There is a relationship between the luminosity & surface temperature based upon the initial mass of a star its age its composition (usually a small effect) The initial studies of the relation between the absolute magnitudes (equivalent to luminosities) and spectral types (broadly equivalent to temperature) were perform (independently) by Ejnar Hertzsprung (Danish, 1905) and Henry Norris Russell (USA, 1913). Thus the plots of luminosity vs temperature (or absolute magnitudes vs spectral types) are often referred to as Hertzsprung-Russell (or HR) diagrams.

[Image from Hipparchus WWW site]

[Image from Greg Bothun]

Stars of different initial masses follow different evolutionary paths within the luminosity-temperature plane. However Stars spend most of their (active) lives within a relatively narrow band within the luminosity-temperature plane known as the Main Sequence. This fact is the key behind Main Sequence fitting

However, instead of plotting stars directly on the actual luminosity-temperature plane, an equivalent plot, known as a Color-Magnitude (CM) diagram is often used instead. The reasons are as follows:

To 1st-order, the spectrum emitted by a star is a black body.

• Thus rather than actually measure & plot (in Kelvin) temperature of every star, it is easier & quicker to simply measure & plot the ratio of the intensity of the star in two spectral bands. This ratio is then directly related to the black body function and hence temperature
  • For primarily historical reasons, the ratio is usually expressed as the difference (in magnitudes) between two standard (optical/IR) spectral bands and is known as the color
    • Traditionally, the most commonly used color is the difference between the B and V bands (centered at 440 & 550 nm, respectively) and usually written as simply B - V.

• rather than actually measure & plot (in W m^-2) the total flux of every star, it is easier to simply measure & plot the flux in a standard (optical/IR) spectral band. Again since the emitted spectra are black bodies, this is directly related to the total flux.
  • Traditionally, the most commonly used band is the V band (550 nm) and usually written as simply V.

• if the distances to all the stars have been determined, then this might be a plot of B - V versus M_V (absolute V band magnitude)
• if the distances to all the stars have NOT been determined (say for a star cluster), then this might be a plot of B - V versus m_V (apparent V band magnitude)