Structure of the equivalent Newtonian systems in MOND N -body simulations: Density profiles and the core-cusp problem

Aims. We investigate the core-cusp problem of the ? cold dark matter (? CDM) scenario in the context of the modified Newtonian dynamics (MOND) paradigm while exploiting the concept of an equivalent Newtonian system (ENS). Methods. By means of particle-mesh N-body simulations in MOND, we explored the processes of galaxy formation via cold dissipationless collapse and the merging of smaller substructures. From the end states of our simulations, we recovered the associated ENS and studied the properties of their dark matter halos. We compared the simulation results with simple analytical estimates with a family of ?-models. Results. We find that the dark matter density of ENSs of most spherical cold collapses have a markedly cored structure, particularly for the lowest values of the initial virial ratios. End states of some simulations with initially clumpy conditions have more complex profiles, and some of their ENSs exhibit a moderate cusp, with the logarithmic density slope always shallower than one. Conclusions. In contrast to what one would expect from theoretical and numerical arguments in ? CDM, these results seem to point towards the fact that the absence of a central DM cusp in most observed galaxies would be totally consistent in a MONDian description