March 7, 2016

Stellar collisions: Role of collisions in cluster dynamics

Why we care about stellar collisions?

Stellar collisions and their role in the evolution of stellar clusters were the subject of a conference held at the American Museum of Natural History, NY, in 2000. The proceeding book is a very good starting point to explore these subjects and get a picture of our present understanding of them. Or just read on…

The various regimes and various cases.

First, we define and determine a few key quantities in this page.

This allows to distinguish between parabolic collisions for which V_rel << V_ast, the regime relevant for open and globular clusters, and hyperbolic collisions,V_rel > V_ast, which are highly supersonic and may happen in the center of galactic nuclei. A third category are collisions occurring between bound partners in a binary star, either because of the perturbation of the pair by a third star (elliptic collision), or as a result of “normal” binary evolution (“circular collision”).
Elliptic encounters were found to occur between MS stars in N-body simulations (see for instance Portegies Zwart & McMillan 2002) and are probably the main channel for collisions in young or globular clusters. As they usually occur at large eccentricities, they are physically similar to parabolic encounters and probably don’t require specific hydro calculations.
Circular encounters, i.e. the merger of two stars in a circularized binary has been studied in particular detail in the context of two compact objects. Such mergers may have outstanding observational consequences and are extremely unlikely to occur between two single, unbound, stars. An important example is the merger of 2 neutron stars, a source of gravitational waves, r-elements and possibly the engine powering gamma ray bursts (see the review by Rasio & Shapiro 1999). For the time being, no attempt is made here to treat this category in any detail.

Of course, one has also to distinguish between the various stellar species that take part in a collision. Collisions between pre-MS star may play an important role in young clusters and contribute to populate the high-end of the mass function. Collisions between 2 MS star or a MS star and a Giant are the more likely to occur in mature clusters (in binaries) or galactic nuclei (between single stars).

In the figure below we show the cumulative collision probability integrated over the lifetime of three stellar models. The second star is assumed to be point-like. In each case, two limiting regimes are considered. At low relative velocities V_rel << V_ast, the collisional cross-section scales like R_star (solid lines); at very high velocities V_rel >> V_ast, we recover the geometrical cross section, ~ R_star^2 (dashed lines). Stellar evolution models are from Schaller et al. 1992 and Meynet et al. 1994. The evolution is only shown up to He-flash. The solid dot shows the end of the MS phase.

Relative collision probability in the life of a star

Cumulative collision probability (normalized to 1) integrated over the lifetime of three stellar models.

Collisions between a compact star and a more extended object are less probable, mainly because compact objects are less numerous (the cross section itself is only 2-4 times smaller than for collisions between 2 identical extended objects), but not vanishingly rare and may result in outstanding objects. Collisions between 2 compact objects can occur with a significant probability only as a result of binary evolution. Note that interactions with field stars in clusters shrinks the orbit of compact binaries and, thus, may highly increase the number of compact-compact mergers (see, for instance the work of Shara & Hurley 2002, for a nice example).

A very special case, of great interest for galactic nuclei, is the encounter between a star and a black hole (M>>100 M_sun), a tidal disruption.

What we need to know.

On a purely stellar dynamical point of view, a collision between two stars can be described by a few simple quantities: the number of surviving stars (2, 1 or 0), their masses and the modulus and direction of the post-collisional relative velocity (if both stars survive). This completely determines the kinematical outcome of the collision only if CM frame of the surviving star(s) is the same as the one for the incoming star, i.e. if one can neglect the kick given to the star(s) by asymmetrical gas ejection.

In order to know how the collision products (stars that have undergone collision) evolve and, in particular, what their observational properties will be, one also need to know the post-collisional stellar stellar structure, in particular the chemical and angular momentum profiles, which may be unlike any produced by “normal” stellar evolution. In principle, this more precise information requires more detailed hydrodynamical simulations (but see the fluid sorting method, in the page of methods). After a collision, the star returns to hydrostatic equilibrium in a few hours. However, it is swollen by the dissipated orbital energy and recontracts to thermal equilibrium over a much longer time-scale, T_therm. Due to this increased size, a further collision is more likely, much more so if the star is part of a binary. This means that one cannot always assume that the star instantaneously returns to thermal equilibrium. For these reasons, it seems that realism cannot be achieved in simulations of stellar clusters (where a significant number of collision occurs) without resorting to in-line ‘live’ computation of the stellar evolution of collision products. Unfortunately, stellar evolution codes able to cope with strongly rotating stars with a pecular composition gradient, if they exist at all, are still far from being intervention-free black boxes (see Modest working group 2).