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Astrophysics applies the principles of physics to understand the universe — from individual stars to the large-scale structure and evolution of the cosmos. This optional topic (AQA Option D) covers astronomical distances, stellar classification and evolution, the Hertzsprung-Russell diagram, cosmology, and the evidence for the Big Bang. Astrophysics draws together ideas from almost every other area of the course — thermal physics, waves, nuclear physics, and gravity all play essential roles.
Distances in astronomy are so vast that everyday units are impractical. Three key units are used:
Key Definition: An astronomical unit (AU) is the mean distance from the Earth to the Sun: 1 AU ≈ 1.496 × 10¹¹ m. It is useful for distances within the solar system.
Key Definition: A light-year (ly) is the distance that light travels in one year: 1 ly ≈ 9.46 × 10¹⁵ m. It is useful for distances to nearby stars and within galaxies.
Key Definition: A parsec (pc) is the distance at which a star has a parallax angle of one arcsecond: 1 pc ≈ 3.086 × 10¹⁶ m ≈ 3.26 ly. It is the preferred unit in professional astronomy.
| Unit | Equivalent in metres | Equivalent in light-years | Typical use |
|---|---|---|---|
| AU | 1.496 × 10¹¹ | 1.58 × 10⁻⁵ | Solar system distances |
| Light-year | 9.46 × 10¹⁵ | 1 | Interstellar distances |
| Parsec | 3.086 × 10¹⁶ | 3.26 | Professional astronomy |
| Megaparsec (Mpc) | 3.086 × 10²² | 3.26 × 10⁶ | Intergalactic/cosmological |
Stellar parallax is the most direct method for measuring the distance to nearby stars. As the Earth orbits the Sun, nearby stars appear to shift position against the background of very distant stars.
Method:
d (in parsecs) = 1/p (in arcseconds)
For example, if a star has a parallax angle of 0.5 arcseconds, its distance is 1/0.5 = 2 parsecs.
Limitations: Parallax angles become too small to measure accurately for stars beyond about 100 pc with ground-based telescopes. The Hipparcos satellite extended this to about 1000 pc, and the Gaia satellite (launched 2013) can measure parallaxes for stars up to tens of thousands of parsecs away.
For more distant objects, astronomers use standard candles — objects of known luminosity. By comparing the known luminosity with the observed brightness (flux), the distance can be calculated.
Cepheid variable stars are pulsating stars whose period of brightness variation is directly related to their luminosity (the period-luminosity relationship, discovered by Henrietta Leavitt in 1912). By measuring the period of a Cepheid, its luminosity is determined, and hence its distance.
Type Ia supernovae are thermonuclear explosions of white dwarf stars that always reach approximately the same peak luminosity (about 10⁹ times the luminosity of the Sun). They are visible across enormous cosmological distances and serve as standard candles for measuring distances to remote galaxies. Type Ia supernovae were crucial in the 1998 discovery that the expansion of the universe is accelerating.
Stars can be classified by their spectral type (based on surface temperature and absorption lines) and by their position on the Hertzsprung-Russell diagram.
Stars are classified using the letters O, B, A, F, G, K, M (remembered by "Oh Be A Fine Girl/Guy, Kiss Me"):
| Class | Colour | Surface Temperature (K) | Key Absorption Lines |
|---|---|---|---|
| O | Blue | > 30 000 | Ionised helium |
| B | Blue-white | 10 000–30 000 | Neutral helium |
| A | White | 7 500–10 000 | Strong hydrogen (Balmer series) |
| F | Yellow-white | 6 000–7 500 | Ionised metals |
| G | Yellow | 5 200–6 000 | Ionised and neutral metals |
| K | Orange | 3 700–5 200 | Neutral metals |
| M | Red | 2 400–3 700 | Molecular bands (TiO) |
The Sun is a G2V star (G-type, main sequence) with a surface temperature of approximately 5 800 K.
The spectral class depends on surface temperature because different temperatures cause different elements to be ionised or excited, producing characteristic absorption lines in the star's spectrum.
Key Definition: The apparent magnitude (m) of a star is a measure of how bright it appears from Earth. A lower (or more negative) magnitude means a brighter star. The scale is logarithmic: a difference of 5 magnitudes corresponds to a factor of 100 in brightness.
Key Definition: The absolute magnitude (M) of a star is the apparent magnitude the star would have if it were placed at a standard distance of 10 parsecs from the observer.
The relationship between apparent magnitude (m), absolute magnitude (M), and distance (d in parsecs) is:
m − M = 5 log₁₀(d/10)
The quantity (m − M) is called the distance modulus. If m − M > 0, the star is further than 10 pc; if m − M < 0, it is closer than 10 pc.
Key Definition: Wien's Displacement Law states that the peak wavelength (λ_max) of the black-body radiation emitted by a star is inversely proportional to its surface temperature.
