`  `

## The Hertzsprung-Russell Diagram

There are stars both smaller and bigger than the Sun. The lifetime of the Sun is 10 billion years. More massive stars burn the fuel more quickly and, despite the fact tha have more fuel, have shorter lifetimes. The following relation holds:

star lifetime = mass / rate of energy liberated = mass / M3.5 = 1/mass 2.5 where we used the relation: luminosity (which is energy radiated at all wavelengths per second) = M3.5.

Smaller stars than the Sun but large enough to obtain ignition, red dwarfs, burn the fuel more slowly and might last hundreds of billions of years. Stars with masses less than approx. 3 times the mass of the Sun get so hot in the core that they can burn (fuse) atoms of helium to produce carbon; the temperature is not enough in these stars to make anything else. More massive stars burn carbon to oxygen, and then to silicon and finally iron. Iron is a very stable nucleus and no nuclei heavier than iron are produced in stars. Regardless of their mass, most stars spend most of the time burning hydrogen.

Two astronomers, Hertzsprung and Russell, noticed that when they plotted, for each star, its luminosity vs. its temperature, most stars would cluster along a line. (Note: luminosity is the energy that the star radiates at all wavelengths in one second; recall -see the Tutorial - that the luminosity L = 4 x 3.14 x R2 x T4, where s = the Stefan-Boltzman constant. In the figure below, the luminosity of a star is given with respect to the luminosity of the Sun).

The temperature of the star is its surface temperature - recall that we can think of a star as a "black body" that emits radiation with a peak emission given by its temperature. Stars hotter than the Sun are bluish, while cooler ones are reddish.
The place where stars bunch up in the diagram is called the "main sequence". More massive and luminous stars are at the top; less luminous, cooler stars are at the bottom.

For most of its life a star stays in one point of the diagram. However, towards the end of its life, a star like the Sun will move right and up of the diagram, in the so called "red giant branch". In this branch, where stars have converted part of their hydrogen fuel (12 % in mass) into He, the core of a star starts to contract while the outer layer expands and become cooler (red giants have a lower temperature than the original star). When this happens to the Sun, 4-5 billion years from now, the outer reaches of our star will hit the Earth and perhaps Mars.
In the meantime, the core contracts so rapidly that helium (He) becomes so hot that it burns quickly into carbon (He flash). The outer layers are blown off and the star crosses the diagram right to left (i.e., its surface temperature increases) very quickly - this is called "the horizontal branch". Finally the inner core will forms a "white dwarf" that, having burned up its fuel, slowly cools until it will not be visible.

Stars three times or more massive than the Sun will be able to maintain high temperatures in the core for longer periods of time and will be able to burn other elements as well.

Planetary nebula NGC 6720. The colored shadows give us information about the elements produced by the star. Credits:Howard Bond (ST ScI) and NASA

It is important to realize that the Hertzsprung-Russell diagram is a snapshot of the luminosity and temperature of all stars at a given moment; most stars are seen on the main sequence because they move off sequence for relatively brief periods of time (in the case of the Sun for hundreds of million of years compared to a lifetime of 10 billion years). Main sequence stars spend 10% of their life outside "main sequence".

The following table is given to provide a more complete picture of how the properties of stars are influenced by their mass.