# Thread: The Barnes-Hut Algorithm as a solution for N-Body Problem

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## The Barnes-Hut Algorithm as a solution for N-Body Problem

Originally Posted by Shaula
12) Do you accept that computational hydrodynamics and n-body simulations are the right way to do this?
.
I have found a very interesting article about The N-Body Problem.

http://beltoforion.de/article.php?a=...imulator&hl=en

"A region of space contains the number of N bodies. Each body has its own potential and a resulting force field. This could be charges causing an electrical field (Coulomb's law) or planets in space (Law of Gravity). The potential of the bodies can be summed up yielding a combined potential which depends on the location of each of the bodies and its physical properties (i.e. mass or charge). According the Newtons first law the bodies themself will experience an acceleration caused by the field."

As we add high number of objects it become too complicated:

"Lets assume Fij is the force acting between particles i and j. The total number of force calculations needed to compute the state of the system is N*(N-1) and according to Newtons third law every force has an opposite forces equal to itself: Fij = -Fji. The total number of force calculations can then be reduced to:

The problem is of order O(N2). If the number of particles double the number of calculations quadrupels. If the number of particles is increased by factor ten the number of calculations increases by a factor of 100 and so on... From this simple relation it is clear that computing the N-Body problem for large numbers of particles will quickly become very costly in terms of computational power. A more effective algorithm that scales better with increasing number of particles is needed."

There is a solution for that and it's called: "The Barnes-Hut Algorithm".
"The Barnes-Hut Algorithm describes an effective methood for solving n-body problems. It was originally published in 1986 by Josh Barnes and Piet Hut [1]. Instead of directly summing up all forces it is using a tree based approximation scheme which reduces the computational complexity of the problem from O(N2) to O(N log N)."

So far so good.
Now, let's focus in Animation 1:

"Animation 1: The animation shows a distribution of 5000 particles. The quadrants that are shown are the ones that are used for calculating the force excerted on the particle at the origin of the coordinate system. The higher θ is, the fewer the number of nodes that are necessary for the force calculation (and the larger the error)."

So, now that I have better understanding on this issue, I wonder how our scientists in Zurich have used the simulation for the spiral galaxy:

1. Did they set in the calculation only real stars measurements in the density wave (spiral arms) and outside the arms?
2. Did they set special quadrants for the stars in the spiral arms and outside the spiral arms? (This is very critical in my opinion)
3. What is the ratio in the milky way between the star densities in the arms to the one outside the arms that they have used (Is it 10% or close to 20%)?
Last edited by Dave Lee; 2018-May-21 at 05:33 PM.

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Originally Posted by Dave Lee
1. Did they set in the calculation only real stars measurements in the density wave (spiral arms) and outside the arms?
2. Did they set special quadrants for the stars in the spiral arms and outside the spiral arms? (This is very critical in my opinion)
3. What is the ratio in the milky way between the star densities in the arms to the one outside the arms that they have used (Is it 10% or close to 20%)?
1. The stars formed, they didn't put them in to start with. They started with gas + dark matter
2. That is not how the Barnes-Hut approach works. You don't manually set regions. Read up on the parameter theta.
3. I've told you before - they did not code in these kinds of parameters. They emerged from the model. Which is the whole point of the model.

I know you either won't read them or will skim them for bits to quote out of context but for anyone else interested:
Barnes-Hut: https://en.wikipedia.org/wiki/Barnes...Hut_simulation
ERIS: https://en.wikipedia.org/wiki/Eris_(simulation)
The ERIS paper: https://arxiv.org/pdf/1103.6030.pdf
GASOLINE: http://gasoline-code.com/docs.html

Have fun.

3. Originally Posted by Shaula
I know you either won't read them or will skim them for bits to quote out of context but...
That'll be enough of that, please. Keep it polite.

4. Originally Posted by Dave Lee

I have found a very interesting article about The N-Body Problem.

http://beltoforion.de/article.php?a=...imulator&hl=en

"A region of space contains the number of N bodies. Each body has its own potential and a resulting force field. This could be charges causing an electrical field (Coulomb's law) or planets in space (Law of Gravity). The potential of the bodies can be summed up yielding a combined potential which depends on the location of each of the bodies and its physical properties (i.e. mass or charge). According the Newtons first law the bodies themself will experience an acceleration caused by the field."

