Astrophysics & Cosmology: Reading the Universe from Light Alone

Look up on a clear night and every point of light is a sun. The faint smudge you can sometimes spot in Andromeda is a galaxy of a trillion suns about 2.5 million light-years away. The light reaching your eye left it before our species existed. There is no way to travel there, take a sample, or send a probe. And yet astronomers can tell you the star's mass, its temperature, how long it has left to live and how far away it is, from the colour and the brightness of that light.

That is the odd thing about this subject: it is the one place in physics where you may not touch, and the whole discipline is built on inference. A graduate learns to see a point of light as an equation: brightness falls with the square of distance, colour tells temperature, and the stretching of its wavelengths tells how the space between us is growing. Out of three such ideas comes the age of the universe.

Light is all we get: the cosmic distance ladder

A lamp twice as far away looks four times fainter, because its light spreads over four times the area. This inverse-square law is the first tool of astronomy: if you know how bright something really is, its apparent brightness tells you its distance. Magnitudes are astronomers' logarithmic scale for brightness, and the working form is the distance modulus:

The hard part is knowing the true brightness, M. For nearby stars, geometry gives it directly: as the Earth goes round the sun, a nearby star seems to shift against the background. Its parallax angle p, in arcseconds, gives distance 1/p parsecs. The Gaia satellite has measured Proxima Centauri's parallax as about 768 milliarcseconds, so it is 1.30 pc, 4.25 light-years away. Past a few thousand parsecs parallax fails, and astronomers climb a ladder instead: Cepheid variable stars, whose pulsation period fixes their luminosity (Henrietta Leavitt, 1912), and then Type Ia supernovae, exploding white dwarfs that are all about equally bright, at around absolute magnitude −19.3, visible across billions of light-years.

Each rung is calibrated on the one before. That chain is why a 5% mistake near the bottom spreads to everything above, which matters later in this piece.

A star is a balance, and its mass sets its life

A star is a ball of gas in which two things fight. Gravity pulls everything inward. Pressure from the hot gas pushes outward. The heat is replenished by fusion in the core (the binding-energy story from Particle & Nuclear Physics, 34/86). If the core cools, gravity squeezes it, it heats up and burns faster: the balance is self-correcting. Because of that, mass is almost the only thing that decides a main-sequence star's luminosity, size and temperature.

The fuel runs out faster than you would think. A star's luminosity grows steeply with mass, roughly as M^3.5 for stars a few times the sun. Its fuel grows only as M. So the lifetime, fuel divided by burn rate, drops as about M^−2.5. Worked for the sun: it fuses about 10% of its hydrogen, converting 0.7% of the mass to energy, so its lifetime is 0.1 × 0.007 × Mc² ÷ L ≈ 10 billion years. A star of ten solar masses burns 4,400 times brighter and lasts of order tens of millions of years. Move the mass.

The plot is a Hertzsprung–Russell diagram: temperature (hot on the left) against luminosity. Stars burning hydrogen fall on a band across it, the main sequence, where the sun sits in the middle. Every star ever catalogued is a point on that diagram, and its position, together with its mass, tells the stage of its life.

When the balance fails: white dwarfs, neutron stars, black holes

When the core's fuel is spent, nothing replaces the heat, and gravity wins. What stops the collapse depends on the mass left behind. For stars like the sun, electrons are squeezed until the Pauli principle resists: a white dwarf the size of the Earth. In 1930–31 Subrahmanyan Chandrasekhar showed that this support fails above about 1.4 solar masses (the Chandrasekhar limit; Nobel Prize 1983). Beyond that, the core collapses until protons and electrons merge into neutrons, a neutron star about 12 km across, with a teaspoon weighing billions of tonnes. And above a limit near two to three solar masses, nothing known can hold it up: a black hole.

A black hole has one size, the radius inside which not even light escapes. In general relativity (34/85) it is:

The sun would be a black hole 3 km wide, and the Earth one under 9 mm. Black holes are not cosmic vacuum cleaners; from afar they pull as any other mass does. In 2015 the LIGO detectors recorded the gravitational waves of two black holes of about 36 and 29 solar masses merging (GW150914), the first direct detection, and in 2019 and 2022 the Event Horizon Telescope imaged the shadows of the black holes at the centres of the galaxy M87 and of our own.

The density line is the surprise. A black hole's average density, mass over the volume inside its horizon, falls as 1/M². The 6.5-billion-sun hole in M87 is, on average, lighter than air.

Galaxies spin too fast: the dark matter evidence

Kepler's law for planets says the farther out you go, the slower you orbit. Stars in a galaxy should do the same: outside the bright disk, where little mass is visible, their orbital speed should fall. In the 1970s Vera Rubin and Kent Ford measured the Andromeda galaxy, and later Rubin, Ford and Norbert Thonnard measured many more. The speeds did not fall. They stayed flat to the edge of the visible disk. The simplest reading is that there is unseen mass, more than the visible stuff, spread in a huge halo. The same hint, from the Coma cluster, had been noticed by Fritz Zwicky in 1933.

More evidence agrees: light bending by galaxy clusters (gravitational lensing), the hot gas in clusters, and the pattern of the cosmic microwave background all say the same. The Bullet Cluster, a collision of two clusters studied in 2006, shows the lensing mass separated from the hot gas, which is hard for a pure gravity change to mimic. The Planck 2018 values for the cosmic budget are about 5% ordinary matter, 27% dark matter and 68% dark energy.

