The central surface density of "dark halos" predicted by MOND
  Prompted by the recent claim, by Donato et al., of a quasi-universal central
surface density of galaxy dark matter halos, I look at what MOND has to say on
the subject. MOND, indeed, predicts a quasi-universal value of this quantity
for objects of all masses and of any internal structure, provided they are
mostly in the Newtonian regime; i.e., that their mean acceleration is at or
above a0. The predicted value is qSm, with Sm= a0/2 pi G= 138 solar masses per
square parsec for the nominal value of a0, and q a constant of order 1 that
depends only on the form of the MOND interpolating function. This gives in the
above units log(Sm)=2.14, which is consistent with that found by Doanato et al.
of 2.15+-0.2. MOND predicts, on the other hand, that this quasi-universal value
is not shared by objects with much lower mean accelerations. It permits halo
central surface densities that are arbitrarily small, if the mean acceleration
inside the object is small enough. However, for such low-surface-density
objects, MOND predicts a halo surface density that scales as the square root of
the baryonic one, and so the range of the former is much compressed relative to
the latter. This explains, in part, the finding of Donato et al. that the
universal value applies to low acceleration systems as well. Looking at
literature results for a number of the lowest surface-density disk galaxies
with rotation-curve analysis, I find that, indeed, their halo surface densities
are systematically lower then the above "universal" value. The prediction of Sm
as an upper limit, and accumulation value, of halo central surface densities,
pertains, unlike most other MOND predictions, to a pure "halo" property, not to
a relation between baryonic and "dark matter" properties.
