The hunt for self-similar core collapse

Core collapse is a prominent evolutionary stage of self-gravitating systems. In an idealised collisionless approximation, the region around the cluster core evolves in a self-similar way prior to the core collapse. Thus, its radial density profile outside the core can be described by a power law, $\rho \propto r^{-\alpha}$. We aim to find the characteristics of core collapse in $N$-body models. In such systems, a complete collapse is prevented by transferring the binding energy of the cluster to binary stars. The contraction is, therefore, more difficult to identify. We developed a method that identifies the core collapse in $N$-body models of star clusters based on the assumption of their homologous evolution. We analysed different models (equal- and multi-mass), most of which exhibit patterns of homologous evolution, yet with significantly different values of $\alpha$: the equal-mass models have $\alpha \approx 2.3$, which agrees with theoretical expectations, the multi-mass models have $\alpha \approx 1.5$ (yet with larger uncertainty). Furthermore, most models usually show sequences of separated homologous collapses with similar properties. Finally, we investigated a correlation between the time of core collapse and the time of formation of the first hard binary star. The binding energy of such a binary usually depends on the depth of the collapse in which it forms, for example from $100\,kT$ to $10^4\,kT$ in the smallest equal-mass to the largest multi-mass model, respectively. However, not all major hardenings of binaries happened during the core collapse. In the multi-mass models, we see large transfers of binding energy of $\sim 10^4\,kT$ to binaries that occur on the crossing timescale and outside of the periods of the homologous collapses.Comment: 12 pages, 5 tables, 14 figures, Accepted for publication in A&

Do star clusters form in a completely mass-segregated way?

ALMA observations of the Serpens South star-forming region suggest that stellar protoclusters may be completely mass segregated at birth. Independent observations also suggest that embedded clusters form segregated by mass. As the primordial mass segregation seems to be lost over time, we aim to study on which timescale an initially perfectly mass-segregated star cluster becomes indistinguishable from an initially not mass-segregated cluster. As an example, the Orion Nebula Cluster (ONC) is also discussed. We used $N$-body simulations of star clusters with various masses and two different degrees of primordial mass segregation. We analysed their energy redistribution through two-body relaxation to quantify the time when the models agree in terms of mass segregation, which sets in only dynamically in the models that are primordially not mass segregated. A comprehensive cross-matched catalogue combining optical, infrared, and X-ray surveys of ONC members was also compiled and made available. The models evolve to a similar radial distribution of high-mass stars after the core collapse (about half a median two-body relaxation time, $t_\mathrm{rh}$) and become observationally indistinguishable from the point of view of mass segregation at time $\tau_\mathrm{v} \approx 3.3\,t_\mathrm{rh}$. In the case of the ONC, using the distribution of high-mass stars, we may not rule out either evolutionary scenario (regardless of whether they are initially mass segregated). When we account for extinction and elongation of the ONC, as reported elsewhere, an initially perfectly mass-segregated state seems to be more consistent with the observed cluster.Comment: A&A (in press), 17 pages, 15 figures, data available at CD

Warping the young stellar disc in the Galactic Centre

We examine influence of the circum-nuclear disc (CND) upon the orbital evolution of young stars in the Galactic Centre. We show that gravity of the CND causes precession of the orbits which is highly sensitive upon the semi-major axis and inclination. We consider such a differential precession within the context of an ongoing discussion about the origin of the young stars and suggest a possibility that all of them have originated in a thin disc which was partially destroyed due to the influence of the CND during the period of ~6Myr.Comment: proc. conf. "The Universe Under the Microscope - Astrophysics at High Angular Resolution", 21-25 April 2008, Bad Honnef, German

The giants that were born swiftly -- Implications of the top-heavy stellar initial mass function on the birth conditions of globular clusters

Recent results suggest that the initial mass function (IMF) of globular clusters (GCs) is metallicity and density dependent. Here it is studied how this variation affects the initial masses and the numbers of core collapse supernovae (CCSNe) required to reproduce the observed iron spreads in GCs. The IMFs of all of the investigated GCs were top-heavy implying larger initial masses compared to previous results computed assuming an invariant canonical IMF. This leads to more CCSNe being required to explain the observed iron abundance spreads. The results imply that the more massive GCs formed at smaller Galactocentric radii, possibly suggesting in-situ formation of the population II halo. The time until star formation (SF) ended within a proto-GC is computed to be 3.5 - 4 Myr, being slightly shorter than the 4 Myr obtained using the canonical IMF. Therefore, the impact of the IMF on the time for which SF lasts is small.Comment: published in MNRAS, 13 pages, 12 figure

The properties of dynamically ejected runaway and hyper-runaway stars

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 (>~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; Gamma(v) goes like 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.Comment: Now matching published ApJ versio

Violating laws providing for the circulation of goods in foreign transactions from the perspective of criminal law

Katedra trestního právaDepartment of Criminal LawFaculty of LawPrávnická fakult