of fusion (the 4H->He mass defect), should be somewhere in the fusion or the p-p chain article.
Calculate how many hydrogen atoms get fused into helium atoms per second to maintain the luminosity. You'll have to convert between units.
And voilà. You have a function that converts hydrogen into helium per time unit.

It's not going to win you any awards for accurate modelling, but maybe it'll do for your particular needs.

Let us know should you get stuck.

16. Jun 16, 2015

### Staff: Mentor

Oh, my mistake. That's not what I meant by a 'side reaction'. Those are the actual steps in the P-P chain. For what you're wanting I don't think they even need to be calculated now that I think about it.

It depends on the star and the cycle of its life its in. Space certainly isn't filled with energy unless your just talking about the light output. Most stars have some sort of stellar wind, and high mass/post main sequence stars can eject immense amounts of material: https://en.wikipedia.org/wiki/Stellar_wind

Post-main-sequencestars nearing the ends of their lives often eject large quantities of mass in massive ( solar masses per year), slow (v = 10 km/s) winds. These include red giants and supergiants, and asymptotic giant branch stars. These winds are understood to be driven by radiation pressure on dust condensing in the upper atmosphere of the stars.

Stellar winds from main-sequencestars do not strongly influence the evolution of lower mass stars such as the Sun. However, for more massive stars such as O stars, the mass loss can result in a star shedding as much as 50% of its mass whilst on the main sequence: this clearly has a significant impact on the later stages of evolution.

17. Jun 17, 2015

### Ranguna

Right. Theres no need to to calculate all that since the output is always the same.

Found a powerpoint explaining all that, but I don't understand half of it, but no worries, I don't need that yet.

I got stuck just by reading your comment.. I don't even know how to convert between units, I'm an economics student programming a scientific game so excuse me if I don't understand most of the scientific calculations.
I found this article on the forum but I don't understand some parts either, I belive that Garth's replay has everything I need but I don't know how to apply my data on it.

Last edited: Jun 17, 2015
18. Jun 17, 2015

### Bandersnatch

One full p-p or CNO chain fuses 4 H nuclei into a He nucleus with the release of 26 MeV (mega electronvolts) of energy.

A star has luminosity L (your input variable). Luminosity uses units of power, so it's energy/second.
To maintain it, N number of fusion chains must be completed per second so that:

$L =N * 26 MeV / 1 sec$

You need to match the units of energy there, so covert whatever you get the luminosity in into MeV (or the other way around). If you get L in Watts, divide it by 1.6*10^-13. If you get L in terms of solar luminosity (L☉), multiply it by 3.85*10^26 to get Watts, then convert to MeV as before.

Taking the Sun as an example, L☉=1

$\frac{1*3.85*10^{26}}{1.6*10^{-13}}=N*26$

$N \approx 9*10^{37}$ reactions every second.

Every second 4*N hydrogen atoms turn into N helium atoms.

If you take every star to be born with 75% H and 25% He by mass, the initial number of available atoms of each of the elements is just a function of mass.
You'll then have a function that each second reduces the number of H by 4N and adds 1N of He. You just need to find out how many atoms of H and He are there in the first place:
Take the mass of a star M. If in units of solar mass, convert to grams by multiplying by 2*10^33. In each gram there will be approximately NH atoms of hydrogen:

$N_H / 1 g = 3/4*N_A/A_{rH}$

where NA is the Avogadro's constant and ArH is the atomic weight of hydrogen.
For helium, correspondingly:

$N_{He} / 1 g = 1/4*N_A/A_{rHe}$

Multiply those by the total mass in grams to get the total number of atoms. The atomic weights may just as well be taken to be 1 for H and 4 for He here.

(somebody care to check for cock-ups, be my guest)

Notice how both the number of atoms and luminosity are functions of mass, so that in the end that is the sole variable which determines the evolution of composition over time.

Let me know if something's not clear.

Last edited: Jun 17, 2015
19. Jun 17, 2015

### Ranguna

This will take me a while to understand, I'll post back once I test all this.

20. Jun 17, 2015

### Bandersnatch

Note there was a mistake in the last two equations. Now corrected.

Don't hesitate to ask for clarifications. It's not terribly well presented as it is.