The central surface density of "dark halos" predicted by MOND

Abstract

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.