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MODEST Working Group 4:
Stellar Collisions

Collision image Collisions between stars in dense stellar systems are thought to produce tell-tale `stellar exotica,' i.e. stars with a peculiar structure and evolution, like blue stragglers or very massive stars. They also influence the overall dynamics by changing the number, masses and orbits of stars. In galactic nuclei, collisional mass loss contributes to the feeding of massive black holes. Our goals are to understand and describe stellar collisions through hydrodynamical simulations and (semi)analytical calculations and to develop numerical methods to incorporate that knowledge into stellar dynamical models.

Contact: Pau Amaro-Seoane

Note: Comments/inputs to improve these pages are welcome.

(The original version was written by Marc Freitag in 2004)

Jump to: Semi-analytical methods | SPH simulations | Grid simulations | Miscellaneous

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. 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). See this diagram. 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 massive black hole (M>>100 M_sun).

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, below). 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).


Two classes of methods have been developed that aim at 'guessing' the result of a stellar collision without resorting to an explicit hydrodynamical simulation. So far they have been applied only for MS--MS collisions.

Spitzer & Saslaw model (high velocity collisions)

          Lombardi's fluid sorting (low velocity collisions)

The hope is to get a semi-analytical method to get detailed prediction about the outcome of collisions (masses, velocities and stellar structure(s)) with only a tiny fraction of the computational burden of full-fledged hydrodynamical simulations. Indeed, even with a relatively low resolution (of order 10000 particles), an SPH simulation requires at least a few hours of CPU time on a standard PC.  It is thus clear that incorporating 'live' hydrodynamics into stellar dynamical simulation is still not an option, except maybe for the slowest stellar dynamics schemes (i.e. direct N-body) and for clusters in which collisions are rare.

What is SPH?

Smoothed Particle Hydrodynamics is a Lagrangian particle-based method that has been widely used to tackle all kinds of astrophysical problems, from planetesimal fragmentation to cosmological structure formation. For a description of the method and of its achievements, we refer to reviews by Benz (1990), Monaghan (1992,1999,2001) or Rasio (1999). Peter J. Cossins has written a chapter of his thesis reviewing the subject (2010). For a minimalist introduction to SPH, taken from Freitag (2000), follow this link.

SPH simulations of stellar collisions

SPH codes do not impose any restriction on the geometry of the problem, are best suited for highly dynamical situations (rather than quasi-hydrostatic ones), adapt naturally to a wide range of spatial scales and don't waste computational resources on void spaces. For all these reasons, SPH is particularly well suited to the simulation of stellar collisions. And indeed, most investigations in that field were done using SPH, as this (incomplete) list of SPH collision simulation papers testifies.

All the data for the ~15000 SPH simulations of MS-MS collisions by Freitag and Benz (2004), are on-line

On-line animations

... by Marc Freitag, James Lombardi and Joshua Barnes

On-line ressources

SPH in astrophysics is alive and well! I have created a direct (tiny) link to the most recent papers on SPH:

Unfortunately, most web sites concerned with SPH seem to be a bit out-dated, with a lot of dead links. Here is an exception found so far: The on-line course on computational physics, by Franz Vesely, at the University of Vienna, features a chapter on SPH
... And for the curious, a few links illustrating the versatility of the SPH approach...

Not much here for the time being, except an (incomplete) list of papers on collision simulations with grid methods. Any help to develop this section very welcome...

Visit also the page about NS--NS coalescence by Max Ruffert, with nice images and animations.

To get an idea about the recent (2003 and Jan 2004) scientific activities and issues about collisions in cluster dynamics, see the slides presented during the Modest-4 held in Geneva in Jan 2004 for this working group (coll_report_marc_freitag.pdf). You may also have a look at the list of  collision-related topics disscussed during this meeting (coll_discussion_modest4.pdf).

All the data for the ~15000 SPH simulations of MS-MS collisions by Freitag and Benz (2004), is now on-line!

Maintained, updated and new material added by Pau Amaro-Seoane; comments and contributions welcome. Last Update: 2009-12-10