Computational modelling of the companion star and its interaction with Sol

[gdpetti]

Just a thought.

If things reflect each other like the stock market reflects the need to deflect public attention, then perhaps that line from the session on May 17, 2014 is a guide? Seems April as a 'drop dead date' has always been a popular line with these C's, even if not used in that particular reference, and 'eleven months' was the term of choice. IMO, the market should play dead before April, if the charts are aligned like the stars, anything too far out of the ecliptic, soon corrects itself to maintain balance, same as the planets in a star system or stars in a galactic system, no? If this April date isn't correct, then perhaps it's just another example of hyperdimensional teasing of the channel? ;D but then the markets are known for their penchant for 'dead cat bounces', which help to keep the game going even as the ship is sinking.... 'good till the last drop'.... of distraction that is.... 'as in the days of Neo'... they never see it coming, hiding in plain sight.

 

[axj]

Another "random" thought that may be either relevent, or utter nonsense (more likely lol).
When interpreting data, we operate within a definite framework. In Astronomy, the framework is 3D reality and most often, nonelectric "empty" space. Most importantly, we automatically think of physical reality as devoid of consciousness/information as an underlying, and yet unassuming unconscious assumption.

Until there is some practical reality someday to gravitational waves, all we see of the outer space is what and how photons at whatever wavelengths arrive and how they are detected, etc. We see what the universe allows us to see in other words.
Now to give an analogy, on a hot day, the ground is heated by the sun and a strong gradient of temperature builds up in the air right above it. Light that travels almost parallel to the ground is strongly refracted, which gives the mirage effect. Light from other directions, especially the one whose propagation is parallel to the temperature gradient is as usual. Thus, there is a certain privileged direction where we have a bizarre optical distortion because of the nature of the medium. Now suppose that the solar system is in a discharge mode with Nemesis. We can imagine a connecting thread, straight or otherwise, making the connection between the objects. The question one could ask is how does light propagate in the direction of that thread. Does it cause some optical distortion that makes any object observed in that direction fall below detection threshold? If it is the case, than maybe we have a blindspot in that very particular direction.

The thing is that as a planet with so much density of consciousness (at least in potential), it is possible that the universe offers us with a special treatment such as that we cannot extrapolate from systems we observe from the outside (any double star system) to what we can see from the inside. The image of the fish in the ocean comes to mind. Solar eclipses and other "coincidences" may be a way to remind us that we indeed occupy a special place in the "local?" universe.

To draw more from mythology, if we take the story of Atlantis literally, how come such a civilization that conquered the solar system couldn't anticipate what happened? One possibility is the above-mentioned possible blind-spot, another possibility is transdimentional phenomena. For instance, it is very possible that a cycle-ending cometary bombardment would be caused by a certain ratio X of comets from 3D, and another ratio from comets that suddenly emerge from elsewhere. Same with Nemesis. One component of its behaviour could be 3D physics, and another part could be from (3+n)D physics. Since the Wave is "realm merging" of some sort, which is hard to describe/model/predict/define etc., the only rational (not logic) approach to the thing would be that: If we see Nemesis, there is a possibility that it is there, but if we don't see it, it doesn't mean that it isn't there, it just means that there is a possibility that it isn't there, which implies a possibility that it is there. Since the rules of the games are blurred, and the rules of the known cannot be applied with certainty to the rules of the unknown, it's only a matter of conjecture.
OSIT FWIW

Interesting! Sounds like a question for the Cs.

I agree. Another good question might be if the companion star has already been discovered and whether amateur astronomers may be able to find it if told where to look.

 

[tohuwabohu]

I think the Cs wont answer the question if we don't try to answer them first. Perhaps only in general sense.

The last time I posted results of the simulation I discovered that the energy is not conserved and therefore the results were inaccurate. I imporved the algorithm a little bit.
The final algorithm utilizes fourth order integration method coupled with adaptive time stepping. This way the accuracy is maintained even for very close encounters. The energy is not conserved anymore because the trans-neptunian objects (TNOs) are treated as test particles. They have negligible masses compared to the stars and other planets thus the results are acceptable and the execution speed is increased. Moreover of interest are only small asteroids that are now impacting Earth so we can make some comparisons hopefully.

 

[tohuwabohu]

The accuracy can therefore be checked only by visually inspecting the transformation pattern of a uniformly distributed patch of particles upon interaction with the stars and planets. This is collisional simulation – the impacts against the planets and stars are checked and recorded. When a test particle has distance smaller than a radius of the given object (planet or star, measured from its center) an impact event is recorded containing data of interest like time of the event, impact velocity and others. The particle is afterwards discarded.

The impact velocity is calculated from the relative velocity of the impacting particle and the impacted object. The atmospheric effects are neglected thus the impact velocity can be larger than in reality. Nonetheless this quantity is only informative. Most of the bolides will be destroyed upon entering the atmosphere and only small fragments will impact the surface. The aim is to see what it takes in terms of the spatial density of the TNO and companion distance to match the current fireball influx.

