Star Colors and the Color Index 

The total luminosity is a measure of all the energy the star puts out over all wavelengths, from the far infrared to the extreme ultraviolet. Astronomers refer to this as the star's bolometric luminosity.

But that's not what we observe. A single detector is not sensitive to all wavelengths, so we typically only observe a fraction of the star's luminosity. The star's luminosity is typically measured in different, well-defined spectral regions, for example using the UBV(RI) filter system.

For example, Sirius:
Sirius' Magnitudes

We define a color index as a difference of magnitudes, ie the U-B color index, or the B-V color index. For Sirius, these would be:
Sirius' Color Indices
Conventions: Okay, here's a cute applet to play around with which explores blackbody radiation and the color indices.

The Bolometric Correction

So how do we measure the bolometric magnitude of a star? We usually don't! We measure the magnitude of the star in some filter (say, V) and apply a bolometric correction, ie:

For example, we said the (bolometric) absolute magnitude for the Sun was M = 4.76. It's absolute V magnitude is 4.83, so its bolometric correction is BC=4.76-4.83=-0.07.

The Color-Color Diagram

We can plot stars on a color-color diagram, which looks like this: