Cosmic distance ladder
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The cosmic distance ladder refers to the methods by which astronomers determine the distances to celestial objects. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung.
Many of the rungs involve standard candles — objects whose intrinsic brightness is known. By comparing the intrinsic brightness with the apparent brightness, one can derive a distance.
At the base of the ladder are radar observations of Venus and other planets, which allow one to determine the distance between them and the Earth, and by extension, the size of the Earth's orbit.
Some of the succeeding rungs are:
- Parallax
- main sequence fitting
- Cepheid variables
- Type Ia Supernovae or the Tully-Fisher relation
- Redshifts
The field of astronomy which measures distances is known as astrometry. Astrometry has been greatly enhanced with the launch of space-based observatories such as Hipparcos, which can make extremely precise measurements that serve to strengthen the links between the different rungs in the cosmic distance ladder.
How it works
note: section needs review by a professional!
As an example of how the ladder-principle works, consider the distance attributed to a quasar, say, "9 billion lightyears". This figure was arrived at in one single step: the amount of redshift in the quasar's spectrum was measured, and directly translated to a distance figure.
In reality, there is actually no direct way to establish this particular relationship. Instead, the conversion depends on a chain of means to determine relative distances between objects. Whenever these relative methods overlap, they can be used to put the complete chain together.
A real direct distance-measurement to an astronomical object is only possible on a relatively small scale (in astronomical terms). Reflection of laserbeams can be used to measure the distance to the moon, reflection of radar to measure the distance to the nearest planet (Venus). The latter measurement serves as the basis for the parallax-based trigonometric method which allows for a direct determination of the distance to stars in the neighborhood of our sun. Beyond a certain scale, parallax will no longer be meaningful and relative methods are used instead.
Relative methods (have to) depend on the only type of information that we get from distant objects: the emitted light. This can be quantitative information (apparent brightness) or qualitative (redshift in the spectrum). The former is typically useful for middle-distance, the latter for distances on a cosmological scale. The general idea is that methods which are used on the higher end of the scale, are calibrated using the methods that serve for the lower end of the scale. Ultimately, the direct method of parallax is used to calibrate the first relative method.
The method based on brightness depends on the simple relationship between absolute and apparent brightness of similar objects observed from different distances. This is the already mentioned standard candle method. When you put a lightsource twice as far, its apparent brightness will only be one quarter of the absolute. Turning this around, you can get a relative distance by measuring the brightness. Note that this will only be true if the objects do actually have the same luminosity, and in the assumption that there are no substances between observer and object which significantly interfere. Another way to put it, is that the accuracy of these type of relationships depends on how sure we are of the similarity of the objects and interstellar space. In general, the accuracy also lowers with increasing distance. This is because less light is available, because there is more uncertainty about the opacity of space alongside the path of the light, and because brighter objects (which can thus be observed over greater distances) are simply less common. At the very high end of the scale, only entire galaxies (with all associated uncertainties as to their "similarity")can thus be used as standard candles. Just below that are certain types of the very luminous supernovas, and at the lower end of the scale variable stars like cepheids, and regular stars based on their position in the main sequence.
The confidence in the "standardness" of these different standard candles is based on theories about the formation and evolution of stars and galaxies, and is thus also subject to uncertainties in those aspects. As always, the more common objects are also more likely to be available nearby. Thus, especially the confidence in the reliability of the main sequence theory is reinforced by calibration via the direct parallax method. Something which is more difficult or impossible for cepheids, supernovas and galaxies since they are too rare and/or too far away.
To summarize: the distance of the quasar was based on the amount of redshift in the spectrum. On the lower end, the redshift-method was calibrated by using entire galaxies and Type Ia supernovas as standard candles. This, in turn, was calibrated by cepheids, and main sequence on the lower end. At the very basis of the distance ladder, finally, we find parallax measurements of sufficient amounts of variable and main sequence-stars.
It is thus clear that possible inaccuracies will pile up, and that a reliable determination of distances at the lowest rung of the ladder is very important.