Re: NGC 1350
- From: "David Ewan Kahana" <dek@xxxxxxx>
- Date: 10 Oct 2005 04:37:51 -0700
Bobby D. Bryant wrote:
> On Fri, 07 Oct 2005, "Sverker Johansson" <lsj@xxxxxxxxx> wrote:
>
> > Murf wrote:
> >> > DOUG SAID
> >> > We don't need no stinking belief.
> >>
> >> My point exactly -
> >>
> >> However, I have a quick question (sorry if this is a starter question
> >> for 8 year olds on "Space")
> >>
> >> If a spiral galaxy can contain over a hundred billion stars, what is
> >> the latest view on how many galaxys have bee detected?
> >>
> >> Thanks! I would like to use this as a throw away line in a
> >> presentation I am doing.
> >
> > Too many to bother counting. Many billions of galaxies are
> > visible with a large telescope. Tens or hundreds of billions.
> >
> > Or put it this way: typical spacing between galaxies is
> > on the order of a million light years. We can see galaxies
> > up to a distance on the order of ten billion light years.
>
> I've been wondering...
>
> The stuff we see at great distances lies in less-expanded space.
> It seems "obvious" that the normal rules for calculating volume
> should apply... but it also seems that there's something subtly
> wrong with using the normal formula. If you do, it seems that
> you must allow for a higher density of galaxies at greater
> distances.
>
Since we also are looking back over very long times when
we are looking out to great distances, you're quite right.
There is something wrong with using the normal formula,
and it's not at all obvious that the normal rules for
calculating volume should apply, in fact it's obvious
that if space is expanding the normal rules do not
apply. So people don't in fact use the normal rules,
not before doing some careful work. After doing that
work however, it turns out that you can get away with
using the normal rules, just like Sverker did.
If we were able to look back far enough, one would
predict that we shouldn't see any galaxies at all if the
big bang model is correct, because in that theory there
was some point in time at which there were no galaxies to see,
because no stars had formed as yet. Look still further
back than that time and the only thing you'll be able to see
is the cosmic microwave background radiation.
The basic underlying problem is that there are inevitably
going to be various definitions of distance involved when
one talks about galaxies, because we can't simply do the
measurement by taking a ruler and finding out how many times
we have to lay it end to end to get to even the nearest galaxy.
Neither can we do what we do if we want to measure say, the
distance to the moon. If we wanted to do that, we could simply
send a radar pulse to a reflector on the moon's surface, measure
the round trip time, and divide by the speed of light. For
a very distant galaxy that we see, it turns out in fact that
it's possible, depending on the cosmological parameters, that
we could send out a pulse of light towards the galaxy, and it
would never even get there, no matter how long we waited.
Nevertheless we can imagine trying to do these various things
to measure the distance to a galaxy in the context of general
relativity.
Then, combined with observational information we can then often
give various estimated distances to galaxies. One of the most
common types of distance you'll hear discussed is the
so-called comoving distance, which is a natural quantity
in an isotropic, homogeneous expanding universe. In all such
universes, there is a quantity called the universal scale
factor, a(t), which increases with time.
To understand what the comoving distance is, first
suppose that you could measure the distance between two
very nearby objects at some fixed time by laying rulers
end to end and counting up how many you needed.
The distance you get that way is called an infinitesimal
`proper' distance. Now suppose you measure again the distance
between these two objects at some later time, and you get a new
`proper' distance which is larger.
If multiplying the new distance, measured at the later time,
by the ratio of the scale factor of the universe at the original
time to the scale factor of the universe at the later time
gives you back the original proper distance, then you know
that the change in the measured distance can be accounted for
by the change in the scale factor of the universe. Two such
objects are said to be moving exactly with the `Hubble flow' or
to be _comoving_ with the expansion of the universe.
So you can clearly also define a distance between such objects
which remains constant in time, if you just divide out the ratio
of the scale factors at different times.
That distance is what's called the comoving distance. You
can imagine extending the idea of comoving distance all
the way out to a very distant galaxy, by adding up lots of
infinitesimal proper distances along a straight line out
to the galaxy. Let's call the comoving distance so defined,
d_c.
