## The new findings about the structure of Milky from TGD viewpointI 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 r
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 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. - 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=mv
_{1}^{2}/ρ, where ρ is the orthogonal distance from cosmic string. Here v_{1}^{2}has dimensions of velocity squared being proportional to v_{1}^{2}∝ GT, T=dM/dl the string tension of cosmic string. - Newton's law v
^{2}/r= v_{1}^{2}/r gives the observed constant velocity spectrumv=v _{1}.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 requires estimate for the gravitational Planck constant
h _{gr}=GMm/v_{0}assignable to te flux tubes connecting mass m to central mass M. - The first guess for v
_{0}would be asv _{0}=v_{1}.The value of v _{1}is approximately v_{1}= 10^{-3}/3 (unit c=1 are used) (see this). - 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. - The first guess for M would be as the mass of galaxy x× 10
^{12}× 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 valueΛ _{gr}= h_{gr}/m= GM/v_{0}=r_{S}/2v_{0}(c=1) .For v _{0}=v_{1}this would give Λ_{gr}= 4.5× 10^{3}ly for x=1.5. Note that the colossal void extends from 150 ly to 8× 10^{3}ly. This guess is very probably too large since M should correspond to a mass within R_{0}or perhaps even within r_{0}. - A more reasonable guess is that the mass corresponds to mass within R
_{0}=60,000 ly or perhaps even radius r_{0}=150 ly. r_{0}turns out to make sense and gives a connection between the two observations.
- The first guess for M would be as the mass of galaxy x× 10
- The quantization condition for angular momentum reads as
mv _{1}ρ= n× h_{gr}/2 π .This would give ρ _{n}= n× ρ_{0}, ρ_{0}=GM/[2π v_{1}× v_{0}] =Λ_{gr}/[2π v_{1}] .The radii ρ _{n}are integer multiples of a radius ρ_{0}.- Taking M=M
_{gal}, the value of ρ_{0}would be for the simplest guess v_{0}=v_{1}about ρ_{0}=2.15× 10^{6}ly. This is roughly 36 times larger than the value of the radius R_{0}=6× 10^{4}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. - By scaling M down by factor 1/36 one would obtain R
_{0}=6× 10^{4}ly and M= M_{gal}/36=.033.× M_{gal}: this mass should reside within R_{0}ly, actually within radius Λ_{gr}. Remarkably, the estimate for Λ_{gr}= 2π v_{1}M gives Λ_{gr}= 127 ly, which is somewhat smaller than r_{0}= 150 ly associated with void. The model therefore relates the widely different scales r_{0}and R_{0}assignable with the two findings to each other in terms of small parameter v_{0}appearing in the role of dimensionless gravitational "fine structure constant" > α_{gr}= GMm/2h_{gr}= v_{0}/2.
- Taking M=M
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 or the article Three astrophysical and cosmological findings from TGD point of view. |