Re: Hubble deep field question

In article <GP6el.1549$aI1.879@xxxxxxxxxxxxxxxxxxxx>,
"Craig Franck" <craig.franck@xxxxxxxxxxx> writes:
I'm reading "Chasing Hubble's Shadows" by Jeff Kanipe, and he
states on page 140 that "blobjects" at redshift 6 that were
13,000 light years across would appear 0.2 seconds of arc in
size.

Let's check that with Ned Wright's cosmology calculator:
http://www.astro.ucla.edu/~wright/CosmoCalc.html

What we want is the "angular size distance." The calculator gives
1.2 Gpc, and the next line of the output gives the angular scale
directly. One fifth of an arcsecond at z=6 is about 1.2 kpc or about
4000 light years, so 13000 light years would be closer to 0.6 arcsec.

An interesting property of the angular size distance is that it
reaches a maximum around z=1.5 (for the current best estimate of
cosmological parameters). Beyond that, objects are magnified, and
the angular size distance decreases. Of course object surface
brightnesses drop drastically as they are magnified, which is why
distant objects are hard to detect.

But that's assuming the light left when the object was 12.7
billion light years away.

It's assuming a specific cosmological model, which will also give a
light travel time. According to the calculator, the light left the
object 12.7 Gyr ago, but the object was much closer to us then than
it is now.

I had thought that the objects would have been much closer when
the light first left and it took 12.7 billion years to reach us because
of cosmic expansion,

Yes, that's right.

which would not have made the objects look smaller.

I'm not sure how you figure that. Look at the explanations of the
angular size distance linked from Ned's calculator. In general,
there's a complicated relationship between angular size distance and
other distances.

At redshift 6 they would be traveling at about 0.9c,

More like 0.96 if you are thinking of Doppler shift, but it's not
best to think of cosmological redshift that way. See Ned's
explanatory material.

but how would you figure out how far away they were when the light
first left from that?

As noted on Ned's calculator, there are many different distances.
What you probably mean is the "proper distance" (which Ned calls
"co-moving radial distance"), which is now 27.5 G-light-year. When
the light was emitted, the scale factor of the Universe was 7 times
smaller than now (1+z), so the proper distance then was about 3.9
G-light-year. Unless I'm confused, but I don't think so.

--
Steve Willner Phone 617-495-7123 swillner@xxxxxxxxxxxxxxx
Cambridge, MA 02138 USA
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