Photometric systems

The magnitude of a star depends on the system with which one is measuring it. Astronomers have settled on a number of different photometric systems, each one based on a particular passband (i.e. a particular combination of filter and detector and telescope). One should always remember to specify the system when quoting the magnitude of a star.

Most astronomers working in the optical use the UBVRI photometric systems. These are five different passbands which stretch from the blue end of the visible spectrum to beyond the red end. They were set up many years ago by several astronomers:

put references to Johnson, Morgan, Cousins, etc. here

The systems are defined by particular combinations of glass filters and photomultiplier tubes, since there were created back in the days before CCDs existed. Since photomultipliers and CCDs have very different spectral sensitivities (photomultipliers are more efficient in the blue, CCDs in the red), it is difficult to make the effective passband of a CCD-based instrument match that of a photomultiplier-based instrument. In 1990, Michael Bessell came up with a recipe for making filters out of common colored glasses which would reproduce pretty closely the official Johnson-Cousins UBVRI passbands.

reference to Bessell paper, plus figures of the UBVRI passbands

The UBVRI passbands are called broadband because they span wide swaths of wavelengths. The spectral resolution of the passbands is small:

                               central wavelength
  spectral resolution  R  =  ----------------------   =  approx 5
                               width of passband

For some applications, astronomers use filters which transmit a much smaller range of wavelengths; a common filter used to measure light emitted by hydrogen atoms is centered at 6563 Angstroms and roughly 20 Angstroms wide:

                               6563 Angstroms
  spectral resolution  R  =  ----------------------   =  approx 330
                                20 Angstroms

A narrowband filter like this requires much longer exposure times to build up the same signal as a broadband filter. Since telescope time is so precious, astronomers tend to use broadband systems. That's one reason for the popularity of the UBVRI system.

When writing the magnitude of a star, astronomers use an abbreviation to denote the photometric system of the measurement:

       V = 1.03    means   "magnitude of this star in the V system is 1.03"
       B = 0.46    means   "magnitude of this star in the B system is 0.46"

There is also a convention to use lower-case letters for raw measurements and upper-case letters for fully reduced values:

       b = 1.18    means   "a measurement made through a B filter"
       B = 1.22    means   "the same measurement after a full reduction"

Zero point

So, once one has settled on the equipment one will use -- which sets the photometric system -- one still faces the question of the magnitude zero-point. The choice is arbitrary. Astronomers have chosen to use the bright star Vega as their starting point.

figure showing Vega in Lyra

In the UBVRI systems, the star Vega is defined to have a magnitude of zero.(*)

* Actually, this is not quite true: the zero point is defined strictly by the mean measurements of a set of bright stars (which may include Vega), rather than by Vega alone. However, since Vega always ends up with a magnitude within a few percent of zero, the simple rule "Vega's magnitude is zero" suffices for almost all purposes.

That is,

     Vega's magnitude in U-band:     U = 0.0
     Vega's magnitude in B-band:     B = 0.0
     Vega's magnitude in V-band:     R = 0.0
     Vega's magnitude in R-band:     V = 0.0
     Vega's magnitude in I-band:     I = 0.0

Stellar "colors"

When ordinary people use the word "color" to describe a star, then mean "what is the tint perceived by the eye?" One star might have a color of "pale orange", another "bluish-white".

But astronomers use the word "color" in very different way. To them, "color" is a measure of the magnitude difference of a star in two passbands .... relative to the magnitude difference of Vega in the same passbands. Let me illustrate with an example or two.

Consider the stars Vega (a hot star), Antares (a very cool star), and Rigel (a very hot star). We can measure their magnitudes in the B and V passbands.

                 B             V           (B-V)
-----------------------------------------------------------
   Vega         0.00          0.00         0.00

   Antares

   Rigel

An astronomer would say, "Antares has a color index of (B-V) = xxx", or less formally "Antares has a color of xxx", or, even less formally, "Antares is red." Any color index less than zero (indicating a temperature hotter than Vega's roughly 10,000 K) means a star is "blue"; any color index greater than zero (indicating a temperature less than Vega's) means a star is "red".