Large-scale filaments--Newtonian vs. modified dynamics
  Eisenstein Loeb and Turner (ELT) have recently proposed a method for estimating the dynamical masses of large-scale filaments, whereby the filament is modeled by an axisymmetric, isothermal cylinder, for which ELT derive a global relation between the (constant) velocity dispersion and the total line density. We first show that the model assumptions of ELT can be relaxed materially: an exact relation between the velocity and line density is derived for any cylinder (not necessarily axisymmetric), with an arbitrary constituent distribution function (so isothermality need not be assumed). We then consider the same problem in the context of the modified dynamics (MOND). After a brief comparison between scaling properties in the two theories, we study idealized MOND model filaments. A preliminary application to the segment of the Perseus-Pisces filament treated by ELT, gives MOND M/L estimates of order 10 s.u., compared with the Newtonian value of about 450, which ELT find. In spite of the large uncertainties still besetting the analysis, this instance of MOND application is of particular interest because: 1. Objects of this geometry have not been dealt with before. 2. It pertains to large-scale structure. 3. The typical accelerations involved are the lowest so far encountered in a semi-virialized system. 
Mordehai Milgrom (Condensed-Matter Physics, Weizmann Institute)