A stellar atmosphere is the outer region that determines the escaping spectrum and matches the interior stellar structure to its radiation boundary conditions. A photosphere is the layer near unit optical depth, not a zero-temperature boundary. The inward intensity at the outer surface vanishes when there is no external illumination.
The distribution of radiation from a star with wavelength or frequency, including its continuum and absorption lines. Continuum colors and temperature-dependent line strengths provide complementary estimates of effective temperature. Spectra of an unresolved binary star may need to be separated by eclipse observations or their different velocity shifts before the component effective temperatures can be inferred.
A stellar abundance can be expressed as an elemental or isotopic mass fraction, or as a number ratio to hydrogen. Inferring it from a spectral line requires a model for level populations, opacity, radiation and velocity fields. Agreement between suitable ionization stages and weak photospheric lines tests whether the adopted stellar atmosphere is adequate.
The abundance of chemical elements heavier than helium in astronomical material. A metal mass fraction measures their combined mass; spectroscopic abundance ratios are other measures of metallicity and need not be numerically identical to that fraction.
The fraction of total mass in chemical elements heavier than helium, so the hydrogen mass fraction, helium mass fraction and metal mass fraction satisfy . Despite the astronomical name, this includes elements such as carbon and oxygen that are not chemical metals.
When radiative rates compete with or dominate collisions, level populations need statistical equilibrium coupled to radiative transfer, rather than thermal population laws at the local temperature. Radiation from other depths can make the local radiation field differ from the Planck function. This changes ionization and spectral-line strengths, so a geometrically thin atmosphere may still require non-LTE abundance modelling.
A heated layer above a photosphere can have an outward temperature increase. Strong lines formed there may show emission where an outward-cooling photosphere would produce absorption. The energy maintaining the temperature inversion is additional atmospheric heating; the exact height and transfer regime vary between stars.
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 . Exponential field-coherence decay produces a Lorentzian line shape with full angular-frequency width . 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 has a field-coherence decay time . Its Lorentzian line shape has angular-frequency half-width and full width . 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.
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 ; 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 , field correlation survives only when no such collision occurs during the delay. Thus its magnitude decays as . The Wiener-Khinchin theorem gives the normalized Lorentzian line shapeIts full width at half maximum is in angular frequency or 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, is frequency, is the line centre, and is the half width at half maximum: , so the full width is . 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 and levels of doubly ionized oxygen makes temperature sensitive. A constant-collision-strength approximation is . Increasing temperature strengthens the higher-excitation auroral line and lowers . Density, extinction and nonthermal electrons require separate treatment; the 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.
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