An Etymological Dictionary of Astronomy and Astrophysics
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Statistics: The correlation coefficient of two random variables X and Y is in general defined as the ratio of the Cov(X,Y) to the two standard deviations of X and Y. It varies between 1 and -1 corresponding to complete correlation or anticorrelation.

Anticorrelation, from → anti- + → correlation.

Pâdhambâzâneš, from pâd-, → anti-, + hambâzâneš, → correlation.

1) In radio astronomy, a process performed by an → autocorrelator.
2) In statistics, a linear relation between values of a random variable over time.
3) In electronics, a technique used to detect cyclic activity in a complex signal.

Autocorrelation, from → auto- "self" + → correlation.

Xod-hambâzâneš, from xod- "self" + hambâzâneš, → correlation.

A mathematical function that describes the correlation between two values of the same variable at different points in time.

→ autocorrelation; → function.

A relation between the → entropy of a given → state of a → thermodynamic system and the → probability of the state: S = k . ln Ω where S is the entropy of the system, k is → Boltzmann's constant, and Ω the thermodynamic probability of the state. Boltzmann's relation connects → statistical mechanics and → thermodynamics. Ω is the number of possible → microstates of the system, and it represents the → randomness of the system. The relation also describes the statistical meaning of the → second law of thermodynamics. This expression has been carved above Boltzmann's name on his tombstone in Zentralfreihof in Vienna. Same as → Boltzmann's entropy formula.

→ Boltzmann's constant; → relation.

The highest correlation between linear functions of two data sets when specific restrictions are imposed upon them.

→ canonical; → correlation.

General: The degree to which two or more attributes or measurements on the same group of elements show a tendency to vary together; the state or relation of being correlated.
Statistics: The strength of the linear dependence between two random variables.

From M.Fr. corrélation, from cor- "together," → com- + → relation.

Hambâzâneš , from ham-→ com- + bâzâneš→ relation.

A number between -1 and 1 which measures the degree to which two variables are linearly related.

→ correlation; → coefficient.

In radio astronomy, the process performed by a → cross correlator or the result of the process.

→ cross; → correlation.

A correlation between two variables such that as one variable becomes large, the other also becomes large, and vice versa. The correlation coefficient is between 0 and +1. Also called positive correlation.

→ direct; → correlation.

An equation that describes how the → angular frequency, ω, of a wave depends on its → wave number, k. For the simplest of waves, where the speed of propagation, c, is a constant, ω(k) = ck. If the → phase velocity depends on k, that is for a dispersive medium, the function ω(k) is nonlinear.

→ dispersion; → relation.

An empirical power-law correlation between the luminosity (L) and the velocity dispersion of stars (σ) in the center of a elliptical galaxies. The original relation can be expressed mathematically as: L ∝ σ^γ, where the index γ is observed to be approximately equal to 4, but depends on the range of galaxy luminosities that is fitted. → Tully-Fisher relation.

After the astronomers Sandra M. Faber and Robert Earl Jackson, who first noted this relation in 1976 (ApJ 204, 668); → relation.

An → empirical relationship between the internal → velocity dispersion of → molecular clouds and their size. The velocity dispersions are derived from molecular → linewidths, in particular those of → carbon monoxide. It was first established on star forming regions and found to be: σ (km s^-1) = 1.10 L (pc)^0.38, where σ is the velocity dispersion and L the size. The relation holds for 0.1 ≤ L ≤ 100 pc. More recent set of cloud data yield: σ (km s^-1) = L (pc)^0.5. This relation indicates that larger molecular clouds have larger internal velocity dispersions. It is usually interpreted as evidence for → turbulence in molecular clouds. Possible sources of interstellar turbulence include the following processes operating at various scales: galactic-scale (→ differential rotation, → infall of extragalactic gas on the galaxy), intermediate-scale (expansion of → supernova remnants, → shocks, → stellar winds from → massive stars), and smaller-scale processes (→ outflows from → young stellar objects).

First derived by Richard B. Larson, American astrophysicist working at Yale University (Larson, 1981, MNRAS 194, 809). See Falgarone et al. (2009, A&A 507, 355) for a recent study; → relation.

A measure of how well data points fit a straight line. When all the points fall on the line it is called a perfect correlation. When the points are scattered all over the graph there is no correlation.

→ linear; → correlation.

The relation between the stellar luminosity of a galaxy and its physical size. More at → mass-size relation.

→ luminosity; → size; → relation.

The famous equation proposed by Einstein as a consequence of his special theory of relativity describing the equivalence of mass and energy: E = mc², where E is energy, m is the equivalent amount of mass, and c is the velocity of light.

→ mass; → energy; → relation.

A relationship between luminosity and mass for stars that are on the main sequence, specifying how bright a star of a given mass will be. Averaged over the whole main sequence, it has been found that L = M^3.5, where both L and M are in solar units. This means, for example, that if the mass is doubled, the luminosity increases more than 10-fold.

→ mass; → luminosity; → relation.

A correlation between the → stellar mass (or → luminosity) and the → gas metallicity of → star-forming galaxies (Lequeux et al. 1979) according to which massive galaxies have higher gas metallicities. Several large galaxy surveys, such as the → Sloan Digital Sky Survey (SDSS), have confirmed that galaxies at all → redshifts with higher stellar masses retain more metals than galaxies with lower stellar masses. Besides the dependence on stellar mass, other studies have found further dependences of gas metallicity on other physical properties at a given mass, such as → specific star formation rate, → star formation rate, and stellar age. These higher dimensional relations could provide additional constraints to the processes that regulate the metal enrichment in galaxies. In addition to gas metallicity, also the → stellar metallicity of galaxies is found to correlate with the stellar mass, suggesting the mass-metallicity relation already existed at early epochs of galaxy evolution (Lian et al., 2017, MNRAS 474, 1143, and references therein).

→ mass; → metallicity; → relation.

The relation between the → stellar mass and the physical size of a galaxy. Studies show that the sizes increase with stellar mass, but that the relation weakens with increasing → redshift. Separating galaxies by their → star formation rate, model simulations show that → passive galaxies are typically smaller than → active galaxies at a fixed stellar mass. These trends are consistent with those found in observations; the level of agreement between the predicted and observed size-mass relations is of the order of 0.1 dex for redshifts < 1 and 0.2-0.3 dex from redshift 1 to 2. Known also as the → luminosity-size relation (Furlong et al., 2016, MNRAS 465, 722, and references therein).

→ mass; → size; → relation.

An observationally determined relationship between the → morphological classification of galaxies and the → environments in which they are located. Specifically, the morphology-density relation indicates that early-type galaxies (→ ETG) are preferentially located in high density environments, whereas late-type galaxies (→ LTG) are preferentially found in low density environments. Hence, spiral galaxies are rare in the high densities of clusters and are common in the lower density group environments. Early-type galaxies, on the other hand, are common in clusters and are rarely found in isolation.

→ morphology; → density; → relation.

A correlation between two variables such that as one variable's values tend to increase, the other variable's values tend to decrease.

→ negative; → correlation.