Computational modelling of the companion star and its interaction with Sol

[MusicMan]

Thank you guys for your support, I appreciate it very much. Well step by step the informations keep adding little by little so we will see where it will lead. I am just afraid that the associate professor position will left me with less time on my hands. Moreover teaching is not only time consuming but also exhausting. But the bright side is I can support others some more as mkrnhr said. So what can I do, I will just enjoy the ride and see where it takes me.

MusicMan I agree with you, moreover I think that the inner solar system is loaded with dust which is then collected as the Earth sweeps through it on her orbital journey. But of course I cannot prove it because we are working with very limited data here. Perhaps the amount of dust in the atmosphere even seasonally oscillates.

I am just trying to understand what is going on in some general terms, and if the companion throws a lot of rocks into the inner solar system then the dust is integral part of it. We can enjoy the fact that one can get to same results via different ways. So perhaps some dust expert is scratching his head as he is looking at his dust samples and thinks that something is not right. :)

On the subject of dust, you would imagine that the particles of lesser mass would be the ones most affected by the gravitational pull of passing objects, so that they would be the ones that arrive first.
In other words, if you are starting to see a lot of smaller meteorites, flashing through the sky, then the larger ones will be following on their heels, and it's time to take cover.

I guess its impossible to calculate that sort of thing, maybe you could model a medium size object, and extrapolate backwards for the smaller ones, and forwards for the larger ones.
A good size to aim for would be an object that could flatten a city.
Anything larger would be even more of a worry.
Anything less might only be startling to most people, and could be neglected.

 

[Mikey]

Hi tohuwabohu, I just skimmed this thread from the beginning and wanted to congratulate you for your multi-year work so far. The project you've undertaken is difficult and has many unknown variables, but from what I've seen, and as far as I can tell, you made the best out of it and are applying proper scientific methods. I've got background in applied mechanical engineering too, and specialized a little bit in numerical methods in linear elastostatics, so I at least got a 'feeling' for what you're doing and can appreciate it. I think if you wait for more current observational data on body influx and use it as a feedback for your model (as you've been doing), you actually might get somewhere! And on top of that, I'm sure you've learned a ton of new and useful things pertaining to your profession. So, I think it's a win-win scenario for you! Also, I think writing a paper about it is a good idea, even if you only self-publish it. I'm definitively going to read it! Keep up the work!

Also, I've been wondering, having worked with both OpenCL and OpenGL, if moving the math to the GPU (via OpenCL or similar APIs) might be possible. You might get at least an order of magnitude faster calculations. I know that not every calculation is parallelizable, so it depends of course on the problem.

Edit: It seems gravity simulations lend themselves well to the GPU: https://www.youtube.com/watch?v=HR7SgCKu8Oc

 

[tohuwabohu]

MusicMan, according to the simulation the gravity well affects all particles in the same manner and it doesn't depend on their size or mass. Nevertheless the dust microparticles are also very much affected by the electromagnetic forces. For example the solar wind tends to blow the smallest particles out of the solar system. But because I have only mechanical model so far, there is no difference between the dust and the large bodies, and therefore I cannot make accurate predictions.

The most I could do was already shown in the figures 24 to 26. One can extrapolate the graphs to the left to have a feel what is the count of the dust particles that is flowing into the atmosphere. In general it will be some very large number like billion or trillion depending what is the limiting size of the microparticles.

 

[tohuwabohu]

Hello Data,
thank you for your encouraging words. I am doing what I can with the limited amount of data and slowly but surely I think I am going somewhere with the thread. I am thinking that when I will come to a point where I couldn't get any new ideas I will concentrate my energy to write an article about the analysis that is presented here.

Well the OpenCL implementation might help but it would require above all powerful hardware which is capable of high performance in double precision. I do not have such equipment nor do I plan to buy it simply because I think that the money can be spent much better elsewhere where it is needed and where it can help others.
Another thing to consider is whether also quite complicated algorithms could be efficiently parallelizable. This is questionable because mostly only the basic n^2 algorithms with simple time stepping schemes are presented to show the raw power of GPUs. And only with potential softening and in single precision.

For example right now I am literally battling with very simple simulation where only the sun, companion and planets are present. That is there are only 11 bodies present. Yet I have found that parallel performance in this simple case is even worse compared to single thread performance because of the communication overhead and necessary synchronization. I am doing this to have better initial conditions for the cometary swarm problem and it also needs to be evolved for 26 Myr. One would say that it is very simple problem and in one hour it should be over right? But this is not the case because to ensure the stability of the planets the time step has to be very small. Right now I use 9 hrs step size and on single thread this yields 26000 fps. So one can easily calculate how long it takes to simulate 26 million years.

