An Etymological Dictionary of Astronomy and Astrophysics

1. The ratio of an object’s → linear size (l)
   to its → angular size (δθ, in → radians), that is D_A = l/δθ. It is used to convert observed angular separations into proper separations at the source.
   
   

2. In cosmology, a distance defined as the ratio of an object’s physical transverse size (l) to its angular size (δθ). It is used to convert angular separations in telescope images into proper separations at the source. The angular diameter distance is defined by: D_A = l / δθ.

Consider a light source of size l at r = r₁ and t = t₁ subtending an angle δθ at the origin (r = 0, t = t₀). The proper distance between the two ends of the object is related to δθ by:

δθ = l / [a(t₁). r₁], where a(t₁) is the → scale factor at the present epoch. Therefore, D_A = r₁ / (1 + z).

The angular diameter distance has the particularity that it does not increase infinitely with z→ ∞. It gets its maximum value at a → redshift of ~ 1 and then decreases for higher z. Therefore, more distant objects appear larger in angular size. This is explained by considering the size of the Universe when the light of the object was emitted. At that time the Universe was smaller and therefore the object occupied a larger fraction of the size of the Universe. In other words, objects appear larger because the entire Universe acts
as a → gravitational lense.

See also: → angular; → diameter; → distance.