As we add high number of objects it become too complicated:

"Lets assume Fij is the force acting between particles i and j. The total number of force calculations needed to compute the state of the system is N*(N-1) and according to Newtons third law every force has an opposite forces equal to itself: Fij = -Fji. The total number of force calculations can then be reduced to:

The problem is of order O(N2). If the number of particles double the number of calculations quadrupels. If the number of particles is increased by factor ten the number of calculations increases by a factor of 100 and so on... From this simple relation it is clear that computing the N-Body problem for large numbers of particles will quickly become very costly in terms of computational power. A more effective algorithm that scales better with increasing number of particles is needed."

There is a solution for that and it's called: "The Barnes-Hut Algorithm".
"The Barnes-Hut Algorithm describes an effective methood for solving n-body problems. It was originally published in 1986 by Josh Barnes and Piet Hut [1]. Instead of directly summing up all forces it is using a tree based approximation scheme which reduces the computational complexity of the problem from O(N2) to O(N log N)."

So far so good.
Now, let's focus in Animation 1:

"Animation 1: The animation shows a distribution of 5000 particles. The quadrants that are shown are the ones that are used for calculating the force excerted on the particle at the origin of the coordinate system. The higher θ is, the fewer the number of nodes that are necessary for the force calculation (and the larger the error)."

So, now that I have better understanding on this issue, I wonder how our scientists in Zurich have used the simulation for the spiral galaxy:

1. Did they set in the calculation only real stars measurements in the density wave (spiral arms) and outside the arms?
2. Did they set special quadrants for the stars in the spiral arms and outside the spiral arms? (This is very critical in my opinion)
3. What is the ratio in the milky way between the star densities in the arms to the one outside the arms that they have used (Is it 10% or close to 20%)?
My bold. Can you tell us, in appropriate mathematical detail, why you think so?

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Originally Posted by Shaula
1. The stars formed, they didn't put them in to start with. They started with gas + dark matter
The ERIS paper: https://arxiv.org/pdf/1103.6030.pdf.
Thanks for the great article.

"High-resolution particles were further split into 13 million dark matter particles and an equal number of gas particles, for a final dark and gas particle mass of mDM = 9.8 × 10^4 M
and mSPH = 2×10^4 M, respectively."

So, the total mass in one gas particle is 2×10^4 M while the total mass of Dark matter particle is 9.8 × 10^4 M.

Star particle creation from gas particle:

"Each star particle is created stochastically with an initial mass m∗ = 6 × 10^3 M, and the gas particle that spawns the new star has its own mass reduced accordingly"

Questions:

1. Star creation - In real life, is it feasible to create star from Gas? Don't we need a Nebulae for that?
Is it realistic to assume that almost 1/3 of the gas particle (2×10^4 M = 20 × 10^3 M) has been converted to star particle (6 × 10^3 M)?

2. Time frame - There is no time frame in the simulation for the star creation from gas and for setting the density wave structure.
In other words - How long (in real life) it is expected to create all the requested stars?
Please be aware that the Sun had set one orbital cycle around the galaxy in 240 Million years.
So, how many cycles is needed for the simulation to set the density wave? Based on requested Number of cycles, we can extract the requested time to create the spiral
arms.

3. Hydrodynamic Vs Gravity Force

It is stated: "Here we report a new cosmological N-body/smooth particle hydrodynamic (SPH) simulation of extreme dynamic range in which a close analog of a Milky Way disk galaxy arises naturally"

If I understand it correctly :

The whole propose of the N-Body simulation is to evaluate the outcome of the gravity between the objects. So, it isn't just the simple gravity force between a particle to the center, it is mainly monitor the forces between one particle to all the other particles in the simulation, including Gas, dark matter and stars. In total - 18.6 million particles at the same moment.
However, as the gravity calculation between the particles is too complicated, we are using "The Barnes-Hut Algorithm".
"The Barnes-Hut Algorithm describes an effective method for solving n-body problems. It was originally published in 1986 by Josh Barnes and Piet Hut [1]. Instead of directly summing up all forces it is using a tree based approximation scheme which reduces the computational complexity of the problem from O(N2) to O(N log N)."

