Cosmic distance ladder

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 of an astronomical object is possible only 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 and methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity.

The ladder analogy arises because no single 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.

Extragalactic distance ladder

Direct measurement

The Astonomer
Statue of an astronomer and the concept of the cosmic distance ladder by the parallax method, made from the azimuth ring and other parts of the Yale–Columbia Refractor (telescope) (c 1925) wrecked by the 2003 Canberra bushfires which burned out the Mount Stromlo Observatory; at Questacon, Canberra, Australian Capital Territory.

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. The precise measurement of stellar positions is part of the discipline of astrometry.

Astronomical unit

Direct distance measurements are based upon the astronomical unit (AU), which is the distance between the Earth and the Sun. Kepler's laws provide precise ratios of the sizes of the orbits of objects orbiting the Sun, but provides no measurement of the overall scale of the orbit system. Radar is used to measure the distance between the orbits of the Earth and of a second body. From that measurement and the ratio of the two orbit sizes, the size of Earth's orbit is calculated. The Earth's orbit is known with an absolute precision of a few meters and a relative precision of a few 1×10−11.

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 orbit of Earth is determined with high precision using radar measurements of distances to Venus and other nearby planets and asteroids,[1] and by tracking interplanetary spacecraft in their orbits around the Sun through the Solar System.


Stellar parallax motion from annual parallax. Half the apex angle is the parallax angle.

The most important fundamental distance measurements come from trigonometric parallax. As the Earth orbits the Sun, the position of nearby stars will appear to shift slightly against the more distant background. These shifts are angles in an isosceles triangle, with 2 AU (the distance between the extreme positions of Earth's orbit around the Sun) making the base leg of the triangle and the distance to the star being the long equal length legs. The amount of shift is quite small, measuring 1 arcsecond for an object at 1 parsec's distance (3.26 light-years) of the nearest stars, and thereafter decreasing in angular amount as the distance increases. Astronomers usually express distances in units of parsecs (parallax arcseconds); light-years are used in popular media.

Because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars which are near enough to have a parallax larger than a few times the precision of the measurement. Parallax measurements typically have an accuracy measured in milliarcseconds.[2] In the 1990s, for example, the Hipparcos mission obtained parallaxes for over a hundred thousand stars with a precision of about a milliarcsecond,[3] providing useful distances for stars out to a few hundred parsecs. The Hubble telescope WFC3 now has the potential to provide a precision of 20 to 40 microarcseconds, enabling reliable distance measurements up to 5,000 parsecs (16,000 ly) for small numbers of stars.[4][5] In 2018, Data Release 2 from the Gaia space mission provides similarly accurate distances to most stars brighter than 15th magnitude.[6]

Stars have a velocity relative to the Sun that causes proper motion (transverse across the sky) and radial velocity (motion toward or away from the Sun). The former is determined by plotting the changing position of the stars over many years, while the latter comes from measuring the Doppler shift of the star's spectrum caused by motion along the line of sight. For a group of stars with the same spectral class and a similar magnitude range, a mean parallax can be derived from statistical analysis of the proper motions relative to their radial velocities. This statistical parallax method is useful for measuring the distances of bright stars beyond 50 parsecs and giant variable stars, including Cepheids and the RR Lyrae variables.[7]

Cosmic distance ladder
Parallax measurements may be an important clue to understanding three of the universe's most elusive components: dark matter, dark energy and neutrinos.[8]
Hubble stretches the stellar tape measure ten times further
Hubble precision stellar distance measurement has been extended 10 times further into the Milky Way.[9]

The motion of the Sun through space provides a longer baseline that will increase the accuracy of parallax measurements, known as secular parallax. For stars in the Milky Way disk, this corresponds to a mean baseline of 4 AU per year, while for halo stars the baseline is 40 AU per year. After several decades, the baseline can be orders of magnitude greater than the Earth–Sun baseline used for traditional parallax. However, secular parallax introduces a higher level of uncertainty because the relative velocity of observed stars is an additional unknown. When applied to samples of multiple stars, the uncertainty can be reduced; the uncertainty is inversely proportional to the square root of the sample size.[10]

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 historically 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. Those measurements however suffer from uncertainties in the deviation of the object from sphericity. Binary stars which are both visual and spectroscopic binaries also can have their distance estimated by similar means, and don't suffer from the above geometric uncertainty. The common characteristic to these methods 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 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, 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 provide fundamental distance estimates to supernovae in other galaxies.[11] Though valuable, such cases are quite rare, so they serve as important consistency checks on the distance ladder rather than workhorse steps by themselves.

