From: metzler@pablo.physics.lsa.umich.edu (Chris Metzler)
Newsgroups: sci.physics,sci.astro
Subject: Re: reported dark matter observation (PART 1)
Date: 6 Jan 1993 01:15:25 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

Here's the deal.  What Rick Mushotzky and collaborators did is use
ROSAT (a German X-ray satellite) to measure carefully the gas mass
and total mass of a small group of galaxies.  This let them calculate
a value for Omega, which turns out to be much higher than previous
efforts in this regard.

That's the short version.  Here comes the long version.  (from here on
out, I'm assuming the Cosmological Constant \Lambda = 0)  We'll do this
in three steps.

1.  Mass estimates for groups and clusters of galaxies are important because
they give you a way to get at \Omega_o, the ratio of the mean mass density of
the universe to the critical value.  If \Omega_o > 1, the universe is closed,
the Hubble expansion should slow down, stop and reverse, and everything should
eventually collapse back upon itself.  If \Omega_o < 1, the universe is open
and should continue in free expansion forever.  If \Omega_o = 1, the
universe is flat and should expand forever but asymptotically approach
no-expansion.  So cosmologically speaking, \Omega_o is the quantity of
interest.

Now, how do cluster masses let us get at \Omega_o?  Assume for a second
that we know the total mass of a cluster of galaxies, as well as the
total mass in normal, baryonic-type matter.  In the absence of any
significant dissipation (and dissipation should not be important on
these huge scales), all the matter in the cluster should have fallen
in from the same volume.  Then the ratio of the mass in baryons to
the total mass (the baryon fraction of the cluster) should equal
the ratio of the average baryon density in that original volume to the
average total density in that original volume,

	M            <rho      >
         baryon          baryon
        -------    = -----------  .
         M            <rho     >
          tot             total


Now, overdensities that result in clusters of galaxies are not that
huge ( ~10^-3).  So, we introduce only a very small error by considering
these average densities to be representative of the universe as a whole.
Then dividing the numerator and the denominator by the critical density,
we get

	M            <Omega      >
         baryon            baryon
        -------    = -------------  .
         M           <Omega     >
          tot              total

where \Omega_baryon is the ratio of the mean baryon (normal matter)
density of the universe to the critical value, and \Omega_total is 
the ratio of the average total density (considering all components
in the universe) to the critical value.  Note that \Omega_total
is what we above described as \Omega_o, the quantity of interest.
We thus have that \Omega_o is equal to \Omega_baryon divided by
the baryon fraction of the cluster.  The very-successful theory
of Big Bang Nucleosynthesis tells us what \Omega_baryon is; the
X-ray observations tell us what the baryon fraction of clusters
are by measuring the two masses.

Up to this point, efforts to do this keep coming up over and over
with values for \Omega_o of 0.1-0.3.

Urp, gotta run, my ride's here.  Parts 2 and 3 will explain how
they got their mass values, and what it may mean.  Sorry to break
thought like this; rest'll come later tonight.


-- 
SNAILMAIL:                                       AT&TMAIL:
Chris Metzler                                    313-764-4607 (office)
Department of Physics, University of Michigan    313-996-9249 (home)
Randall Lab, 500 E. University
Ann Arbor, MI  48109-1120 USA

E-MAIL:  metzler@pablo.physics.lsa.umich.edu