 

[tohuwabohu]

I finished the simulation of the companion star together with the solar system including the planets.
I found proper initial conditions for the Sun and companion when the simulation starts from their farthest point on their orbit from the barycenter. The orbits are shown in Fig. 44.

So this was a success. I experimented also with variable perihelion distance and found that the distance should be not less than 45 AU because else the companion captures Pluto the dwarf planet and carries it off of the solar system. It was circling around the companion for the rest of the simulation which took three periods. So I guess the perihelion distance ought to be somewhere around 50 AU.

Well I then modified the orbital period of the companion to one tenth of the 26 million years to see the effect of the planetary positions on the aphelion distance. Well I reduced it in order to save time. So the simulation took only one day. I left the companion revolve for several orbital periods (Fig. 45). The barycenter moves to the left so the starting position was on the right most orbit.

One can see that indeed the aphelion distance and thus also the orbital period changes after each perihelion visit. This confirms that the planets have pronounced effect on the companion star. The perihelion distance for this case was 50 AU.

 

[tohuwabohu]

It is interesting to note that although the aphelion distance changes, the perihelion distance was stable and did not change at all without external influences (outside of the solar system).

But not only the companion star is affected by the planetary positions. Even though from the distance the sun's orbital path looks like it is very simple and straightforward (Fig. 46), upon closer inspection it is far from simple (Fig. 47).

It's spirals in spirals in spirals... Because each planet pulls the sun in its direction the resulting orbital path is a superposition of all the planetary influences. Just like the summation of vectors. It is clear that the initial conditions are a function of the planetary positions. I would say that the most accurate would be to take the snapshot of the whole system and apply it on the 26 million year problem. But first I should check the results of the previous run to see whether the results can be improved with proper initial conditions.

 

[goyacobol]

It is interesting to note that although the aphelion distance changes, the perihelion distance was stable and did not change at all without external influences (outside of the solar system).

But not only the companion star is affected by the planetary positions. Even though from the distance the sun's orbital path looks like it is very simple and straightforward (Fig. 46), upon closer inspection it is far from simple (Fig. 47).

It's spirals in spirals in spirals... Because each planet pulls the sun in its direction the resulting orbital path is a superposition of all the planetary influences. Just like the summation of vectors. It is clear that the initial conditions are a function of the planetary positions. I would say that the most accurate would be to take the snapshot of the whole system and apply it on the 26 million year problem. But first I should check the results of the previous run to see whether the results can be improved with proper initial conditions.

tohuwabohu,

Not being a scientist or a mathematician I am not sure what the colors in Fig. 46 represent. It sounds reasonable that the planets and their size and position would be part of the equation. Does Fig. 47 represent the spiraling effect of the sun and it's companion star?

Thank you for your continued research. :)

 

[MusicMan]

I'm wondering if we should take into account the comments from the C's that indicate that the sun is the equivalent of a 'proton', and the companion star is the equivalent of an 'electron', macroscopically. So there are electromagnetic effects to consider.
From this point of view, what elementary particle could we compare the planets to, and would we consider Pluto, recently in the news - I wonder if the ptb are taking a sneaky look at the companion at the same time as they are viewing Pluto..

 

[tohuwabohu]

It is interesting to note that although the aphelion distance changes, the perihelion distance was stable and did not change at all without external influences (outside of the solar system).

But not only the companion star is affected by the planetary positions. Even though from the distance the sun's orbital path looks like it is very simple and straightforward (Fig. 46), upon closer inspection it is far from simple (Fig. 47).

It's spirals in spirals in spirals... Because each planet pulls the sun in its direction the resulting orbital path is a superposition of all the planetary influences. Just like the summation of vectors. It is clear that the initial conditions are a function of the planetary positions. I would say that the most accurate would be to take the snapshot of the whole system and apply it on the 26 million year problem. But first I should check the results of the previous run to see whether the results can be improved with proper initial conditions.

tohuwabohu,

Not being a scientist or a mathematician I am not sure what the colors in Fig. 46 represent. It sounds reasonable that the planets and their size and position would be part of the equation. Does Fig. 47 represent the spiraling effect of the sun and it's companion star?

Thank you for your continued research. :)

You are right goyacobol, I forgot to explain whats in the figures, sorry. This just shows how important clear communication is.

Fig. 46 shows the inner solar system. So the sun is in the centre and the colored circles are the orbital paths of the four planets that are closest to the sun - Mercury, Venus, Earth and Mars. I should note that in the simulation all planets were included. The sun is also moving due to the initial conditions and due to the influence of the planets and the yellow line is the path along which the sun moves.
Fig. 47 is simply a magnification of the solar path. So to say a close up on the sun in Fig. 46. The companion star is not present in the figures.

