Astronomy 2e · Galaxies
Properties of Galaxies
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In 30 seconds
Once astronomers knew galaxies were real, the next questions were physical: How big are they? How bright? How massive? What are they made of? The answers turned out to be both humbling and strange. Galaxies range from dwarf systems of a few million stars to giants a hundred times the Milky Way's luminosity, and they come in two basic flavors — red, gas-poor ellipticals and blue, gas-rich spirals. The strangest result came from weighing them: when astronomers measure how fast gas and stars orbit inside galaxies, they find the visible matter cannot account for the motion. Galaxies rotate as if they contain far more mass than we can see — evidence for Dark matter Invisible mass detected only through gravity Full entry → extending far beyond the visible disk.
This topic covers the standard measurements: mass (from rotation curves and stellar motions), luminosity and size, color and stellar content, and the mass-to-light ratio that exposes dark matter. It also introduces the Tully–Fisher relation L ∝ v⁴ for spiral galaxies Full entry →, a connection between a spiral's brightness and its rotation speed that becomes a powerful distance tool in the next topic.
Why this matters
Galaxy properties are the raw material for nearly all of extragalactic astronomy. Luminosities and masses tell us how galaxies compare with one another and how many of each kind exist; colors reveal stellar populations and star-formation history; mass-to-light ratios are our best evidence for dark matter, one of the great unsolved problems in physics. The Tully–Fisher relation (and its elliptical-galaxy cousins) are rungs on the extragalactic distance ladder (Topic 4), and galaxy masses feed directly into how we interpret clusters, the expansion of the universe, and dark matter on the largest scales. For exams, rotation curves and dark matter are the highest-yield ideas in this topic.
The college version
Core Concepts
Weighing a spiral: rotation curves
The mass of a spiral galaxy is measured from its Rotation curve Orbital speed vs radius for gas/stars in a galaxy Full entry → — the orbital speed of gas and stars versus distance from the center. Astronomers measure Doppler shifts of the 21-cm radio line of neutral hydrogen (and of optical lines from stars) across the disk. For matter in a circular orbit, the mass inside radius r is
M(<r) = v²r / G
where v is the orbital speed at radius r and G is the gravitational constant. If most of the mass were in the bright, central parts, orbital speeds should fall off as r increases (as the planets' speeds do with distance from the Sun). Instead, observed rotation curves are flat: speed stays roughly constant far beyond the visible disk. A constant v with growing r means M(<r) keeps growing — there is mass out there that emits almost no light. That invisible component is called dark matter, and it dominates the mass of spiral galaxies, typically extending to many times the visible disk's radius.
Weighing an elliptical: velocity dispersion
Ellipticals have no organized rotation, so their masses come from the random motions of their stars. The spread of stellar speeds along the line of sight — the Velocity dispersion Spread of stellar speeds in a galaxy Full entry →, σ — measures how "hot" the stellar swarm is. Using the Virial theorem Kinetic energy ≈ gravitational potential energy in bound systems Full entry → (which relates the total kinetic energy of a bound system to its gravitational potential energy), astronomers convert σ and the galaxy's size into a mass. Typical ellipticals turn out to be comparable in mass to spirals, and like spirals they are dominated by dark matter in their outer parts.
Luminosity and size
Galaxy luminosities span an enormous range — roughly a factor of a billion. Dwarf galaxies have absolute magnitudes around −8 to −14 (from a few × 10⁵ to ~10⁷ times the Sun's luminosity), while giant ellipticals and bright spirals reach 10¹¹ solar luminosities or more. Sizes follow: dwarf galaxies span roughly 1–10 kiloparsecs, giants reach ~100 kpc or more, and the Milky Way's disk is about 30 kpc (~100,000 light-years) across. The Luminosity function Number of galaxies per luminosity interval Full entry → — the number of galaxies per luminosity interval — rises steeply toward the faint end: dwarf galaxies vastly outnumber giants.
Colors and stellar populations
A galaxy's color is a shortcut to its stellar content. Red galaxies are dominated by old, cool stars; blue light comes from young, hot, massive stars that live only briefly, so blue galaxies must be forming stars now. Ellipticals are red (old stars, no gas, no star formation); spirals and irregulars are bluer (gas-rich, active star formation in their arms). Color therefore tells the same story as morphology: red = finished forming stars, blue = still building.
Mass-to-light ratio and dark matter
The mass-to-light ratio (M/L, in solar units) compares a galaxy's total mass with its luminosity. Ordinary stellar populations have M/L of a few; galaxies measured through rotation curves or velocity dispersions typically show M/L of ten to a hundred or more, and dwarf spheroidal galaxies show extreme values. A high M/L means most of the mass is not in the stars we see: dark matter. Combining all measurements, dark matter outweighs ordinary (baryonic) matter in galaxies by roughly a factor of five to ten on cosmic scales (a commonly taught reference; the exact ratio depends on assumptions and is still being refined).