We claim that "Gravity is the dominant force". So, where is that dominant force in the simulation?

Unfortunately, I couldn't find even one word about gravity in this article. How can they discuss about N-Body simulation without verifying the gravity forces?

Please remember that the estimated mass of each gas particles is of 2×10^4 M, and the estimated mass of each star is 2×10^4 M. So where is the gravity calculation for that?
If it is there, then why they don't highlight that important information?
Last edited by Dave Lee; 2018-May-23 at 06:19 PM.

6. My educated guess is that the writers made the reasonable presumption that their target readership already understood that gravity was the principal force and that vast clouds of diffuse gas behaved as fluids, so they saw no need to clutter their papers up with what was common knowledge for this purpose. If they had to write for novices at all levels they might need ten or more times as many pages to cover everything that is covered in entry-level physics.

7. Originally Posted by Dave Lee
1. Star creation - In real life, is it feasible to create star from Gas? Don't we need a Nebulae for that?
Nebulae are clouds of gas, specifically hydrogen and helium, along with small amounts of oxygen, water vapor, etc, and dust consisting of heavier elements.

8. Originally Posted by Dave Lee
Unfortunately, I couldn't find even one word about gravity in this article. How can they discuss about N-Body simulation without verifying the gravity forces?
What forces caused by the presence of mass do you think they might be simulating? I'll give you three guesses.

Anyway, apart from the fact it is about solving an N-body problem to simulate the formation of galactic structures (i.e. it is about gravity), gravity is explicitly mentioned at least three times in the paper.

So where is the gravity calculation for that?
In the source code.

"The simulation follows the interactions of more than 60 million particles of dark matter and gas. A lot of physics goes into the code--gravity and hydrodynamics, star formation and supernova explosions--and this is the highest resolution cosmological simulation ever done this way," said Guedes, who is currently a postdoctoral researcher at the Swiss Federal Institute of Technology in Zurich (ETH Zurich).
https://news.ucsc.edu/2011/08/eris-simulation.html
Last edited by Strange; 2018-May-23 at 09:12 PM.

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Originally Posted by Strange
it is about solving an N-body problem to simulate the formation of galactic structures (i.e. it is about gravity), gravity is explicitly mentioned at least three times in the paper.
Originally Posted by Hornblower
My educated guess is that the writers made the reasonable presumption that their target readership already understood that gravity was the principal force and that vast clouds of diffuse gas behaved as fluids.
If B- Body problem is based on gravity and if due to the Simulation model, after several cycles of the Gas + Stars + dark matter around the galaxy center, the density wave had been emerged from the model;:

Originally Posted by Shaula
They emerged from the model. Which is the whole point of the model.
Then, where is the gravity impact on the dense wave outcome?
Why don't we call it - GRAVITY DENSE WAVE?

10. Originally Posted by Dave Lee
Then, where is the gravity impact on the dense wave outcome?
As you have been told multiple times, it is a result of gravitational interactions.

Why don't we call it - GRAVITY DENSE WAVE?
Because the waves are not dense.
Because they already have a name.
Because that is an unnecessarily long name.
Because it is a wave of density not a wave of gravity.
Because we already have "gravity waves" (a very different thing).
Because we already have "gravitational waves" (a very different thing).
Because everyone(*) knows that galactic structures are created by gravity.

(*) Nearly everyone.
Last edited by Strange; 2018-May-24 at 11:23 AM. Reason: another because

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Originally Posted by Dave Lee
Why don't we call it - GRAVITY DENSE WAVE?
Simple: At the 1991 International Symposium of Naming Odd Things (better known by its acroynm), GRAVITY DENSE WAVE tied with MYSTERIOUS SKIN RASH for last place in the voting.

