What Is a Standard Candle? Objects of Known Brightness Used as Rulers
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If you know how bright something really is, comparing that with how bright it looks gives its distance. Finding objects whose true brightness can be established is the whole problem, and the ones that work carry the entire scale of the universe.
The principle
Light spreads out as it travels, so the apparent brightness of a source falls off with the square of the distance, which means that a source of known intrinsic output has a distance that follows directly from how bright it appears. That relationship is simple and the difficulty lies entirely in establishing the intrinsic output, since nothing announces how bright it really is. The solution is to find classes of object whose intrinsic brightness can be determined from something else about them, either because all members of the class are essentially identical or because an observable property correlates with the output. Corrections are then needed for anything that dims the light on the way, particularly dust, and for the expansion of the universe at large distances, both of which introduce their own uncertainties.
The objects that work
A small number of classes carry most of the distance scale:
- •Cepheid variable stars, which pulsate with a period that correlates tightly with their intrinsic brightness, discovered in the early twentieth century
- •RR Lyrae variables, similar in principle, fainter and useful in older stellar populations
- •Type Ia supernovae, exploding white dwarfs whose peak brightness is nearly uniform after a correction, visible across enormous distances
- •The brightest stars in a galaxy, and the tip of a particular branch on the brightness and colour diagram, both used as secondary indicators
- •Certain relationships between a galaxy's rotation or velocity spread and its total output
- •Each works over a limited range, which is why they must be chained together
The distance ladder
No single method covers the whole range, so distances are built up in steps with each calibrating the next, which is why the arrangement is called a ladder. The bottom rung is geometry, measuring the apparent shift of nearby stars as the Earth moves around the sun, which requires no assumptions and reaches a limited distance. Those stars calibrate the pulsating variables, which reach nearby galaxies. Those galaxies calibrate the supernovae, which reach across the observable universe. The structure is powerful and fragile, since an error at any rung propagates to everything above it, and a great deal of careful work goes into the calibration steps for exactly that reason. Independent methods that bypass rungs, including gravitational wave events that supply a distance directly, are valuable precisely because they test the chain rather than extending it.
The woman who found the first rung
The relationship that made the ladder possible was established by Henrietta Swan Leavitt, working at Harvard Observatory in the early twentieth century among a group of women employed to measure and catalogue photographic plates at low pay and without the authority to direct their own research. Examining variable stars in a nearby satellite galaxy, where all the stars are at effectively the same distance, she found that the brighter ones pulsated more slowly and that the relationship was tight enough to be useful. Because the distance was common to all of them, apparent brightness stood in for intrinsic brightness and the relation could be established without knowing any distance at all. That single result made it possible to measure distances to other galaxies, which led directly to the demonstration that the universe extends far beyond our own galaxy and that it is expanding.
The disagreement
The current state of the field includes a genuine and unresolved discrepancy that these methods produced. Measurements of the expansion rate of the universe made by climbing the distance ladder give one value, and measurements inferred from the radiation left over from the early universe give a noticeably different value, and the gap is larger than either method's stated uncertainty. That disagreement has persisted and sharpened as both measurements improved, which is the opposite of what would happen if it were a simple error, and it has become one of the central problems in cosmology. Possible resolutions include an unrecognised systematic error in one method, an unrecognised error in the other, or genuinely new physics affecting the early universe. The situation is a good illustration of measurement precision creating a problem rather than resolving one.
The takeaway
Apparent brightness falls with the square of distance, so knowing the true output gives the distance, and establishing that output is the entire difficulty. Pulsating variables with period-brightness relations and exploding white dwarfs of nearly uniform peak brightness do most of the work. Each covers a limited range, so distances are chained, and an error at one rung propagates to everything above.