The effect of the dynamical state of clusters on gas expulsion and infant mortality

The star formation efficiency (SFE) of a star cluster is thought to be the critical factor in determining if the cluster can survive for a significant (>50 Myr) time. There is an often quoted critical SFE of ~30 per cent for a cluster to survive gas expulsion. I reiterate that the SFE is not the critical factor, rather it is the dynamical state of the stars (as measured by their virial ratio) immediately before gas expulsion that is the critical factor. If the stars in a star cluster are born in an even slightly cold dynamical state then the survivability of a cluster can be greatly increased.Comment: 6 pages, 2 figures. Review talk given at the meeting on "Young massive star clusters - Initial conditions and environments", E. Perez, R. de Grijs, R. M. Gonzalez Delgado, eds., Granada (Spain), September 2007, Springer: Dordrecht. Replacement to correct mistake in a referenc

The mass-to-light ratio of rich star clusters

We point out a strong time-evolution of the mass-to-light conversion factor eta commonly used to estimate masses of unresolved star clusters from observed cluster spectro-photometric measures. We present a series of gas-dynamical models coupled with the Cambridge stellar evolution tracks to compute line-of-sight velocity dispersions and half-light radii weighted by the luminosity. We explore a range of initial conditions, varying in turn the cluster mass and/or density, and the stellar population's IMF. We find that eta, and hence the estimated cluster mass, may increase by factors as large as 3 over time-scales of 50 million years. We apply these results to an hypothetic cluster mass distribution function (d.f.) and show that the d.f. shape may be strongly affected at the low-mass end by this effect. Fitting truncated isothermal (Michie-King) models to the projected light profile leads to over-estimates of the concentration parameter c of delta c ~ 0.3 compared to the same functional fit applied to the projected mass density.Comment: 6 pages, 2 figures, to appear in the proceedings of the "Young massive star clusters", Granada, Spain, September 200

Dynamic Evolution of a Quasi-Spherical General Polytropic Magnetofluid with Self-Gravity

In various astrophysical contexts, we analyze self-similar behaviours of magnetohydrodynamic (MHD) evolution of a quasi-spherical polytropic magnetized gas under self-gravity with the specific entropy conserved along streamlines. In particular, this MHD model analysis frees the scaling parameter $n$ in the conventional polytropic self-similar transformation from the constraint of $n+\gamma=2$ with $\gamma$ being the polytropic index and therefore substantially generalizes earlier analysis results on polytropic gas dynamics that has a constant specific entropy everywhere in space at all time. On the basis of the self-similar nonlinear MHD ordinary differential equations, we examine behaviours of the magnetosonic critical curves, the MHD shock conditions, and various asymptotic solutions. We then construct global semi-complete self-similar MHD solutions using a combination of analytical and numerical means and indicate plausible astrophysical applications of these magnetized flow solutions with or without MHD shocks.Comment: 21 pages, 7 figures, accepted for publication in APS

Dense Stellar Populations: Initial Conditions

This chapter is based on four lectures given at the Cambridge N-body school "Cambody". The material covered includes the IMF, the 6D structure of dense clusters, residual gas expulsion and the initial binary population. It is aimed at those needing to initialise stellar populations for a variety of purposes (N-body experiments, stellar population synthesis).Comment: 85 pages. To appear in The Cambridge N-body Lectures, Sverre Aarseth, Christopher Tout, Rosemary Mardling (eds), Lecture Notes in Physics Series, Springer Verla

The long-term survival chances of young massive star clusters

We review the long-term survival chances of young massive star clusters (YMCs), hallmarks of intense starburst episodes often associated with violent galaxy interactions. We address the key question as to whether at least some of these YMCs can be considered proto-globular clusters (GCs), in which case these would be expected to evolve into counterparts of the ubiquitous old GCs believed to be among the oldest galactic building blocks. In the absence of significant external perturbations, the key factor determining a cluster's long-term survival chances is the shape of its stellar initial mass function (IMF). It is, however, not straightforward to assess the IMF shape in unresolved extragalactic YMCs. We discuss in detail the promise of using high-resolution spectroscopy to make progress towards this goal, as well as the numerous pitfalls associated with this approach. We also discuss the latest progress in worldwide efforts to better understand the evolution of entire cluster systems, the disruption processes they are affected by, and whether we can use recently gained insights to determine the nature of at least some of the YMCs observed in extragalactic starbursts as proto-GCs. We conclude that there is an increasing body of evidence that GC formation appears to be continuing until today; their long-term evolution crucially depends on their environmental conditions, however.Comment: invited refereed review article; ChJA&A, in press; 33 pages LaTeX (2 postscript figures); requires chjaa.cls style fil

Homological flows & star formation

SIGLEAvailable from British Library Document Supply Centre-DSC:D063836 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A taxonomic algorithm for bar-building orbits

Recently it has been realized that the major structures observed in rotating disc galaxies, i.e. bars and spirals, can be supported by regular as well as by chaotic orbits. The fact that the building of a structure cannot be attributed just to quasi-periodic orbits associated with a single orbital family, creates the need to classify the trajectories of the particles in structure supporting and structure non-supporting within a time interval of interest. Our goal is to present a simple algorithm that detects and classifies the orbits which reinforce the rectangularity of the outer envelope of a bar, independently of their regular or chaotic character. Our bar is a two-dimensional (2D) response bar, formed when an external potential estimated from near-infrared observations of an early-type barred-spiral galaxy, is imposed to a set of initial conditions. For this purpose we use a method based on tracing patterns in sequences of characters, which indicate sign changes of the (Cartesian) coordinates. These sign changes occur when as integrate an orbit for a timetand we follow it in 2D subspaces of the phase space [( etc.]. A sign change indicates crossing of an axis during the integration. In the case we describe in our paper the bar in the inner parts is supported by regular orbits following the x1 flow, while the outer envelope of the bar is supported mainly by chaotic orbits at higher energies. With our method, at a given Jacobi constant, first we assess the contribution to the local surface density of a large number of orbital segments. This is done by integrating their initial conditions for 10 pattern rotations. We depict this information on grey-scale maps. We have realized that this contribution is independent of the regular or chaotic character of the integrated orbits. Then, by analysing the arrays of sign changes we have registered during the orbital integrations, we separate the trajectories that shape the outer structure of the bar in two classes. They follow mainly boxy or/and diamond-like morphologies within the time of integration. By repeating the method at several Jacobi constants (EJ) we find that the majority of the orbits that support the morphological feature we study, i.e. the boxiness of the bar, are found in a narrow ΔEJ interval. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS

On time-dependent orbital complexity in gravitational N-body simulations

We implement an efficient method to quantify time-dependent orbital complexity in gravitational $N$-body simulations. The technique, which we name DWaTIM, is based on a discrete wavelet transform of velocity orbital time series. The wavelet power-spectrum is used to measure trends in complexity continuously in time. We apply the method to the test cases N=3 Pythagorean- and a perturbed N=5 Caledonian configurations. The method recovers the well-known time-dependent complexity of the dynamics in these small-$N$ problems. We then apply the technique to an equal-mass collisional N=256 body simulation ran through core-collapse. We find that a majority of stars evolve on relatively complex orbits up to the time when the first hard binary forms, whereas after core-collapse, less complex orbits are found on the whole as a result of expanding mass shells.Comment: 17 pages, 15 figures, 2 tables, accepted for publication in MNRA