12. Take a look at the 2D galaxy collision simulator at the bottom of the first page. It starts with no visible spiral pattern and ends up looking very much like M51 after one revolution. There is an example of the companion's gravitational perturbation stirring the pot to create a spiral pattern in a previously unperturbed hypothetical galaxy. Very nicely done in my opinion.

13. Originally Posted by Strange
What forces caused by the presence of mass do you think they might be simulating? I'll give you three guesses.

Anyway, apart from the fact it is about solving an N-body problem to simulate the formation of galactic structures (i.e. it is about gravity), gravity is explicitly mentioned at least three times in the paper.

In the source code.

https://news.ucsc.edu/2011/08/eris-simulation.html
Is there more information on the initial conditions beyond "they chose a halo with an appropriate mass and merger history to host a galaxy like the Milky Way and "rewound the tape" back to the initial conditions. Zooming in on the small region that evolved into the chosen halo, they added gas particles and greatly increased the resolution of the simulation." Was there any presumed origin for the added gas particles other than "they were added"? How were they added? Were they in motion? How were they distributed? What element ratios? A more concerning, question is, if the added particles would have been present prior to the start of the simulation, then why didn't they have an impact prior to that point in time? That's like saying we'll create an orbital model and just insert another moon around the Earth as if it suddenly materialized out of nothing and assuming it had no prior effect, then running the simulation from that point forward. The text indicates that's exactly what they did, just creating additional particles in an already-stable environment.

14. Originally Posted by mkline55
Is there more information on the initial conditions beyond "they chose a halo with an appropriate mass and merger history to host a galaxy like the Milky Way and "rewound the tape" back to the initial conditions. Zooming in on the small region that evolved into the chosen halo, they added gas particles and greatly increased the resolution of the simulation." Was there any presumed origin for the added gas particles other than "they were added"? How were they added? Were they in motion? How were they distributed? What element ratios? A more concerning, question is, if the added particles would have been present prior to the start of the simulation, then why didn't they have an impact prior to that point in time? That's like saying we'll create an orbital model and just insert another moon around the Earth as if it suddenly materialized out of nothing and assuming it had no prior effect, then running the simulation from that point forward. The text indicates that's exactly what they did, just creating additional particles in an already-stable environment.
They are starting with simplified models, not exact descriptions of every little detail of a particular galaxy. When they find the subsequent simulation to be in good general agreement with real galaxies, they can add more fine structure to their models until they either get good matches with the real thing or exceed the computer's capabilities while trying.

15. Originally Posted by Hornblower
They are starting with simplified models, not exact descriptions of every little detail of a particular galaxy. When they find the subsequent simulation to be in good general agreement with real galaxies, they can add more fine structure to their models until they either get good matches with the real thing or exceed the computer's capabilities while trying.
I was hoping for some reassurance that they did not quadruple the mass in the initial conditions and expect that those initial conditions could have existed. I can see keeping the mass the same, and dividing it up into smaller and smaller particles as a valid direction to take, but the articles all say they added particles/gas. That means added mass. Back to the earth/Moon example. If the initial condition has the moon orbiting at 384K KM in a nearly circular orbit in 27 days, then I can't just take the model and make the Earth four times as massive to see where it goes. The initial orbit of the moon would be wrong. It could not have been in that nearly circular 27-day orbit at that distance. So again, if they quadrupled the mass in their galaxy model, then the initial conditions are already wrong. If they simply kept the mass the same and divided it into smaller particles, then it's a different story.

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Originally Posted by Strange
As you have been told multiple times, it is a result of gravitational interactions.
Thanks

So, the density wave is a "result of gravitational interactions" between all the particles in the simulation model.
This "gravitational interactions" set a higher Gas + Stars particles density in the density wave. (about 10% to 20% more than the average density in the simulation model).
Therefore, by definition the increased density must be a direct outcome of "gravity interactions" between the particles in the Simulation.

Hence, why do you claim that:
Originally Posted by Strange
it is a wave of density not a wave of gravity.
I'm not sure that I fully understand this statement.
What kind of force had set this density wave? Don't you agree that it is due to gravitational interactions?
If it is not gravitational interactions (gravity force), what kind of force had set this density wave?

