The Life of a Star

I recently posted about the Hertzsprung-Russel diagram, which shows stars arranged by their color and brightness:

The diagram neatly shows how these properties are not independent; rather, stars are found to be grouped into distinct populations corresponding to different regions of the HR diagram. But why does the HR diagram look like this?

In this post I argued that the stars in the diagram are not actually representative of stars as such, as bright distant stars are over-represented in the HYG database on which the diagram was based. Even if correcting for this, however, the patterns displayed in the diagram would remain.

The energy output of stars stems from nuclear fusion in their core: light isotopes fuse into heavier isotopes, releasing large amounts of energy in the process. The energy heats the star's core, and by convection and radiation the heat is transported to the star's surface. From there it radiates into space in the form of infrared, visible and ultraviolet light - what we perceive as sunshine.

The internal heat of the star leads to an outward pressure which is counterbalanced by the star's gravitational pull upon itself. The size of the star is determined by the equilibrium between those two competing forces - outward radiation pressure and indward gravitational pressure. This balance affects the pressure and temperature in the stellar core, which determine the efficiency of fusion and therefore the release of heat and radiation. While a star thus has several interdependent mechanisms at play in determining its dynamics, it should be clear that its mass is of crucial importance.

Stars are formed when clouds of hydrogen and other elements contract under the effects of gravity. This converts gravitational energy to thermal energy, heating the gas, and when the temperature and density of the gas crosses a certain threshold fusion commences; a star is born.

In fusing hydrogen to heavier elements the star slowly depletes is reserve of hydrogen. The smaller the star, the lower its internal pressure and temperature, since there is less gravity that must be balanced out. Small stars are generally extremely long-lived and relatively cool; these are the stars found on the lower-right tail of the main sequence in the HR diagram. On the other hand, larger stars need a higher temperature and pressure to balance gravity, and fusion thus proceeds at a faster rate. Such stars output more energy, deplete their hydrogen supply faster, and have shorter lives. These bright, hot stars are found toward the upper-left end of the main sequence.

As a hydrogen-fusing star's temperature and brightness are both determined largely by its mass these properties do not vary independently, but correlate, giving rise to the pattern we see as the main sequence in th HR diagram.

When a star eventually begins to deplete its hydrogen supply it leaves the main sequence; its fate is then determined by its mass. In any case, the end of hydrogen fusion causes the outward radiation pressure to fall, allowing the star's outer layers to fall in towards the core under the influence of gravity. This collapse re-heats the regions around the core, allowing hydrogen fusion to resume in these regions. This in turn causes the outer layer of the star to expand, decreasing the surface temperature of the star. This is the red giant phase, corresponding roughly to the stars found in the upper-right part of the HR diagram.

Details on this and the subsequent delevopments depend on the star's convective properties and its mass. A sufficiently massive star may at one point reach a temperature in its core enabeling fusion of helium into heavier elements, followed by progressively faster and more energetic phases of fusion of even heavier elements, ultimately producing isotopes as heavy as iron-56, ending in the final demise of the star as a nova, leaving behind a stellar remnant such as a black hole.

Lighter stars may end up as white dwarfs, in which no fusion takes place to supply the star with energy. Instead these very small stars glow ever fainter as they cool down over the course of billions of years.

There are of course many further details and variations to the possible successions of events described above, but I hope that the discussion presented in this post gives a suffcient idea about the mechanisms producing the patterns found in the HR diagram and in the distribution of star sizes.