λ_max T = 2.898 × 10⁻³ m K (Wien's constant)
This allows the surface temperature of a star to be determined from its observed spectrum — specifically, from the wavelength at which the emission is most intense.
A hotter star has a shorter peak wavelength (bluer), while a cooler star has a longer peak wavelength (redder).
Described diagram — Black-body radiation curves at different temperatures: The horizontal axis is wavelength (λ) and the vertical axis is spectral radiance (intensity per unit wavelength). Several curves are plotted, one for each temperature (e.g. 3 000 K, 5 000 K, and 8 000 K). Each curve starts at zero for very short wavelengths, rises to a peak, then falls off gradually at longer wavelengths. Higher-temperature curves have their peak shifted to shorter wavelengths (to the left), in accordance with Wien's law. Higher-temperature curves also have a much higher peak intensity — the peak height increases dramatically with temperature (the total area under the curve, proportional to total power, scales as T⁴ by the Stefan-Boltzmann law). The 3 000 K curve peaks in the infrared (red star), the 5 000 K curve peaks in the visible range (yellow-white star like the Sun), and the 8 000 K curve peaks in the blue-ultraviolet region (blue-white star). At any given wavelength, a hotter body emits more radiation than a cooler body.
Question: The star Rigel has a peak emission wavelength of 263 nm. Calculate its surface temperature.
Solution:
Rearranging Wien's law: T = 2.898 × 10⁻³ / λ_max
T = 2.898 × 10⁻³ / (263 × 10⁻⁹)
T = 2.898 × 10⁻³ / 2.63 × 10⁻⁷
T = 11 020 K ≈ 11 000 K
This places Rigel as a B-type star (blue-white), consistent with its observed colour.
Exam Tip: In Wien's law calculations, make sure the peak wavelength is in metres (not nanometres) before substituting into the equation. A common error is to forget to convert nm to m, giving an answer that is out by a factor of 10⁹.
The total power (luminosity, L) radiated by a star, assuming it radiates as a black body, is:
L = σAT⁴ = 4πr²σT⁴
where σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W m⁻² K⁻⁴), A is the surface area, r is the stellar radius, and T is the surface temperature.
Key points:
Question: The Sun has a surface temperature of 5 800 K and a radius of 6.96 × 10⁸ m. Calculate its luminosity. Verify that this is consistent with the accepted value of L_Sun ≈ 3.85 × 10²⁶ W.
Solution:
L = 4πr²σT⁴
L = 4π × (6.96 × 10⁸)² × 5.67 × 10⁻⁸ × (5800)⁴
Step 1: r² = (6.96 × 10⁸)² = 4.844 × 10¹⁷ m²
Step 2: 4πr² = 4π × 4.844 × 10¹⁷ = 6.087 × 10¹⁸ m²
Step 3: T⁴ = (5800)⁴ = 1.132 × 10¹⁵ K⁴
Step 4: L = 6.087 × 10¹⁸ × 5.67 × 10⁻⁸ × 1.132 × 10¹⁵
L = 6.087 × 10¹⁸ × 6.418 × 10⁷ = 3.91 × 10²⁶ W
This is within 2% of the accepted value, confirming the calculation.
The intensity (flux, F) of radiation received from a star decreases with distance according to the inverse square law:
F = L/(4πd²)
where F is the flux (W m⁻²), L is the luminosity (W), and d is the distance to the star (m). This is because the luminosity is spread uniformly over a sphere of area 4πd².
This equation is fundamental — it connects the measurable quantity (flux received at Earth) with the intrinsic property (luminosity) and the distance. If any two of these three quantities are known, the third can be calculated.
Question: A star has a luminosity of 8.0 × 10²⁸ W. The flux (intensity) measured at Earth is 2.5 × 10⁻⁹ W m⁻². Calculate the distance to the star in metres and in parsecs. (1 pc = 3.086 × 10¹⁶ m)
Solution:
Step 1: Rearrange F = L/(4πd²) for d. d² = L/(4πF) d = √(L/(4πF))
Step 2: Substitute values. d = √(8.0 × 10²⁸ / (4π × 2.5 × 10⁻⁹)) d = √(8.0 × 10²⁸ / 3.142 × 10⁻⁸) d = √(2.546 × 10³⁶) d = 1.60 × 10¹⁸ m
Step 3: Convert to parsecs. d = 1.60 × 10¹⁸ / 3.086 × 10¹⁶ = 51.8 pc
Exam Tip: When using F = L/(4πd²), ensure all quantities are in SI units. The flux is what you measure at Earth (W m⁻²), the luminosity is the total power output of the star (W), and d is in metres. This equation is the basis for determining distances to stars using standard candles.
The HR diagram is one of the most important tools in astrophysics. It plots luminosity (or absolute magnitude) on the vertical axis against surface temperature (or spectral class) on the horizontal axis.
Important: Temperature increases from right to left on the horizontal axis (the opposite of normal convention). This is a historical convention that must be followed.
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