Gravitation on large scales
Abstract
A sample of dwarf and spiral galaxies with extended rotation curves is analysed, assuming that the fraction of dark matter is small. The objective of the paper is to prepare a framework for a theory, based on fundamental principles, that would give fits of the same quality as the phenomenology of dark halos. The following results are obtained: 1) The geodesics of massive systems with low density (Class I galaxies) can be described by the metric ds^2 = b^{1}(r)dr^2  b(r)dt^2 + r^2 dOmega^2 where b(r) = 1  {2 over c^2}({{GM} over r} + gamma_f M^{1/2}) In this expression Gamma_f is a new fundamental constant which has been deduced from rotation curves of galaxies with circular velocity V_c^2 >= 2 {{GM} over r} for all r 2) The above metric is deduced from the conformal invariant metric ds^2 = B^{1}(r)dr^2  B(r)dt^2 + r^2 dOmega^2 where B(r) = 1  {2 over c^2}({{GM} over r} + Gamma_f M^{1/2} + {1 over 3} {Gamma_f^2 over G}r) through a linear transform, u, of the linear special group SL(2, R) 3) The term {2 over c^2}Gamma_f M^{1/2} accounts for the difference between the observed rotation velocity and the Newtonian velocity. The term {2 over {3c^2}}{Gamma_f^2 over G}r is interpreted as a scale invariance between systems of different masses and sizes. 4) The metric B is a vacuum solution around a mass M deduced from the least action principle applied to the unique action I_a = 2 a int (g)^{1/2} [R_{mu kappa}R^{ mu kappa}  1/3(R^{alpha}_{alpha})^2] dx^4 built with the conformal Weyl tensor 5) For galaxies such that there is a radius, r_0, at which {{GM} over r_0} = Gamma M^{1/2} (Class II), the term Gamma M^{1/2} might be confined by the Newtonian potential yielding stationary solutions. 6) The analysed rotation curves of Class II galaxies are indeed well described with metrics of the form b(r) = 1  {2 over c^2}({{GM} over r} + (n + 1) Gamma_0 M^{1/2}) where n is an integer and Gamma_0 = {1 over the square root of 3}Gamma_f 7) The effective potential is determined and found to be E(Gamma, r) = {Gamma^2 over G}r 8) A quantized model is deduced from a Schrodingertype equation  {{D^2} {{d^2 Psi(r)} over {dr^2}}} = {[E  {{G M} over r}] Psi(r)} where D^2 is the product of the energy Gamma M^{1/2} by the square of the radius r where {{G M} over r} = {Gamma_f M^{1/2}}. The boundary conditions are given by Psi (0) = 0 and the effective potential 9) The data are in agreement with the hypothesis of quantization, but that hypothesis is not proved because, the masstolight ratio being a ''free'' variable, it is always possible to shift a Gammacurve out of its best ''energy level''. However, if one moves a Gammafit from an ''energy level'' to the next, the fitting of the curve becomes clearly poorer. 10) The Newtonian masstolight ratios of Class I galaxies range from ~7 to ~75. The masstolight ratios of the same objects deduced from the Gammadynamics are reduced to 1.1 <= M_{dyn}/L <= 7.4. For Class II galaxies, the range of the Newtonian masstolight ratios of the sample is 10 <= M_{lum+dark}^N/L <= 40. It is reduced to 1.7 <= M_{dyn}/L <= 4.2 when using the quantized version of the Gammadynamics. It is approximately 3.5 M_odot/L_odot for Sb galaxies and 2 M_odot/L_odot for Sc galaxies. 11) None of the Gammafits are poorer than the models with dark halos of the reference articles. The Gammadynamics is sensitive to the integrated mass through the term Gamma M^{1/2}, and to the mass and density through the Newtonian term {G M} over r. This kind of coupling is particularly efficient in galaxies like NGC 1560 whose rotation curve shows conspicuous structure.
 Publication:

Joint European and National Astronomical Meeting
 Pub Date:
 1997
 Bibcode:
 1997jena.confE.305G