E.5.2 Evolution of stars

Stellar Stability, Evolution, and End States

1. Imagine lying under a clear night sky, marveling at the stars.
2. Have you ever wondered what keeps these massive spheres of gas stable for billions of years?
3. Or why some stars quietly fade into white dwarfs while others end their lives in spectacular explosions, collapsing into black holes?

The Balance that Sustains a Star: Stellar Stability

1. Stars are engaged in a constant tug-of-war between two opposing forces: gravity and radiation pressure.
2. Gravity, driven by the star’s immense mass, pulls it inward, seeking to collapse it.
3. Meanwhile, nuclear fusion in the star’s core generates energy that creates an outward radiation pressure, pushing against gravity.
4. When these forces are perfectly balanced, the star remains stable.

Why Does Fusion Create Outward Pressure?

1. At the core of a star, hydrogen nuclei (protons) fuse to form helium through nuclear fusion.
2. This process releases energy because the mass of the resulting helium nucleus is slightly less than the combined mass of the hydrogen nuclei.
3. The lost mass is converted into energy according to Einstein’s equation: $$E=\mathrm{\Delta }m{c}^2$$
4. This energy radiates outward, generating pressure that counteracts the inward pull of gravity.
5. Stable stars maintain equilibrium through the balance of inward gravitational pressure and outward radiation pressure generated by nuclear fusion.

Classifying Stars: The Hertzsprung-Russell (HR) Diagram

1. The HR diagram is one of the most important tools in astrophysics.
2. It plots luminosity (brightness) on the vertical axis and surface temperature on the horizontal axis, with temperature increasing to the left.

Main Features of the HR Diagram

1. Main Sequence:
   • A diagonal band where most stars, including the Sun, are found.
   • These stars are fusing hydrogen into helium in their cores.
2. Red Giants and Supergiants:
   • Found in the upper-right region of the diagram.
   • These stars are large, cool, and luminous.
3. White Dwarfs:
   • Located in the lower-left region.
   • These stars are small, hot, and faint.

What Can the HR Diagram Tell Us?

1. A star’s temperature and luminosity determine its position on the diagram.
2. Stars with the same radius lie along diagonal lines because luminosity depends on both temperature and surface area, as described by the Stefan-Boltzmann law:

$$L=\sigma A{T}^4$$

where

• $L$ is the luminosity ($\mathrm{W}$)
• $A$ is the surface area (${\mathrm{m}}^2$)
• $T$ is the absolute temperature of the body ($K$)
• $\sigma$ is the Stefan-Boltzmann constant ($\frac{\mathrm{W}}{{\mathrm{m}}^2\cdot {\mathrm{K}}^4}$)

The Role of Mass in Stellar Evolution

A star’s mass is the most critical factor in determining its life cycle. Let’s follow the journey of a star from its birth to its ultimate fate.

Main Sequence Phase

1. During this phase, the star is stable, fusing hydrogen into helium in its core.
2. Stars spend about 90% of their lifetimes in this phase.
3. Massive stars burn their fuel far more quickly than smaller stars, meaning they leave the main sequence much sooner.

Evolution Off the Main Sequence

1. When a star exhausts the hydrogen in its core, the balance between radiation pressure and gravity is disrupted.
2. What happens next depends on the star’s mass:
   • Low to Medium Mass Stars (less than 8 solar masses):
     • These stars expand into red giants as helium fusion begins in their cores.
     • Eventually, they shed their outer layers, forming a planetary nebula, and leave behind a dense core—a white dwarf.
   • High Mass Stars (greater than 8 solar masses):
     • These stars become red supergiants.
     • When fusion stops at iron (the most stable element), the core collapses, triggering a supernova explosion.
     • The remnant becomes either a neutron star or a black hole, depending on the mass.

The End States of Stars

The ultimate fate of a star depends on the mass of its core after fusion ceases:

White Dwarfs

1. Formed from the remnants of low to medium-mass stars.
2. Supported byelectron degeneracy pressure, a quantum mechanical effect that prevents further collapse.
3. Extremely dense: a white dwarf with the mass of the Sun would have a radius similar to Earth.

Neutron Stars

1. Formed when the core of a massive star collapses.
2. Composed almost entirely of neutrons, supported by neutron degeneracy pressure.
3. Incredibly dense: a neutron star with the mass of the Sun would have a radius of only about 10 km.

Black Holes

1. Formed when the core’s mass exceeds the Oppenheimer-Volkoff limit.
2. The gravitational pull is so strong that not even light can escape, creating a region of space called the event horizon.

Reflection

Stars are not just distant points of light; they are dynamic systems governed by the laws of physics. Their evolution, from stable main sequence stars to their dramatic end states, reveals the delicate balance between gravity and radiation pressure.