One can divide the stars in MW to the stars in the galactic disk and those in the galactic halo. The halo has gigantic structures consisting of clouds and streams of stars rotating around the center of the MW. These structures have been identified as a kind of debris thought to reflect the violent past of the MW involving collisions with smaller galaxies.

The scientists investigated 14 stars located in two different structures in the Galactic halo, the Triangulum-Andromeda (Tri-And) and the A13 stellar over-densities, which lie at opposite sides of the Galactic disc plane. Earlier studies of motion of these two diffuse structures revealed that they are kinematically associated and could relate to the Monoceros Ring, a ring-like structure that twists around the Galaxy. The position of the two stellar over-densities could be determined as each lying about 5 kiloparsec (14000 ly) above and below the Galactic plane. Chemical analysis of the stars made possible by their spectral lines demonstrated that they must must originate from MW itself, which was a complete surprise.

The proposed model for the findings is in terms of vertical vibrations of galactic disk analogous to those of drum membrane. In particular the fact that the structures are above and below of the Monoceros Ring supports this idea. The vibrations would be induced by the gravitational interactions of ordinary and dark matter of galactic halo with a passing satellite galaxy. The picture of the the article (see this) illustrates what the pattern of these vertical vibrations would look like according to simulations.

In TGD framework this model is modified since dark matter halo is replaced with cosmic string. Due to the absence of the dark matter halo, the motion along cosmic string is free apart from gravitational attraction caused by the galactic disk. Cosmic string forces the migrated stars to rotate around to the cosmic string in plane parallel to the galactic plane and the stars studied indeed belong to ring like structures: the prediction is that these rings rotate around the axis of galaxy.

One can argue that if one has stars are very far from galactic plane - say dwarf galaxy - the halo model of dark matter suggests that the orbital plane arbitrary but goes through galactic center since spherically symmetric dark matter halo dominates in mass density. TGD would predict that the orbital plane is parallel to to the galactic plane.

Are the oscillations of the galactic plane necessary in TGD framework?

- The large size of and the ring shape of the migrated structures suggests that oscillations of the disk could have caused them. The model for the oscillations of MW disk would be essentially that for a local interaction of a membrane (characterized by tension) with its own gravitational field and with the gravitational field of G passing by. Some stars would be stripped off from the membrane during oscillations.

- If the stars are local knots in a big knot (galaxy) formed by a long flux tube as TGD based model for galaxy formation suggests, one can ask whether reconnections of the flux tube could take place and split from the flux tube ring like structures to which migrating stars are associated. This would reduce the situation to single particle level and

it is interesting to see whether this kind of model might work. One can also ask whether the stripping could be induced by the interaction with G without considerable oscillations of MW.

- G moves past the MW and strips off stars and possibly also larger structures from MW: denote this kind of structures by O. Since the stripped objects at the both sides of the MW are at the same distance, it seems that the only plausible direction of motion of G is along the cosmic string along which galaxies are like pearls in necklace.

G would go through MW! If the model works it gives support for TGD view about galaxies.

One can of course worry about the dramatic implications of the head on collisions of galaxies but it is interesting to look whether it might work at all. On the other hand, one can ask whether the galactic blackhole for MW could have been created in the collision possibly via fusion of the blackhole associated with G with that of MW in analogy with the fusion of blackholes detected by LIGO.

- A reasonable approximation is that the motions of G and MW are not considerably affected in the collision. MW is stationary and G arrives with a constant velocity v along the axis of cosmic string above MW plane. In the region between galactic planes of G and MW the constant accelerations caused by G and MW have opposite directions so that one has

g

_{tot}= g_{G}-g_{MW}between the galactic planes and above MW plane

g

_{tot}= -g_{G}+g_{MW}between the galactic planes and below MW plane ,g

_{tot}= -g_{G}- g_{MW}above both galactic planes ,

g

_{tot}= g_{G}+ g_{MW}below both galactic planes .

The situation is completely symmetric with respect to the reflection with respect to galactic plane if one assumes that the situation in galactic plane is not affected considerably. Therefore it is enough to look what happens above the MW plane.

