The equivalent width of a spectral line is a measure of the area of the line on a plot of intensity versus wavelength in relation to underlying continuum level. It is found by forming a rectangle with a height equal to that of continuum emission, and finding the width such that the area of the rectangle is equal to the area in the spectral line. It is a measure of the strength of spectral features that is primarily used in astronomy. [1]
Formally, the equivalent width is given by the equation [2]
Here, represents the underlying continuum intensity, while represents the intensity of the actual spectrum (the line and continuum). Then represents the width of a hypothetical line which drops to an intensity of zero and has the "same integrated flux deficit from the continuum as the true one." [2] This equation can be applied to either emission or absorption, but when applied to emission, the value of is negative, and so the absolute value is used.
In other words, if the continuum level is constant and the area under/above the emission/absorption line (compared to the continuum) is (the integral above), then (further highlighting the continuum-level dependence). Therefore, for a fixed line strength (), the equivalent width will be smaller for a brighter continuum.
The equivalent width is used as a quantitative measure of the strength of spectral features. The equivalent width is a convenient choice because the shapes of spectral features can vary depending upon the configuration of the system which is producing the lines. For instance, the line may experience Doppler broadening due to motions of the gas emitting the photons. The photons will be shifted away from the line center, thus rendering the height of the emission line a poor measure of its overall strength. The equivalent width, on the other hand, "measures the fraction of energy removed from the spectrum by the line," regardless of the broadening intrinsic to the line or a detector with poor resolution. [3] Thus the equivalent width can in many conditions yield the number of absorbing or emitting atoms, by using the curve of growth. [1]
For example, measurements of the equivalent width of the Balmer alpha transition in T Tauri stars are used in order to classify individual T Tauri stars as being classical or weak-lined. [2] Also, the equivalent width is used in studying star formation in Lyman alpha galaxies, as the equivalent width of the Lyman alpha line is related to the star formation rate in the galaxy. [4] The equivalent width is also used in many other situations where a quantitative comparison between line strengths is needed.
In physics, coherence length is the propagation distance over which a coherent wave maintains a specified degree of coherence. Wave interference is strong when the paths taken by all of the interfering waves differ by less than the coherence length. A wave with a longer coherence length is closer to a perfect sinusoidal wave. Coherence length is important in holography and telecommunications engineering.
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In mathematics, a self-adjoint operator on an infinite-dimensional complex vector space V with inner product is a linear map A that is its own adjoint. If V is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of A is a Hermitian matrix, i.e., equal to its conjugate transpose A∗. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this basis is a diagonal matrix with entries in the real numbers. This article deals with applying generalizations of this concept to operators on Hilbert spaces of arbitrary dimension.
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In astronomy, the spectral index of a source is a measure of the dependence of radiative flux density on frequency. Given frequency in Hz and radiative flux density in Jy, the spectral index is given implicitly by
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Laser linewidth is the spectral linewidth of a laser beam.
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In the study of heat transfer, Schwarzschild's equation is used to calculate radiative transfer through a medium in local thermodynamic equilibrium that both absorbs and emits radiation.
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