Surface brightness

Galaxies are resolved objects, so that in addition to measuring their total luminosity, it is possible to measure the surface brightness from each point in the image.

The surface brightness is the flux per unit solid angle of the image.

The surface brightness is independent of distance (to first order). This is because the flux coming from an object decreases as 1/d2 for an object is located at distance d, while the solid angle subtended by the object decreases also as
1/d2. Thus the surface brightness at a given point on the surface of the galaxy is a well-defined distance-independent quantity.

The units to measure surface brightness are magnitudes per square arcsecond.

Note that the surface brightness is not an additive quantity! If two galaxies, whose individual surface brightnesses are I1 and I2, overlap somewhat, the total surface brightness from the region of overlap is not
I1 + I2!
For example, if
I1 = I2= 21 mag/arcsec2, then the total SB is 20.25 mag/arcsec2, because the total amount of light from the two galaxies is 2 * 10-21/2.5 = 10-20.25/2.5.