Dynamical friction. I. General considerations: the coefficient of dynamical friction

Abstract

In this paper it is shown that a star must experience dynamical friction, i.e., it must suffer from a systematic tendency to be decelerated in the direction of its motion. 'This dynamical friction which stars experience is one of the direct consequences of the fluctuating force acting on a star due to the varying complexion of the near neighbors. From considerations of a very general nature it is concluded that the coefficient of dynamical friction, η, must be of the order of the reciprocal of the time of relaxation of the system. Further, an independent discussion based on the two-body approximation for stellar encounters leads to the following explicit formula for the coefficient of dynamical friction: η = 4πm_l (m_l + m₂)G²/v³ log_e [D₀|u|²/G(m₁+m₂)]∫ ₀ ^v N(v₁) dv₁, where m_l and m₂ denote the masses of the field star and the star under consideration, respectively; G, the constant of gravitation; Do, the average distance between the stars; |u|², the mean square velocity of the stars; N(v₁) dv₁, the number of field stars with velocities between v₁ and v₁ + dv₁; and, finally, v, the velocity of the star under consideration. It is shown that the foregoing formula for η is in agreement with the conclusions reached on the basis of the general considerations. Finally, some remarks are made concerning the further development of these ideas on the basis of a proper statistical theory.