# Magnitudes and Colors

## Flux

Astronomers usually measure the *flux* of an object by collecting
light with a telescope, sending it through a known filter, and then
determining the power. The flux is the power per unit area, and the
area is given by the size of the telescope. After calibrating the
detector using standard stars, and correcting for the absoprtion in the
atmosphere, the flux in the filter band is known. This process is known
as *photometry*.

## Magnitude

But astronomers usually give their photometric results in terms of
magnitudes. The magnitude of an object is given by

m = -2.5 log[Flux/F0]

where "log" is the common or base-10 logarithm, and F0 is standard
zeroth-magnitude flux for the chosen filter. If the filter is
a blue filter, then the magnitude is denoted as *B*.
For a yellow-green filter, close to the peak sensitivity of the eye,
the magnitude is denoted as *V* for visual.
An ultraviolet filter gives *U* magnitudes.
Another common set of standard filters, with narrower passbands than the
*UBV* filters, is the *uvby* for ultraviolet, violet, blue
and yellow.
Bright objects have more negative magnitudes than faint objects.
The brightest star is Sirius, with a magnitude of -1.6.
The faintest stars visible with the naked eye from a dark site
are about sixth magnitude. The faintest
objects visible with the Hubble Space Telescope are about 28th
magnitude, which implies a flux nearly one trillion times smaller
than the flux of Sirius.

## Color

When astronomers measure the flux of an object at two or more
wavelengths, they can take ratios of fluxes. Since the logarithm of a
ratio is the difference in the logarithms, these flux ratios are
defined by subtracting the magnitudes in different filter bands:
such as *U-B* or *B-V*.
In the *UBV* system, the zeroth magnitudes fluxes are defined
for a bright nearby star with a temperature of 10,000 K [Vega].
Thus *B-V = 0* corresponds to a temperature of 10,000 K,
while a star with the temperature of the Sun (5,770 K) has
a *B-V* color of 0.65.

## Absolute Magnitude

If a star is far away, it is faint and has a large magnitude.
A ten-fold increase in distance results in a factor of 100
decrease in flux, which is an increase of 5 magnitudes.
Astronomers define an *absolute magnitude* that is independent of
the distance of a star and only depends on the intrinsic properties of
the object: the absolute magnitude is the magnitude the star would have
if it were 10 parsecs away from the Earth. The relation between
the absolute magnitude *M*, the apparent magnitude *m*
and the distance *D* is

M = m - 5 log(D/[10 pc])

Tutorial:
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© 1996-2004 Edward L.
Wright. Last modified 20 Feb 2004