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Wednesday, March 14, 2018 3:27

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I learned in FB about very interesting finding about the angular rotation velocities of stars near the edges of the galactic disks (see this). The rotation period is about one giga-year. The discovery was made by a team led by professor Gerhardt Meurer from the UWA node of the International Centre for Radio Astronomy Research (ICRAR). Also a population of older stars was found at the edges besides young stars and interstellar gas. The expectation was that older stars would not be present.

These velocities are in reasonable accuracy same for all spiral galaxies irrespective of the size. The constant velocity spectrum for distant stars implies that ω proportional to 1/r. Hence it is important do identify the value of radius precisely. I understood that outside boundary stars are not formed. 10^{5} ly for Milky Way with factor of order 2 accuracy.

Could one understand this in TGD framework?

- The notion of gravitational Planck constant h
_{gr}introduced first by Nottale is central in TGD, where dark matter corresponds to a hierarchy of Planck constants h_{eff}=n×h . One would have

hbar_{eff} =n×hbar= hbar_{gr}= GMm/v_{0}

for the magnetic flux tubes connecting masses M and m and carrying dark matter. For flux loops from M back to M one would have

hbar_{gr}= GM^{2}/v_{0}.

v_{0} is a parameter with dimensions of velocity. The first guess (which turns out to be wrong) is v_{0} =v_{rot}, where v_{rot} corresponds to the rotation velocity of distant stars – roughly v_{rot}=5c/6 . v_{rot} would be determined by the string tension of long flux tube in which galaxies correspond to knots: stars would correspond to local knots of these galactic knots. If so, the radius for the edge of galactic disk would correspond to the size of the galactic knot. If stars are sub-knots of galactic knot in long flux tube, also old stars could be present in the edge region.

- Assume quantization of dark angular momentum with unit h
_{gr}for the galaxy. Using L = Iω, where I= MR^{2}/2 is moment of inertia, this gives

MR^{2}ω/2= L = m×hbar_{gr} =2m×GM^{2}/v_{0}

giving

ω= 2m×hbar_{gr}/MR^{2} = 2m×GM/(R^{2}v_{0})= m× 2πg_{gal}/v_{0} , m=1,2,.. ,

where g_{gal}= GM/πR^{2} is surface gravity of galactic disk.

If the average surface mass density of the galactic disk and the value of m do not depend on galaxy, one would obtain constant ω as observed (m=1 is the first guess but also other values can be considered). ω =v/r is however larger at smaller radii down to r ≈ 1 kpc below which it becomes essentially constant. That part of galactic knot would rotate like rigid body: this is known as cusp-core problem in halo models of dark matter.

- For the rotation period one obtains

T= v_{0}/m×g_{gal}, m=1,2,…

Does the prediction make sense for Milky Way? For M= 10^{12}M_{Sun} represents a lower bound for the mass of Milky Way. The upper bound is roughly by a factor 2 larger. For the lower value of M the average surface gravity g _{gal} of Milky Way would be approximately g_{gal} ≈ 10^{-10}g for R= 10^{5} ly and by a factor 1/4 smaller for R= 2× 10^{5} ly. Here g=10 m/s^{2} is the acceleration of gravity at the surface of Earth. m=1 corresponds to the maximal period.

For the lower mass M= 10^{12}M_{Sun} and larger radius R=2× 10^{5}ly one obtains T≈ 10^{7}/m years. This prediction for T is too small by a factor 100. For M= 2×10^{12}M_{Sun} this value of T is replaced with T/2.

Something clearly goes wrong. v_{0} should be by a factor of order 100 larger than v_{rot}.

- Interestingly, one has R/r=60 for R= 2× 10
^{5}ly and r ≈ 1 kpc (r is the radius of rigidly rotating part of galaxy). This in turn implies that ω is by a factor R/r=60 larger at the surface of the rigidly rotating part of galaxy.Should one apply the quantization condition at this surface using ω = v

_{rot}/r instead of ω=v_{rot}/R? This would conform with the fact that the quantization condition assumes rigid body. This would give T=.6 Gy. Scaling of R=2×10^{5}ly by factor 1.2 would give T= 9 Gy.

- But does it make sense to identify the entire mass of galaxy as the mass associated with rigid body like part? It could since dark matter and energy associated with flux tube dominates the mass density and also the possible dark mass outside the rigid body part rotates like rigid body!
- Is this assumption consistent with the assumption that also the stars outside rigid body type region are sub-knots in galactic flux tube? It could be if they have low enugh string tension (mass density) due to thickening. They could be also flux loops which have separated (evaporated) from the galactic knot by reconnection and perhaps decayed to ordinary matter. If their contribution to the total mass is small, as it should be (about 10 per cent), one can approximate the dark mass within rigid body part with total mass.

v_{0}= v_{rot}(R/r) means that gravitational Planck constant is proportional to the size scale of the object. The trivial explanation would be that quantum size scale is identifiable as gravitational Compton length h_{gr}/M= GM/v_{0}.

What about the universality of T? It seems that one understand it in TGD based model for galaxy as a knot in cosmic string. Suppose that the length L of the the galactic string is proportional to R:

L= kR ,

where k does not depend on galaxy. This part would contain both the rigid part and the loops associated with the visible matter split from galactic string. Suppose that v_{0}= v_{rot}(R/r). By substituting to T= (M/πR^{2 v0 one obtains T= Gkvrot/πr= Gkω(r)/π= 2Gk/T giving T=(Gk)}^{1/2} ,

which is indeed independent on galaxy.

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

Articles and other material related to TGD.

Source: http://matpitka.blogspot.com/2018/03/tgd-based-models-explains-why-rotation.html