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MODEST Working Group 4:
Collisions between stars in dense stellar systems are thought to
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
of stars. In galactic nuclei, collisional mass loss contributes to the
feeding of massive black holes. Our goals are to understand and
stellar collisions through hydrodynamical simulations and
(semi)analytical calculations and to develop numerical methods to
incorporate that knowledge into stellar dynamical models.
Note: Comments/inputs to improve these pages are welcome.
(The original version was written by Marc Freitag in 2004)
methods | SPH simulations | Grid simulations | Miscellaneous
Role of collisions in cluster
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
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
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
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
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,
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
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.
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
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
composition gradient, if they exist at all, are still far from being
intervention-free black boxes (see Modest working group
fluid sorting (low velocity collisions)
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
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.
- Smoothed Particle Hydrodynamics (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
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
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
All the data for the ~15000 SPH simulations of MS-MS collisions by
Freitag and Benz (2004), are on-line
... by Marc Freitag
, James Lombardi
and Joshua Barnes
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
Here is an exception found so far:
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...
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
comments and contributions welcome. Last Update: