Appearance
12.4 — Galaxies and the Structure of the Universe
In 1920 two astronomers argued in public about whether the spiral nebulae are objects inside the Milky Way or separate galaxies. Nobody knew whether the universe was one galaxy across or unimaginably larger.
Hubble settled it in 1924 by finding Cepheid variables in Andromeda and applying Leavitt's relation (Chapter 11.9). The distance came out far beyond any plausible size for the Milky Way.
The universe went from one galaxy to hundreds of billions, in a single measurement.
The Milky Way from inside
Measuring your own galaxy is harder than measuring someone else's, because you are inside it and dust blocks the view.
Structure:
| Component | Extent | Contents |
|---|---|---|
| Disc | 100,000 ly across, 1000 ly thick | Young stars, gas, dust, spiral arms |
| Bulge/bar | 10,000 ly | Old stars, central black hole |
| Halo | 200,000+ ly | Globular clusters, old stars, dark matter |
The Sun is 26,000 light years from the centre, in a minor arm, orbiting at about 230 km/s with a period of roughly 230 million years.
So the Sun has completed about 20 orbits since it formed, and about one since the dinosaurs appeared.
How the shape was determined. Optical light is blocked by dust in the disc — you can see only a few thousand light years along the plane. The 21 cm hydrogen line (Chapter 7.6) passes straight through, and mapping its Doppler shifts across the sky reveals the spiral structure.
And Harlow Shapley located the centre in 1918 by mapping globular clusters, which sit in the halo above the dust. They are not centred on the Sun; they are centred on a point 26,000 light years away in Sagittarius.
The Milky Way is a barred spiral, which was not established until infrared surveys in the 1990s and 2000s.
And it is not isolated. It is currently absorbing the Sagittarius Dwarf Galaxy, and its halo contains streams of stars from previous mergers. Galaxy formation is a history of cannibalism.
Galaxy types
Hubble's classification of 1926, still used, arranges galaxies in a "tuning fork".
Ellipticals (E0–E7). Smooth, featureless, little gas or dust, mostly old red stars, little star formation. Range from dwarf ellipticals with a million stars to giant cD galaxies with 10^{13}.
Spirals (Sa–Sc and barred SBa–SBc). A disc with arms, a central bulge, ongoing star formation in the arms. The sequence runs from tightly wound arms with a large bulge to loosely wound arms with a small one.
Lenticulars (S0). A disc with no arms — the transition case.
Irregulars. No structure, often gas-rich and actively forming stars. The Magellanic Clouds are the nearest examples.
Hubble thought this was an evolutionary sequence, with ellipticals as "early type" and spirals as "late type". He was wrong, and the terminology survives anyway. Ellipticals are generally the end products of mergers, not the beginning.
Spiral arms are not structures
A common misconception: the arms are not fixed patterns of stars.
If they were, they would wind up. The inner disc rotates faster than the outer, so an arm made of the same stars would be wrapped into a tight coil within a few rotations.
Worked example. At 26,000 ly the orbital period is 230 Myr; at 40,000 ly it is roughly 350 Myr. Over 10 billion years the inner region completes 43 orbits and the outer 29 — a difference of 14 full turns. Any material arm would be wound beyond recognition.
The resolution is density wave theory. The arms are a pattern that rotates more slowly than the stars, like a traffic jam. Stars pass through the arm, are compressed, and pass out the other side.
The compression triggers star formation, and the brightest young stars are short-lived (Chapter 12.1), so they die before leaving the arm. The arms are bright because they contain the young stars, not because they contain more stars.
The mass contrast between arm and inter-arm is only 10–20 %. The light contrast is far larger.
Rotation curves
This is where the trouble starts.
Newtonian prediction. For a mass distribution concentrated in the centre, like the solar system:
v(r) = \sqrt{\frac{GM(r)}{r}}
Once you are outside most of the mass, M(r) is constant and:
v \propto \frac{1}{\sqrt{r}}
Check it against the solar system, where 99.86 % of the mass is in the Sun:
| Planet | Distance (AU) | Speed (km/s) | 1/\sqrt{r} prediction |
|---|---|---|---|
| Mercury | 0.387 | 47.4 | 47.9 |
| Earth | 1.000 | 29.8 | 29.8 |
| Jupiter | 5.203 | 13.1 | 13.1 |
| Neptune | 30.07 | 5.4 | 5.4 |
Exact. Keplerian falloff, as it must be.
Now do the same for a galaxy.
The measurement. Use the 21 cm line or optical emission lines and measure the Doppler shift as a function of radius (Chapter 2.5). The gas disc extends well beyond the visible stars, so the curve can be traced far out.
The result: the curve is flat.
v(r) \approx \text{constant}
out to two or three times the visible radius, and sometimes further.
Vera Rubin and Kent Ford measured this systematically through the 1970s, first for Andromeda and then for dozens of galaxies. Every one was flat.
What flatness implies
v = \sqrt{\frac{GM(r)}{r}} = \text{constant} \quad\Longrightarrow\quad M(r) \propto r
The enclosed mass must keep growing linearly with radius, far beyond where the light stops.
And the density profile that gives this:
M(r) = \int_0^r 4\pi r'^2\rho(r')dr' \propto r \quad\Longrightarrow\quad \rho \propto \frac{1}{r^2}
An extended halo with density falling as 1/r^2, rather than the sharply concentrated distribution the light shows.
Worked example: the Milky Way
At the Sun's radius, r = 8.2 kpc = 2.53\times10^{20} m, v = 230 km/s:
M(r) = \frac{v^2r}{G} = \frac{(2.3\times10^{5})^2(2.53\times10^{20})}{6.674\times10^{-11}} = \frac{(5.29\times10^{10})(2.53\times10^{20})}{6.674\times10^{-11}}
= \frac{1.338\times10^{31}}{6.674\times10^{-11}} = 2.00\times10^{41}\ \text{kg} = 1.0\times10^{11}M_\odot
A hundred billion solar masses within the Sun's orbit, which is roughly consistent with the visible stars.
Now at 50 kpc, where the rotation is still about 200 km/s:
M = \frac{(2\times10^{5})^2(1.54\times10^{21})}{6.674\times10^{-11}} = 9.2\times10^{41}\ \text{kg} = 4.6\times10^{11}M_\odot
Four and a half times more mass, in a region containing very few stars.
And out to the halo's edge at about 200 kpc, dynamical estimates give 1.5\times10^{12}M_\odot.
\boxed{\text{The Milky Way's visible matter is about 6 \% of its total mass.}}
The wider evidence
Rotation curves alone would be a puzzle. There are six independent lines, and they agree.
1. Galaxy clusters
Fritz Zwicky, 1933, applied the virial theorem to the Coma Cluster.
The virial theorem (Chapter 1.6) says that for a bound gravitating system in equilibrium:
2\langle KE\rangle = -\langle PE\rangle
Measure the velocity dispersion from Doppler shifts, and the total mass follows:
M \approx \frac{5\sigma^2R}{G}
Zwicky found a mass 400 times the visible. He called the missing component dunkle Materie — dark matter.
He was ignored for forty years. Partly because his estimate was too high (the modern factor is about 10, not 400, mostly because his distance scale was wrong), and partly because he was famously abrasive.
2. Hot gas in clusters
X-ray observations show clusters filled with gas at 10^{7}–10^{8} K.
For that gas to be bound rather than evaporating, the cluster must be much more massive than its galaxies. The required mass matches the dynamical estimate.
3. Gravitational lensing
Chapter 6.6 established that mass bends light. Measuring the distortion of background galaxies gives the foreground mass, with no assumption that anything is in equilibrium.
Strong lensing produces multiple images and Einstein rings. Weak lensing produces a statistical shear in the shapes of thousands of background galaxies, and mapping it gives a mass map.
The lensing masses agree with the dynamical ones, which rules out any explanation that depends on the system being out of equilibrium.
4. The Bullet Cluster
The single most persuasive piece of evidence, from 2006.
Two galaxy clusters collided at about 4500 km/s.
The hot gas — about 90 % of the ordinary matter — collided and slowed, because gas is collisional. It sits between the two clusters, glowing in X-rays.
The galaxies passed through each other, because stars almost never hit.
And weak lensing shows the mass centred on the galaxies, not the gas.
\boxed{\text{The mass and the ordinary matter are in different places.}}
This is very hard to explain by modifying gravity, because a modified force law would still put the extra gravity where the visible matter is. The gas is where the baryons are, and the gravity is somewhere else.
5. The cosmic microwave background
Chapter 12.6 covers it properly. The CMB power spectrum's peak heights depend on the ratio of ordinary to total matter, and they give:
\Omega_b = 0.049, \qquad \Omega_m = 0.315
So 84 % of the matter is not ordinary. This measurement is completely independent of anything involving galaxies.
6. Structure formation
Ordinary matter could not have clumped fast enough.
Before recombination at 380,000 years (Chapter 12.6), ordinary matter was coupled to radiation and could not collapse — radiation pressure smoothed out any overdensity.
Dark matter does not interact with radiation, so it could begin clumping much earlier. By the time the ordinary matter was released, the dark matter had already built gravitational wells for it to fall into.
Without that head start, structure formation is far too slow to produce the galaxies we see. Simulations without dark matter do not reproduce the observed universe; simulations with it do, in remarkable detail.
The evidence considered together
No single line is conclusive on its own. Together they are.
Six methods, on scales from a single galaxy to the whole observable universe, using dynamics, X-rays, lensing, the CMB and simulations, all give the same answer: about five times as much gravitating matter as visible matter.
And the specific value agrees between methods that share no assumptions. The CMB, which knows nothing about galaxies, gives the same \Omega_m as cluster dynamics.
Chapter 12.7 examines what it might be, and the alternatives.
Large-scale structure
Galaxies are not scattered randomly.
The hierarchy:
| Scale | Structure | Size |
|---|---|---|
| 10^{5} ly | Galaxy | Milky Way |
| 10^{7} ly | Group | Local Group (~80 galaxies) |
| 10^{8} ly | Cluster | Virgo (~1500 galaxies) |
| 10^{9} ly | Supercluster | Laniakea |
| >10^{9} ly | Filaments and voids | The cosmic web |
The cosmic web. Redshift surveys — CfA, 2dF, SDSS — mapped millions of galaxy positions and revealed that they lie on filaments and sheets surrounding enormous voids.
Voids are 100–300 million light years across and nearly empty. They occupy most of the volume.
The Sloan Great Wall is 1.4 billion light years long.
And this structure is reproduced by simulations starting from the tiny density fluctuations seen in the CMB and evolving them under gravity with cold dark matter. The Millennium and IllustrisTNG simulations match the observed statistics quantitatively.
The end of the hierarchy
Above about 300 million light years, the universe is homogeneous.
Take any two cubes of that size anywhere and they contain the same average density to within a fraction of a percent.
\boxed{\text{The cosmological principle: on large enough scales, the universe is homogeneous and isotropic.}}
This is an assumption in the Friedmann equations (Chapter 12.5) and it is also a measured fact, confirmed by galaxy surveys and by the CMB's uniformity to one part in 10^{5}.
Some claimed structures exceed this scale — the Hercules–Corona Borealis Great Wall at 10 billion light years, the Giant GRB Ring — and their statistical significance is disputed. If real, they would be a problem for the standard model.
Galaxy evolution
Galaxies were smaller, bluer, clumpier and more irregular in the past, and they grew by merging.
JWST's early results were a surprise. It found galaxies at redshift 10–14 — within 300 million years of the Big Bang — that appear more massive and more mature than expected.
Whether this is a real problem for the standard model is unresolved. Possible explanations include underestimated stellar masses from assuming the wrong initial mass function, an unexpectedly efficient early star formation, or genuinely more rapid structure growth.
It is being actively worked on, and it is a good example of a new instrument creating a puzzle rather than confirming expectations.
The Milky Way and Andromeda will merge in about 4.5 billion years. They are approaching at 110 km/s. Almost no stars will collide — the stellar density is so low that a direct hit is essentially impossible — but the discs will be disrupted and the merged remnant will be an elliptical, sometimes nicknamed Milkomeda.
The Sun will probably be flung into a wider orbit and will survive, though by then it will be nearing the end of its life anyway (Chapter 12.1).
Where this shows up in your life
Dark matter is 85 % of the matter in the universe and nobody knows what it is. That is not a small gap in knowledge.
Gravitational lensing is now a routine tool, used to weigh clusters, find distant galaxies magnified by foreground mass, and constrain cosmological parameters.
The 21 cm line maps our own galaxy and is the target of experiments trying to observe the cosmic dark ages before the first stars.
And the fact that you can see the Milky Way at all — a faint band across the sky — is you looking edge-on through the disc of the galaxy you live in, from 26,000 light years out.
What the next chapter fixes
Galaxies are receding, and the recession is not motion through space. Chapter 12.5 derives the Friedmann equations from general relativity, explains why cosmological redshift is not a Doppler shift and what it actually is, defines the scale factor and the several distinct meanings of "distance" in an expanding universe, and works through the Hubble tension that Chapter 11.9 raised.