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

Understand

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.