- If G is more massive, one can say that it attracts the material in MW and can induce oscillatory wave motion, whose amplitude could be however small. This would induce the reconnections of the cosmic string stripping objects O from MW, and O would experience upwards acceleration g
_{tot}= g_{G}-g_{MW}towards G (note that O also rotates around the cosmic string). After O has passed by G, it continues its motion in vertical direction and experiences deceleration g_{tot}= -g_{G}- g_{MW}and eventually begins to fall back towards MW.

One can parameterize the acceleration caused by G as g

_{G}=(1+x)× g_{MW}, x>1 so that the acceleration felt by O in the middle regions between the planes is g_{tot}=g_{G}-g= x × g_{MW}. Above planes of both G and MW the acceleration is g_{tot}= -(2+x) g_{MW}.

- Denote by T the moment when O and G pass each other. One can express the vertical height h and velocity v of O in the 2 regions above MW as

h(t)= (g

_{G}-g_{MW})2t^{2}, v=(g_{G}-g_{MW})t for t<T ,

h(t)= [(g

_{G}+g_{MW})/2](t-T)^{2}+ v(T)(t-T)+h(T) , v(T)= (g_{G}-g_{MW})T ,

h(T) = [(g

_{G}-g_{MW})/2] T^{2}for t>T .Note that time parameter T tells how long time it takes for O to reach G if its has been stripped off from MW. A naive estimate for the value of T is as the time scale in which the gravitational field of galactic disk begins to look like that of point mass.

This would suggest that h(T) is of the order of the radius R of MW so that one would have using g

_{G}= (1+x)g_{MW}

T∼ (1/x)

^{1/2}(2R/g_{MW})^{1/2}.

- The direction of motion of O changes at v(T
_{max})=0. One has

T

_{max}= (2g_{G}/(g_{G}+g_{MW}) T ,

h

_{max}= -[(g_{G}+g_{MW})/2] (T_{max}-T)^{2}+ v(T)(T_{max}-T)+h(T) .

- For t>T
_{max}one has

h(t)= -[(g

_{G}+g_{MW})/2] (t-T_{max})^{2}+h_{max},

h

_{max}=-(g_{G}+g_{MW})2(T_{max}-T)^{2}+h(T) .

Expressing h_{max}in terms of T and parameter x= (g_{G}g_{MW})/g_{MW}one has

h

_{max}= y(x)g_{MW}(T^{2}/2) ,

y(x)= x(5x + 4)/2(2+x) ≈ x for small values of x .

- If one assumes that h
_{max}>h_{now}, where h_{now}∼ 1.2× 10^{5}ly the recent height of the objects considered, one obtains an estimate for the time T from h_{max}>h_{now}giving

T> [2(2+x)/x(5x+4)]

^{1/2}T_{0}, T_{0}=h_{now}g_{MW}.

Note that T

_{max}<2T holds true.

- It is easy to find (one can check the numerical factors here) that g
_{MW}can be expressed at the limit of infinitely large galactic disk as

g

_{MW}= 2π G (dM/dS)= 2GM/R^{2},

where R is the radius of galactic disk and dM/dS= M/π R

^{2}is the density of the matter of galactic disk per unit area. This expression is analogous to g= GM/R^{2}_{E}at the surface of Earth.

- One can express the estimate in terms of the acceleration g= 10 m/s
^{2}as

g

_{MW}≈ 2g (R_{E}/R)^{2}(M/M_{E}) .

The estimate for MW radius has lower bound R=10

^{5}ly, MW mass M∼ 10^{12}M_{Sun}, using M_{Sun}/M_{E}=3×10^{6}and R_{Earth}≈ 6× 10^{6}m, one obtains g_{MW}∼ 2× 10^{-10}g.

- Using the estimate for g
_{MW}one obtains T> [2(2+x)/[x(5x+4)]]^{1/2}T_{0}with

T

_{0}∼ 3× 10^{9}years .

The estimate T∼ (1/x(

^{1/2}(2R/g_{MW})^{1/2}proposed above gives T>(1/x)^{1/2}× 10^{8}years. The fraction of ordinary mass from total mass is roughly 10 per cent of the contribution of the dark energy and dark particles associated with the cosmic string. Therefore x<.1 is a reasonable upper bound for x parametrizing the mass difference of G and MW. For x≈ .1 one obtains T in the range 1-10 Gy.

For a summary of earlier postings see Latest progress in TGD.

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