Now, fixing how the scale factor a varies with time,
even deciding whether the whole process makes any sense
at all in light of the observations, is clearly not a
trivial process. You have to connect the mathematics,
which I'm only hinting at here, to the observations.
What astronomers actually measure about galaxies is the
spectrum of light that comes from them, their position on
the sky, and any other observational characteristics which
they choose to quantify and can measure, such as angular
size and brightness, or possibly the observation of particular
types of stars in them, or other structure of the galaxy.
>>From the light spectrum of a galaxy, one can extract the
galaxy's redshift, z, as long as one sees identifiable
spectral lines in the spectrum. Here's a nice discussion
of how the process works:
http://cas.sdss.org/dr4/en/proj/basic/universe/redshifts.asp
The redshift, as it turns out, for galaxies that happen to
move with the expansion of the universe is directly and
easily related to the ratio of the universal scale factors
at the time when the light is observed (now) and the time
when it was emitted. So we can convert redshifts to comoving
distances.
Now there are other ways of defining distances. For example,
we might want to know how far apart are two galaxies at the
same redshift, separated by a small angle on the sky. This
distance can be defined, too, and this is called the transverse
comoving distance. This turns out to be relatively easily
related to d_c. Call this one d_t.
Here's yet another distance we can define. Suppose we knew
that some object has a definite physical size, because,
for example it's a very special kind of object whose size
we just happen to know. Then we expect that its angular size,
measured on the sky, will decrease as it becomes further and
further away from us in comoving distance. If you divide the
transverse physical size of the object by its measured
angular diameter you get yet another distance, called the
angular diameter distance, d_a. This distance has the very
funny property that, in general relativity it does not
increase forever, for a fixed with increasing d_c. It stops
increasing and actually turns over when the redshift
(related to d_c) becomes bigger than about 1. That means
that an object of a fixed physical size actually starts to
appear larger and larger in angular size on the sky
when it gets far enough away. This is the fisheye effect
that Robert was talking about. d_a turns out to be easily
related to d_t.
There are a lot more distances we can talk about, but I'll
just mention one other very important one. This is the luminosity
distance. Suppose we know that some object has a certain absolute
luminosity, that is: we know exactly how bright it actually
is. In that case, we can assume that the inverse square law
for the decay of the brightness of an object with distance
holds, and add up the total flux of light we obtain from
the object (the so-called bolometric flux). Then dividing
the luminosity by 4 pi times the flux, and taking the square
root gives a distance. This is the luminosity distance d_l.
Luminosity distance turns out to be very easily related to both
d_t and d_a.
Making sense of cosmology involves looking at how all
of these distances are inter-related. For very small
redshifts, the rule is that they all agree very closely,
but for very large redshifts they begin to differ
significantly. Exactly how they differ at large redshifts
depends on the parameters of the cosmological model.
> Can someone comment on this? I don't even know the question I'm
> trying to ask. There's just omething about seeing denser space at the
> periphery of our field of view that bothers me.
>
>
> Also, could someone tell the difference between more expanded and less
> expanded space, other than by how crowded the neighborhood is? I
> suppose the microwave background would be hotter. Anything else you
> would notice or measure?
>
I'm not sure quite what you mean here ... we would always have to
look at things in space to get any idea about what's happening
of course, space all by itself is not really something you can
look at.
If your question is, can we detect that the scale factor of
the observable universe was actually smaller for some objects
at the very extreme range of our vision, then the answer is yes,
in a way.
Fluctuations in the microwave background temperature have been
measured. This radiation comes from matter at close to the
largest possible observable lookback times or distances: roughly
14000 Megaparsecs away in comoving distance. These
temperature fluctuations have a characteristic spectrum of
angular sizes which can also be related to physical sizes using
some theory, and thus also are related to fluctuations which
must have existed in the actual spacetime metric at that time.
So you can see some effects of `less expanded space' in the
microwave background, I'ld say.
David
.
- References:
- [OT] NGC 1350
- From: Bobby D. Bryant
- Re: NGC 1350
- From: DougC
- Re: NGC 1350
- From: Murf
- Re: NGC 1350
- From: DougC
- Re: NGC 1350
- From: Murf
- Re: NGC 1350
- From: Sverker Johansson
- [OT] NGC 1350
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