What you are looking at
Each point is how fast a real galaxy turns at one distance from its centre, measured from the light of its hydrogen gas. The lines under the points are what the gravity of its stars and gas alone would give: far out they fall short. Add a dark matter halo, fit it, and read how much unseen mass the galaxy needs. The second tab puts every point of 153 galaxies on one plot: the radial acceleration relation.
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Glossary
- Rotation curve
- How fast stars and gas circle a galaxy's centre at each radius. In a disk galaxy it rises quickly and then stays about flat, far past where the light fades.
- Why it matters If the visible mass were all, the speed would fall off far out, as the planets' speeds do round the Sun.
- SPARC
- Spitzer Photometry and Accurate Rotation Curves: 175 disk galaxies with infrared photometry from the Spitzer space telescope and rotation curves from radio and optical data (Lelli, McGaugh and Schombert 2016). The module uses the 163 with quality 1 or 2.
- Why it matters One homogeneous sample, so every galaxy is modelled the same way.
- Measured speed, with error bars
- The rotation speed at each radius, from the Doppler shift of hydrogen's 21 cm radio line and of Hα light, corrected for the disk's tilt. The bar is its measured uncertainty.
- Radius (kpc)
- Distance from the galaxy's centre in kiloparsecs. One kiloparsec is about 3260 light-years; the Sun sits about 8 kpc from the centre of the Milky Way.
- Stars and gas (baryons)
- The ordinary matter we can see. The stars line comes from the 3.6 µm infrared light of the disk and bulge; the gas line from the atomic hydrogen measured, with helium added. Stars and gas together is V_bar² = V_gas|V_gas| + Υ_d V_disk² + Υ_b V_bul².
- Why it matters Its gap below the points is what a halo has to fill.
- Mass-to-light ratio Υ
- How many solar masses of stars each solar luminosity of 3.6 µm light stands for. Stellar population models give about 0.5 for disks and 0.7 for bulges; the fit lets it move with a prior of 0.1 dex round those values.
- Why it matters Heavier stars could fill some of the gap, but not as far out as the points go.
- Dark matter halo
- A roughly round cloud of matter that gives off no light, larger than the visible galaxy. The model adds its speed to the baryons': V² = V_bar² + V_halo².
- NFW halo (V₂₀₀, c)
- The density profile cold dark matter simulations give (Navarro, Frenk and White 1996), steep to the centre. V₂₀₀ is the speed at r₂₀₀, where the halo's mean density is 200 times the universe's critical density; the concentration c says how much of its mass sits near the middle.
- Why it matters It is what the standard cosmology predicts, so how well it fits is a test.
- Pseudo-isothermal halo (ρ₀, r_c)
- A halo with a flat-density core of radius r_c and central density ρ₀, falling as 1/r² outside. It is an empirical shape, not a prediction.
- Why it matters Dwarfs such as DDO 154 often fit a core better than the NFW cusp: the cusp-core problem.
- Fit
- Least squares (Levenberg–Marquardt): the halo's two numbers, Υ, distance and inclination move together until the model passes as close to the points as their error bars allow. Distance and inclination may move within the catalogue's errors, as Li et al. 2020 let them.
- χ²/ν (reduced chi-squared)
- The sum of each point's miss squared, in units of its error bar, divided by the number of points minus the numbers the fit sets. Near 1 is a good fit; far above 1 the model misses.
- Why it matters It turns 'does the line go through the points' into one number.
- Dark share
- Of all the mass inside the last measured radius, the share the halo provides. In most galaxies it is well over half.
- Why it matters It says how much of the galaxy is matter no telescope has seen.
- Distance and inclination used
- The galaxy's distance sets its size and the stars' mass; its tilt converts the speed seen along the line of sight into the true one. The catalogue gives each with an error; the fit may move them within it.
- Radial acceleration relation
- At every measured radius of every galaxy, the acceleration the rotation shows, g_obs = V²/r, against what stars and gas give by Newton, g_bar = V_bar²/r. All 153 galaxies fall on one curve (McGaugh, Lelli and Schombert 2016).
- Why it matters One curve for galaxies of every size is a strong clue to how dark matter, or gravity, behaves.
- g† (acceleration scale)
- The acceleration where the relation bends away from g_obs = g_bar, about 1.2 × 10⁻¹⁰ m/s²: a hundred-billionth of the Earth's gravity. The module fits it to the sample as you change Υ.
- Scatter (dex)
- How far the points sit from the fitted curve, on average, in powers of ten: 0.13 dex is about 35%.
- MOND
- Modified Newtonian Dynamics (Milgrom 1983): instead of unseen mass, gravity itself grows stronger than Newton's below an acceleration a₀ about equal to g†.
- Why it matters It predicts the relation from the visible mass alone, but struggles in galaxy clusters and with the cosmic microwave background.
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