 

[tohuwabohu]

Firstly the spatial and temporal accuracy is checked on a uniform patch of particles. The patch with dimensions 2x20 AU contains 10,000 particles with average heliocentric distance 100 AU. The particles are initially on a stable circular orbit. As the companion approaches, the patch starts to bulge. Afterwards the companion passes through the patch and creates a wake. The patch is intentionally colored using two different colors to better perceive the transformation. It can be seen that the wake is now correct – resembles sphere and behaves like a wave. The tunnel in the wake is formed by the particles that impacted the companion and were discarded. No object was attached to the companion. It can happen but only for objects that are moving more along the path of companion (in a colinear fashion).

The figure shows the evolution of the patch (from left to right, top to bottom).

 

[tohuwabohu]

One can notice that the distribution was maintained also after the transform and that even for very close encounters (particles right on the sides of the tunnel) the spatial/temporal accuracy is excellent.

By the wave like behavior is meant that the particles propagate and even scatter similarly to a wave. This can be observed in figure below where the sequence shows what happens next as the wake approaches the solar system and interacts with the sun and the planets. The sun being very massive creates big secondary wave that propagates back at the companion. The back scattered wave is nonetheless much less spatially dense and the companion then diffuses the particles even more as it hurls them back into the inner solar system. Also the planets contribute to the scattering but in much lesser extent. Even if it is not readily visible the interaction with the planets is observable on a smaller scale. Moreover even small initial change in trajectory of a particle can lead to large deviations in the end.

One leg of the patch (particles to the right of the passing companion in previous post) was slowed down by the companion so much that it collapses into the inner solar system as the companion shoots past the perihelion. This is visible in the attached figure in the last picture where the sling like formation interacts already with Saturn as it tightens around the sun. I will call the sling-like formation the destabilized tail.
The wake always precedes the companion whereas the destabilized tail follows the companion.

 

[tohuwabohu]

Effect of heliocentric distance

Here the effect of the heliocentric distance of a patch of 10,000 uniformly distributed particles on a stable circular orbit is investigated. The number of Earth crossing objects is recorded for each case upon companion passes through the patch and creates the primary wake. The patch has dimensions 1x10 AU thus the number of objects in the patch also corresponds to the spatial density of 1000 AU-2.

The results are summarized in Tab. 1 below. The total number of Earth crossing objects is shown in the second column. These are the objects that cross the Earth orbit. The influx of the objects into Earth orbit in number per year is shown in the third column. Influx duration is time in years it took for the patch to pass through the inner solar system. The averaged spatial density is calculated from the number of objects located in the inner solar system in a snapshot taken once a year. The maximal density is the same only the maximum is taken from all snapshots taken.

Tab. 1 Effect of heliocentric distance on influx and density

Heliocentric distance [AU]	Number of Earth crossing objects	Influx of objects [#/year]	Influx duration [years]	Average spatial density [#/AU2]	Max spatial density [#/AU2]
900	4413	339.5	13	67.6	109
800	3945	232.1	17	48.8	71
700	3648	214.6	17	42.0	65
600	3399	212.4	16	43.1	63
500	3213	200.8	16	40.9	57
400	3076	205.1	15	38.5	54
300	1971	179.2	11	35.0	47
200	2521	210.1	12	42.9	71
100	4392	313.7	14	62.8	135

It is surprising that the influx is very large for heliocentric distance 900 AU. It is also good to keep in mind that the velocities of all objects do change with the heliocentric distance which affects the diffusion and spread of objects upon interaction. These results are done for constant initial density of asteroids. Nonetheless in reality the density diminishes with increasing heliocentric distance [1, 2]. Therefore the influx would be larger for lower distances.

References:
[1] Duncan, M., Quinn, T., & Tremaine, S. The formation and extent of the solar system comet cloud. 1987, AJ, 94.
[2] Dones, L., Levison, H., Duncan, M., & Weissman, P. Simulations of the formation of Oort cloud. 2000, in AAS/Division of Planetary Sciences Meet., vol. 32.

 

[tohuwabohu]

To resolve the regular initial distribution and zero eccentricities a small deviations in the TNOs initial velocities were introduced which destroy the uniformity. The change in velocity (and slightly also eccentricity) did not change the results in a significant way.

There are differences compared to the regular distribution but the overall trend remains the same. The patch is more spread after the encounter with the companion and also the distribution of the objects is perturbed. This can be seen in Fig. 3 where the objects that penetrated into the inner solar system are colored pink. The figure shows distribution of these objects in the patch at the beginning and also at the end of the simulation. Obviously only the objects lying in a very narrow spiral-like area are thrown towards the Earth (Fig. 4). The figure shows spiral of constant width. This knowledge was utilized to decrease the area that needs to be modeled and in the simulation only the spiral-like area is populated by the TNOs to decrease the computation time.

 

[tohuwabohu]

Clearly the TNOs having nonzero inclination and eccentricity could also cross the earth orbit if they were approached by the companion under correct angle. The spiral like patch would be then more diffused and larger portion of the space would have to be modeled. This is not pursued mainly because of computer limitations.