One more issue:
On every full orbital cycle in the simulation model, more and more particles have been attracted by gravity force to the density wave.
I have no idea how many orbital cycles they had to do before getting the requested density wave.
In any case, they have started with a density wave of Zero and ended at density wave which is estimated at a value of up to 20%.
Can we assume that they have ended the simulation at our current time, which represents orbital cycles of about 13 Billion years?
How many billion years are needed to set a 10% density wave (in the simulation)?
Last edited by Dave Lee; 2018-May-24 at 04:31 PM.

17. Originally Posted by Dave Lee
I'm not sure that I fully understand this statement.
What kind of force had set this density wave? Don't you agree that it is due to gravitational interactions?
The "wave" (i.e. the regular variations) are in the density of the (bright) stars. The cause may be gravity but they are not waves of gravity. We already have things named gravity waves and other things called gravitational waves.

And, anyway, what does it matter what they are called. They could be called "Fred", as long as everyone knows what the name refers to.

18. Originally Posted by mkline55
Is there more information on the initial conditions beyond "they chose a halo with an appropriate mass and merger history to host a galaxy like the Milky Way and "rewound the tape" back to the initial conditions. Zooming in on the small region that evolved into the chosen halo, they added gas particles and greatly increased the resolution of the simulation." Was there any presumed origin for the added gas particles other than "they were added"? How were they added? Were they in motion? How were they distributed? What element ratios? A more concerning, question is, if the added particles would have been present prior to the start of the simulation, then why didn't they have an impact prior to that point in time? That's like saying we'll create an orbital model and just insert another moon around the Earth as if it suddenly materialized out of nothing and assuming it had no prior effect, then running the simulation from that point forward. The text indicates that's exactly what they did, just creating additional particles in an already-stable environment.
The (first) actual paper reporting on these results is here. Indeed, dividing unrealistically massive simulation particles into (still unrealistically but not quite so much) less massive ones is a common simulation feature.
That links also lists 342 later papers citing this one, which should give a lot of ground for further examination.

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Originally Posted by mkline55
Is there more information on the initial conditions beyond "they chose a halo with an appropriate mass and merger history to host a galaxy like the Milky Way and "rewound the tape" back to the initial conditions. Zooming in on the small region that evolved into the chosen halo, they added gas particles and greatly increased the resolution of the simulation." Was there any presumed origin for the added gas particles other than "they were added"? How were they added? Were they in motion? How were they distributed? What element ratios? A more concerning, question is, if the added particles would have been present prior to the start of the simulation, then why didn't they have an impact prior to that point in time? That's like saying we'll create an orbital model and just insert another moon around the Earth as if it suddenly materialized out of nothing and assuming it had no prior effect, then running the simulation from that point forward. The text indicates that's exactly what they did, just creating additional particles in an already-stable environment.
If you look at the paper it explains it in more detail - they used low resolution simulations which only had dark matter to create the initial seed halo with the same mass as the Milky Way. They then took the low resolution results and upsampled it using a standard method to generate fine scale perturbations. They then further broke down the intermediate scale particles in it into dark matter and gas particles. So they didn't add any mass, they instead assumed minimal baryonic contribution at large scales (i.e. the baryonic component was minimally interacting, like dark matter) and then replaced the particles with an equivalent mass of gas and dark matter particles. They also assumed that there was plenty of early merging activity, but that recently there had been far less (to allow the system to come to a quasi-equilibrium condition as a condensing dark matter halo). Finally they didn't simulate elemental abundances - the star formation model was fairly simple, assuming that once a seed density was reached star formation could be simulated by a stochastic process.

I suspect it is just a case of the articles getting it wrong, at least for ERIS.

