# 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])
```

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