DYNAMICAL FRICTION IN HEAD-ON GALAXY COLLISIONS .1. ANALYTICAL CALCULATIONS AND RESTRICTED 3-BODY SIMULATIONS

The accretion of a small satellite by a big elliptical galaxy is ackno wledged as a key phenomenon in the dynamics of galaxies. It is held re sponsible for the formation of most fine structures which are observed in ellipticals. Circular orbits for the satellite have been studied i n most work so far. However, they may not be representative of the gen eral phenomenon, as their geometry prevents the process from being tim e-dependent in a genuine way. Here is the first of two articles devote d to the dynamical study of orbital decay during a head-on encounter. Analytical calculations give access to the mechanism of dynamical fric tion during the event. They consist in the coupled solution of the lin earised Poisson and collisionless Boltzmann equations. Our results con firm that time now plays an active role: the drag force undergone by t he satellite derives from the transient response of the galaxy and dep ends on the full past history of the event. As a consequence, dynamica l friction is not strictly proportional to the local density as classi cally expected from Chandrasekhar's formula. Our study is refined by a harmonic analysis of the process. We extend these results by means of restricted three-body simulations. They allow us to deal with a compa ct satellite and to follow the accretion until merging with the galaxy . We adopt the Multiple Three-Body Algorithm, which naturally accounts for dynamical friction and proves equivalent to the analytical method inasmuch as self-gravity of the galactic wake is unimportant. A satel lite along a radial trajectory is braked in a steplike way: its orbita l energy is essentially dissipated when it crosses the galactic core. We discuss the dependence of this process on the parameters of the col lision: initial energy, mass and radius of the intruder. The size is m ost important, because it determines both the nature of the galactic r esponse and the ultimate fate of the object. However, we do not proper ly describe the strong distortion of the inner galaxy when hit by the intruder, nor do we include the disruption of the satellite in the tid al field of the elliptical. These issues will be discussed in a forthc oming article (Seguin and Dupraz 1994: Paper II) in the light of self- consistent N-body simulations and within a broader study of eccentric collisions between the galaxy and the satellite.