20. Originally Posted by Shaula
If you look at the paper it explains it in more detail - they used low resolution simulations which only had dark matter to create the initial seed halo with the same mass as the Milky Way. They then took the low resolution results and upsampled it using a standard method to generate fine scale perturbations. They then further broke down the intermediate scale particles in it into dark matter and gas particles. So they didn't add any mass, they instead assumed minimal baryonic contribution at large scales (i.e. the baryonic component was minimally interacting, like dark matter) and then replaced the particles with an equivalent mass of gas and dark matter particles. They also assumed that there was plenty of early merging activity, but that recently there had been far less (to allow the system to come to a quasi-equilibrium condition as a condensing dark matter halo). Finally they didn't simulate elemental abundances - the star formation model was fairly simple, assuming that once a seed density was reached star formation could be simulated by a stochastic process.

I suspect it is just a case of the articles getting it wrong, at least for ERIS.
Thanks Shaula and NGC3314. That makes a lot more sense than "added particles".

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Originally Posted by Strange
The "wave" (i.e. the regular variations) are in the density of the (bright) stars. The cause may be gravity but they are not waves of gravity. We already have things named gravity waves and other things called gravitational waves.

And, anyway, what does it matter what they are called. They could be called "Fred", as long as everyone knows what the name refers to.
Yes I fully agree. The name doesn't matter.

However, the cause for the density is Gravitational interaction (Please - without may be).

Hence, gravitational interactions between the particles in the Simulation is the ultimate cause for the Density Wave.

In the same token:

Gravitational interactions between the matter (Stars, Nebulae...) in the spiral arm is the ultimate cause for the spiral Arms in the Galaxy.

I hope that we all agree with that.
Last edited by Dave Lee; 2018-May-25 at 01:09 PM.

22. Originally Posted by Dave Lee
I hope that we all agree with that.
I'm glad you do, finally. It's been a journey.

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Originally Posted by Dave Lee
Gravitational interactions between the matter (Stars, Nebulae...) in the spiral arm is the ultimate cause for the spiral Arms in the Galaxy.

I hope that we all agree with that.
Gravitational interactions are the ultimate cause for the spiral Arms in the Galaxy. Not just the ones between matter in the spiral arm. Whether it is down to the bar/disk interactions or the effect of mergers/companions it is these interactions that drive the formation and stability of the density wave pattern. The actual internal interactions of the bodies in the overdensity may have a second order effect but it is not the main driver for the pattern forming or persisting.

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Originally Posted by Shaula
Gravitational interactions are the ultimate cause for the spiral Arms in the Galaxy.
Thanks

That's good enough for me at this point.

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Originally Posted by Strange
What forces caused by the presence of mass do you think they might be simulating? I'll give you three guesses.

Anyway, apart from the fact it is about solving an N-body problem to simulate the formation of galactic structures (i.e. it is about gravity), gravity is explicitly mentioned at least three times in the paper.

In the source code.
""The simulation follows the interactions of more than 60 million particles of dark matter and gas. A lot of physics goes into the code--gravity and hydrodynamics, star formation and supernova explosions--and this is the highest resolution cosmological simulation ever done this way," said Guedes, who is currently a postdoctoral researcher at the Swiss Federal Institute of Technology in Zurich (ETH Zurich)"

https://news.ucsc.edu/2011/08/eris-simulation.html

Two questions with regards to Zurich simulation:

1. Did they try to run the Simulation without dark matter?

2. We see some far end spiral galaxies with estimated age of less than 600 Million years .
If I understand it correctly, in Zurich they have set the simulation for a reference of 13 Billion years. However, did they also try to run the simulation for that short time frame?
In other words, is it feasible to get a full spiral galaxy in only 600 Million years?

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Originally Posted by Dave Lee
1. Did they try to run the Simulation without dark matter?
Density waves can form spiral structure without dark matter. But the kinematics of the resulting galaxies area not in accordance with observations. ERIS is orders of magnitude more complex than the basic models which are indifferent to the matter and dark matter balance because it includes things like radiative effects. So to answer the question they wouldn't have run this particular simulation without dark matter because the results of many previous simulations showed it was required.

