Hertzsprung-Russell Diagram

The HR diagram

• Danish astronomer Ejnar Hertzsprung, and American astronomer Henry Noris Russell, independently plotted the luminosity of different stars against their temperature.
• Luminosity, relative to the Sun, is on the y-axis and goes from dim (at the bottom) to bright (at the top).
• Temperature, in degrees kelvin, is on the x-axis and goes from hot (on the left) to cool (on the right). Note that the temperature axis is reversed compared to a normal graph.

Regions of the HR diagram

• Hertzsprung and Russell found that stars are clustered in distinct areas:
• Most stars are clustered in a band called the main sequenceThe diagonal band running from hot, bright stars (top-left) to cool, dim stars (bottom-right) on the HR diagram. Stars spend most of their lives on the main sequence while fusing hydrogen into helium.. For main sequence stars, luminosity increases with surface temperature.
• A smaller number of stars are clustered above the main sequence in two areas: red giants and red supergiants. These stars show an increase in luminosity at cooler temperatures. The only explanation for this is that these stars are much larger than main sequence stars.
• Below and to the left of the main sequence are the white dwarf stars. These stars are hot, but not very luminous. Therefore, they must be much smaller than main sequence stars.
• The HR diagram only shows stars that are in stable phases. Transitory phases, such as supernovae, happen quickly in relation to the lifetime of a star. Black holes cannot be seen since they emit no light.

Evolutionary path of sun-like stars

• The evolutionary path of stars similar to the Sun can be described using an HR diagram. The path is labelled A → B → C → D:

• Protostar to main sequence (A to B): the protostar collapses from a cold cloud of gas. Initially, it is visible as a very dim cool star as it moves onto a fixed position on the main sequence. Its position on the main sequence is determined by the star's mass.
• Main sequence to red giant (B to C): on the main sequence, the star is stable while it fuses hydrogen into helium nuclei. Once hydrogen fusion stops, the star begins to collapse under gravity. This heats up the core until further nuclear reactions reignite the star. The massive increase in temperature causes the star to expand into a red giant, which could be 100 times the current diameter of the Sun. As the outer layers move further from the core, its surface temperature will be lower (about 3 000 K), and the extremely large surface area causes it to be much more luminous.
• Red giant to white dwarf (C to D): when the supply of helium runs out in the star, nuclear fusion stops and the star collapses into a white dwarf. The surface temperature of a white dwarf is generally very hot (about 10 000 K). Due to the small surface area of a white dwarf, its luminosity is very low.

Lifetimes of stars

• The brightest stars have very short lifetimes (a few million years). These stars use up nuclear fuel at a much higher rate.
• The dimmest stars have extremely long lifetimes in comparison (about $10^{12}$ years). These stars use up nuclear fuel at a much slower rate.
• Crucially, stars on the main sequence with high luminosities are massive and very bright. A star that is $10^6$ times brighter than the Sun will use up its nuclear fuel $10^6$ times faster. A star that has a mass 100 times that of the Sun will live about $\frac{100}{10^6} = 10^{-4}$ times as long.