Standard candles

Almost all astronomical objects used as physical distance indicators belong to a class that has a known brightness. By comparing this known luminosity to an object's observed brightness, the distance to the object can be computed using the inverse-square law. These objects of known brightness are termed standard candles, coined by Henrietta Swan Leavitt.[12]

The brightness of an object can be expressed in terms of its absolute magnitude. This quantity is derived from the logarithm of its luminosity as seen from a distance of 10 parsecs. The apparent magnitude, the magnitude as seen by the observer (an instrument called a bolometer is used), can be measured and used with the absolute magnitude to calculate the distance D to the object in kiloparsecs (where 1 kpc equals 1000 parsecs) as follows:


where m is the apparent magnitude and M the absolute magnitude. For this to be accurate, both magnitudes must be in the same frequency band and there can be no relative motion in the radial direction.

Some means of correcting for interstellar extinction, which also makes objects appear fainter and more red, is needed, especially if the object lies within a dusty or gaseous region.[13] The difference between an object's absolute and apparent magnitudes is called its distance modulus, and astronomical distances, especially intergalactic ones, are sometimes tabulated in this way.


Two problems exist for any class of standard candle. The principal one is calibration, that is the determination of 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 of that class with well-known distances to allow their true absolute magnitude to be determined with enough accuracy. The second problem lies in recognizing members of the class, and not mistakenly using a standard candle calibration on an object which does not 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.

A significant issue with standard candles is the recurring question of how standard they are. For example, all observations seem to indicate that Type Ia supernovae that are of known distance have the same brightness (corrected by the shape of the light curve). The basis for this closeness in brightness is discussed below; however, the possibility exists that the distant Type Ia supernovae have different properties than nearby Type Ia supernovae. The use of Type Ia supernovae is crucial in determining the correct cosmological model. If indeed the properties of Type Ia supernovae are different at large distances, i.e. if the extrapolation of their calibration to arbitrary distances is not valid, ignoring this variation can dangerously bias the reconstruction of the cosmological parameters, in particular the reconstruction of the matter density parameter.[14]

That this is not merely a philosophical issue can be seen from the history of distance measurements using Cepheid variables. In the 1950s, Walter Baade discovered that the nearby Cepheid variables used to calibrate the standard candle were of a different type than the ones used to measure distances to nearby galaxies. The nearby Cepheid variables were population I stars with much higher metal content than the distant population II stars. As a result, the population II stars were actually much brighter than believed, and when corrected, this had the effect of doubling the distances to the globular clusters, the nearby galaxies, and the diameter of the Milky Way.

Standard siren

Gravitational waves originating from the inspiral phase of compact binary systems, such as neutron stars or black holes, have the useful property that both the amplitude and shape of the emitted gravitational radiation depend strongly on the chirp mass of the system. By observing the waveform, the chirp mass can be computed. With the chirp mass and the measured amplitude, distance to the source can be determined. Further, gravitational waves are not subject to extinction due to an absorbing intervening medium. (They are subject to gravitational lensing, however.) Thus, such a gravitational wave source is a "standard siren" of known loudness.[15]

The amplitude and shape of the detected gravitational radiation allows the distance to be computed. Therefore, a standard siren can be used as a distance indicator on a cosmic scale. When the collision can be observed optically as well (in the case of a kilonova such as GW170817), the Doppler shift can be measured and the Hubble constant computed.[16][17]

Standard ruler

Another class of physical distance indicator is the standard ruler. In 2008, galaxy diameters have been proposed as a possible standard ruler for cosmological parameter determination.[18] More recently the physical scale imprinted by baryon acoustic oscillations (BAO) in the early universe has been used. In the early universe (before recombination) the baryons and photons scatter off each other, and form a tightly-coupled fluid that can support sound waves. The waves are sourced by primordial density perturbations, and travel at speed that can be predicted from the baryon density and other cosmological parameters. The total distance that these sound waves can travel before recombination determines a fixed scale, which simply expands with the universe after recombination. BAO therefore provide a standard ruler that can be measured in galaxy surveys from the effect of baryons on the clustering of galaxies. The method requires an extensive galaxy survey in order to make this scale visible, but has been measured with percent-level precision (see baryon acoustic oscillations). The scale does depend on cosmological parameters like the baryon and matter densities, and the number of neutrinos, so distances based on BAO are more dependent on cosmological model than those based on local measurements.

Light echos can be also used as standard rulers,[19][20] although it is challenging to correctly measure the source geometry.[21][22]

Galactic distance indicators

With few exceptions, distances based on direct measurements are available only out to about a thousand parsecs, which is a modest portion of our own Galaxy. For distances beyond that, measures depend upon physical assumptions, that is, the assertion that one recognizes the object in question, and the class of objects is homogeneous enough that its members can be used for meaningful estimation of distance.

Physical distance indicators, used on progressively larger distance scales, include:

Main sequence fitting

When the absolute magnitude for a group of stars is plotted against the spectral classification of the star, in a Hertzsprung–Russell diagram, evolutionary patterns are found that relate to the mass, age and composition of the star. In particular, during their hydrogen burning period, stars lie along a curve in the diagram called the main sequence. By measuring these properties from a star's spectrum, the position of a main sequence star on the H–R diagram can be determined, and thereby the star's absolute magnitude estimated. A comparison of this value with the apparent magnitude allows the approximate distance to be determined, after correcting for interstellar extinction of the luminosity because of gas and dust.

