The distribution of dark and luminous matter inferred from extended rotation curves

Abstract

A better understanding of the formation of mass structures in the universe can be obtained by determining the amount and distribution of dark and luminous matter in spiral galaxies. To investigate such matters a sample of 12 galaxies, most with accurate distances, has been composed of which the luminosities are distributed regularly over a range spanning 2 1 2 orders of magnitude. Of the observed high quality and extended rotation curves of these galaxies decompositions have been made, for four different schemes, each with two free parameters. For a "maximum disc fit" the rotation curves can be well matched, yet a large range of mass-to-light ratios for the individual galaxies is required. For the alternative gravitational theory of MOND the rotation curves can be explained if the fundamental parameter associated with MOND is allowed as a free parameter. Fixing that parameter leads to a disagreement between the predicted and observed rotation curves for a few galaxies. When cosmologically motivated NFW dark matter halos are assumed, the rotation curves for the least massive galaxies can, by no means, be reproduced; cores are definitively preferred over cusps. Finally, decompositions have been made for a pseudo isothermal halo combined with a universal M/L ratio. For the latter, the light of each galactic disc and bulge has been corrected for extinction and has been scaled by the effect of stellar population. This scheme can successfully explain the observed rotations and leads to sub maximum disc mass contributions. Properties of the resulting dark matter halos are described and a ratio between dark and baryonic mass of ∼ 9 for the least, and of ∼ 5, for the most luminous galaxies has been determined, at the outermost measured rotation.

The physics of galactic spin

“…RC of these galaxies are used in subsequent figures. Bottom, density element contours in the oblate, for which the z and r dependence of are linked via (8), and in the disk, for which the z and r dependence of are assumed to be independent, after Perek [43]. Both profiles are shown in a vertical plane through the center.…”

“…Figure 1a shows RC behavior typical of non-interacting galaxies [7]. Figure 2 shows RC data at very large r [8]; key characteristics are in Table 1.…”

“…Table 1 lists galaxy characteristics. (a) Galaxies studied by Bottema and Pestaña [8], who considered this set to represent diverse galaxies with data collected under favorable conditions to high radius. (b) Large proximal spirals.…”

Implications of Geometry and the Theorem of Gauss on Newtonian Gravitational Systems and a Caveat Regarding Poisson’s Equation

“…Newton's law is spherically symmetric: yet, axisymmetric disk geometry is currently assumed in most models of the periodic, circular, rotational motions observed for gravitationally-bound galactic interiors, e.g., [3][4][5][6][7][8]. The coin shape has been the focus in galactic dynamics since 1964 [3] after Perek [9] declared, without proof and erroneously [10], that density (ρ) variations in the oblate spheroid shape required for spinning bodies [11] are independent in the z and r directions (the vertical distance along Data sources are [36,37].…”

“…Data on Andromeda compiled by Sofue [7]. Data on the other galaxies are from the compilation of Bottema and Pestano [8] who considered these rotation curves (RC) to be collected under optimal conditions. The three galaxies shown have RC similar to the archetypes of non-interacting galaxies [51], where velocities most typically increase with r and then become flat.…”