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abstract: 'Dissipationless collapses in Modified Newtonian Dynamics (MOND) are studied by using a new particle-mesh N-body code based on our numerical MOND potential solver. We found that low surface-density end-products have shallower inner density profile, flatter radial velocity-dispersion profile, and more radially anisotropic orbital distribution than high surface-density end-products. The projected density profiles of the final virialized systems are well described by Sersic profiles with index $m \lsim 4$, down to $m\sim 2$ for a deep-MOND collapse. Consistently with observations of elliptical galaxies, the MOND end-products, if interpreted in the context of Newtonian gravity, would appear to have little or no dark matter within the effective radius. However, we found impossible (under the assumption of constant mass-to-light ratio) to simultaneously place the resulting systems on the observed Kormendy, Faber-Jackson and Fundamental Plane relations of elliptical galaxies. Finally, the simulations provide strong evidence that phase mixing is less effective in MOND than in Newtonian gravity.'
author:
- Carlo Nipoti
- Pasquale Londrillo
- Luca Ciotti
title: Dissipationless collapses in MOND
---

Introduction
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In Bekenstein & Milgrom’s (1984, hereafter BM) Lagrangian formulation of Milgrom’s (1983) Modified Newtonian Dynamics (MOND), the Poisson equation $$\nabla^2{\phi_{\rm N}}=4\pi G\rho
\label{eqPoisson}$$ for the Newtonian gravitational 