Everything about The Cosmic Distance Ladder totally explained
The
cosmic distance ladder (also known as the
Extragalactic Distance Scale) is the succession of methods by which astronomers determine the
distances to celestial objects. A real
direct distance measurement to an astronomical object is only possible for those objects that are "close enough" (within about a thousand
parsecs) to earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances with methods that work at larger distances. The ladder analogy arises because no one technique can measure distances at all ranges encountered in astronomy. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung.
Direct methods of distance determination
At the base of the ladder are
fundamental distance measurements, in which distances are determined directly, with no physical assumptions about the nature of the object in question. These direct methods are:
The precise measurement of stellar positions is part of the discipline of
astrometry.
Parallax-based methods
The most important fundamental distance measurements come from
parallax. The Earth's motion around the sun causes small shifts in stellar positions. These shifts are angles in a right
triangle, with 1
AU making the short leg of the triangle and the distance to the star being the long leg. One
parsec is the distance of a star whose parallax is one
arc second. Astronomers usually express distances in units of parsecs;
light-years are used in popular media, but almost invariably values in light-years have been converted from numbers tabulated in parsecs in the original source.
Because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars whose parallax is larger than the
precision of the measurement. In the
1990s, the
Hipparcos mission obtained parallaxes for over a hundred thousand stars with a precision of about a
milliarcsecond, providing useful distances for stars out to a few hundred parsecs.
Another fundamental distance method is
statistical and secular parallax. This technique combines measurements of the motions and brightnesses of members of a selected, homogeneous group of stars in a statistical way to deduce an average distance to the group. It remains an important technique for the Cepheids and the
RR Lyrae variables.
Moving cluster parallax is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster. Only
open clusters are near enough for this technique to be useful. In particular the distance obtained for the
Hyades has been an important step in the distance ladder.
Other individual objects can have fundamental distance estimates made for them under special circumstances. If the expansion of a gas cloud, like a
supernova remnant or
planetary nebula, can be observed over time, then an
expansion parallax distance to that cloud can be estimated.
Binary stars which are both
visual and
spectroscopic binaries also can have their distance estimated by similar means. The common characteristic to these is that a measurement of angular motion is combined with a measurement of the absolute
velocity (usually obtained via the
Doppler effect). The distance estimate comes from computing how far away the object must be to make its observed absolute velocity appear with the observed angular motion.
Expansion parallaxes in particular can give fundamental distance estimates for objects that are very far away, because supernova ejecta have large expansion velocities and large sizes (compared to stars). Further, they can be observed with radio
interferometers which can measure very small angular motions. These combine to mean that some supernovae in other galaxies have fundamental distance estimates. Though valuable, such cases are quite rare, so they serve as important consistency checks on the distance ladder rather than workhorse steps by themselves.
Astronomical unit
The use of the parallax method usually requires
precise determination of the distance between the Earth and the Sun (the radius of the Earth's orbit), called the
Astronomical Unit (AU).
Other astronomical distance measures build outward from this.
Historically, observations of
transits of Venus were crucial in determining the AU; in the first half of the 20th Century, observations of
asteroids were also important. Presently the AU is determined with high precision using radar measurements of
Venus and other nearby planets and asteroids, and by tracking interplanetary
spacecraft in their orbits around the
Sun through the
Solar System.
Kepler's Laws provide precise
ratios of the sizes of the orbits of objects revolving around the Sun, but not a real measure of the orbits themselves. Radar provides a value in
kilometers for the difference in two orbits' sizes, and from that and the ratio of the two orbit sizes, the size of Earth's orbit comes directly.
Distance determination based on physical assumptions
Almost all of these physical distance indicators are
standard candles. These rely upon recognizing an object as belonging to some class, which has some known
absolute magnitude, measuring its
apparent magnitude, and using the
inverse square law to infer the distance needed to make the "candle" appear at its observed brightness. Some means of accounting for
interstellar extinction, which also makes objects appear fainter, is also needed. The difference between absolute and apparent magnitudes is called the
distance modulus, and astronomical distances, especially intergalactic ones, are sometimes tabulated in this way.
Physical distance indicators, used on progressively larger distance scales, include:
Dynamical parallax, using orbital parameters of visual binaries to measure the mass of the system and the mass-luminosity relation to determine the luminosity
Main sequence fitting, usually for open clusters of stars
Cepheids and novae
Individual galaxies in clusters of galaxies
The Tully-Fisher relation
Type Ia supernovae
Redshifts and Hubble's Law
Two problems exist for any class of standard candle. The principal one is calibration, determining exactly what the absolute magnitude of the candle is. This includes defining the class well enough that members can be recognized, and finding enough members with well-known distances that their true absolute magnitude can be determined with enough accuracy. The second lies in recognizing members of the class, and not mistakenly using the standard candle calibration upon an object which doesn't belong to the class. At extreme distances, which is where one most wishes to use a distance indicator, this recognition problem can be quite serious.
(Another class of physical distance indicator is the standard ruler, but few of these are used at this time.)
A succession of distance indicators, which is the distance ladder, is needed for determining distances to other galaxies. The reason is that objects bright enough to be recognized and measured at such distances are so rare that few or none are present nearby, so there are too few examples close enough with reliable trigonometric parallax to calibrate the indicator. For example, Cepheid variables, one of the best indicators for nearby spiral galaxies, can't be satisfactorily calibrated by parallax alone. The situation is further complicated by the fact that different stellar populations generally don't have all types of stars in them. Cepheids in particular are massive stars, with short lifetimes, so that'll only be found in places where stars have very recently been formed. Consequently, because elliptical galaxies usually have long ceased to have large-scale star formation, they won't have Cepheids. Instead, distance indicators whose origins are in an older stellar population (like novae and RR Lyrae variables) must be used. However, RR Lyrae variables are less luminous than Cepheids (so they can't be seen as far away as Cepheids can), and novae are unpredictable and an intensive monitoring program — and luck during that program — is needed to gather enough novae in the target galaxy for a good distance estimate.
Because the more distant steps of the cosmic distance ladder depend upon the nearer ones, the more distant steps include the effects of errors in the nearer steps, both systematic and statistical ones. The result of these propagating errors means that distances in astronomy are rarely known to the same level of precision as measurements in the other sciences, and that the precision necessarily is poorer for more distant types of object.
Another concern, especially for the very brightest standard candles, is their "standardness": how homogeneous the objects are in their true absolute magnitude. For some of these different standard candles, the homogeneity is based on theories about the formation and evolution of stars and galaxies, and is thus also subject to uncertainties in those aspects. For the most luminous of distance indicators, the Type Ia supernovae, this homogeneity is known to be poor; however, no other class of object is bright enough to be detected at such large distances, so the class is useful simply because there's no real alternative.
The observational result of Hubble's Law, the proportional relationship between distance and the speed with which a galaxy is moving away from us (usually referred to as redshift) is a product of the cosmic distance ladder. Hubble observed that fainter galaxies are more redshifted. Finding the value of the Hubble constant was the result of decades of work by many astronomers, both in amassing the measurements of galaxy redshifts and in calibrating the steps of the distance ladder. Hubble's Law is the primary means we've for estimating the distances of quasars and distant galaxies in which individual distance indicators can't be seen.
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