Runaway stars are stars observed to have large peculiar velocities. Two mechanisms are thought to contribute to the ejection of runaway stars, both involve binarity (or higher multiplicity). In the binary supernova scenario a runaway star receives its velocity when its binary massive companion explodes as a supernova (SN). In the alternative dynamical ejection scenario, runaway stars are formed through gravitational interactions between stars and binaries in dense, compact clusters or cluster cores. Here we study the ejection scenario. We make use of extensive N-body simulations of massive clusters, as well as analytic arguments, in order to to characterize the expected ejection velocity distribution of runaways stars. We find the ejection velocity distribution of the fastest runaways (v 80 km s −1 ) depends on the binary distribution in the cluster, consistent with our analytic toy model, whereas the distribution of lower velocity runaways appears independent of the binaries properties. For a realistic log constant distribution of binary separations, we find the velocity distribution to follow a simple power law; Γ(v) ∝ v −8/3 for the high velocity runaways and v −3/2 for the low velocity ones. We calculate the total expected ejection rates of runaway stars from our simulated massive clusters and explore their mass function and their binarity. The mass function of runaway stars is biased towards high masses, and depends strongly on their velocity. The binarity of runaways is a decreasing function of their ejection velocity, with no binaries expected to be ejected with v > 150 km s −1 . We also find that hyper-runaways with velocities of hundreds of km s −1 can be dynamically ejected from stellar clusters, but only at very low rates, which cannot account for a significant fraction of the observed population of hyper-velocity stars in the Galactic halo.

Aims. We study the probability of close encounters between stars from a nuclear cluster and a massive black hole (10 4 M M • 10 8 M ). The gravitational field of the system is dominated by the black hole in its sphere of influence. It is further modified by the cluster mean field (a spherical term) and a gaseous disc/torus (an axially symmetric term) causing a secular evolution of stellar orbits via Kozai oscillations. Intermittent phases of high eccentricity increase the chance that stars become damaged inside the tidal radius of the central hole. Such events can produce debris and lead to recurring episodes of enhanced accretion activity. Methods. We introduce an effective loss cone and associate it with tidal disruptions during the high-eccentricity phases of the Kozai cycle. By numerical integration of the trajectories forming the boundary of the loss cone, we determine its shape and volume. We also include the effect of a relativistic advance of the pericentre. Results. The potential of the disc has the efffect of enlarging the loss cone, therefore, the predicted number of tidally disrupted stars should grow by factor of 10 2 . On the other hand, the effect of the cluster mean potential, together with the relativistic pericentre advance, act against the eccentricity oscillations. In the end we expect the tidal disruption events to be approximately ten times more frequent in comparison with the model in which the three effects -the cluster mean field, the relativistic pericentre advance, and the Kozai mechanism -are all ignored. The competition of different influences suppresses the predicted star-disruption rate as the black hole mass increases. Hence, the process under consideration is more important for intermediate-mass black holes, M • 10 4 M .

The observation of quasars at very high redshift such as Pōniuā’ena is a challenge for models of super-massive black hole (SMBH) formation. This work presents a study of SMBH formation via known physical processes in star-burst clusters formed at the onset of the formation of their hosting galaxy. While at the early stages hyper-massive star-burst clusters reach the luminosities of quasars, once their massive stars die, the ensuing gas accretion from the still forming host galaxy compresses its stellar black hole (BH) component to a compact state overcoming heating from the BH–BH binaries such that the cluster collapses, forming a massive SMBH-seed within about a hundred Myr. Within this scenario the SMBH–spheroid correlation emerges near-to-exactly. The highest-redshift quasars may thus be hyper-massive star-burst clusters or young ultra-compact dwarf galaxies (UCDs), being the precursors of the SMBHs that form therein within about 200 Myr of the first stars. For spheroid masses ≲ 109.6 M⊙ a SMBH cannot form and instead only the accumulated nuclear cluster remains. The number evolution of the quasar phases with redshift is calculated and the possible problem of missing quasars at very high redshift is raised. SMBH-bearing UCDs and the formation of spheroids are discussed critically in view of the high redshift observations. A possible tension is found between the high star-formation rates (SFRs) implied by downsizing and the observed SFRs, which may be alleviated within the IGIMF theory and if the downsizing times are somewhat longer.