Re: Fully formed 8-11 billion year old galaxies observed.

From: Brian Tung (brian_at_isi.edu)
Date: 07/08/04 

Date: Thu, 8 Jul 2004 22:36:24 +0000 (UTC)

starman wrote:
> True but at what phase of the universe's evolution was it effectively
> expanding faster than the speed of light?

This question is a bit ill-formed. It's like asking at what speed is a
rubber band being stretched. The answer depends on what section of the
rubber band you're talking about. In the case of the rubber band, a
natural section is to take two points at opposite "ends" of the rubber
band, and to measure the rate at which the distance between those points
is increasing.

In the case of the universe, however, there isn't an obvious choice of
two points, especially since the topology of the universe isn't well
established. Rather, because the expansion of the universe appears to
be fairly uniform (that is, the rate of "stretching" is the same here
as it is anywhere), we give the expansion in terms of some abstract
"scale."

For instance, we say that in a flat universe, the scale goes as time
raised to the two-thirds power. That is to say, if two points in the
universe are separated by distance d at some time t after the Big Bang,
then after time 8t, they are separated by distance 4d, because 8 raised
to the two-thirds power is 4:

    8^(2/3) = (8^2)^(1/3) = cbrt(8^2) = cbrt(64) = 4

where cbrt is the cube root function.

This means that whether or not two points are separating at a speed
faster than that of light, at some time t, depends on how far apart
they are at that time. The galaxies in the Virgo cluster have never
receded from us at the speed of light, because they are too close to
us. Even now, a typical distance to a galaxy in the Virgo cluster is
"only" 60 million light-years or so. But the galaxy whose distance
now is estimated to be 32 billion light-years--obviously, that galaxy
has (at least for part of the history of the universe) been receding
from us at more than the speed of light, since the universe is thought
to be only about 13.6 billion years old.

It seems paradoxical that we should be able to detect that galaxy, if
it is receding from us at more than the speed of light. One can liken
the photons from the galaxy as bugs that travel along a rubber band
that is constantly stretching out. Amazingly, one can show that even
if the ends of the rubber band are separating faster than the bugs can
crawl, the bugs can *still* make it from one end to the other--the
photons still make it from that distant galaxy all the way to us.

Brian Tung <brian@isi.edu>
The Astronomy Corner at http://astro.isi.edu/
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