The new findings about the structure of Milky Way from TGD viewpoint

I learned about two very interesting findings forcing to update the ideas about to the structure of Milky Way and allowing to test the TGD inspired Bohr model of galaxy based on the notion of gravitational Planck constant (see this, this, this, and this)

The first popular article tells about a colossal void extending from radius r₀=150 ly to a radius of r₁= 8,000 ly (ly=light year) around galactic nucleus discovered by a team led by professor Noriyuki Matsunaga. What has been found that there are no young stars known as Cepheids in this region. For Cepheids luminosity and the period of pulsation in brightness correlate and from the period for pulsation one can deduce luminosity and from the luminosity the distance. There are however Cepheids in the central region with radius about 150 ly.

Second popular article tells about the research conducted by an international team led by Rensselaer Polytechnic Institute Professor Heidi Jo Newberg. Researchers conclude that Milky Way is at least 50 per cent larger than estimated extending therefore to R_gal= 150,000 ly and has ring like structures in galactic plane. The rings are actually ripples in the disk having a higher density of matter. Milky way is said to be corrugated: there are at least 4 ripples in the disk of Milky Way. The first apparent ring of stars about at distance of R₀=60,000 ly from the center. Note that R₀ is considerably larger than r₁=8,000 ly: the ratio is R₀/r₁= 15/2 so that this findings need not have anything to do with the first one.

Consider now the TGD based quantum model of galaxy. Nottale proposed that the orbits of planets in solar system are actually Bohr orbits with gravitational Planck constant (different for inner and outer planets and proportional to the product of masses of Sun and planet). In TGD this idea is developed furthe (see this): ordinary matter would condense around dark matter at spherical cells or tubes with Bohr radius. Bohr model is certainly over-simplification but can be taken as a starting point in TGD approach.

Could Bohr orbitology apply also to the galactic rings and could it predict ring radii as radii with which dark matter concentrations - perhaps at flux tubes - are associated? One can indeed apply Bohr orbitology by assuming TGD based model for galaxy formation.

1. Galaxies are associated with long cosmic string like objects carrying dark matter and energy (as magnetic energy) (see this and this). Galaxies are like pearls along necklace and experience gravitational potential which is logarithmic potential. Gravitational force is of form F=mv₁²/ρ, where ρ is the orthogonal distance from cosmic string. Here v₁² has dimensions of velocity squared being proportional to v₁²∝ GT, T=dM/dl the string tension of cosmic string.
   
   
2. Newton's law v²/r= v₁²/r gives the observed constant velocity spectrum
   

   v=v₁ .
   

   The approximate constancy originally led to the hypothesis that there is dark matter halo. As a matter of fact, the velocity tends to increase). Now there is no halo but cosmic string orthogonal to galactic plane: the well-known galactic jets would travel along the string. The prediction is that galaxies are free to move along cosmic string. There is evidence for large scale motions.
   
   

This was still just classical Newtonian physics. What comes in mind that one could apply also Bohr quantization for angular momentum to deduce the radii of the orbits.

1. This requires estimate for the gravitational Planck constant
   

   h_gr=GMm/v₀
   

   assignable to te flux tubes connecting mass m to central mass M.
   
   

2. The first guess for v₀ would be as
   

   v₀=v₁ .
   

   The value of v₁ is approximately v₁= 10^-3/3 (unit c=1 are used) (see this).
   
   

3. What about mass M? The problem is that one does not have now a central mass M describable as a point mass but an effective mass characterizing the contributions of cosmic string distributed along string and also the mass of galaxy itself inside the orbit of star. It is not clear what value of central mass M should be assigned to the galactic end of the flux tubes.
   

   One can make guesses for M.
   
   

   1. The first guess for M would be as the mass of galaxy x× 10¹²× M(Sun), x∈ [.8-1.5]. The corresponding Schwartschild radius can be estimated from that of Sun (3 km) and equals to .48 ly for x=1.5. This would give for the mass independent gravitational Compton length the value
      

      Λ_gr= h_gr/m= GM/v₀=r_S/2v₀ (c=1) .
      

      For v₀=v₁ this would give Λ_gr= 4.5× 10³ ly for x=1.5. Note that the colossal void extends from 150 ly to 8× 10³ ly. This guess is very probably too large since M should correspond to a mass within R₀ or perhaps even within r₀.
      
      

   2. A more reasonable guess is that the mass corresponds to mass within R₀=60,000 ly or perhaps even radius r₀=150 ly. r₀ turns out to make sense and gives a connection between the two observations.
      
      
4. The quantization condition for angular momentum reads as
   

   mv₁ρ= n× h_gr/2 π .
   

   This would give
   

   ρ_n= n× ρ₀ , ρ₀=GM/[2π v₁× v₀] =Λ_gr/[2π v₁] .
   

   The radii ρ_n are integer multiples of a radius ρ₀.
   
   

   1. Taking M=M_gal, the value of ρ₀ would be for the simplest guess v₀=v₁ about ρ₀=2.15× 10⁶ ly. This is roughly 36 times larger than the value of the radius R₀=6× 10⁴ ly for the lowest ring. The use of the mass of the entire galaxy as estimate for M of course explains the too large value.
      
      
   2. By scaling M down by factor 1/36 one would obtain R₀=6× 10⁴ ly and M= M_gal/36=.033.× M_gal: this mass should reside within R₀ ly, actually within radius Λ_gr. Remarkably, the estimate for Λ_gr= 2π v₁M gives Λ_gr= 127 ly, which is somewhat smaller than r₀= 150 ly associated with void. The model therefore relates the widely different scales r₀ and R₀ assignable with the two findings to each other in terms of small parameter v₀ appearing in the role of dimensionless gravitational "fine structure constant" α_gr= GMm/2h_gr= v₀/2.
      
      

The TGD inspired prediction would be that the radii of the observed rings are integer multiples of basic radius. 4 rings are reported implying that the outermost ring should be at distance of 240,000 ly, which is considerably larger than the claimed updated size of 150,000 ly. The simple quantization as integer multiples would not be quite correct. Orders of magnitude are however correct.

This would suggest that visible matter has condensed around dark matter at Bohr quantized orbits or circular flux tubes. This dark matter would contribute to the gravitational potential and imply that the velocity spectrum for distance stars is not quite constant but increases slowly as observed . The really revolutionary aspect of this picture is that gravitation would involve quantum coherence in galactic length scales. The constancy of the CMB temperature supports gravitational quantum coherence in cosmic scales.

For details see the chapter TGD and Astrophysics of "Physics in Many-sheeted Space-time" or the article Three astrophysical and cosmological findings from TGD point of view.

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