What I wanted to say by these pictures is that contrary to the popular belief that the sun is static or that it is moving simply along some straight line, the sun moves in a very complex way. And exactly this was the culprit with the 26 million year simulation I made. I did not realized this and thus the initial conditions were wrong. This resulted in the companion star being ejected from its periodic orbit. I will write about the simulation in next posts.

 

[tohuwabohu]

I'm wondering if we should take into account the comments from the C's that indicate that the sun is the equivalent of a 'proton', and the companion star is the equivalent of an 'electron', macroscopically. So there are electromagnetic effects to consider.
From this point of view, what elementary particle could we compare the planets to, and would we consider Pluto, recently in the news - I wonder if the ptb are taking a sneaky look at the companion at the same time as they are viewing Pluto..

Well MusicMan, you are jumping way ahead. But to clarify if the sun is a proton and the companion star is an electron then the solar system is perhaps nucleus and the planets are then neutrons. But I think with the knowledge we have about solar system we can do better than this.

I have a feeling that this thread will inevitably lead to the plasma theory simply because it is part of the puzzle. It's just we have to go step by step carefully so as to not miss some gems along the path... ;)

 

[goyacobol]

It is interesting to note that although the aphelion distance changes, the perihelion distance was stable and did not change at all without external influences (outside of the solar system).

But not only the companion star is affected by the planetary positions. Even though from the distance the sun's orbital path looks like it is very simple and straightforward (Fig. 46), upon closer inspection it is far from simple (Fig. 47).

It's spirals in spirals in spirals... Because each planet pulls the sun in its direction the resulting orbital path is a superposition of all the planetary influences. Just like the summation of vectors. It is clear that the initial conditions are a function of the planetary positions. I would say that the most accurate would be to take the snapshot of the whole system and apply it on the 26 million year problem. But first I should check the results of the previous run to see whether the results can be improved with proper initial conditions.

tohuwabohu,

Not being a scientist or a mathematician I am not sure what the colors in Fig. 46 represent. It sounds reasonable that the planets and their size and position would be part of the equation. Does Fig. 47 represent the spiraling effect of the sun and it's companion star?

Thank you for your continued research. :)

You are right goyacobol, I forgot to explain whats in the figures, sorry. This just shows how important clear communication is.

Fig. 46 shows the inner solar system. So the sun is in the centre and the colored circles are the orbital paths of the four planets that are closest to the sun - Mercury, Venus, Earth and Mars. I should note that in the simulation all planets were included. The sun is also moving due to the initial conditions and due to the influence of the planets and the yellow line is the path along which the sun moves.
Fig. 47 is simply a magnification of the solar path. So to say a close up on the sun in Fig. 46. The companion star is not present in the figures.

What I wanted to say by these pictures is that contrary to the popular belief that the sun is static or that it is moving simply along some straight line, the sun moves in a very complex way. And exactly this was the culprit with the 26 million year simulation I made. I did not realized this and thus the initial conditions were wrong. This resulted in the companion star being ejected from its periodic orbit. I will write about the simulation in next posts.

tohuwabohu,

Thanks for the explication. I guessed correctly on Fig. 46 but the Fig. 47 is more clear now.

 

[tohuwabohu]

Here I will try to explain how was the 26 million years simulation made. Basically it was very similar to what is shown in Fig. 39 only there are complete rings which were populated by one million objects and in the 26 Myr run I could use only up to 1000 objects to finish the simulation in reasonable time.

Therefore I populated the objects in a tight patch that would be basically part of a ring. It is the part that interacted with the inner solar system so it was very small (the pink particles in Fig. 40 to Fig. 43 if you can imagine where they were initially). I calculated that for the orbital period of 3600 years the patch has to be placed at distance 470 AU from the sun. The 3600 year period is the period of the destabilized tail after the patch interacts with the companion. The companion was placed at distance 550 AU.

The velocity of the companion and of the sun was prescribed according to the two body simulation. This proved to be wrong as the companion didn't return to the point of origin. The planets were also present and can be seen in the figures. Their velocities were determined from the ephemeris data.

Few snapshots from the beginning of the simulation are shown in the following figures. The situation after 1900 years is shown in Fig. 48. Trajectories are shown for some of the bodies but not for all. In the figure you can see the solar system as it ethereally floats through the space not knowing that it will soon be hit by the destabilized tail region. The bodies that are part of the primary wave have already interacted with the solar system and now are seen to be leaving it for good. These bodies are scattered in all directions. As was mentioned earlier the primary wave always precedes the companion and one can see that the companion already passed the perihelion and is off for its orbital journey. The destabilized tail is about to 'wrap' around the solar system.

