Stars, Cosmology and the Expanding Universe

Telescopes and magnitude

Astronomers gather light with telescopes (refracting, reflecting) and measure how bright stars appear.

• Apparent magnitude (m): how bright a star looks from Earth. A smaller/more negative number = brighter. A difference of 5 magnitudes = a brightness factor of 100.
• Absolute magnitude (M): the apparent magnitude a star would have at a standard distance of 10 parsecs — a true measure of luminosity.

Distances: 1 parsec (pc) ≈ 3.09 × 10¹⁶ m; 1 light-year is the distance light travels in a year.

Classifying stars

• Black-body radiation: stars approximate black bodies. Wien's law links peak wavelength to temperature: λ_max ∝ 1/T (hotter stars are bluer). Stefan's law: power output P = σAT⁴.
• Spectral classes (OBAFGKM) run from hottest/bluest (O) to coolest/reddest (M).
• The Hertzsprung–Russell (H–R) diagram plots luminosity against temperature; most stars lie on the main sequence, with giants, supergiants and white dwarfs in distinct regions.

Stellar evolution (outline)

A star forms from collapsing gas/dust, fuses hydrogen on the main sequence, then becomes a red giant. Its end depends on mass:

• Low mass (like the Sun): sheds outer layers → white dwarf.
• High mass: explodes as a supernova, leaving a neutron star or, if massive enough, a black hole.

A supernova is also used as a "standard candle" to measure large distances.

The expanding universe

• Doppler effect / red shift: light from receding galaxies is shifted to longer (redder) wavelengths: z = Δλ/λ ≈ v/c.
• Hubble's law: recession velocity is proportional to distance: v = H₀d (H₀ = Hubble constant). This shows the universe is expanding.
• Running the expansion backwards leads to the Big Bang theory. Key evidence: the cosmic microwave background radiation (CMBR) and the observed abundance of light elements.

Worked example

A galaxy's spectral line is red-shifted so that z = 0.02. Estimate its recession speed.

• v ≈ zc = 0.02 × 3.0×10⁸ = 6.0 × 10⁶ m/s (moving away from us). ✓

Common mistakes

• Getting magnitude backwards — smaller/more negative = brighter.
• Confusing apparent (how it looks) with absolute (true, at 10 pc) magnitude.
• Forgetting red shift means galaxies are moving away (expanding universe).

Exam tips

• Use Wien's law (hotter → shorter λ_max) and Stefan's law (P = σAT⁴).
• Interpret the H–R diagram and outline stellar evolution by mass.
• Link red shift + Hubble's law to the expanding universe and the Big Bang (CMBR evidence).

Key facts to remember

• Apparent vs absolute magnitude (absolute = at 10 pc); smaller = brighter; classify stars by temperature (OBAFGKM, H–R diagram).
• Wien's law (λ_max ∝ 1/T) and Stefan's law (P = σAT⁴); evolution: main sequence → red giant → white dwarf / supernova → neutron star or black hole.
• Red shift (z = Δλ/λ ≈ v/c) + Hubble's law (v = H₀d) → expanding universe → Big Bang (evidence: CMBR).