In a gravitationally-bound star cluster such as the Hyades, the stars formed at approximately the same age and lie at the same distance. This allows relatively accurate main sequence fitting, providing both age and distance determination.

Extragalactic distance scale

Extragalactic distance indicators[26]
Method Uncertainty for Single Galaxy (mag) Distance to Virgo Cluster (Mpc) Range (Mpc)
Classical Cepheids 0.16 15–25 29
Novae 0.4 21.1 ± 3.9 20
Planetary Nebula Luminosity Function 0.3 15.4 ± 1.1 50
Globular Cluster Luminosity Function 0.4 18.8 ± 3.8 50
Surface Brightness Fluctuations 0.3 15.9 ± 0.9 50
D–σ relation 0.5 16.8 ± 2.4 > 100
Type Ia Supernovae 0.10 19.4 ± 5.0 > 1000

The extragalactic distance scale is a series of techniques used today by astronomers to determine the distance of cosmological bodies beyond our own galaxy, which are not easily obtained with traditional methods. Some procedures utilize properties of these objects, such as stars, globular clusters, nebulae, and galaxies as a whole. Other methods are based more on the statistics and probabilities of things such as entire galaxy clusters.

Wilson–Bappu effect

Discovered in 1956 by Olin Wilson and M.K. Vainu Bappu, the Wilson–Bappu effect utilizes the effect known as spectroscopic parallax. Many stars have features in their spectra, such as the calcium K-line, that indicate their absolute magnitude. The distance to the star can then be calculated from its apparent magnitude using the distance modulus.

There are major limitations to this method for finding stellar distances. The calibration of the spectral line strengths has limited accuracy and it requires a correction for interstellar extinction. Though in theory this method has the ability to provide reliable distance calculations to stars up to 7 megaparsecs (Mpc), it is generally only used for stars at hundreds of kiloparsecs (kpc).

Classical Cepheids

Beyond the reach of the Wilson–Bappu effect, the next method relies on the period-luminosity relation of classical Cepheid variable stars. The following relation can be used to calculate the distance to Galactic and extragalactic classical Cepheids:


Several problems complicate the use of Cepheids as standard candles and are actively debated, chief among them are: the nature and linearity of the period-luminosity relation in various passbands and the impact of metallicity on both the zero-point and slope of those relations, and the effects of photometric contamination (blending) and a changing (typically unknown) extinction law on Cepheid distances.[29][30][31][32][33][34][35][36][37]

These unresolved matters have resulted in cited values for the Hubble constant ranging between 60 km/s/Mpc and 80 km/s/Mpc. Resolving this discrepancy is one of the foremost problems in astronomy since some cosmological parameters of the Universe may be constrained significantly better by supplying a precise value of the Hubble constant.[38][39]

Cepheid variable stars were the key instrument in Edwin Hubble's 1923 conclusion that M31 (Andromeda) was an external galaxy, as opposed to a smaller nebula within the Milky Way. He was able to calculate the distance of M31 to 285 Kpc, today's value being 770 Kpc.

As detected thus far, NGC 3370, a spiral galaxy in the constellation Leo, contains the farthest Cepheids yet found at a distance of 29 Mpc. Cepheid variable stars are in no way perfect distance markers: at nearby galaxies they have an error of about 7% and up to a 15% error for the most distant.


SN 1994D (bright spot on the lower left) in the NGC 4526 galaxy. Image by NASA, ESA, The Hubble Key Project Team, and The High-Z Supernova Search Team

There are several different methods for which supernovae can be used to measure extragalactic distances.

Measuring a supernova's photosphere

We can assume that a supernova expands in a spherically symmetric manner. If the supernova is close enough such that we can measure the angular extent, θ(t), of its photosphere, we can use the equation

where ω is angular velocity, θ is angular extent. In order to get an accurate measurement, it is necessary to make two observations separated by time Δt. Subsequently, we can use

where d is the distance to the supernova, Vej is the supernova's ejecta's radial velocity (it can be assumed that Vej equals Vθ if spherically symmetric).

This method works only if the supernova is close enough to be able to measure accurately the photosphere. Similarly, the expanding shell of gas is in fact not perfectly spherical nor a perfect blackbody. Also interstellar extinction can hinder the accurate measurements of the photosphere. This problem is further exacerbated by core-collapse supernova. All of these factors contribute to the distance error of up to 25%.

Type Ia light curves

Type Ia supernovae are some of the best ways to determine extragalactic distances. Ia's occur when a binary white dwarf star begins to accrete matter from its companion star. As the white dwarf gains matter, eventually it reaches its Chandrasekhar limit of .