Tully–Fisher and other correlations
For spiral galaxies, the Tully–Fisher relation links luminosity to rotation speed:
L ∝ v⁴ (approximately)
Bright spirals rotate faster. Because rotation speed is easy to measure (via the Doppler width of the 21-cm line) and does not depend on distance, Tully–Fisher gives an independent luminosity — and therefore a distance — for spirals far beyond Cepheid range (Topic 4). A similar relation, the M–σ relation, links the mass of a galaxy's central supermassive black hole to the velocity dispersion of its bulge; it connects galaxy properties to the active-galaxy phenomena of Chapter 27. Spiral galaxies also contain substantial gas — neutral hydrogen (H I), molecular clouds, and dust — which fuels star formation; ellipticals are nearly gas-free.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| Rotation-curve speed being the galaxy's "speed through space" | Circular orbital speed of its gas/stars | It measures internal orbital motion, not bulk motion of the galaxy |
| Dark matter existing only in clusters | Dark matter in individual galaxies | Flat rotation curves show halos around single galaxies |
| A blue galaxy being "younger" than a red one | Blue = forming stars now | Both may be ~13 Gyr old; blue means recent/ongoing star formation, red means it has stopped |
| Ellipticals having no dark matter | Ellipticals having no gas | Ellipticals have dark halos; they just lack star-forming gas |
| A galaxy's M/L being like a star's | Galaxy M/L including dark matter | Galaxy M/L of 10–100+ vs a few for stars alone |
| Tully–Fisher applying to ellipticals | It applies to spirals | Ellipticals use velocity-dispersion-based relations instead |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Imagine swinging a ball on a string: the string's pull tells you how heavy the ball is. Astronomers do the same with galaxies — they watch how fast the outer parts orbit and use gravity to "weigh" the galaxy. The surprise: the outer parts orbit way too fast for the stars we can see to hold them, like the ball being heavier than the string and your hand suggest. So galaxies must be full of invisible "dark" stuff — dark matter — that we can't see but can feel through gravity.
Worked example
Step 1 — measure. The 21-cm line maps neutral hydrogen across a spiral galaxy. At 10 kpc from the center the gas orbits at 200 km/s; at 20 kpc it still orbits at about 200 km/s.
Step 2 — compute enclosed mass. Using M(<r) = v²r/G with v = 200 km/s = 2 × 10⁵ m/s, G = 6.67 × 10⁻¹¹ N·m²/kg², and 1 kpc ≈ 3.1 × 10¹⁹ m:
- At r = 10 kpc: M ≈ (4 × 10¹⁰) × (3.1 × 10²⁰) / (6.7 × 10⁻¹¹) ≈ 1.9 × 10⁴¹ kg ≈ 9 × 10¹⁰ M☉
- At r = 20 kpc: double r with the same v → M ≈ 1.9 × 10¹¹ M☉
Step 3 — interpret. Between 10 and 20 kpc the enclosed mass roughly doubles, yet the galaxy's light output beyond 10 kpc is tiny. The extra mass emits essentially no light: it is dark matter. If the galaxy's mass were only in its stars, the rotation curve would fall like the planets' speeds fall with distance from the Sun — it doesn't. (Numbers rounded as teaching values; verify against current sources.)
This one measurement — flat rotation curve → growing enclosed mass — is the cleanest single piece of evidence that galaxies are embedded in halos of dark matter.
Key takeaways
- Rotation curves (spirals): flat beyond the visible disk → mass keeps increasing → dark matter halo.
- Mass formula (circular orbit): M(<r) = v²r/G — if v is constant while r grows, the enclosed mass grows.
- Ellipticals: mass from velocity dispersion + virial theorem, not rotation.
- Luminosities span ~10⁵–10¹¹+ L☉; sizes ~1–100+ kpc; dwarfs vastly outnumber giants (steep luminosity function).
- Red = old stars, no star formation; blue = young stars, star formation happening now.
- M/L ratio of 10–100+ in galaxies = most of the mass is dark; dark matter outweighs visible matter in galaxies.
- Tully–Fisher (spirals): L ∝ v⁴ — a distance tool for the next topic.
- Galaxies: spirals gas-rich and star-forming; ellipticals gas-poor and "red and dead."
Check yourself
5 review questions from the chapter. Try each one, then open the answer.
Why do flat rotation curves imply dark matter?
Show answer
If mass were only in the visible stars, orbital speeds would fall with radius; instead they stay roughly constant, and M(<r) = v²r/G keeps growing with r — mass must exist beyond the visible disk, emitting little or no light.
Write the formula for the mass enclosed inside a circular orbit, and define each symbol.
Show answer
M(<r) = v²r/G, where v is the circular orbital speed at radius r and G is the gravitational constant (6.67 × 10⁻¹¹ N·m²/kg²). It gives the total mass inside radius r.
How do astronomers weigh an elliptical galaxy, and why can't they use a rotation curve?
Show answer
From the velocity dispersion of their stars and the virial theorem: their random (not rotational) motions plus the galaxy's size give the mass. Ellipticals rotate too slowly for a rotation-curve analysis.
A galaxy is smooth and red. What does its color tell you about its star formation?
Show answer
Red light comes from old, cool stars; there are no young blue stars, so star formation has essentially stopped — typical of an elliptical.
What does the Tully–Fisher relation say, and why is it useful?
Show answer
For spirals, luminosity is proportional to rotation speed to roughly the fourth power (L ∝ v⁴): brighter spirals rotate faster. Because rotation speed is distance-independent, the relation turns a measured speed into a luminosity, and hence a distance.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- Rotation curve
- Orbital speed vs radius for gas/stars in a galaxy
- Dark matter
- Invisible mass detected only through gravity
- Velocity dispersion
- Spread of stellar speeds in a galaxy
- Virial theorem
- Kinetic energy ≈ gravitational potential energy in bound systems
- Luminosity function
- Number of galaxies per luminosity interval
- Mass-to-light ratio (M/L)
- Total mass ÷ luminosity (in solar units)
- Tully–Fisher relation
- L ∝ v⁴ for spiral galaxies
- H I region
- Neutral hydrogen gas (traced by the 21-cm line)
Sources & references
This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.
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