At distance 300 AU the inner solar system is partially shielded from the meteor shower by the companion – the tunnel is aligned with the sun and as a result the influx of objects is decreased (Fig. 5). This effect is dependent on the position and relative velocity of the companion and the TNOs and can be reproduced also in 3D.

 

[tohuwabohu]

To sum the results the values directly from the simulation are shown in Fig. 6 and Fig. 7 for the influx and density. The time on the x axis is time for the companion to reach perihelion.

The peaks correspond to the patch distance from the right peak for distance 900 AU to the left peak for distance 100 AU. These represent only the 10 AU in the radial direction. In the tangential direction the spiral-like area was only 1 AU wide. It would be better to make continuous spiral from nine patches with radial width 100 AU but this would require 10 times more objects to maintain the initial 1000 AU-2 spatial density and each simulation would take few days to complete. There is also option to use lower spatial resolution but in that case the accuracy will suffer. Also first it has to be determined how is the influx and the density in the inner solar system affected by the spatial density in the patch at the beginning. For now the estimated trend is approximated by the red line.

The maximum influx at the perihelion almost matches the initial spatial density of the TNOs – the influx is close to 800 objects/year. The maximum in density is roughly one quarter of the influx.

 

[tohuwabohu]

Effect of spatial density

The effect of spatial density was investigated on a patch with heliocentric distance 900 AU. The initial density was scaled from 100 AU-2 to 100,000 AU-2. This time also the number of impacts is recorded. The results are shown in Tab. 2. By the influx is meant sustained influx of the bodies into the inner solar system and spatial density in column 4 refers to sustained density of the TNOs in the inner solar system. By sustained is meant that it would be valid if the Oort cloud would be modeled as continuous (not only a patch).

Tab. 2 Effect of the initial spatial density

Initial spatial density [#/AU2]	Number of Earth crossing objects	Influx of objects [#/year]	Spatial density [#/AU2]	Number of Earth impacts	Earth impacts per year
100	500	66	11	-	-
200	992	136	22	-	-
625	2996	410	75	-	-
1000	4383	610	116	1	0.08
2500	11483	1600	305	1	0.08
10000	45860	6302	1295	1	0.08
100000	458627	62996	12266	16	1.33

 

[tohuwabohu]

As can be seen from Fig. 8 (and from Tab. 2) the relation between the initial density of the TNOs and the influx into inner solar system is linear. The same can be said for the spatial density of the TNOs in the inner solar system.

This conclusion is logical because all objects from the spiral are thrown into the inner solar system thus the more the area is populated the higher the influx and density. Clearly even the initial spatial density of 100,000 AU-2 is not enough in terms of Earth impacts or atmospheric entries that are now present. Here only assumption can be made on the number of impacts because the relationship can hardly be obtained from the small number of events. If the probability of impact is linearly dependent on the influx and density then the results can be easily scaled to any initial spatial density of the TNOs.

 

[psychegram]

Well this is just stunning. Absolutely amazing work.

It seems that the simulations suggest a much smaller influx of cometary bodies than has in fact been observed. However, it seems (unless I am misinterpreting something) that the smallest perihelion you test is 100 AU. But according to the 98/07/04 transcript, perihelion is rather less than this:

A: They are moving in tandem with one another along a flat, elliptical orbital plane. Outer reaches of solar system are breached by passage of brown companion, thus explaining anomalies recently discovered regarding outer planets and their moons.
Q: (A) […] Elliptical orbit means there is perihelion and aphelion. I want to know what will be, or what was, or what is the closest distance between this brown star and the sun? What is perihelion? Can we know this, even approximately. Is it about one light year, or less or more?
A: Less, much less. Distance of closest passage roughly corresponds to the distance of the orbit of Pluto from Sun.
Q: (A) Okay. Now, this closest pass, is this something that is going to happen?
A: Yes.
Q: (A) And it is going to happen within the next 6 to 18 years?
A: 0 to 14.

Now, ignoring the large perihelion increase in the number of Earth-crossing objects, which as you note is likely an artifact of the model originating in the use of a constant number density, it seems that the increase with perihelion distance (beyond about 300 AU) is quite strong. Therefore, how do the results change if perihelion is closer to 50 AU? And how do they change if the number density is more realistic?

 

[MusicMan]

It would be interesting to know whether the brown star has scooped up Pluto in its passing, hence the reason Pluto is no longer regarded as a planet.
This could also contribute to your Mass anomaly.

 

[tohuwabohu]

It would be interesting to know whether the brown star has scooped up Pluto in its passing, hence the reason Pluto is no longer regarded as a planet.
This could also contribute to your Mass anomaly.

This could definitely happen depending on the position of Pluto on its orbit. I think a 3D model would be helpful so perpahs later I will look into it. Nonetheless the inclination of the companion is also unknown so for now I am modeling it in the plane of ecliptic.