Once reached, the star becomes unstable and undergoes a runaway nuclear fusion reaction. Because all Type Ia supernovae explode at about the same mass, their absolute magnitudes are all the same. This makes them very useful as standard candles. All Type Ia supernovae have a standard blue and visual magnitude of

Therefore, when observing a Type Ia supernova, if it is possible to determine what its peak magnitude was, then its distance can be calculated. It is not intrinsically necessary to capture the supernova directly at its peak magnitude; using the multicolor light curve shape method (MLCS), the shape of the light curve (taken at any reasonable time after the initial explosion) is compared to a family of parameterized curves that will determine the absolute magnitude at the maximum brightness. This method also takes into effect interstellar extinction/dimming from dust and gas.

Similarly, the stretch method fits the particular supernovae magnitude light curves to a template light curve. This template, as opposed to being several light curves at different wavelengths (MLCS) is just a single light curve that has been stretched (or compressed) in time. By using this Stretch Factor, the peak magnitude can be determined.

Using Type Ia supernovae is one of the most accurate methods, particularly since supernova explosions can be visible at great distances (their luminosities rival that of the galaxy in which they are situated), much farther than Cepheid Variables (500 times farther). Much time has been devoted to the refining of this method. The current uncertainty approaches a mere 5%, corresponding to an uncertainty of just 0.1 magnitudes.

Novae in distance determinations

Novae can be used in much the same way as supernovae to derive extragalactic distances. There is a direct relation between a nova's max magnitude and the time for its visible light to decline by two magnitudes. This relation is shown to be:

Where is the time derivative of the nova's mag, describing the average rate of decline over the first 2 magnitudes.

After novae fade, they are about as bright as the most luminous Cepheid variable stars, therefore both these techniques have about the same max distance: ~ 20 Mpc. The error in this method produces an uncertainty in magnitude of about ±0.4

Globular cluster luminosity function

Based on the method of comparing the luminosities of globular clusters (located in galactic halos) from distant galaxies to that of the Virgo Cluster, the globular cluster luminosity function carries an uncertainty of distance of about 20% (or 0.4 magnitudes).

US astronomer William Alvin Baum first attempted to use globular clusters to measure distant elliptical galaxies. He compared the brightest globular clusters in Virgo A galaxy with those in Andromeda, assuming the luminosities of the clusters were the same in both. Knowing the distance to Andromeda, Baum has assumed a direct correlation and estimated Virgo A's distance.

Baum used just a single globular cluster, but individual formations are often poor standard candles. Canadian astronomer René Racine assumed the use of the globular cluster luminosity function (GCLF) would lead to a better approximation. The number of globular clusters as a function of magnitude is given by:

where m0 is the turnover magnitude, M0 is the magnitude of the Virgo cluster, and sigma is the dispersion ~ 1.4 mag.

It is important to remember that it is assumed that globular clusters all have roughly the same luminosities within the universe. There is no universal globular cluster luminosity function that applies to all galaxies.

Planetary nebula luminosity function

Like the GCLF method, a similar numerical analysis can be used for planetary nebulae (note the use of more than one!) within far off galaxies. The planetary nebula luminosity function (PNLF) was first proposed in the late 1970s by Holland Cole and David Jenner. They suggested that all planetary nebulae might all have similar maximum intrinsic brightness, now calculated to be M = −4.53. This would therefore make them potential standard candles for determining extragalactic distances.

Astronomer George Howard Jacoby and his colleagues later proposed that the PNLF function equaled:

Where N(M) is number of planetary nebula, having absolute magnitude M. M* is equal to the nebula with the brightest magnitude.

Surface brightness fluctuation method

Galaxy cluster Abell 2218 gravitaitonal lens
Galaxy cluster

The following method deals with the overall inherent properties of galaxies. These methods, though with varying error percentages, have the ability to make distance estimates beyond 100 Mpc, though it is usually applied more locally.

The surface brightness fluctuation (SBF) method takes advantage of the use of CCD cameras on telescopes. Because of spatial fluctuations in a galaxy's surface brightness, some pixels on these cameras will pick up more stars than others. However, as distance increases the picture will become increasingly smoother. Analysis of this describes a magnitude of the pixel-to-pixel variation, which is directly related to a galaxy's distance.

D–σ relation

The D–σ relation, used in elliptical galaxies, relates the angular diameter (D) of the galaxy to its velocity dispersion. It is important to describe exactly what D represents, in order to understand this method. It is, more precisely, the galaxy's angular diameter out to the surface brightness level of 20.75 B-mag arcsec−2. This surface brightness is independent of the galaxy's actual distance from us. Instead, D is inversely proportional to the galaxy's distance, represented as d. Thus, this relation does not employ standard candles. Rather, D provides a standard ruler. This relation between D and σ is

Where C is a constant which depends on the distance to the galaxy clusters.

