Large-scale filaments: Newtonian versus modified dynamics

Eisenstein, Loeb, & Turner (ELT) have recently proposed a method for estimating the dynamical masses of large-scale filaments, whereby the filament is modeled by an infinite, axisymmetric, isothermal, self-gravitating, radially virialized cylinder, for which ELT derive a global relation between the (constant) velocity dispersion and the total line density. We show that the model assumptions of ELT can be relaxed materially: an exact relation between the rms velocity and the line density can be derived for any infinite cylinder (not necessarily axisymmetric) with an arbitrary constituent distribution function (so isothermality need not be assumed). We also consider the same problem in the context of the modi tied Newtonian dynamics (MOND). After we compare the scaling properties in the two theories, we study two idealized MOND model filaments, one with assumptions similar to those of ELT, which we can only solve numerically, and another, which we solve in closed form. A preliminary application to the same segment of the Perseus-Pisces filament treated by ELT gives MOND MIL estimates of order 10(M/L)., compared with the Newtonian value M/L similar to 450(H-0/100 km s(-1) Mpc(-1))(M/L). that 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; and (3) the typical accelerations involved are the lowest so far encountered in a semivirialized system - only a few percent of the critical MOND acceleration-leading to a large predicted mass discrepancy.