### redshift-angular size relation

**(angular size-redshift relation, angular diameter distance)**
(how observed size depends on redshift)

The **redshift-angular size relation**
(or **angular size-redshift relation** or **angular diameter distance**)
is a function of redshift (or distance) that yields a ratio
associated with that redshift. The ratio is that of
an object's (e.g., galaxy's) width versus the angle that
it traverses over the celestial sphere at that redshift.
In Euclidean space, such a ratio is straight-forward, but given
the universe's overall expansion and curvature, and that
long-distance observations look backward in time, this function is
not so straight-forward and is of interest. Functions can be derived
for various Lambda-CDM model parameters and **Friedmann models**, and
observations and analysis revealing the actual relation can be used
to select and tweak such models.

One strategy is to compare the brightness with the angular size
of distant galaxies, e.g., by measuring the angular size of the
brightest galaxies (radio galaxies are suitable) at various redshifts,
assuming they would have similar size. Other proxies for size have
been tried, including some function of brightness, and also additional
galaxy characteristics.

The models under consideration as well as observation indicate that
beyond a certain redshift/distance, the angle no longer decreases
with smaller with distance, but actually increases. While this is
non-intuitive if your intuition takes Euclidean space as its basis,
the universe was much smaller then, yet is spread over the entire
celestial sphere, so objects must appear "larger". And
despite appearing "larger" to us, they still appear dimmer with
distance because their light broadcast in all directions must
eventually span our current larger universe.

(*astrophysics,cosmology,measure*)
**Further reading:**

http://en.wikipedia.org/wiki/Angular_diameter_distance

https://ned.ipac.caltech.edu/level5/March02/Sahni/Sahni4_5.html

**Referenced by pages:**

redshift-magnitude relation

Index