This method has the potential to become one of the strongest methods of galactic distance calculators, perhaps exceeding the range of even the Tully–Fisher method. As of today, however, elliptical galaxies aren't bright enough to provide a calibration for this method through the use of techniques such as Cepheids. Instead, calibration is done using more crude methods.

Overlap and scaling

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, cannot yet be satisfactorily calibrated by parallax alone, though the Gaia space mission is expected to solve that specific problem. The situation is further complicated by the fact that different stellar populations generally do not have all types of stars in them. Cepheids in particular are massive stars, with short lifetimes, so they will 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 will not 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, 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[40]; however, no other class of object is bright enough to be detected at such large distances, so the class is useful simply because there is 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. Edwin 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 have for estimating the distances of quasars and distant galaxies in which individual distance indicators cannot be seen.

See also


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  • An Introduction to Modern Astrophysics, Carroll and Ostlie, copyright 2007.
  • Measuring the Universe The Cosmological Distance Ladder, Stephen Webb, copyright 2001.
  • Pasachoff, JM & Filippenko, AV, The Cosmos: Astronomy in the New Millennium, Cambridge: Cambridge University Press, 4th edition, 2013 ISBN 9781107687561.
  • The Astrophysical Journal, The Globular Cluster Luminosity Function as a Distance Indicator: Dynamical Effects, Ostriker and Gnedin, May 5, 1997.
  • An Introduction to Distance Measurement in Astronomy, Richard de Grijs, Chichester: John Wiley & Sons, 2011, ISBN 978-0-470-51180-0.

External links

Alpha Persei Cluster

The Alpha Persei Cluster, also known as Melotte 20 or Collinder 39, is an open cluster in the constellation of Perseus. To the naked eye, the cluster consists of several blue spectral type B type stars. The most luminous member is the ~2nd magnitude white-yellow supergiant Mirfak, also known as Alpha Persei. Bright members also include Delta, Sigma, Psi, 29, 30, 34 and 48 Persei. The Hipparcos satellite and infrared color-magnitude diagram fitting have been used to establish a distance to the cluster of ~172 pc. The distance established via the independent analyses agree, thereby making the cluster an important rung on the cosmic distance ladder. The age of this cluster is about 50-70 million years.

Coma Star Cluster

The Coma Star Cluster in Coma Berenices, designated Melotte 111 after its entry in the catalogue of star clusters by P. J. Melotte, is a small but nearby star cluster in our galaxy, containing about 40 brighter stars (magnitude 5 to 10) with a common proper motion. The Hipparcos satellite and infrared color-magnitude diagram fitting have been used to establish a distance to the cluster's center of approximately 86 parsecs (280 ly). The distance established via the independent analyses agree, thereby making the cluster an important rung on the cosmic distance ladder. The open cluster is roughly twice as distant as the Hyades and covers an area of more than 7.5 degrees on the sky. The cluster is approximately 450 million years old. In the FOV of a good field glass most of its stars can be seen simultaneously. The brighter stars of the cluster make out a distinctive "V" shape as seen when Coma Berenices is rising.

It used to represent Leo's tail, but Ptolemy III, in around 240 BC, renamed it for the Egyptian queen Berenice's sacrifice of her hair in a legend.

David J. Lane (astronomer)

David J. Lane (born 1963) is a Canadian astronomer at Saint Mary's University, the past president of the Royal Astronomical Society of Canada, director of the Burke-Gaffney astronomical observatory, owner of the Abbey-Ridge Observatory, and creator of the planetarium software entitled the Earth Centered Universe. Asteroid 117032 Davidlane is named in his honour, and the asteroid lies in the main asteroid belt between Mars and Jupiter.

Lane created the first software that enables Twitter users to request images of the Universe from an astronomical observatory (i.e., the Burke-Gaffney Observatory). The impetus is to foster awareness of the Universe by enabling citizens to readily access an observatory using social media, a project that has been heralded as an important innovation by international media.Lane, and fellow Canadian astronomer Paul Gray, discovered supernovas 1995F in NGC 2726, SN 2005B in UGC 11066, and 2005ea in MCG+10-16-61. Kathryn Aurora Gray examined images acquired by Lane via his Abbey-Ridge Observatory and discovered a supernova in UGC 3378 (SN 2010lt). Kathryn subsequently became the youngest person to have discovered a supernova.Lane was a featured guest on comet hunter David H. Levy's internet radio show: Let's Talk Stars.Observations from Lane's astronomical observatory have also been used to improve the cosmic distance ladder.


Dimensionaut is the debut (and as of 2018 only) album by British-based band Sound of Contact, and was released worldwide May 2013. Production of the album was a collaborative effort between Simon Collins and Dave Kerzner, two of the band's founding members. As of March 2014, two singles off the album have been released.Dimensionaut was mixed by veteran sound engineer Nick Davis, known for working with Genesis.