What dark matter is is open. Most physicists favour a new, weakly interacting particle (searches such as LZ and XENONnT have so far found nothing) or a very light field such as the axion. A minority, following Mordehai Milgrom's 1983 MOND, modify the law of gravity at tiny accelerations, which fits galaxy rotation curves well but struggles with clusters and the microwave background. No candidate has been detected.

The universe expands, and its age depends on the numbers

In the 1920s Georges Lemaître and Edwin Hubble found that distant galaxies are receding, and the farther they are the faster. The relation is the Hubble law, v = H₀ d. It does not mean galaxies fly outward from a centre: space between them stretches, so every galaxy sees the same picture. Run the expansion backwards and everything was once denser and hotter. The rough age is the Hubble time 1/H₀, about 14.5 billion years for H₀ = 67.4. The exact age needs the mix of matter and dark energy that slowed and then sped the expansion. For a flat universe with matter fraction Ω_m and dark-energy fraction Ω_Λ = 1 − Ω_m:

With Planck 2018's values, H₀ = 67.4 ± 0.5 km/s/Mpc and Ω_m = 0.315, it gives 13.8 billion years. But there is a live argument. Measurements built on the distance ladder, led by the SH0ES team (Adam Riess), give 73.04 ± 1.04. The two differ by more than their errors. The Chicago–Carnegie group of Wendy Freedman, using a different rung (the tip of the red giant branch), reported about 70 and argues the tension is weaker than claimed. Whether the gap comes from errors in the ladder, in the early-universe model, or from new physics is the Hubble tension, and it is not settled.

Note that the matter fraction matters as much as H₀. A universe with only matter (Ωm = 1) would be two-thirds of the Hubble time old, 9.7 billion years for H₀ = 67.4, younger than some of the oldest stars. That conflict in the 1990s was one of the clues that pointed to dark energy, confirmed by the supernova teams in 1998 (Nobel Prize 2011).

The universe as a cooling oven

Expansion stretches light's wavelengths, which cools it: the radiation's temperature scales as 1 + z, where z is the redshift. Today the leftover glow of the early universe, the cosmic microwave background (CMB), is at 2.7255 K. It was predicted in 1948 and found by accident by Penzias and Wilson in 1965 (Nobel Prize 1978). At redshift 1090, about 372,000 years after the beginning, the universe was a 3,000 K gas, cool enough that electrons and protons combined into atoms and light could finally travel freely. That light is what we see now, mapped by COBE, WMAP and Planck.

Go earlier, and it is hotter than the centre of a star, and nuclear physics returns. At about three minutes, at roughly a billion kelvin, protons and neutrons fused into deuterium and helium. The predicted helium fraction, about a quarter of the mass, matches what we see in the oldest gas clouds, and is one of the most solid pillars of the Big Bang model. Slide through it. At the far end, the universe is as hot as the particle colliders of Particle & Nuclear Physics (34/86).

What a graduate just sees

• Brightness falls with distance squared, so a known brightness is a ruler. Every distance in astronomy is a chain of such rungs.
• A point of light is a temperature, a size and a mass. Position on the HR diagram tells the star's life stage.
• Big stars live fast: lifetime goes as about M^−2.5.
• Stars end as white dwarfs, neutron stars or black holes, by mass: roughly 1.4 and 2 to 3 solar masses are the thresholds.
• Orbit speed measures the mass inside; flat rotation curves mean mass that does not shine.
• Expansion is stretching of space, not an explosion into space, and redshift is the stretching of light.
• The age and size of the universe come from two or three numbers (H₀, Ωm, ΩΛ), so measuring them well matters.
• Temperature falls as the universe grows: look farther, and you see a hotter, simpler universe.

Where it shows up next

• Particle & Nuclear Physics (34/86): the binding-energy curve is why stars stop at iron, and the early universe is the highest-energy experiment there is.
• General Relativity (34/85): black holes, gravitational waves and the expansion equations are all that theory at work.
• Observing: Hubble, JWST (its record: a galaxy confirmed at redshift 14.44, about 280 million years after the Big Bang, reported in 2025), Gaia, LIGO, the Event Horizon Telescope, and the Vera C. Rubin Observatory, named for the dark-matter pioneer.
• In daily life: GPS needs general relativity, space telescopes need cryogenics and precise optics, and astronomy has produced image-processing and data-analysis methods that spread into medicine and machine learning.

If you want to go deeper

• 📘 Textbook. Bradley Carroll and Dale Ostlie, An Introduction to Modern Astrophysics (2nd edition, Pearson 2007; reissued by Cambridge University Press in 2017). The long, standard survey of stars and galaxies.
• 📘 Textbook. Barbara Ryden, Introduction to Cosmology (2nd edition, Cambridge, 2016). Compact and clear, with the Friedmann equations built up step by step.
• 📘 Gentler. Steven Weinberg, The First Three Minutes (Basic Books, 1977; updated 1993), and Katie Mack, The End of Everything (Astrophysically Speaking) (Scribner, 2020).
• 🌐 Free course. MIT OpenCourseWare 8.286 The Early Universe (Fall 2013, Alan Guth): video lectures and slides on the Big Bang model, the CMB and inflation.