On Fri, 4 May 2001, Mr. Wu wrote:

> ?Dear Sir,
> 
> I have some questions concerning the topic 'Dark Matter'.
> 
> First, we said that the dark matter helps us to determine the fate of
> our universe because it helps us to estimate the amount of gravity
> inside the universe.
> But, why must we determine the density of the universe to assess the
> gravity, but not the total mass of the universe?

	Good question.  The technical answer is that in the equations
of general relativity which describe the expansion of the universe,
the terms cancel out such that you are left with a term which is
proportional to the overall mass density and a term which is proportional
to the expansion constant.  This nice form comes about since the
universe has roughly the same mass density everywhere and is expanding
uniformly everywhere.  Thus, you can write the equations to describe
the expansion emanating from any arbitrary point, since the
expansion is occuring from every point in the same way.  When you write
the equations, you actually have first to write down an expression for
the total mass of your miniature example case.  But, you can reduce the
equation and the total mass is reduced to just a density term and the
expansion term which is the Hubble constant.
	Physically, you can think of it as an explosion of a set amount
of mass.  If the explosion occurs and the pieces of mass are very close
together (more dense), the gravity of the pieces will be stronger and will
change the motion of the mass.  If the explosion occurs such that the
mass pieces are farther apart (less dense), then their gravitational
attraction to each other will be comparatively weaker.  Thus, for the
same mass, the density (being how far apart the pieces are) is important.

> Second, is compact object a possible candidate for dark matter?

	Compact objects such as MACHOS are becoming less and less likely
as dark matter candidates.  They do exist and there is exciting research
being conducted now as astronomers search for them, but it appears as
though they can only contribute a few percent of the total missing mass.

> Third, how can we estimate the distance of the galaxy from the center of
> the cluster which helps us to plot the rotation curves?

	There are at least two important sources of information
about dark matter which we determine from studying galactic motions.
The first and best known is the rotation curve method which you mentioned.
Astronomers can measure the rotation velocity of material within a galaxy
as it orbits the galactic center.  This measurement is made on an
individual galaxy, not on a cluster.  Galaxies have structures which
can be categorized.  By observing the radiation from the material in a
galaxy and then by noting the structure of the galaxy, the center can
be determined and the velocity of the galactic stars and gas around that
center can be measured.

Michael Scott Armel
Center for Particle Astrophysics