Full-sky Astrometric Mapping Explorer

Full-sky Astrometric Mapping Explorer (or FAME) was a proposed astrometric satellite designed to determine with unprecedented accuracy the positions, distances, and motions of 40 million stars within our galactic neighborhood (distances by stellar parallax possible). This database was to allow astronomers to accurately determine the distance to all of the stars on this side of the Milky Way galaxy, detect large planets and planetary systems around stars within 1,000 light years of the Sun, and measure the amount of dark matter in the galaxy from its influence on stellar motions. It was to be a collaborative effort between the United States Naval Observatory (USNO) and several other institutions. FAME would have measured stellar positions to less than 50 microarcseconds. The NASA MIDEX mission was scheduled for launch in 2004. In January 2002, however, NASA abruptly cancelled this mission, mainly due to concerns about its price tag which grew from $160 million to $220 million.

This would have been an improvement over the High Precision Parallax Collecting Satellite (Hipparcos) which operated 1989-1993 and produced various star catalogs. Astrometric parallax measurements form part of the cosmic distance ladder, and can also be measured by other Space telescopes such as Hubble (HST) or ground-based telescopes to varying degrees of precision.

Compared to the FAME accuracy of 50 microarcseconds, the Gaia mission is planning 10 microarcseconds accuracy, for mapping stellar parallax up to a distance of tens of thousands of light-years from Earth.

Length measurement

Length measurement is implemented in practice in many ways. The most commonly used approaches are the transit-time methods and the interferometer methods based upon the speed of light. For objects such as crystals and diffraction gratings, diffraction is used with X-rays and electron beams. Measurement techniques for three-dimensional structures very small in every dimension use specialized instruments such as ion microscopy coupled with intensive computer modeling.

For a discussion of astronomical methods for determining cosmological distances, see the article Cosmic distance ladder.

Messier 106

Messier 106 (also known as NGC 4258) is an intermediate spiral galaxy in the constellation Canes Venatici. It was discovered by Pierre Méchain in 1781. M106 is at a distance of about 22 to 25 million light-years away from Earth. M106 contains an active nucleus classified as a Type 2 Seyfert, and the presence of a central supermassive black hole has been demonstrated from radio-wavelength observations of the rotation of a disk of molecular gas orbiting within the inner light-year around the black hole. NGC 4217 is a possible companion galaxy of Messier 106. A Type II supernova was observed in M106 in May 2014.

Neutron star merger

A neutron star merger is a type of stellar collision. It occurs in a fashion similar to the rare brand of type Ia supernovae resulting from merging white dwarfs. When two neutron stars orbit each other closely, they spiral inward as time passes due to gravitational radiation. When the two neutron stars meet, their merger leads to the formation of either a more massive neutron star, or a black hole (depending on whether the mass of the remnant exceeds the currently poorly known Tolman–Oppenheimer–Volkoff limit). The merger can also create a magnetic field that is trillions of times stronger than that of Earth in a matter of one or two milliseconds. These events are believed to create short gamma-ray bursts. The mergers are also believed to produce kilonovae, which are transient sources of fairly isotropic longer wave electromagnetic radiation due to the radioactive decay of heavy r-process nuclei that are produced and ejected during the merger process.In October 2018, astronomers reported that GRB 150101B, a gamma-ray burst event detected in 2015, may be directly related to the historic GW170817, a gravitational wave event detected in 2017, and associated with the merger of two neutron stars. The similarities between the two events, in terms of gamma ray, optical and x-ray emissions, as well as to the nature of the associated host galaxies, are "striking", suggesting the two separate events may both be the result of the merger of neutron stars, and both may be a kilonova, which may be more common in the universe than previously understood, according to the researchers.Also in October 2018, scientists presented a new third way (two earlier methods, one based on redshifts and another on the cosmic distance ladder, gave results that do not agree), using information from gravitational wave events (especially those involving the merger of neutron stars, like GW170817), of determining the Hubble Constant, essential in establishing the rate of expansion of the universe.

Observational cosmology

Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors.


Parallax (from Ancient Greek παράλλαξις (parallaxis), meaning 'alternation') is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects when observed from different positions, so parallax can be used to determine distances.

To measure large distances, such as the distance of a planet or a star from Earth, astronomers use the principle of parallax. Here, the term parallax is the semi-angle of inclination between two sight-lines to the star, as observed when Earth is on opposite sides of the Sun in its orbit. These distances form the lowest rung of what is called "the cosmic distance ladder", the first in a succession of methods by which astronomers determine the distances to celestial objects, serving as a basis for other distance measurements in astronomy forming the higher rungs of the ladder.

Parallax also affects optical instruments such as rifle scopes, binoculars, microscopes, and twin-lens reflex cameras that view objects from slightly different angles. Many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception; this process is known as stereopsis. In computer vision the effect is used for computer stereo vision, and there is a device called a parallax rangefinder that uses it to find range, and in some variations also altitude to a target.

