Modeling Colliding Galaxy Clusters and Dark Matter

Science is about making models.  We make a conceptual model of
something (in other words, we guess how it works), then we figure out
what that model would predict, we compare those predictions to
observations, and then we either discard, modify, or (for the time
being) accept that the model could be correct. (Recently I stumbled
across an entertaining video of Richard Feynman explaining this
method.)  Ideally, the model is conceptually simple, with as few
moving parts as possible, yet is able to match a rich variety of data.
Sometimes this modeling process is about something really fundamental,
such as how gravity works; other times the modeling process is just
about estimating something we can't measure directly.  For example, a
scale which doesn't read the correct weight can still be used to infer
your weight, as long as you have a workable model such as "reads about
ten pounds too heavy" or "reads about half the true weight."

My student Will Dawson recently finished some work which is a really nice example of the latter kind of modeling.  We have been studying colliding clusters of galaxies; our lives are too short to see the collision play out, so we have to make a model which allows us to extrapolate from the current (just post-collision) state back to the time of maximum impact.

A good analogy: given a photograph and a speed gun reading taken a
split-second after an automobile collision, reason backward from that
to infer the velocity of collision and the time since collision.  The
main difference is that the galaxy clusters mostly go right through
each other because the space between the galaxies is so big.  The hot
gas clouds filling those spaces do collide, leaving a pancake of hot
gas in the middle while the galaxies continue on (eventually to slow
down and turn around due to gravity).  We are interested in what
happens to the dark matter: the Bullet Cluster and the Musketball
Cluster show that it is mostly collisionless, but "mostly" is
something we really want to quantify, for reasons I'll explain in a
future post.

But first, we have to make a model of the collision.  Speed guns and
spectrographs can only tell how fast the galaxies are moving toward us
or away from us; they say nothing about how fast they are moving in
the transverse direction (in the plane of the sky).  To study dark
matter we need to know the full three-dimensional velocity, and we
want to know what it was at the time of collision, rather than what it
is right now, after the collision.  This is closely related to how
much time has passed since the collision (by collision I really mean
the maximum overlap of the two clusters), because the observed
separation since the collision could have been achieved by moving at a
high velocity for a short time, or moving at a low velocity for a long
time.  Making things more complicated, the separation we observe is
only the transverse part of the separation.  So a collision which
occurs along the line of sight will give us a large velocity on our
speed gun but a small apparent separation, while the same collision
viewed transversely will exhibit a small part of the velocity and a
large part of the separation.  We don't know what angle we are viewing
the system at, so the true velocity could be just about anything.

Like a rock climber inching up a chimney, the way out of this is to
push against two extremes.  If we observe any line-of-sight velocity,
the motion can't be completely transverse; in fact we can rule out a
range of near-transverse geometries because they would require an
absurdly large three-dimensional velocity.  (Absurdly large is defined
here as larger than the free-fall velocity from infinity.)  Similarly,
if we observe any transverse separation we can rule out a range of
nearly line-of-sight geometries because they would require absurdly
large three-dimensional separation.  (Absurdly large is defined here
as requiring longer than the age of the universe to reach that
separation.)

Still, we are left with a range of geometries in the middle; at the
extremes of that range the geometries aren't completely ruled out, but
look pretty unlikely.  Here Will applied another important concept:
marginalizing over all remaining possibilities.  His code ranges over
all possible geometries, tabulating how well they match the data, and
thus produces a probability distribution.  So we don't know exactly
how fast the collision was, but we can be 99% confident it is within
have a certain broad range, 90% confident it is within a certain
smaller range, etc.

This was a pretty big advance in sophistication compared to the way
previous studies had estimated the collision velocity and time since
collision.  Using this technique, Will demonstrated that what
astronomers don't know can hurt them---not knowing the angle from
which we are viewing a collision results in substantial uncertainty in
the quantities we need to know to study the behavior of dark matter.
To narrow things down to a useful range, we need additional
information about a collision.  (In the case of the Bullet Cluster,
the shock gives this information, but most collisions have not shown
an observable shock.)

Will also used his new technique to estimate that it has been about
700 million years since the Musketball Cluster collided, compare to
"only" 200 million years for the Bullet Cluster.  This is good for the
study of dark matter because people would be justifiably skeptical of
conclusions about the nature of dark matter based on just one kind of
collision (a recent, high-speed collision of massive clusters such as
the Bullet).  Studying a range of collision conditions--including less
recent, lower-speed collisions of less-massive clusters such as the
Musketball--gives us a much better chance of identifying universal
properties of dark matter with high confidence.