Re: Cosmology

["John S. Denker" <jsd@MONMOUTH.COM>]

I wrote
> > The space between measuring sticks can expand, leaving each stick
> > unchanged.  The space between galaxies can expand, leaving each galaxy
> > unchanged.

Then at 08:26 PM 2/11/01 -0700, Jim Green wrote:

> Ah, but, John, they tell me that the space between galaxies does _not_
> expand but that the space between super clusters does - this is what (for
> the moment) I can't understand.  Next I will deal with the rest of what I
> don't understand.  Maybe I am to assume that the binding between local
> clusters is strong enough so that the binding is rigid, but that the
> binding between super clusters is sufficiently weak such that it is not
> rigid.

That's about right.

>   All this seems a bit arbitrary.

It's not arbitrary.  It's like asking why a chunk of pine floats, while a
chunk of quartz sinks.  It depends on the properties of the items (size and
mass).  It also depends on what criterion we're comparing against (density
of water in this analogy).

Let's run the numbers.

1) Start with the solar system.  The mass is on the order of 1 solar mass,
and the distance is on the order of 1 AU.  That gives a characteristic time
on the order of 1 year (actually 1/2pi years) i.e. the time it takes the
orbital velocity to change by roughly 100%.

We need to compare that with something, namely the Hubble time.  That wants
to tear things apart with a timescale of about a billion years.  Clearly
this isn't going to faze anything as tightly bound as the solar system.

2) Next consider the galaxy.  Plug in for galactic mass and typical
intragalactic distances.   Obtain a timescale on the order of 40 million
years.  Clearly the galaxy is bound;  the Hubble expansion can't tear it apart.

3) Next consider a pair of very-close galaxies, like our Milky Way and the
Large Magellanic Cloud.  That's bound also.

4) Next consider a pair of galaxies with typical galactic mass and
reasonable not-too-small INTERgalactic distance.  If we consider only that
pair, they would not be bound.

5) Next consider a cluster of galaxies.  This has the same distance-scale
as the previous case, but we get to use the mass of the entire
cluster.  The way I figure it, given the size of a typical cluster and the
number of galaxies in it, such things are right on the edge of being bound. (*)

6) Next consider a supercluster.  If my numbers are correct, these are also
right on the edge. (*)

7) Presumably bigger things are unbound.  Note that the timescale goes like
(density^-1.5) so anything with much less density than a supercluster will
be unbound.

Note (*) at some point you have to drag in arguments about the infamous
"missing mass".  A lot of things appear to be more tightly bound than can
be explained by the mass of the stars we can see.  So it's not
super-obvious what mass to use in marginal cases.

References:
  http://www.geocities.com/atlasoftheuniverse/virgo.html
  http://www.seds.org/messier/g-group.html
  http://www.seds.org/messier/more/virgo.html
  http://www.seds.org/messier/more/mw.html