Stellar Mid-Life and Old Age

The life cycle of stars features a crucial balance between outward pressure and the inward pull of gravity.

Main-Sequence Age Changes

Initial core composition at birth:
- 73% hydrogen
- 25% helium
Final core composition by the end of life:
- 10% hydrogen
- 88% helium
Result: As stars evolve, they produce fewer but more massive atomic nuclei.
- Pressure declines, leading to gravity having a chance to dominate.
- The core contracts gradually, resulting in increased temperature over time.

The increase in core density and temperature accelerates fusion processes, leading to an increase in luminosity overall.

Luminosity changes are represented in a graphical form across various stellar types:
- The Y-axis of graphs represents Luminosity while the X-axis represents temperature (K).
- Significant points marked as Zero-age main sequence and termination of core hydrogen fusion.

As core fusion runs out of fuel, the lack of energy production leads to:
- Rapid contraction of the core.
- Increased core density due to the same mass occupying a smaller volume.
- Continued rise in core temperature due to gravitational energy.

The increase in density and temperature causes fusion to reignite in the surrounding shell.
The combination of gravitational energy and new fusion energy enables outer layers to expand.
The expansion cools the outer surface gas, showcasing a notable transition in the star's life cycle.

Stars within a cluster share:
- Common age
- Similar chemical composition
- Equidistant positioning from earth.
Individual stars exhibit varied mass and age, impacting their evolutionary rates.

NGC 2362, Pleiades, M41, M11, Coma, Hyades, and Praesepe noted with variety in luminosity and temperature statistics.
- Contains detailed graphs plotting luminosity against temperature similar to previous graphs.

Challenge #1: Is the core hot enough for new fusion? Determined by:
- If the core is indeed hot enough, new fusion reactions can ignite, stabilizing core size and allowing shell fusion to continue, partially restoring outer layers to normal.
- If not, the core collapses and outer layers are lost during the star's dying process.

In a one solar mass star:
- The dead helium core contracts for an extended period, approximately 100 million years, significantly shorter than its main-sequence life of 10 billion years.
- During contraction, core temperature escalates from 10^7 K to 10^8 K.
- The process involves the transition from hydrogen to helium shell fusion.
The outer layers expand substantially, reaching radii up to 100 solar radii, but surface temperatures drop to around 4000 K.
This stage is known as “ascending the giant branch” in the Hertzsprung-Russell (HR) diagram.

Detailed HR diagram showcasing comparison of various stellar classifications such as red giants, subgiants and main sequence stars across a continuum of luminosity and spectral classification from BAF to KM.
Creates a clear picture of how stars progress through luminosity and temperature.

Following core helium ignition, a one solar mass star adjusts to its new structure, burning helium over a span of 50 million years.
It appears on the "horizontal branch" in the HR diagram with its position determined by previous mass loss and structural changes.

Helium fusion eventually ceases leaving a dead carbon core.
- This exhausted state triggers a repeat cycle of previous transformations.
A solar-mass star expands massively into a red supergiant over approximately 10,000 years, revisiting the central challenge: is it hot enough for ensuing fusion tasks?

Temperature Requirement for Carbon Fusion:
- Carbon fusion necessitates core temperatures around 600 million K.
- A one solar-mass star maxes out at 300 million K, leading the core to inevitably collapse into a white dwarf.
The star's outer layers are expelled into space as a planetary nebula.

Stars with mass greater than one solar mass undergo extended cycles of nuclear fusion and face differentiated gravitational scenarios:
- More mass correlates with increased gravitational energy leading to elevated core temperatures allowing ongoing nuclear reactions.
- Intermediate elements such as oxygen, neon, magnesium, silicon, and iron are synthesized in stratified shell-like structures.

Challenge #2: Is the core primarily composed of iron?
- If not yet iron and sufficiently heated, the star will proceed with additional fusion phases, akin to layering shells of an onion.
A particularly massive star (20 solar masses) showcases intense burning rate catastrophes:
- Carbon burned in 1000 years, oxygen in 1 year, silicon in just 1 week.
- Marked transitions in nuclear fission and fusion energies fundamentally alter stellar evolution trajectories.

In cases where stars contain predominantly iron in their core:
- This results in an energy dead end as iron does not undergo further nuclear reactions to release energy. Picture skiing at the lunar energy valley.
The core then collapses into a neutron star or a black hole, leading to dramatic events such as supernovae, where outer layers are forcefully expelled.