A photograph adds together many wavelengths
Imagine photographing the same galaxy through five colored windows. Each window lets through a different, overlapping range of wavelengths. The camera adds the photons that get through; it does not keep a little label saying which wavelength each photon had. Astronomers call such a window a filter. The result is five brightness measurements, a very compressed description of the incoming light.
The full distribution of light across wavelengths is its spectrum. Two spectra can produce nearly the same five measurements even when their fine details differ. This is why a beautiful color image can give a much less definite distance than a spectrum containing recognizable narrow lines. More detailed measurements cost observing time, especially for faint galaxies.
Reading: Doi et al. · Brammer
Expansion moves features; it does not paint everything red
As the universe expands, travelling light stretches to longer wavelengths. The redshift tells us the stretch factor. A feature emitted near four thousand Angstrom arrives near six thousand Angstrom when the redshift is one half. An Angstrom is one ten-billionth of a metre; visible light occupies several thousand of them.
Many galaxy spectra have a broad change in brightness near four thousand Angstrom. Numerous absorption lines in stellar atmospheres suppress the light on its blue side. As this change crosses a pair of filters, one filter begins to receive light from a different side of the feature. Their brightness ratio can change appreciably. The position of a recognizable change carries more distance information than the statement that the whole galaxy is red.
Reading: Hogg et al. · Bruzual & Charlot
Young stars behind dust can resemble old stars
Massive, hot stars shine strongly in blue light and use their fuel quickly. After a brief episode of star formation, these stars disappear first. Longer-lived stars then supply a redder mixture of light. Changing the mixture also changes the absorption features; the strength of the four-thousand-Angstrom break depends on the population and its chemical composition.
Dust offers another route. Small grains absorb and scatter light, generally reducing the short-wavelength signal more strongly. A young galaxy behind enough dust can have broad-band colors like those of an older, clearer galaxy. Dust changes the slope smoothly across these optical filters; redshift moves the features along the wavelength axis. Five broad measurements can blur that distinction.
The age of a real galaxy is also more complicated than one birthday. New stars may keep forming among old ones. A model in which all stars formed at once is useful for seeing how a spectrum changes with time, but its fitted age describes that model. A real age estimate therefore requires an explicit account of how stars formed over time.
Reading: Bruzual & Charlot · Calzetti et al.
Several distances can survive the same measurement
An astronomer tests many trial redshifts, stellar mixtures and dust amounts. Each trial predicts five filter brightnesses. Trials close to the measured values receive more weight, with the measurement errors setting how close is close enough. Adding the weights of the different stellar and dust explanations produces a probability distribution over redshift.
Sometimes this distribution has two separated hills. One hill may describe an older nearby population; another may move a different spectral shape farther away. Reporting only the tallest hill hides the other explanation. A small calibration change can even swap which hill is tallest, although the measurements have changed very little.
A useful extra filter measures the wavelengths where the competing spectra disagree. A spectrum can identify individual lines and settle the distance more directly. The task is to find the next observation that separates the surviving explanations. That is how a set of colored pictures begins to become a map with depth.
Reading: Brammer · SDSS DR17 imaging fluxes and flux calibration