Correlations

Are there any connections among these properties? Are hot stars big? Are heavy stars small? Connections are most easily uncovered graphically. Two types of graphs have been most rewarding, the mass-luminosity diagram and the color-magnitude diagram.

1. The mass-luminosity diagram. Make a table of star properties, for as many stars as you can. Make a graph with mass on one axis, M (what's M?) on the other. Put one dot on the graph for each star in the table. The result is a graph with a lot of dots on it. The dots might form some recognizable pattern, or they might be distributed randomly. The former is what actually occurs: Most of the dots lie along a more-or-less straight region running from the dim, light (low mass) region towards the bright, heavy region. About 10% of the dots don't follow this pattern. These outliers tend to be either significantly brighter, or significantly dimmer, than most others of the same mass.

   This pattern is known as the 'mass-luminosity relation.' In words: the bright stars are the ones with large mass and the dim stars are those of low mass.

2. The color-magnitude diagram. Use the table of star properties as before. This time make a graph with temperature (or color index, or spectral class) on one axis, M on the other. Put the dots on the paper as before. Again a pattern emerges. The cool stars are the dim ones, the hot stars are the bright ones. Again there are about 10% that don't respect the connection. These are hot stars which are dimmer than most others of the same temperature, and cool stars which are brighter than most others of the same temperature. Alternatively, these may be described as dim stars which are anomalously hot, or bright stars which are unusually cool. These outliers tend to be the same as those which didn't obey the mass-luminosity relation.

   Thus the great majority of stars have correlated temperature and luminosity. The cool ones are dim, the hot ones bright. The region of the picture where their dots lie is called the 'main sequence' and the stars whose dots lie on the main sequence are referred to as main sequence stars. The main sequence stars are the same ones which follow the mass-luminosity relation.

   What of the others? The radiation laws reveal the cause of their unusual placement: those which are hot but dim must be small; cool but bright must be large. Thus most stars are main sequence stars; the other, exceptional ones, are 'dwarfs' and 'giants'.

   The color-magnitude diagram is also called the temperature-luminosity diagram, but most often is called the 'H-R diagram', after the names of the two people who originally used it, the Danish astronomer E. Hertzsprung and the American Henry Norris Russell. It is the single most powerful synthesis of stellar data and we will use it heavily in what follows.