TGD based model explains why the rotation periods of galaxies are same

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. 10⁵ ly for Milky Way with factor of order 2 accuracy.

Could one understand this in TGD framework?

1. 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/v₀

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= GM²/v₀.

v₀ is a parameter with dimensions of velocity. The first guess (which turns out to be wrong) is v₀ =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.

MR²ω/2= L = m×hbar_gr =2m×GM²/v₀

giving

ω= 2m×hbar_gr/MR² = 2m×GM/(R²v₀)= m× 2πg_gal/v₀ , m=1,2,.. ,

where g_gal= GM/πR² 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.

T= v₀/m×g_gal, m=1,2,…

Does the prediction make sense for Milky Way? For M= 10¹²M_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^-10g for R= 10⁵ ly and by a factor 1/4 smaller for R= 2× 10⁵ ly. Here g=10 m/s² is the acceleration of gravity at the surface of Earth. m=1 corresponds to the maximal period.

For the lower mass M= 10¹²M_Sun and larger radius R=2× 10⁵ly one obtains T≈ 10⁷/m years. This prediction for T is too small by a factor 100. For M= 2×10¹²M_Sun this value of T is replaced with T/2.

Something clearly goes wrong. v₀ should be by a factor of order 100 larger than v_rot.

1. Interestingly, one has R/r=60 for R= 2× 10⁵ 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=2×10⁵ ly by factor 1.2 would give T= 9 Gy.

v₀= 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/v₀.

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 v₀= v_rot(R/r). By substituting to T= (M/πR^{2 v₀ one obtains T= Gkv_rot/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.

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