The efficiency of the spiral-in of a black hole to the Galactic centre

We study the efficiency at which a black hole or dense star cluster spirals-in to the Galactic centre. This process takes place on a dynamical friction time scale, which depends on the value of the Coulomb logarithm ln(L). We determine the accurate value of this parameter using the direct N-body method, a tree algorithm and a particle-mesh technique with up to 2 million plus one particles. The three different techniques are in excellent agreement. Our result for the Coulomb logarithm appears to be independent of the number of particles. We conclude that ln(L) = 6.6 +/- 0.6 for a massive point particle in the inner few parsec of the Galactic bulge. For an extended object, like a dense star cluster, ln(L) is smaller, with a value of the logarithm argument L inversely proportional to the object size.Comment: 11 pages, 12 figures, MNRAS, in press revised version following referee's comments, references updated, typos correcte