By P. Mannheim
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Additional resources for Alternatives to Dark Matter and Dark Energy
Galaxies with a small N ∗ or a small central surface brightness Σ0 . 32 and the issue should be regarded as being open at the present time. e. if the only information available is the measured surface brightness of a given galaxy, from that how do we then determine which values of σ0 and r0 to use with each such given galaxy so as to be able to predict the structure of the galactic rotation curve in advance of its measurement, and thereby render dark matter theory falsifiable. Forms such as those of Eqs.
Specifically, the rotation curves of the low luminosity dwarf galaxies are typically found to be rising at the last detected data points, the rotation curves of the intermediate to high luminosity galaxies are found to be flat, while the rotation curves of the very highest luminosity galaxies are found to be mildly falling. While there are many flat rotation curves, there are also many which are seen to be rising, and if these curves are to eventually flatten off, this has yet to be observed. Of these various classes, it is only the high luminosity, flat rotation curve galaxies which are Freeman limit, Tully-Fisher galaxies, with the lower luminosity, non-flat galaxies not enjoying this particular form of universality at all.
While the asymptotic limit of Eq. (118) leads to 2 vdark → 4πβ ∗ c2 σ0 , (120) there is no apparent reason why the dark matter σ0 should be related to the luminous parameters N ∗ and R0 via N∗ σ0 = , (121) 10πR0 and yet without such a fine-tuning between the dark halo and optical disk parameters, the asymptotic halo contribution would not match the inner region peak velocity at all, being either larger or smaller than it. 2R0 to the velocity at r = 10R0 and not require the rotation curve to be flat at all points in between.
Alternatives to Dark Matter and Dark Energy by P. Mannheim