A simple everyday example of parallax can be seen in the dashboard of motor vehicles that use a needle-style speedometer gauge. When viewed from directly in front, the speed may show exactly 60; but when viewed from the passenger seat the needle may appear to show a slightly different speed, due to the angle of viewing.


The Pleiades (), also known as the Seven Sisters and Messier 45, are an open star cluster containing middle-aged, hot B-type stars located in the constellation of Taurus. It is among the nearest star clusters to Earth and is the cluster most obvious to the naked eye in the night sky.

The cluster is dominated by hot blue and luminous stars that have formed within the last 100 million years. Reflection nebulae around the brightest stars were once thought to be left over material from the formation of the cluster, but are now considered likely to be an unrelated dust cloud in the interstellar medium through which the stars are currently passing.Computer simulations have shown that the Pleiades were probably formed from a compact configuration that resembled the Orion Nebula. Astronomers estimate that the cluster will survive for about another 250 million years, after which it will disperse due to gravitational interactions with its galactic neighborhood.

RR Lyrae variable

RR Lyrae variables are periodic variable stars, commonly found in globular clusters. They are used as standard candles to measure (extra)galactic distances, as a part of the cosmic distance ladder. This class of variable star is named after the prototype and brightest example, RR Lyrae.

RR Lyraes are pulsating horizontal branch aging stars of spectral class A or F, with a mass of around half the Sun's. They are thought to have previously shed mass during the Red-giant branch phase, and consequently, they were once stars with similar or slightly less mass than the Sun, around 0.8 solar masses.

The period of pulsation and absolute magnitude of RR Lyraes makes them good standard candles for relatively nearby targets, especially within the Milky Way and Local Group. Beyond the Milky Way they are difficult to detect due to their low luminosity. They are extensively used in globular cluster studies, and also used to study chemical properties of older stars.

Sigma-D relation

The Sigma-D relation, or Σ-D Relation, is the radio surface brightness to diameter relation of a supernova remnant.

Standard ruler

A standard ruler is an astronomical object for which the actual physical size is known. By measuring its angular size in the sky, one can use simple trigonometry to determine its distance from Earth. In simple terms, this is because objects of a fixed size appear smaller the further away they are.

Measuring distances is of great importance in cosmology, as the relationship between the distance and redshift of an object can be used to measure the expansion rate and geometry of the Universe. Distances can also be measured using standard candles; many different types of standard candles and rulers are needed to construct the cosmic distance ladder.

Stellar parallax

Stellar parallax is the apparent shift of position of any nearby star (or other object) against the background of distant objects. Created by the different orbital positions of Earth, the extremely small observed shift is largest at time intervals of about six months, when Earth arrives at exactly opposite sides of the Sun in its orbit, giving a baseline distance of about two astronomical units between observations. The parallax itself is considered to be half of this maximum, about equivalent to the observational shift that would occur due to the different positions of Earth and the Sun, a baseline of one astronomical unit (AU).

Stellar parallax is so difficult to detect that its existence was the subject of much debate in astronomy for hundreds of years. It was first observed in 1806 by Giuseppe Calandrelli who reported parallax in α-Lyrae in his work "Osservazione e riflessione sulla parallasse annua dall’alfa della Lira". Then in 1838 Friedrich Bessel made the first successful parallax measurement, for the star 61 Cygni, using a Fraunhofer heliometer at Königsberg Observatory.

Once a star's parallax is known, its distance from Earth can be computed trigonometrically. But the more distant an object is, the smaller its parallax. Even with 21st-century techniques in astrometry, the limits of accurate measurement make distances farther away than about 100 parsecs (or roughly 300 light years) too approximate to be useful when obtained by this technique. This limits the applicability of parallax as a measurement of distance to objects that are relatively close on a galactic scale. Other techniques, such as spectral red-shift, are required to measure the distance of more remote objects.

Stellar parallax measures are given in the tiny units of arcseconds, or even in thousandths of arcseconds (milliarcseconds). The distance unit parsec is defined as the length of the leg of a right triangle adjacent to the angle of one arcsecond at one vertex, where the other leg is 1 AU long. Because stellar parallaxes and distances all involve such skinny right triangles, a convenient trigonometric approximation can be used to convert parallaxes (in arcseconds) to distance (in parsecs). The approximate distance is simply the reciprocal of the parallax: For example, Proxima Centauri (the nearest star to Earth other than the Sun), whose parallax is 0.7687, is 1 / 0.7687 parsecs = 1.3009 parsecs (4.243 ly) distant.

