Using high-resolution cosmological N-body simulations, we investigate the survival of dark matter satellites falling into larger haloes. Satellites preserve their identity for some time after merging. We compute their loss of mass, energy and angular momentum as they are dissolved by dynamical friction, tidal forces and collisions with other satellites. We also analyse the evolution of their internal structure. Satellites with less than a few per cent of the mass of the main halo may survive for several billion years, whereas larger satellites rapidly sink into the centre of the main halo potential well and lose their identity. Penetrating encounters between satellites are frequent and may lead to significant mass loss and disruption. Only a minor fraction of cluster mass (10-15 per cent on average) is bound to substructure at most redshifts of interest. We discuss the application of these results to the survival and extent of dark matter haloes associated with galaxies in clusters, and to their interactions. We find that a minor fraction of galaxy-size dark matter haloes are disrupted by redshift z=0. The fraction of satellites undergoing close encounters is similar to the observed fraction of interacting or merging galaxies in clusters at moderate redshift

We demonstrate, using a simple analytic model, that the presence of a massive satellite can globally modify the structure and emission properties of an accretion disc to which it is tidally coupled. We show, using two levels of numerical approximation, that the analytic model gives reasonable results. The results are applicable to two astrophysical situations. In the case of an active galactic nucleus, we consider the case of a 10 3 M compact companion to the central black-hole and show that it could modulate the emitted spectrum on a timescale of 10 5 years. In the case of a T Tauri accretion disc, a satellite such as a sub-dwarf or giant planet could modify the disc spectral energy distribution over a substantial fraction of the T Tauri star lifetime.

We describe an algorithm for constructing N -body realisations of equilibrium stellar systems. The algorithm complements existing orbit-based modelling techniques using linear programming or other optimization algorithms. The equilibria are constructed by integrating an N -body system while slowly adjusting the masses of the particles until the time-averaged density field and other observables converge to a prescribed value. The procedure can be arranged to maximise a linear combination of the entropy of the system and the χ 2 statistic for the observables. The equilibria so produced may be useful as initial conditions for N -body simulations or for modelling observations of individual galaxies.

We derive the rates of capture, Ndot, of main sequence turn off stars by the central massive black hole in a sample of galaxies from Magorrian et al. 1998. The disruption rates are smaller than previously believed with Ndot ~ 10^-4 - 10^-7 per galaxy. A correlation between Ndot and black hole mass, M, is exploited to estimate the rate of tidal disruptions in the local universe. Assuming that all or most galaxies have massive black holes in their nuclei, this rate should be dominated by sub-Lstar galaxies. The rate of tidal disruptions could be high enough to be detected in supernova (or similar) monitoring campaigns---we estimate the rate of tidal disruptions to be 0.01 - 0.1 times the supernova rate. We have also estimated the rates of disruption of red giants, which may be significant (Ndot ~> 10^-4 y^-1 per galaxy) for M ~> 10^8 Msun, but are likely to be harder to observe---only of order 10^-4 times the supernova rate in the local universe. In calculating capture rates, we advise caution when applying scaling formulae by other authors, which are not applicable in the physical regime spanned by the galaxies considered here.Comment: MNRAS, Accepted; 9 pages, Late

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