Dynamical Friction in truncated systems

Astrophysical systems where the external regions of a satellite are modified by its motion in the gravitational potential of the principal companion lead to ask whether the dynamical friction inside the satellite changes or not. Here, after having accounted for the satellite as a N-body system, we try to answer this question by means of collisionless N-body simulations. Field particles are distributed according to a truncated Navarro-Frenk-White density profile; we consider three profiles differing for the values of some relevant physical parameters. A first set of simulation, run as a check for our numerical method, verifies that the density and cumulative mass profiles of the isolated host systems do not change in time. Then, the interaction with the test particle is considered. At first, we check if this interaction modifies the density and cumulative mass profiles of the host systems, with simulations not exceeding the infall time of the test particle. Then we focus on the orbits of the test particle in the three different systems. Two values of the test particle mass, three types of orbits (circular, eccentric and radial) and four different initial distances from the centre of the host satellite are considered. According to our simulations, for smaller values of the test particle mass, some differences can be noticed. However, a clear trend with the truncation radius of the halo is not observed, since, for certain orbits, we notice that the infall of the test particle is faster both if we diminish and increase the truncation radius of the system, and, in the end, dynamical friction seems to be little affected by modifications of the external regions of the host system. Further simulations are necessary.