Tully–Fisher relation

In astronomy, the Tully–Fisher relation (TFR) is an empirical relationship between the mass or intrinsic luminosity of a spiral galaxy and its asymptotic rotation velocity or emission line width. It was first published in 1977 by astronomers R. Brent Tully and J. Richard Fisher. The luminosity is calculated by multiplying the galaxy's apparent brightness by 4πd2, where d is its distance from us, and the spectral-line width is measured using long-slit spectroscopy.

Several different forms of the TFR exist, depending on which precise measures of mass, luminosity or rotation velocity one takes it to relate. Tully and Fisher used optical luminosity, but subsequent work showed the relation to be tighter when defined using microwave to infrared (K band) radiation (a good proxy for stellar mass), and even tighter when luminosity is replaced by the galaxy's total baryonic mass (the sum of its mass in stars and gas). This latter form of the relation is known as the Baryonic Tully–Fisher relation (BTFR), and states that baryonic mass is proportional to velocity to the power of roughly 3.5–4.The TFR can be used to estimate the distance to spiral galaxies by allowing the luminosity of a galaxy to be derived from its directly measurable line width. The distance can then be found by comparing the luminosity to the apparent brightness. Thus the TFR constitutes a rung of the cosmic distance ladder, where it is calibrated using more direct distance measurement techniques and used in turn to calibrate methods extending to larger distance.

In the dark matter paradigm, a galaxy's rotation velocity (and hence line width) is primarily determined by the mass of the dark matter halo in which it lives, making the TFR a manifestation of the connection between visible and dark matter mass. In Modified Newtonian dynamics (MOND), the BTFR (with power-law index exactly 4) is a direct consequence of the gravitational force law effective at low acceleration.The analogues of the TFR for non-rotationally-supported galaxies, such as ellipticals, are known as the Faber–Jackson relation and the fundamental plane.

Wilson–Bappu effect

The Ca II K line in cool stars is among the strongest emission lines which originates in the star's chromosphere. In 1957, Olin C. Wilson and M. K. Vainu Bappu reported on the remarkable correlation between the measured width of the aforementioned emission line and the absolute visual magnitude of the star. This is known as the Wilson–Bappu effect. The correlation is independent of spectral type and is applicable to stellar classification main sequence types G, K, and Red giant type M. The greater the emission band, the brighter the star, which is correlated with distance empirically.

The main interest of the Wilson–Bappu effect is in its use for determining the distance of stars too remote for direct measurements. It can be studied using nearby stars, for which independent distance measurements are possible, and it can be expressed in a simple analytical form. In other words, the Wilson–Bappu effect can be calibrated with stars within 100 parsecs from the Sun. The width of the emission core of the K line ( W0 ) can be measured in distant stars, so, knowing W0 and the analytical form expressing the Wilson–Bappu effect, we can determine the absolute magnitude of a star. The distance of a star follows immediately from the knowledge of both absolute and apparent magnitude, provided that the interstellar reddening of the star is either negligible or well known.

The first calibration of the Wilson–Bappu effect using distance from Hipparcos parallaxes was made in 1999 by Wallerstein et al. A later work also used W0 measurements on high-resolution spectra taken with CCD, but a smaller sample.

According to the latest calibration, the relation between absolute visual magnitude (Mv) expressed in magnitudes and W0, transformed in km/s, is the following:

The data error, however, is quite large: about 0.5 mag, rendering the effect too imprecise to significantly improve the cosmic distance ladder. Another limitation comes from the fact that the measurement of W0 in distant stars is very challenging, requires long observations at big telescopes. Sometimes the emission feature in the core of the K line is affected by the interstellar extinction. In these cases an accurate measurement of W0 is not possible.

The Wilson–Bappu effect is also valid for the Mg II k line. However, the Mg II k line is at 2796.34 Å in the ultraviolet, and since the radiation at this wavelength does not reach the earth's surface it can only be observed with satellites such as the International Ultraviolet Explorer.

In 1977, Stencel published a spectroscopic survey that showed that the wing emission features seen in the broad wings of the K line among higher luminosity late type stars, share a correlation of line width and Mv similar to the Wilson–Bappu effect.

Zeta Geminorum

Zeta Geminorum (ζ Geminorum, abbreviated Zeta Gem, ζ Gem) is a star (possibly binary) in the zodiac constellation of Gemini, on the outstretched left 'leg' of the twin Pollux. As a member of the category of variable stars known as classical Cepheids, it has a regular pulsation frequency that is closely related to the luminosity and the star serves as an important calibrator for the cosmic distance ladder. Based on parallax measurements, it is approximately 1,200 light-years from the Sun.Zeta Geminorum is the primary or 'A' component of a multiple star system designated WDS J07041+2034 (the secondary or 'B' component is UCAC2 39130002; the 'C' component is HD 268518; 'D' is UCAC3 222-78010, and 'E' is UCAC2 39129951). Zeta Geminorum's two components are therefore designated WDS J07041+2034 Aa and Ab. Aa is also named Mekbuda.

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