Bullet cluster and TGD based model of dark matter

Sabine Hossenfelder wrote about Bullet Cluster. Usually Bullet Cluster is seen to favor dark matter and disfavor MOND theory introducing a modification of Newtonian gravity. Sabine Hossenfelder saw it differently.

Cold dark matter model (ΛCDM) and MOND are two competing mainstream models explaining the constant velocity spectrum of stars in galaxies.

1. ΛCDM assumes that dark matter forms a spherical halo around galaxy and that its density profile is such that it gives the observed velocity spectrum of distant stars. The problem of the model is that dark matter distribution can have many shapes and it is not easy to understand why approximately constant velocity spectrum is obtained. Also the attempts to find dark matter particles identified as some exoticons have failed one after another. The recent finding that the velocity spectrum of distant stars around galaxies correlates strongly with the density of baryonic matter also challenges this model: it is difficult to believe that the halo would have so universal baryonic mass density.
   
   
2. MOND does not assume dark matter but makes an ad hoc modification of gravitational force for small accelerations. The problem of MOND is that it is indeed an ad hoc modification and it is not easy to see how to make it consistent with general relativity: it is difficult to do cosmology using MOND. For small accelerations (small space-time curvatures) one would expect Newtonian theory to be an excellent approximation.
   
   

Consider now how Bullet Cluster relates to these two options. Bullet cluster is a pair of galaxy clusters which has emerged from collision (see the figure). There exists data at optical wavelenghts about stars. Stars experience only a small gravitational slowing down and are expected to go through the collision region rather fast. Data from X-ray measurements give information about the intergalactic gas associated with clusters. This gas interacts electromagnetically and is slowed down much more and remains in the collision region for a longer time. The red regions in the figure correspond to the gas. Gravitational lensing in turn gives information about space-time curvature and these two regions are farthest away from the collision center. These regions are blue and would naturally correspond to dark matter in ΛCDM model. Both models have severe problems.

1. In cold dark matter model the event would require too high relative velocity for colliding clusters - about c/100. The probability for this kind of collision in cold dark matter model is predicted to be very low - about 6.4×10^-6. Something seems to be wrong with ΛCDM model.
   
   
2. In MOND the relative collision velocities are argued to be much more frequent. Bee however forgot to mention that in MOND the lensing is expected to be associated with X-ray region (hot gas in the center of figure) rather than with the blue regions disjoint from it. This observation is a very severe blow against MOND model.
   
   

The logical conclusion is that there indeed seems to be dark matter there but it is something different from the cold dark matter. What it could be?

What could be the interpretation in TGD?

1. In TGD galaxies are associated with cosmic string or more general string like objects like pearls with necklace: that this is the case is known for decades but for some mysterious reason to me has not been used as guideline in dark matter models. Maybe it is very difficult to see things from bigger perspective than galaxies.
   

   The flux tubes carry Kähler magnetic energy, dark energy, and dark matter in TGD sense having h_eff=n×h. The galactic matter experiences transversal 1/ρ gravitational force predicting constant velocity spectrum for distant stars when baryonic matter is neglected. Note that one avoids a model for the profile of the halo altogether. The motion of the galaxy along the flux tube is free apart from the forces caused by galaxy. The presence of baryonic matter implies that the velocity increases slowly with distance up to some critical radius. By recent findings correlating observed velocity spectrum with density of baryonic matter one can deduce the density of baryonic matter (see this). A possible interpretation is as remnants of cosmic string like object produced in its decay to ordinary matter completely analogous to the decay of the vacuum energy of inflaton field to matter in inflation theory.
   

   The order of magnitude for velocity v_gal for distant stars in galaxies is about v_gal∼ c/1000. In absence of baryonic matter it is predicted to be constant and proportional satisfy v∝ (TG)^1/2, T string tension and G Newton's constant (c=1). T in turn is proportional to 1/R², where R is CP₂ radius. Maximal velocity is obtained for cosmic strings. For magnetic flux tubes resulting when cosmic strings develop 4-D M⁴ projection string tension T and thus v_gal is reduced. One obtains larger velocities if there are several parallel flux tubes forming a gravitational bound state so that tensions add.
   
   

2. By fractality also galaxy clusters are expected to form similar linear structures. Concerning the interpretiong of the Bullet Cluster one can imagine two options.
   
   
   1. The two colliding clusters could belong to the same string like object and move in opposite directions along it. In this case gravitational lensing would be most naturally associated with the flux tube and there would be single linear blue region instead of the two blue spots of the figure.
      
      
   2. The clusters could also belong to different flux tubes, which pass by each other and induce the collision of clusters and the gas associated with them. If the flux tubes are more or less parallel and orthogonal to the plane of the figure, the gravitational lensing would be from the two string like objects and two disjoint blue spots would appear in the figure. This option conforms with the figure.
      

      
      
      

3. The collision velocity would correspond to the relative velocity of flux tubes. Can one say anything about the needed collision velocities? The naive first guess of dimensional analyst is that the rotation velocity v_gal ∝ (TG)^1/2 determining galactic rotation spectrum determines also the typical relative velocity between galaxies. Here T would be the string tension of flux tubes containing galaxy clusters along it. T would gradually decrease during the cosmic evolution as flux tubes gets thicker and magnetic energy density is reduced. The velocity v∼ c/100 suggested by ΛCDM model is 10 times larger than c/1000 for distant stars in galaxies.
   By fractality similar view would apply to galaxy clusters assigned to flux tubes. Cluster flux tubes containing clusters along them could correspond to bound states of parallel galactic flux tubes containg galaxies along them.
   
   
4. The simplest model for collision of flux tubes treats them as parallel rigid strings so that dimensional reduction to D=2 occurs. The gravitational potential is logarithmic potential: V= Klog(ρ). One can use conservation laws of angular momentum and energy to solve the equations of motion just as in 3-D central force problem. The initial and final angular momentum per mass equals to J= v₀a, where a is the impact parameter and v₀ the initial velocity. The initial energy per unit mass equals to e= v₀²/2 and is same in the final state. Conservation law for e gives e= v²/2+Klog(ρ) = v₀²/2.
   Conservation law for angular momentum reads j= v ρsin(φ)=v₀a and gives v =j/ρsin(φ). Velocity is given from v²=(dρ/dt)²+ ρ²(dφ/dt)² and leads together with conservation laws a first order differential equation for &drho;/dt.
   

   Since the potential is logarithmic, there is rather small variation of energy in the collision so that the clusters interact rather weakly. This could produce the same effect as larger relative collision velocity in ΛCDM model with kinetic energy dominating over gravitational potential.
   
   

See the chapter TGD and astrophysics.

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

Articles and other material related to TGD.