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Due to the space expansion, the universe should act as a giant telescope. The farther objects are from us (beyond the redshift of $z\approx 1.5$), the larger (not smaller!) they should appear in the sky. Per Wikipedia:

an object "behind" another of the same size, beyond a certain redshift (roughly z=1.5), appears larger on the sky

This optical effect is explained by the Angular Diameter Distance decreasing with distance in an expanding universe, whether open, closed, or flat:

enter image description here

The smaller the angular diameter distance, the larger the object appears in the sky. Therefore, galaxies of the same size should appear the smallest in the sky at the redshift of about $z\approx 1.5$. The galaxies that are closer to us should naturally appear larger, because they are closer, but, counterintuitively, the galaxies that are farther away from us also should appear larger due to the optical effects of the space expansion. Thus the universe should act as a giant telescope magnifying distant objects the more the further they are.

However, when we look at the most distant objects discovered by the Hubble telescope with the redshift ranging from $z=8.6$ to $z=11.9$, they all appear extremely small on the background of other also very distant (but not as extremely distant) Ultra Deep Field galaxies:

enter image description here

What is the explanation of why more distant galaxies appear the smallest on the Ultra Deep Field image while they should appear the largest according to the angular diameter distance formula?

$$d_A=\cfrac{c}{H_0 q^2_0} \cfrac{(zq_0+(q_0 -1)(\sqrt{2q_0 z+1}-1))}{(1+z)^2}$$

Qmechanic
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safesphere
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1 Answers1

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Two reasons, both to do with comparing like with like.

  1. Measuring the angular diameter of a galaxy is not a trivial matter. Where do you consider the edge of the galaxy to be? Whilst the angular diameter distance decreases at high redshift, the luminosity distance increases as $(1+z)^2 d_A$ and the flux from a galaxy decreases as $(1+z)^{-4} d_A^{-2}$, so very distant galaxies get faint very quickly. The dynamic range achievable in the imaging of "galaxies" at $z\sim 10$ is extremely limited, so that essentially only their bright nuclei or brightest starburst regions are seen above the background.

  2. It is unlikely that galaxies in the present day, or even at $z \sim 2$ are anything like the galaxies observed at $z>6$. The highest redshift objects are either hugely powerful quasars (at $6<z<8$) at where most of the light comes from a compact nucleus, or from starbursts in small proto-galaxy fragments that eventually merge to form the larger galaxies seen in the universe today.

For example, the record holder (or it was at some point), GN-z11 at $z=11.1$ was found to have a half-light radius of only 0.6 kpc (about 20 times smaller than the Milky Way) but to have a star formation rate about 20 times higher than the Milky Way (Oesch et al. 2016).

ProfRob
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