No Arabic abstract
Mass and energy injection throughout the lifetime of a star cluster contributes to the gas reservoir available for subsequent episodes of star formation and the feedback energy budget responsible for ejecting material from the cluster. In addition, mass processed in stellar interiors and ejected as winds has the potential to augment the abundance ratios of currently forming stars, or stars which form at a later time from a retained gas reservoir. Here we present hydrodynamical simulations that explore a wide range of cluster masses, compactnesses, metallicities and stellar population age combinations in order to determine the range of parameter space conducive to stellar wind retention or wind powered gas expulsion in star clusters. We discuss the effects of the stellar wind prescription on retention and expulsion effectiveness, using MESA stellar evolutionary models as a test bed for exploring how the amounts of wind retention/expulsion depend upon the amount of mixing between the winds from stars of different masses and ages. We conclude by summarizing some implications for gas retention and expulsion in a variety of compact ($sigma_v gtrsim 20 , {rm km s^{-1}}$) star clusters including young massive star clusters ($10^5 lesssim M/M_odot lesssim 10^7$, $age lesssim 500$~Myrs), intermediate age clusters ($10^5 lesssim M/M_odot lesssim 10^7$, $age approx 1-4$~Gyrs), and globular clusters ($10^5 lesssim M/M_odot lesssim 10^7$, $age gtrsim 10$~Gyrs).
We study Markovian continuous-time random walk models for Levy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal to zero in zero. The significance of this result is two-fold: i) with regard to the probabilistic derivation of the fractional diffusion equation and also ii) with regard to the concept of site fidelity in the framework of Levy-like motion for wild animals.
Long-term planning poses a major difficulty to many reinforcement learning algorithms. This problem becomes even more pronounced in dynamic visual environments. In this work we propose Hierarchical Planning and Reinforcement Learning (HIP-RL), a method for merging the benefits and capabilities of Symbolic Planning with the learning abilities of Deep Reinforcement Learning. We apply HIPRL to the complex visual tasks of interactive question answering and visual semantic planning and achieve state-of-the-art results on three challenging datasets all while taking fewer steps at test time and training in fewer iterations. Sample results can be found at youtu.be/0TtWJ_0mPfI
We use 3D hydrodynamical models to investigate the effects of massive star feedback from winds and supernovae on inhomogeneous molecular material left over from the formation of a massive stellar cluster. We simulate the interaction of the mechanical energy input from a cluster with 3 O-stars into a giant molecular cloud (GMC) clump containing 3240 solar masses of molecular material within a 4 pc radius. The cluster wind blows out of the molecular clump along low-density channels, into which denser clump material is entrained. We find that the densest molecular regions are surprisingly resistant to ablation by the cluster wind, in part due to shielding by other dense regions closer to the cluster. Nonetheless, molecular material is gradually removed by the cluster wind during which mass-loading factors in excess of several 100 are obtained. Because the clump is very porous, 60-75 per cent of the injected wind energy escapes the simulation domain, with the difference being radiated. After 4.4 Myr, the massive stars in our simulation begin to explode as supernovae. The highly structured environment into which the SN energy is released allows even weaker coupling to the remaining dense material and practically all of the SN energy reaches the wider environment. The molecular material is almost completely dispersed and destroyed after 6 Myr. The escape fraction of ionizing radiation is estimated to be about 50 per cent during the first 4 Myr of the clusters life. A similar model with a larger and more massive GMC clump reveals the same general picture, though more time is needed for it to be destroyed.
Recent research has been constraining the retention fraction of black holes (BHs) in globular clusters by comparing the degree of mass segregation with $N$-body simulations. They are consistent with an upper limit of the retention fraction being $50,%$ or less. In this work, we focus on direct simulations of the dynamics of BHs in star clusters. We aim to constrain the effective distribution of natal kicks that BHs receive during supernova (SN) explosions and to estimate the BH retention fraction. We used the collisional $N$-body code nbody6 to measure the retention fraction of BHs for a given set of parameters, which are: the initial mass of a star cluster, the initial half-mass radius, and $sigma_mathrm{BH}$, which sets the effective Maxwellian BH velocity kick distribution. We compare these direct $N$-body models with our analytic estimates and newest observational constraints. The numerical simulations show that for the one-dimensional (1D) velocity kick dispersion $sigma_mathrm{BH} < 50,mathrm{km,s^{-1}}$, clusters with radii of 2 pc and that are initially more massive than $5 times 10^3,M_odot$ retain more than $20,%$ of BHs within their half-mass radii. Our simple analytic model yields a number of retained BHs that is in good agreement with the $N$-body models. Furthermore, the analytic estimates show that ultra-compact dwarf galaxies (UCDs) should have retained more than $80,%$ of their BHs for $sigma_mathrm{BH} leq 190,mathrm{km,s^{-1}}$. Although our models do not contain primordial binaries, in the most compact clusters with $10^3$ stars, we have found evidence of delayed SN explosions producing a surplus of BHs compared to the IMF due to dynamically formed binary stars. These cases do not occur in the more populous or expanded clusters.
Globular clusters should be born with significant numbers of stellar-mass black holes (BHs). It has been thought for two decades that very few of these BHs could be retained through the cluster lifetime. With masses ~10 MSun, BHs are ~20 times more massive than an average cluster star. They segregate into the cluster core, where they may eventually decouple from the remainder of the cluster. The small-N core then evaporates on a short timescale. This is the so-called Spitzer instability. Here we present the results of a full dynamical simulation of a globular cluster containing many stellar-mass BHs with a realistic mass spectrum. Our Monte Carlo simulation code includes detailed treatments of all relevant stellar evolution and dynamical processes. Our main finding is that old globular clusters could still contain many BHs at present. In our simulation, we find no evidence for the Spitzer instability. Instead, most of the BHs remain well-mixed with the rest of the cluster, with only the innermost few tens of BHs segregating significantly. Over the 12 Gyr evolution, fewer than half of the BHs are dynamically ejected through strong binary interactions in the cluster core. The presence of BHs leads to long-term heating of the cluster, ultimately producing a core radius on the high end of the distribution for Milky Way globular clusters (and those of other galaxies). A crude extrapolation from our model suggests that the BH--BH merger rate from globular clusters could be comparable to the rate in the field.