The Radial Acceleration Relation (RAR): the crucial cases of Dwarf Discs
  and of Low Surface Brightness galaxies
  McGaugh et al. (2016) have found, in a large sample of disc systems, a tight
nonlinear relationship between the total radial accelerations $g$ and their
components $g_b$ arisen from the distribution of the baryonic matter
[McGaugh_2016]. Here, we investigate the existence of such relation in Dwarf
Disc Spirals and Low Surface Brightness galaxies on the basis of [Karukes_2017]
and [DiPaolo_2018]. We have accurate mass profiles for 36 Dwarf Disc Spirals
and 72 LSB galaxies. These galaxies have accelerations that cover the McGaugh
range but also reach out to one order of magnitude below the smallest
accelerations present in McGaugh et al. (2016) and span different Hubble Types.
We found, in our samples, that the $g$ vs $g_b$ relation has a very different
profile and also other intrinsic novel properties, among those, the dependence
on a second variable: the galactic radius, normalised to the optical radius
$R_{opt}$, at which the two accelerations are measured. We show that the new
far than trivial $g$ vs $(g_b, r/R_{opt})$ relationship is nothing else than a
direct consequence of the complex, but coordinated mass distributions of the
baryons and the dark matter (DM) in disc systems. Our analysis shows that the
McGaugh et al. (2016) relation is a limiting case of a new universal relation
that can be very well framed in the standard "DM halo in the Newtonian Gravity"
paradigm.
