Concept

Freeman's law — where it appears

The observation that spiral galaxy discs share nearly the same central surface brightness. It turned out to be partly a selection effect, since a disc much fainter than the sky background is not found by looking, and the low-surface-brightness population was discovered afterwards.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

The rotation curve of NGC 3198, decomposed. Circular speed against radius for a three-component model of NGC 3198: a Hernquist bulge of 1.0×10⁹ M☉, an exponential disc of 2.20×10¹⁰ M☉ with a scale length of 2.6 kpc, and a pseudo-isothermal halo whose asymptotic speed is not chosen but solved for — it is whatever brings the total to the measured 150 km/s at 30 kpc, and comes out at 171 km/s. The components add in quadrature because accelerations add. The disc alone peaks at 5.7 kpc and falls away; the total does not.

A rotation curve that refuses to fall

Beyond the edge of a galaxy's light there is nothing left to enclose, so the orbital speed should fall away as the inverse square root of radius. It does not fall at all, and the shape of that refusal says the missing mass arrives at a constant rate for as far out as anyone can measure.

galaxies · Rotation curves

Tully–Fisher, from two assumptions and no fitting. 44 model galaxies spanning two and a half decades in luminosity, each built from a constant disc surface brightness of 380 L☉ per square parsec with 0.13 dex of scatter and a stellar mass-to-light ratio of 1.4 with 0.1 dex. Nothing about a luminosity–speed relation is put in: the scale length follows from the surface brightness, the mass from the light, and the speed from v² = GM/R. The construction makes L ∝ v⁴ exactly, so the true slope is −10.0 magnitudes per decade of speed. Least squares of magnitude on log speed returns -8.45, and the reverse regression -9.15: the scatter here is scatter in the speed at fixed luminosity, and error in the abscissa flattens a fitted slope, so neither fit returns the value the family was built with and the distance between them is the size of the effect. Residual scatter about the drawn line is 0.54 magnitudes. Observed slopes run from about −7.5 in blue light to −10 in the near infrared, where the mass-to-light ratio is steadiest — which is the same statement as the second assumption above.

A line width that is a distance

The width of a galaxy's hydrogen line depends on how fast it rotates, which depends on its mass, which is tied to its luminosity — so a quantity no distance enters gives an absolute brightness, and the distance follows from the brightness that is seen.

galaxies · Tully–Fisher

What distance does, and does not, do to a galaxy. Three quantities against distance, each relative to its value at 5 Mpc, on logarithmic axes so that a power law is a straight line and its exponent is the slope. Flux falls with slope −2 and angular size with slope −1, both of which are ordinary. Their ratio has slope zero: a galaxy of surface brightness 23.5 magnitudes per square arcsecond has that surface brightness at every distance, and a sky of 22 is brighter than it at every distance too. The contrast against the sky — the quantity that decides whether the thing is detectable at all — is -1.5 magnitudes wherever it is put.

The brightness distance cannot touch

Flux falls as the inverse square of distance and so does solid angle, so their ratio does not fall at all. A galaxy's surface brightness is the same number wherever it is put, which means whole populations can be undetectable at any distance whatever.

galaxies · Surface brightness

Named alongside it

The objects these essays reach for when they reach for this one.

Malmquist bias Mass-to-light ratio The baryonic Tully–Fisher relation Circular velocity Dark halo Dark matter Detection limit Distance indicator Enclosed mass Exponential disc Inclination correction Inverse square law

All concepts