The total flux of light from a galaxy is its inegrated light and tells us something about the stars that make up a galaxy. The light we measure is usually through a passband (just as B or V) and therefore our knowledge must be interpreted in light of the wavelength we are studying. For example, hot stars are typically blue, so a galaxy rich in hot stars will have more blue flux than red flux. The integrated flux of a galaxy becomes the total magnitude after correcting for extinction effects from dust (in the observed galaxy and our own) and correcting for the effects of Doppler shift due to the galaxies velocity with repect to the Sun. In addition, the atmosphere of the Earth produces its own light (sky background) which must be subtracted from the galaxy's light.

Since galaxies are extended sources of light, the total magnitude will depend on how you measure it. The simpliest form is a metric magnitude, where the light is measured through a circular aperture of a set metric (angle on sky) size. If the metric size is small, not all the light is measured. But, if the metric size is too large, then too much sky light enters the aperture lowering the accuaracy of the measurment. Integrated magniude can also be measured out to some surface brightness, where surface brightness is he luminosity divided by the area (in mags per square arcsec, sort of like a luminosity density). Measuring to a known surface brightness produces an isophotal magnitude with an isophotal radius. In addition, a total magnitude can be extrapolated by using a curve of growth, a plot of the metric magnitude with increase aperture size. As the aperture gets larger, the amount of galaxy light should level off to a value that represents all the light emitted by the galaxy.

Absorption/Reddening:

Astrophotograph in the 19th century showed that the dark lanes or holes in the Milky Way did not have sharp edges. That, in fact, detail studies of star clusters at various distances from us showed that the intensity of light from remote stars is reduced as it passes through the sparse material of the interstellar medium. Herschel tried to use star counts to measure the size of the Galaxy and where our position is within it. His result was the diagram below, but what he really discovered was that interstellar extinction limits our line of sight. Not only is the intensity of the light decreased, called interstellar extinction, it is also reddened, called interstellar reddening. The blue component of light is more easily scattered than the red component (which is why the sky is blue during the day, scattered sunlight). Thus, light from remote stars has part of its blue component scattered before it reaches the Earth.

Maps of interstellar reddening demonstrated that the interstellar medium composed mostly of hydrogen and helium gas (99%) and traces of dust. Dust, in an interstellar sense, is very small (few microns in size) particles of carbon and silicon. Dust is fragile because it can be broken down by UV photons, but is very important in dark nebula as sites for the formation of molecules. Interstellar extinction in our own Galaxy is greater in the Galactic plane then above it. A simple cosine law can account for a majority of extinction, although detail radio and far-IR maps make it possible to correct for extinction on a point-by-point basis.

Surface Brightness:

The surface brightness is defined as the flux density per unit solid angle. The geometry of the situation results in the interesting fact that the observed surface brightness is independent of the distance of the observer from the extended source. This slightly counter-intuitive phenomenon can be understood by realising that although the flux density arriving from a unit area is inversely proportional to the distance to the observer, the area on the surface of the source enclosed by a unit solid angle at the observer is directly proportional to the square of the distance. Thus the two effects cancel each other out. Surface brightness is usual expressed as mags per arcsec-2 and given by the following formula: where the constant will be dependent on the units used for luminosity. Area should be in square arcsecs on the sky. The importance of sruface brightness measurments for galaxies is that the luminosity as a function of radius (a galaxy profile) is calculated using this luminosity. The radial distribution of light obvious goes from high luminosity in the center of a galaxy to low luminosities (than zero) at the galaxy edge. But the shape and behavior of this distribution says a grat deal about the structure of a galaxy, its internal kinematics and how it was formed. In ellipticals, the flux is brightest at its center, or core, where gravity has concentrated the most stars. The flux decreases outward into the envelope. Radial light profiles are ploteted as surface brightness as a function of distance from the center of the galaxy. For ellipticals, the galaxy profile is usually best fit by what is called the de Vaucouleurs r1/4 law, meaning the galaxy light decreases at the rate of 1/4 power of the distance from the center.

Spirals, or disk galaxies, often have a two component surface brightness profile, reflecting the bulge and disk components of the galaxy's kinematics. The bulge is often r1/4 in shape with an expontenial disk.