# Stellar evolution

Stellar evolution refers to the life cycle of stars from their formation in nebulae to their final demise. The exact path that evolution takes is dependent on the initial mass of the star.

## Formation

In general, stars start out forming from the gas and dust found in nebulae. Some event such as a supernova[1][2], galaxy collision[3], or the passage of a density wave in a spiral galaxy[4] causes the gas to compress. This causes regions of higher density which will cause a gravitational collapse of the gas towards these higher density regions.

As the gas collapses, it becomes hotter near the centre due to the conversion of gravitational potential energy into kinetic energy causing the gas at the centre to want to expand. Gravity prevents this expansion and more and more gas is attracted, causing the temperature and pressure at the centre to increase to the point where it becomes hot enough for hydrogen to fuse into helium [5]. At this point the star turns on and moves onto the main sequence of the H-R Diagram.

## Main Sequence

The main sequence of the H-R Diagram is defined as the time in a star's evolution where it is fusing hydrogen into helium in its core[6]. During this phase there is a balance between the star's gravity, wanting to collapse it even further and the pressure generated by the fusion occurring in its core. This maintains the star's size. Since the amount of pressure in the star's core is dependant on it's mass, more mass means greater pressure, the rate at which a star consumes its nuclear fuel is also dependant on its mass. This means that more massive stars consume their fuel at a faster rate, and hence are more luminous on the main sequence. It also means that the more massive a star is, the shorter its stay on the main sequence[6]. Once a star has used up the hydrogen in its core, it moves off the main sequence.

## Post Main Sequence

What happens to a star once it leaves the main sequence depends on its initial mass with stars more massive than around 2.2 times the mass of the Sun evolving differently than those smaller than that.

### Less than 2.2 solar masses

Once a star less than 2.2 solar masses has used up the hydrogen in its core, it again begins to collapse. This collapse causes an increase in pressure throughout the star causing the hydrogen in a shell around the now mostly helium core to begin to fuse. This generates more energy than the hydrogen core burning phase, but instead of making the star brighter, it dims because the energy from this shell is used to expand the outer regions of the star, making it cooler as it moves onto the subgiant branch (SGB)[7][8]. As time progresses, the fusing hydrogen shell becomes thinner and thinner and the core denser and denser. Eventually the pressure on the core is so great that electron degeneracy pressure is needed to keep it from further collapse.

Throughout this phase, the hydrogen shell generates a large amount of energy, causing the outer layers of the star (the envelope) to expand greatly. This causes the apparent temperature of the surface of the star to drop and the diameter of the star to increase. This is when the star moves onto the red giant branch (RGB) of the H-R Diagram[6][8].

As the hydrogen shell is burning, the temperature and pressure in the core increases to the point where helium begins to fuse. In stars less than 2.2 solar masses this happens quite rapidly, releasing $10^{11}$ solar luminosities of energy in a few seconds[6]. This helium core flash does not blow the star apart however, as the vast majority of this energy is used to end the electron degeneracy. Once the degeneracy is lifted, the core expands slightly, slowing down the reaction rate and allowing helium core burning[8].

Once the helium in the core has been exhausted, and the hydrogen in the shell exhausted, the star now has a carbon-oxygen (C-O) core with a shell of fusing helium surrounding it. The star has now entered the Asymptotic Giant Branch. The early stages of this phase may have the star pulsing, causing it's magnitude to vary. Later stages of this phase have the star lose most of it's outer envelope of gas due to strong stellar winds forming a planetary nebula. Eventually only the C-O core remains as a white dwarf[5].

### More than 2.2 solar masses

As with stars less than 2.2 solar masses, stars greater than 2.2 solar masses begin to contract once the hydrogen fuel is used up in the core. This also causes a shell of hydrogen to start to fuse around the now quiescent core as with smaller stars. Again this creates more energy than the hydrogen burning in the core, but this energy is used to expand the outer layers of the star and the star moves onto the subgiant branch [6]. As the hydrogen shell burns, it becomes thinner and thinner, causing more and more helium to exist at the core. As temperatures and density at the centre of the core increase, the helium in the core will begin to fuse. Unlike in a star smaller than 2.2 solar masses, this doesn't happen throughout the whole core of a larger star. In this case, the temperature and density increase first only at the centre of the core, the resulting increase in energy production pushes out the outer parts of the core, making them less dense. This throttles that reaction and the helium flash of smaller stars does not occur in larger stars [6].

When a 2.2 solar mass (or larger) star runs out of helium in the core and moves onto the Asymptotic Giant Branch, it not only has a hydrogen shell burning, but also a helium shell about a carbon-oxygen core. This again causes heating in the core and eventually permits the carbon in the core to begin to fuse. At this point there is a fusing carbon core surrounded by a fusing shell of helium which itself is surrounded by a fusing shell of hydrogen[6]. Eventually depending on the mass of the star, the interior begins to look like an onion, with layers of heavier and heavier elements fusing as one heads towards the core. The more massive the star, the more layers. This all stops once the core begins to fill with iron. Iron cannot be fused with iron to produce energy, such a reaction is endothermic and requires energy from the environment so only elements up to iron can be produced in the cores of large stars.

Just before the carbon core burning phase while the hydrogen and helium shells are burning, the stars less than 8 solar masses becomes thermally unstable. This causes it to pulse at a rate in the range of a thousand years or so for stars near 8 solar masses to hundreds of thousands of years for lighter stars [6].

Once fusion stops in a larger star, the core collapses rapidly. This rapid collapse sends a shock wave back up through the star causing it to explode in a supernova explosion. The ultimate fate of the star depends on it's initial mass and mass loss rate during it's final days. Stars with an initial mass less than 20 solar masses become neutron stars whereas those larger than 20 solar masses become black holes [9].

## References

1. Kumar, P. and Johnson, J.L., 2010, Supernovae-induced accretion and star formation in the inner kiloparsec of a gaseous disc, Monthly Notices of the RAS, V404, pp 2170-2176
2. Boss, A.P. And Keiser, S.A., 2010, Who pulled the trigger: A supernova or an asymptotic giant branch star?, Astrophysical Jounal Letters, L1-L5
3. Karl, S.J., Naab, T., Johansson, P.H., Kotarba, H., Boily, C.M., Renaud, F., Theis, C., 2009, One moment in time – Modelling star formation in the Antennae, Astrophysical Journal Letters, V715, ppL88-L93
4. Martinez-Garcia, E.E., Gonzalez-Lopezlira, R.A., Bruzual-A, G., 2009, Spiral density wave triggering of star formation in Sa and Sab galaxies, Astrophysical Journal, V694, pp512-545
5. 5.0 5.1 Iben, I., 1991, Single and binary star evolution, Astrophysical Journal Supplement Series, V76, pp 55-114
6. 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Iben, I., 1967, Stellar evolution within and off the main sequence, Annual Review of Astronomy & Astrophysics. V5, p 571
7. Iben, I., 1967, Stellar evolution. IV. Evolution from the main sequence to the red-giant branch for stars of mass 1, 1.25 and 1.5 solar masses, Astrophysical Journal, V147, p624
8. 8.0 8.1 8.2 Ostlie, D.A. & Carroll, B.W.,1996, An Introduction to Modern Stellar Astrophysics
9. Freyer, C.L., Heger, A., Langer, N., Wellstein, S. 2002, "The limiting stellar initial mass for black hole formation in close binary systems", Astrophysical Journal V578, pp 335-347