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Angular separation vs separation distance with increasing z?



 
 
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  #1  
Old December 26th 16, 11:26 AM posted to sci.astro.research
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Default Angular separation vs separation distance with increasing z?

Suppose two objects are separated on the sky by 1 arc minute, and I can
move them in or out in z as a test example....

Then, as I look out to higher z normally I would think the separation
distance would be larger. This is the case for objects here on
earth....same angle between them but further away means the separation
distance between them is larger

But in the universe, the further out in z the objects are, the smaller
the universe was, so, they are actually closer together, right?

In other words, if a pair of objects at z=1 and another pair at z=6 both
have the same angular separation on the sky (say 1 arc minute), is the
pair at z=6 closer together?

I'm guessing I should use Ned Wright's co moving distance calculator
(somehow) to figure this out?

rt

  #2  
Old December 26th 16, 06:27 PM posted to sci.astro.research
Phillip Helbig (undress to reply)[_2_]
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Posts: 273
Default Angular separation vs separation distance with increasing z?

In article ,
writes:

Suppose two objects are separated on the sky by 1 arc minute, and I can
move them in or out in z as a test example....


OK.

Then, as I look out to higher z normally I would think the separation
distance would be larger. This is the case for objects here on
earth....same angle between them but further away means the separation
distance between them is larger

But in the universe, the further out in z the objects are, the smaller
the universe was, so, they are actually closer together, right?


Perhaps; details depend on the cosmological model.

In other words, if a pair of objects at z=3D1 and another pair at z=3D6 both
have the same angular separation on the sky (say 1 arc minute), is the
pair at z=3D6 closer together?


Perhaps; details depend on the cosmological model.

I'm guessing I should use Ned Wright's co moving distance calculator
(somehow) to figure this out?


What you want is the angular-size distance. By definition, the angular
size distance is the physical separation divided by the angular
separation.

You can use the definition above to calculate the physical separation AT
THE TIME THAT THE LIGHT WAS EMITTED. If the objects are bound, then,
ignoring things irrelevant here, this doesn't change with time. If they
are not bound, then the CURRENT proper separation is (1+z) times that
what you calculated from the observed angle and the angular-size
distance.

So, the physical separation when the light was emitted is the
angular-size distance multiplied by the angle. If the objects are not
bound, then the current separation is a factor of (1+z) larger. This is
sometimes known as the proper-motion distance, although at cosmological
distances proper motion is rarely detectable.

You might think that this distance corresponds to the luminosity
distance, since this is based on the CURRENT area of a sphere
surrounding the source. However, the luminosity distance is another
factor of (1+z) larger. Why? In general, by definition, the luminosity
distance is inversely proportional to the square root of the observed
flux. At cosmological distances, the flux is reduced by a factor of
(1+z) due to the cosmological redshift, and another factor of (1+z)
because the arrival rate of photons is reduced (apply the same argument
to individual photons as you apply to crests of a wave in the
cosmological redshift). So, the flux is reduced by (1+z)^2, meaning
another factor of (1+z) in the distance. Thus, the angular-size
distance is equal to the the luminosity distance divided by (1+z)^2.
This is a very general result and holds in many more cosmological models
than those normally considered.

For a discussion, see my paper:

http://www.astro.multivax.de:8000/he...fo/angsiz.html

(By the way, the Fortran code I wrote in conjunction with this paper was
used in the main Perlmutter et al. paper for which Perlmutter was
awarded the Nobel Prize in 2011.)

This also mentions another effect: the distance can be different from
the standard result (e.g. what Ned's calculator calculates) if the
matter in the universe is clumpy. This is often referred to as the
"Dyer-Roeder distance" in the literature. This is significant only at
high redshifts.

However, it turns out that this doesn't seem to be the case in our
universe. Even if the matter is not distributed completely smoothly, at
least at high redshift (and at low redshift, the inhomogeneity effect
doesn't matter) then the distance one calculates is the same as that in
a homogeneous universe, at least in a statistical sense. I wrote about
this as well:

http://www.astro.multivax.de:8000/he...o/etasnia.html

There is a famous paper by Steven Weinberg (one of the few people who
has worked on pure particle physics AND pure cosmology (as opposed to
astroparticle physics, inflation, big-bang nucleosynthesis, early
universe, etc, which are essentially particle physics applied to
cosmology)) where he shows that this follows from flux conservation,
provided certain assumptions are fulfilled. The data now indicate that
they are.

In fact, it appears that even each individual line of sight is a fair
sample of the universe in that, even if the mass along the line of
sight is not distributed smoothly, the distance calculated from redshift
is the same as if it were. I discuss this he

http://www.astro.multivax.de:8000/he.../etasnia2.html

This doesn't mean that matter is smoothly distributed. We are pretty
sure it is not (cosmic web, etc). However, at low redshift the
small-scale distribution of matter has a negligible effect on the
distance, while at high redshift, the light has travelled far enough
that it has essentially traversed a fair sample of the universe, and
thus the distance is the same as if all the matter were smeared out
smoothly along the line of sight. One could say that voids and
overdense regions (sheets, filaments, etc) "average" out. One has to
put "average" in scare quotes for reasons explained in the paper above.
(The actual details are quite complicated; search for a paper by Nick
Kaiser and John Peacock (arXiv:1503.08506) for the gory details.)

So, although many people (Zeldovich, Dashevskii, Slysh, Sachs,
Kantowski, Dyer and Roeder, Weinberg, Kayser, Linder, myself, Holz,
Bergstr=F6m, Goliath, Gunnarsson, Dahlen, J=F6nsson, Goobar, M=F6rtsell,
Bolejko, Ferreira, Kaiser, Peacock, Lima, Busti, Santos, Clarkson,
Faltenbacher, Uzan, etc) have invested much time worrying about this, in
turns out that it is probably not relevant in our universe. (No-one
debates the fact that in a Dyer-Roeder situation, the Dyer-Roeder
distance is appropriate, but it appears that we don't live in such a
universe.)

This topic is distinct from the possible influence of LARGE-SCALE
inhomogeneities on cosmological distances. See papers by George Ellis,
Roy Maartens, Syksy R=E4s=E4nen, Bagheri, Schwarz, etc. The jury is still
out. Some think that large-scale inhomogeneities can explain
cosmological observations without a cosmological constant, but I would
bet quite a bit that this is not the case. (Whether I'll live long
enough to collect on the bet is a different question.)
  #3  
Old December 28th 16, 04:45 AM posted to sci.astro.research
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Default Angular separation vs separation distance with increasing z?

Thanks,

(is this an appropriate post?)

;-)

rt
 




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