Originally Posted by Dave Lee
2. We see some far end spiral galaxies with estimated age of less than 600 Million years .
If I understand it correctly, in Zurich they have set the simulation for a reference of 13 Billion years. However, did they also try to run the simulation for that short time frame?
In other words, is it feasible to get a full spiral galaxy in only 600 Million years?
The goal of ERIS was to simulate our galaxy. Our galaxy doesn't look like the early phase spirals and didn't form in the same environment. The AMR simulation using ENZO code looked specifically at early universe galaxy evolution, as did EAGLE. Rather than focus on ERIS I'd take a look at other simulations for some answers to this as I believe EAGLE did have early spirals form.

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Originally Posted by Shaula
The goal of ERIS was to simulate our galaxy. Our galaxy doesn't look like the early phase spirals and didn't form in the same environment. The AMR simulation using ENZO code looked specifically at early universe galaxy evolution, as did EAGLE. Rather than focus on ERIS I'd take a look at other simulations for some answers to this as I believe EAGLE did have early spirals form.
Please look at the following image:

https://astronomy.swin.edu.au/cosmos...-type+Galaxies

It seems that SB0/S0 galaxy is the mother of all types of early spiral galaxies.

If I remember correctly, you had informed me that the Zurich simulation had started with some gravitation interaction.

So, does it mean that they have started the simulation from the SB0/S0 type of galaxy?
If so, do we have any idea how long it could take to form the SB0/S0 type of galaxy from day one?

There is another issue with regards to the sun orbital cycles around the galaxy:

https://www.quora.com/How-many-times...ted-the-galaxy
Its age is estimated at 4.567 billion years, so at least 18 and perhaps 20 (20.3).

If that is correct, I would assume that the Milky Way galaxy must be stable at least for the last 4.56 Billion years.

So, by deducting the requested time for the SB0/S0 type of galaxy to be formed and also the last 4.56 Billion years from the total age of the Universe - 13.8 Billion years, than how many Billion years might be left for the Milky Way to be formed?

I also wonder what is the estimated age of the youngest early spiral galaxy that we have found.
Last edited by Dave Lee; 2018-Jun-08 at 10:57 AM.

29. That Hubble "tuning fork" diagram is based on an old galaxy evolution theory which has long since been superceded. If I am not mistaken, the prevailing opinion about large elliptical galaxies is that they are the old end product of mergers of smaller spiral galaxies. The merger action smeared out the original disks, which had various orientations, beyond recognition.

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Originally Posted by Dave Lee
If I remember correctly, you had informed me that the Zurich simulation had started with some gravitation interaction.

So, does it mean that they have started the simulation from the SB0/S0 type of galaxy?
No. It states quite clearly what it starts from in the paper. And I believe I summarised the full simulation path in the other thread. It started from gas. Not a galaxy.

Originally Posted by Dave Lee
If so, do we have any idea how long it could take to form the SB0/S0 type of galaxy from day one?
The page you linked to highlights the issue with the tuning fork diagram as you are using it - it doesn't represent an evolutionary track. See https://en.wikipedia.org/wiki/Hubble...l_significance - this makes a lot of the rest of your questions unanswerable as you are relying on something that isn't true to reason from.

Originally Posted by Dave Lee
If that is correct, I would assume that the Milky Way galaxy must be stable at least for the last 4.56 Billion years.
It probably has been. But there is no need for that assumption. Barring major collisions (and remember they are not needed to trigger the density wave, only an interaction) the sun would be fine.

Originally Posted by Dave Lee
So, by deducting the requested time for the SB0/S0 type of galaxy to be formed and also the last 4.56 Billion years from the total age of the Universe - 13.8 Billion years, than how many Billion years might be left for the Milky Way to be formed?
As I have said, the simulation starts from gas. ERIS shows, pretty unambiguously, that using known physics with minimal inputs (and fairly few assumptions - certainly none of the huge ones you seem to be suggesting were used) you can get a Milky Way like galaxy well within the available time.

Originally Posted by Dave Lee
I also wonder what is the estimated age of the youngest early spiral galaxy that we have found.
About 3 billion years for a grand design spiral. And yes, it could have formed in that time. BX442 has a companion which is a great generator for the density wave. Google is your friend.

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