From: metzler@pablo.physics.lsa.umich.edu (Chris Metzler)
Newsgroups: sci.physics,sci.astro
Subject: Re: reported dark matter observation (PART 2)
Date: 6 Jan 1993 06:02:57 GMT
Organization: University of Michigan Department of Physics
Distribution: world
NNTP-Posting-Host: pablo.physics.lsa.umich.edu

In article <1993Jan5.235706.25449@wam.umd.edu>, mrmuon@next06pg2.wam.umd.edu (Eli John Hawkins) writes:
|> I saw a brief item las night on an overnight news show. It was something  
|> about dark matter having been observed with X-ray astronomy and that it is  
|> supposed to be enough to close the universe.
|> I imagine that someone on the net knows more about this.
|> Has this been published (if so, where) or just announced?:
|> What's the deal?
|> --
|> Eli Hawkins : mrmuon@wam.umd.edu
|> 

OK, here's the rest of the deal.  In the other note I put the short answer
to this question, as well as the description of how baryon mass and total
binding mass estimates give you a value of \Omega_o.  This will explain
how you get those mass estimates, and how this all relates to
Mushotzky et al's announcement.

2.  How do you get the total mass of the cluster when you can't see the
dark matter?  One way is to use gravitational binding arguments on the
group or cluster galaxies.  If you know how far they are from the
center of the cluster, and you know how fast they're going, and you
assume that either the galaxy orbits are circular, or that their
trajectories ("velocity dispersions") are isotropically distributed,
then it's simple physics to calculate the mass of the group or cluster
within a certain radius.  The problem with this, however, is that there's
a lot of reason to believe that the galaxy orbits AREN'T isotropically
distributed -- both "experimental" (i.e. through simulations) and
observational.  In particular, anisotropies in the velocity
dispersions tend to result in underestimates of the binding mass.

A believed-to-be-more-reliable method is to get the binding mass (total
mass within a certain radius) by X-ray observations.  Cluster gas is
hot -- from 10^6 K for small groups to 10^7-10^8 K for rich clusters.
If you assume that the gas is in hydrostatic equilibrium (that is,
that the gravitational force pulling a parcel of gas down is exactly
equal to its pressure support), and also assume the ideal gas law
applies, then you can get a simple formula for the binding mass
within a certain radius.  The observables in the formula are the
radius, the temperature at that radius, and the temperature
and density slope (vs radius) at that radius.  This is believed
to be fairly reliable.  The same N-body plus hydrodynamic simulations
which give underestimated optical mass estimates (using cluster
galaxy velocity dispersions -- see paragraph above) give X-ray
mass estimates that are bang on.

3.  Mushotzky's group measured an X-ray binding mass for this small
group of galaxies and found a very large mass, and thus a very
small baryonic fraction, and thus a large \Omega_o.

This result is in direct contrast with small \Omega_o values (0.1-0.3)
obtained by following the EXACT SAME PROCEDURE, only on rich clusters
of galaxies rather than small groups.

There are four ways to interpret this:

a) This newly announced result is wrong.  I don't know much about the
group they observed, but it's hard for me to see how they were able
to get both a gas temperature, and a temperature slope, at large
radii from the center of the group (~400 kpc or so).  The reason
that this technique has been applied primarily to nearby rich clusters
is because they occupy a large solid angle on the sky, and thus are
easier to observe at several points radially.  And even then, we don't
have reliable measurements of temperatures out very far in the cluster
(~2 Mpc or so); that's the equivalent of what they've done here.  So
I'm not sure how seriously to take this result.

b) The rich cluster observations which predict \Omega_o is low are
wrong.  This is possible, but not very probable.  This is what
theorists would like to be true, and accordingly theorists have
worked very hard to show how this might be true.  What the critiques
boil down to is assailing the assumptions of hydrostatic equilibrium
or of ideal gas-ness.  Certainly the degree of substructure we see
in X-ray surface brightness profiles tells us that in many (perhaps
even most) clusters, the gas hasn't relaxed yet.  And the work I'm
doing suggests that clusters can be out of hydrostatic equilibrium,
have significant substructure, and yet look very relaxed and in
hydrostatic equilibrium if you're looking in the right direction
(this happening about 15% of the time).  But if the gas isn't in
hydrostatic equilibrium, then the total binding mass estimates
ought to be off, and there's no reason to believe that they'd
consistently be off the same way, getting larger as you go to
larger clusters with larger gas masses.  In other words, the fact
that when we do this with different rich clusters, we keep getting
about the same value, tells us that there's probably no problem.

c) Neither set of observations are wrong, but this group of
galaxies is not a representative object; it's an oddity.
Then while the structure of this group may be interesting,
it doesn't tell us anything about \Omega_o per se.

d) Neither set of observations are wrong, and this group of
galaxies is representative.  If this very exciting
possibility is true, then \Omega_o is probably high, because
small groups are more representative of the universe than rich
clusters are.  But then we are faced with explaining why dark
matter is more concentrated in small groups than in rich clusters.
Very strange.

-----------------------------------------

I should point out in closing that the statement I read in the
newspapers to the effect that this is the first observational
evidence that \Omega_o might be high (~1) is false.  Observations
of substructure in clusters suggests a value greater than 0.5, as
do various observations of the galaxy peculiar velocity field.

So in summary, this is a very interesting observation, but how
excited to get is going to take some time to tell.

WHEW!  Hope this wasn't too boring, folks.

-- 
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Chris Metzler                                    313-764-4607 (office)
Department of Physics, University of Michigan    313-996-9249 (home)
Randall Lab, 500 E. University
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