40.3 Content
40.3.1 The Big Bang and Early Universe
Timeline of the early universe:
| Time | Temperature | Events |
|---|---|---|
| 0 | ∞ | Big Bang singularity |
| 10⁻⁴³ s | 10³² K | Planck era; physics unknown |
| 10⁻³⁶ s | 10²⁸ K | Inflation; rapid expansion |
| 10⁻⁶ s | 10¹³ K | Quarks combine into protons/neutrons |
| 3 min | 10⁹ K | Nucleosynthesis: H, He, trace Li |
| 380,000 yr | 3000 K | Recombination; CMB released |
| 200 million yr | ~100 K | First stars form |
In the first seconds, the universe was so hot that photons spontaneously created particle-antiparticle pairs. As expansion cooled the universe, matter became stable. A tiny excess of matter over antimatter (~1 part in 10⁹) gave us the universe we see today.
40.3.2 Interactive: Early Universe Timeline
40.3.3 Hubble’s Law
Edwin Hubble (1929) discovered that galaxies are receding from us, with velocity proportional to distance:
\[v = H_0 d\]
where: - \(v\) = recession velocity (km/s or m/s) - \(H_0\) = Hubble constant ≈ 70 km/s/Mpc ≈ 2.3 × 10⁻¹⁸ s⁻¹ - \(d\) = distance to galaxy
The Hubble constant gives an estimate of the age of the universe: \[t \approx 1/H_0 \approx 13.8\ \text{billion years}\]
40.3.4 Evidence for Expansion: Redshift
Cosmological redshift: As space expands, wavelengths of light stretch:
\[z = \frac{\lambda_{observed} - \lambda_{emitted}}{\lambda_{emitted}} = \frac{v}{c}\]
For non-relativistic speeds (v << c): \[v = cz\]
40.3.5 Interactive: Redshift and Distance
40.3.6 Black Body Radiation and Stars
Stars approximate black bodies—their spectrum depends only on temperature.
Wien’s displacement law: \[\lambda_{max} = \frac{b}{T}\]
where \(b = 2.90 \times 10^{-3}\) m·K
| Surface Temp | Peak λ | Star Colour | Example |
|---|---|---|---|
| 3000 K | 967 nm | Red | Betelgeuse |
| 5800 K | 500 nm | Yellow | Sun |
| 10000 K | 290 nm | Blue-white | Vega |
| 30000 K | 97 nm | Blue | Rigel |
40.3.7 Interactive: Black Body Spectrum
40.3.8 Stellar Spectra Classification
Stars are classified by spectral type (temperature):
| Type | Temperature | Colour | Features |
|---|---|---|---|
| O | 30,000-50,000 K | Blue | Ionised He lines |
| B | 10,000-30,000 K | Blue-white | Neutral He lines |
| A | 7,500-10,000 K | White | Strong H lines |
| F | 6,000-7,500 K | Yellow-white | Weak H, ionised metals |
| G | 5,200-6,000 K | Yellow | Solar-type; Ca lines |
| K | 3,700-5,200 K | Orange | Neutral metals |
| M | 2,400-3,700 K | Red | Molecular bands (TiO) |
“Oh Be A Fine Girl/Guy, Kiss Me”
40.3.9 Absorption Spectra
Dark lines in stellar spectra reveal: - Composition: Which elements are in the star’s atmosphere - Temperature: Which spectral lines are strongest - Radial velocity: Doppler shift of lines - Magnetic fields: Zeeman splitting of lines
40.3.10 The H-R Diagram
The Hertzsprung-Russell diagram plots luminosity vs temperature:
40.3.11 Interactive: H-R Diagram
Key regions:
| Region | Location | Characteristics |
|---|---|---|
| Main sequence | Diagonal band | Hydrogen fusion; stable |
| Red giants | Upper right | He fusion; expanded envelope |
| Supergiants | Top | Massive; short-lived |
| White dwarfs | Lower left | Stellar remnants; no fusion |
40.3.12 Stellar Evolution
| Initial Mass | Main Sequence Life | End State |
|---|---|---|
| < 0.5 M☉ | > 100 billion years | White dwarf |
| 0.5-8 M☉ | 100 million - 10 billion years | White dwarf |
| 8-25 M☉ | 10-100 million years | Neutron star |
| > 25 M☉ | < 10 million years | Black hole |
40.3.13 Nucleosynthesis: Where Elements Come From
| Process | Location | Elements Produced |
|---|---|---|
| Big Bang | Early universe | H, He, trace Li |
| Proton-proton chain | Main sequence (low mass) | He from H |
| CNO cycle | Main sequence (high mass) | He from H |
| Triple-alpha | Red giants | C from He |
| Alpha capture | Giants | O, Ne, Mg, Si |
| Silicon burning | Massive star cores | Up to Fe |
| Supernova | Stellar explosion | Elements > Fe |
| Neutron star mergers | Compact object collision | Heavy r-process elements |
40.3.14 Interactive: Element Origins
40.3.15 The Proton-Proton Chain
The main energy source in Sun-like stars:
Overall reaction: \[4^1_1\text{H} \rightarrow ^4_2\text{He} + 2e^+ + 2\nu_e + 26.7\ \text{MeV}\]
Steps: 1. \(^1\text{H} + ^1\text{H} \rightarrow ^2\text{H} + e^+ + \nu_e\) (slow; rate-limiting) 2. \(^2\text{H} + ^1\text{H} \rightarrow ^3\text{He} + \gamma\) 3. \(^3\text{He} + ^3\text{He} \rightarrow ^4\text{He} + 2^1\text{H}\)
40.3.16 The CNO Cycle
Dominates in stars > 1.3 M☉ (higher temperature needed):
Overall reaction: Same as pp-chain \[4^1_1\text{H} \rightarrow ^4_2\text{He} + 2e^+ + 2\nu_e + 26.7\ \text{MeV}\]
Key difference: Uses C, N, O as catalysts; faster at high temperatures
Fusion releases energy only up to iron (Fe-56). Iron has the highest binding energy per nucleon. Fusing heavier elements requires energy input—this only happens in supernovae.