The Distance Ladder

The elliptical-galaxy counterpart of the Tully–Fisher relation: a link between a galaxy's luminosity and the velocity dispersion of its stars. It is one projection of the tighter Fundamental Plane of elliptical galaxies, which is used as a distance indicator.

Old, pulsating horizontal-branch stars with a well-defined luminosity, especially tight when measured in the infrared. Abundant in globular clusters and the haloes of galaxies, they are a standard candle for old stellar populations and, like the Cepheids, are calibrated directly by parallax.

Gravitational-wave sources whose distance can be read directly from the shape of the waveform, with no calibration ladder at all — the gravitational analogue of a standard candle. A merging neutron-star pair with an electromagnetic counterpart yielded the first standard-siren measurement of the Hubble constant.

A distance method that uses the graininess of a galaxy's light: because a nearer galaxy resolves into fewer, brighter patches of unresolved stars per pixel, the amount of pixel-to-pixel fluctuation measures distance. Best suited to smooth elliptical galaxies and the bulges of spirals.

The sharp, near-constant peak brightness that red giant stars reach just before the helium flash — a robust standard candle that can be measured in a galaxy's halo, away from crowding and dust. It provides an independent route to calibrating Type Ia supernovae, and its Hubble-constant value sits between the Cepheid and CMB results.

An empirical relation for spiral galaxies between how fast they rotate and how luminous they are — the faster the rotation, the brighter the galaxy. Measuring the rotation (from the width of the 21-cm line) then gives the luminosity, and comparing with the apparent brightness gives the distance.

A direct, geometric distance measured from water masers orbiting in the accretion disc around a galaxy's central black hole. By tracking their motion and acceleration, the physical size of the disc is found and compared with its angular size — a one-step distance that anchors the ladder without relying on standard candles.