Catch me if you can: is there a runaway-mass black hole in the Orion Nebula Cluster?

We investigate the dynamical evolution of the Orion Nebula Cluster (ONC) by means of direct N-body integrations. A large fraction of residual gas was probably expelled when the ONC formed, so we assume that the ONC was much more compact when it formed compared to its current size, in agreement with the embedded cluster radius-mass relation from Marks & Kroupa (2012). Hence, we assume that few-body relaxation played an important role during the initial phase of evolution of the ONC. In particular, three body interactions among OB stars likely led to their ejection from the cluster and, at the same time, to the formation of a massive object via runaway physical stellar collisions. The resulting depletion of the high mass end of the stellar mass function in the cluster is one of the important points where our models fit the observational data. We speculate that the runaway-mass star may have collapsed directly into a massive black hole (Mbh > 100Msun). Such a dark object could explain the large velocity dispersion of the four Trapezium stars observed in the ONC core. We further show that the putative massive black hole is likely to be a member of a binary system with appr. 70 per cent probability. In such a case, it could be detected either due to short periods of enhanced accretion of stellar winds from the secondary star during pericentre passages, or through a measurement of the motion of the secondary whose velocity would exceed 10 km/s along the whole orbit.Comment: 10 pages, 6 figures, accepted by Ap

Star-disc interactions in a galactic centre and oblateness of the inner stellar cluster

Structure of a quasi-stationary stellar cluster is modelled assuming that it is embedded in the gravitational field of a super-massive black hole. Gradual orbital decay of stellar trajectories is caused by the dissipative interaction with an accretion disc. Gravitational field of the disc is constructed and its effect on the cluster structure is taken into account as an axially symmetric perturbation. Attention is focused on a circumnuclear region (r<10^4 gravitational radii) where the effects of the central black hole and the disc dominate over the influence of an outer galaxy. It is shown how the stellar system becomes gradually flattened towards the disc plane. For certain combinations of the model parameters, a toroidal structure is formed by a fraction of stars. Growing anisotropy of stellar velocities as well as their segregation occur. The mass function of the inner cluster is modified and it progressively departs from the asymptotic form assumed in the outer cluster. A new stationary distribution can be characterized in terms of velocity dispersion of the stellar sample in the central region of the modified cluster.Comment: Accepted for publication in MNRAS; 12 pages, 10 figure

Fourier Analysis of Stochastic Sampling Strategies for Assessing Bias and Variance in Integration

Each pixel in a photorealistic, computer generated picture is calculated by approximately integrating all the light arriving at the pixel, from the virtual scene. A common strategy to calculate these high-dimensional integrals is to average the estimates at stochastically sampled locations. The strategy with which the sampled locations are chosen is of utmost importance in deciding the quality of the approximation, and hence rendered image. We derive connections between the spectral properties of stochastic sampling patterns and the first and second order statistics of estimates of integration using the samples. Our equations provide insight into the assessment of stochastic sampling strategies for integration. We show that the amplitude of the expected Fourier spectrum of sampling patterns is a useful indicator of the bias when used in numerical integration. We deduce that estimator variance is directly dependent on the variance of the sampling spectrum over multiple realizations of the sampling pattern. We then analyse Gaussian jittered sampling, a simple variant of jittered sampling, that allows a smooth trade-off of bias for variance in uniform (regular grid) sampling. We verify our predictions using spectral measurement, quantitative integration experiments and qualitative comparisons of rendered images.</jats:p