In Fig. 49 and Fig. 50 the situation after 12500 and 25000 years respectively is shown. Even after such short time one can observe how the orbits are affected by the planetary interactions. Some bodies were bound closer to the solar system, others were thrown farther and some were ejected for good. The orbits of most of the object are directed toward the initial position, meaning their aphelion is in that general direction. Nonetheless their orbital period changed. It is surprising how much scattered the orbits are after only such relatively short time (compared to 26 Myr).

The particles are color coded as always. Pink means interaction with the inner solar system and red means close encounter with Earth.

 

[tohuwabohu]

Some of the objects did have Sedna like orbits. Astronomers already noted that such orbit could only be formed by passing star. This is a good sign.

The situation after 25 Myr is shown in Fig. 51. I couldn't afford to run it with the trajectories so only the positions are shown. What is extraordinary is the scale of the image. I already mentioned that the companion star did not return to the point of origin. This is in fact the only flaw in this simulation. The companion is shown with the brown dot and after 25 Myr it is more than 600,000 AU distant from the sun. The original aphelion distance of the companion was approximately 200,000 AU.

The farthest body is over 100 ly (light years) away from the sun. This is over 6 million AU! So the extent to which the bodies were scattered is amazing. It is still observable that most of the bodies are in the direction of their initial position from the sun. Something like a spike is created from the small patch.

I shall gather some statistical data from the simulation.

 

[tohuwabohu]

Here is some statistics. I present the data I gathered from the simulation in Fig. 52. The data are shown in a form of histograms that are arranged into a table. The rows correspond to a snapshot at diferent simulation times. So the first row shows the data extracted after 100,000 years, the second row after 5 million years etc. up to sixth row where the parameters are shown after 25 million years.

In the columns are the three observed quantities - perihelion distance (first column), aphelion distance (second column) and the orbital period (third column). The bin size for perihelion distance is 1 AU, for aphelion distance 100 AU and for orbital period 100 years. So the bars show the number of objects in some range. For example if we are interested in knowing how many objects potentially interact with Earth, then we have to look for the first (most left) bar in the perihelion distance chart, because this bar shows number of objects with perihelion distance less than or equal to 1 AU. The second bar shows number of objects with perihelion distance between 1 AU and 2 AU etc. Similarly also the other charts were created.

The total number of bodies present in the simulation was 900. Looking at the first row we can observe that the distribution is according to the theoretical assumptions. That is the peaks in the charts corresponds to perihelion distance less than 1 AU, to the orbital period 3600 years and logically also to the aphelion distance 470 AU which is in agreement with the initial position of the patch. So after only 100,000 years there is some change in orbital parameters but not significant.

After five million years the situation is nonetheless completely different. One can observe that the bodies with perihelion distance less than 1 AU were almost completely eradicated. There are only 6 such objects which means that 96 % of the original population was ejected from their orbits. The peaks correspond to the space in between the planets. So the planets are doing very good job in clearing their orbital space.
If we look at the aphelion distance chart, there is clear shift in the peak but notice also the different scale on the y-axis. Only 76 objects have aphelion less than 500 AU that is only 8 % compared to the total number resent in simulation. Other objects were ejected.
Looking at the orbital period one can see that it is completely disrupted. There is even gap around 3600 years period. It's like a divide, some of the objects were bound on a closer orbital paths, but most were ejected. There is 69 objects with orbital period less than 3600 years.

The next rows show similar distribution of the quantities but with diminishing number of bodies. After 25 million years there is only 1 object that could potentially interact with Earth. There are two objects with orbital period almost 3600 years but not quite exactly.

This means that if we would treat each object as a potential cometary swarm, then there is small probability that it would survive 26 million years. But the probability gets higher if the swarm consists of a large number of relatively small bodies. In this case even after it interacts with a planet it can reshape and repopulate on its orbital path and hit once again with similar strength.
More precise simulation would require properly populated solar system rings + collisional scattering. This would require enormous computational power.

There were also several impacts. After 25 Myr the impacts are as follows:
Sun ...... 16 hits
Jupiter .. 3 hits
Saturn .. 1 hit
-----------------
Total ..... 20 hits

 

[tohuwabohu]

I could only find one mechanism how such periodic cometary shower might form. And it was presented here. In theory if this would be the case then there should be some dense ring at heliocentric distance 470 AU. Each time the companion passes through this region the cometary shower is either formed anew or reinforced.
The primary wave from such encounter would hit Earth approximately 400 years ago assuming that the companion is near perihelion.

I could not find any resonance with planets and resonance with the companion would be extremely weak because the cometary swarm would circle the sun over 7700 times during one orbital period of the companion.
The simulations were very much time consuming so I will not pursue this further.

Nevertheless during the simulations another path was revealed which I wish to examine closely.