Spectral line ($\nu \simeq {\nu }_0$)

A narrow spectral feature records enhanced emission or absorption near a transition frequency. In a stellar atmosphere, its strength depends on atomic populations, opacity, velocity fields and the source function. Lines therefore diagnose composition as well as the physical atmosphere in which they form.

Two nearby resolved spectral components. A two-line pattern can reflect fine-structure splitting, but counting lines is distinct from assigning a term's spin multiplicity.

The finite width of a spectral line can arise from finite optical coherence or a distribution of resonance frequencies. lifetime broadening and impact-regime pressure broadening often give Lorentzian line shapes; thermal Doppler broadening gives a Gaussian component. The instrument response must also be included when interpreting a measured spectrum.

Broadening for which all participating emitters share the same spectral response, as in a uniform lifetime-limited line. A resonant field can saturate the common transition response. This differs from a distribution of transition frequencies across independently resonant subensembles.

Finite interaction time with a spatially confined optical beam gives a finite spectral response width. Its detailed shape depends on the spatial beam profile, particle trajectory and interaction envelope; a duration alone does not imply a universal Lorentzian profile.

An ensemble-wide distribution of resonance frequencies, such as velocity-dependent Doppler shifts or spatially varying static-field shifts. The observed profile averages the individual responses. A velocity class need not have the full width of the ensemble's thermal Doppler broadening.

Broadening shared by otherwise identical emitters, often described by a common optical coherence time $T_2$. Exponential field-coherence decay produces a Lorentzian line shape with full angular-frequency width $2/T_2$. Population decay, dephasing and collisions can all contribute, with their time constants distinguished.

In the absence of additional dephasing, a transition whose excited-state population has lifetime $T_1$ has a field-coherence decay time $2T_1$. Its Lorentzian line shape has angular-frequency half-width $1/(2T_1)$ and full width $1/T_1$. Population decay time, amplitude decay time and linewidth conventions must therefore be distinguished. Extra dephasing shortens the optical coherence time without necessarily changing the population lifetime.

The locus of midpoints between the two sides of a spectral-line profile at equal intensities. Variations with depth or time diagnose changes in line asymmetry; a null result has finite sensitivity.

A pair of neighbouring spectral lines.

Collisions and fluctuating neighboring-particle electric fields alter atomic energy levels and coherence times, broadening a spectral line. In a simple impact treatment the coherence-decay rate gives a Lorentzian width of order $\Gamma /(2\pi )$; the precise definition of full or half width must be stated. Unlike Doppler broadening, this depends primarily on collision rates and perturber density. In stellar opacity calculations it alters line overlap and the low-opacity windows entering the Rosseland mean opacity.

If phase-randomizing collisions form a Poisson process of mean interval ${\tau }_c$, field correlation survives only when no such collision occurs during the delay. Thus its magnitude decays as $e^{-|\tau |/{\tau }_c}$. The Wiener-Khinchin theorem gives the normalized Lorentzian line shapeIts full width at half maximum is $2/{\tau }_c$ in angular frequency or $1/(\pi {\tau }_c)$ in ordinary frequency. A population lifetime is a different time constant: lifetime-limited amplitude decay at half the population rate introduces the familiar factor of two. The definition of the supplied lifetime must therefore accompany any numerical linewidth.

A spectral line profile with the shape of a Cauchy distribution. In the displayed peak-normalized convention, $\nu$ is frequency, ${\nu }_0$ is the line centre, and $\gamma >0$ is the half width at half maximum: $L({\nu }_0\pm \gamma )=1/2$, so the full width is $2\gamma$. The normalization used for a probability density function differs from this unit-peak convention.

A Voigt profile is the convolution of a Gaussian distribution and a Cauchy distribution. For an absorption line, thermal Doppler broadening contributes the Gaussian core while finite excited-state lifetime contributes the Lorentzian wings. Instrumental broadening and unresolved motions must also be modeled when inferring column density and temperature.

An emission line is a localized excess of specific intensity above the continuum. Heated chromospheric material can give a line source above the photospheric continuum source. Optically thin circumstellar gas can also add line photons through recombination or collisional excitation. Such line formation need not obey a thermal photospheric source prescription.

A forbidden emission line is suppressed by the electric-dipole selection rules but can occur through weaker radiative channels such as magnetic-dipole or electric-quadrupole emission. Its relatively long-lived upper atomic level is vulnerable to collisional de-excitation in dense gas. Low-density astrophysical plasmas can therefore display strong forbidden-line emission even when laboratory dense sources do not.

In a three-level ion, statistical equilibrium must include collisional coupling between both upper levels as well as excitations from the ground. The upper populations solve a two-by-two linear system when expressed relative to the ground population. Their line ratio is a rational function of electron density, interpolating between a collisionally excited low-density limit and a collisional Boltzmann limit. Closely spaced upper energies reduce temperature sensitivity, but neglecting upper-level collisional mixing can bias the inferred density.

For low-density gas with Maxwellian electrons, the excitation-energy difference between the ${}^1{S}_0$ and ${}^1{D}_2$ levels of doubly ionized oxygen makes $(I_{4959}+I_{5007})/I_{4363}$ temperature sensitive. A constant-collision-strength approximation is $R\simeq 7.90e^{32900\mathrm{K}/T_e}$. Increasing temperature strengthens the higher-excitation auroral line and lowers $R$. Density, extinction and nonthermal electrons require separate treatment; the $5007/4959$ pair shares one upper level and is primarily a branching ratio rather than this thermometer.

An absorption line is a deficit of observed spectral specific intensity relative to the surrounding continuum. In a photosphere with temperature falling outward, increased line opacity makes photons emerge from cooler layers than the continuum. For an absorption-dominated LTE source, the Planck function then supplies a smaller line specific intensity. A foreground layer with source below the incident continuum gives another direct transfer description.