Line shapes

The shape of a spectral line — how absorption is distributed in wavenumber around a transition's center ν₀ — is set by the physics of the gas: how fast the molecules move (thermal Doppler broadening) and how often they collide (pressure broadening). AtmosphericAbsorption.jl lets you select the broadening physics with a single profile= keyword on LineByLineModel, while keeping the same line list, partition function, and grid. This page explains the profile family and how to choose among them.

The profile family

Each profile is a more complete physical model than the one before it. Pass any of them as profile=...:

Profile	Constructor	Physics captured
Doppler	Doppler()	Thermal motion only (zero-pressure limit). Gaussian.
Lorentz	Lorentz()	Collisional (pressure) broadening only. Lorentzian.
Voigt	Voigt()	Convolution of Doppler and Lorentz — the standard workhorse.
Speed-dependent Voigt	SpeedDependentVoigt()	Voigt plus the speed dependence of collisional width/shift.
Rautian	Rautian()	Voigt plus velocity-changing (Dicke) collisions — narrows the core.
Speed-dependent Rautian	SpeedDependentRautian()	Speed dependence + Dicke narrowing, without the HT correlation.
Hartmann-Tran	HartmannTran()	Full pCqSDHC: speed dependence + Dicke narrowing + their correlation.

Doppler — thermal broadening

At vanishing pressure the only broadening mechanism is the thermal velocity distribution of the absorbers. The result is a Gaussian whose half-width γ_d scales with √(T/M). Doppler() is the zero-pressure limit of the Voigt profile and is mostly useful for upper-atmosphere / line-core work and teaching.

Lorentz — pressure broadening

Collisions interrupt the radiating dipole and broaden the line into a Lorentzian with a half-width γ_l that grows with pressure. This is the opposite limit — pure collisional broadening with no thermal contribution. In the troposphere this dominates the wings.

Voigt — the convolution

Real lines are both Doppler- and pressure-broadened, so the observed shape is the convolution of a Gaussian and a Lorentzian: the Voigt profile. This is the standard choice for almost all atmospheric work and is the default:

model = LineByLineModel(lines, partition; profile=Voigt())

The convolution has no closed form; it is evaluated through the complex probability function (CPF) — see CPF strategy below.

Speed-dependent Voigt

The collisional width and shift actually depend on the relative speed of the colliding molecules, which the plain Voigt model ignores. Accounting for this speed dependence narrows and subtly reshapes the core. Select it with SpeedDependentVoigt(). The advanced line parameters it needs (γ₂, δ₂) come from load_hitran_nonvoigt.

Rautian and speed-dependent Rautian

Velocity-changing collisions confine a molecule's motion, narrowing the Doppler core below its free-flight width — the Dicke narrowing effect. Rautian() adds this hard-collision narrowing (parameter νVC) to a Voigt line; SpeedDependentRautian() adds it on top of the speed-dependent profile. Both are limits of the same pCqSDHC engine as Hartmann-Tran, with the HT correlation parameter η set to zero, and both reduce to their non-narrowed counterparts when νVC = 0. The effect is largest where the line is Doppler-dominated (low pressure / high altitude); it conserves the integrated line strength while raising the peak.

Hartmann-Tran — the full pCqSDHC model

The Hartmann-Tran profile (the partially-correlated quadratic speed-dependent hard-collision model, pCqSDHC) adds velocity-changing (Dicke narrowing) collisions on top of the speed dependence. It is the most complete line shape in routine use and is recommended when matching reference codes at the highest accuracy. Select it with HartmannTran(). It consumes the full set of advanced columns (γ₂, δ₂, η, ν_VC).

The plot below overlays Voigt and Hartmann-Tran for a slice of the H₂O ν₃ band (real HITRAN HT parameters): the speed dependence subtly narrows and reshapes the line cores — a small but real difference that matters for high-accuracy retrievals.

Getting the advanced parameters

Doppler(), Lorentz(), and Voigt() run from a standard HITRAN or ExoMol line list. SpeedDependentVoigt() and HartmannTran() need the extra Hartmann-Tran columns, which come from HITRAN's authenticated non-Voigt API:

activate_hitran!("your-key")   # or set ENV["HITRAN_API_KEY"]
db = load_hitran_nonvoigt("H2O"; numin=3700, numax=3850, min_strength=0.0, FT=Float64)

This fills the database's advanced columns (γ2_air, δ2_air, η, νVC), after which SpeedDependentVoigt() and HartmannTran() have everything they need.

Line mixing folds in automatically

Voigt, Lorentz, speed-dependent Voigt, and Hartmann-Tran are collisional profiles: wherever a line carries a first-order (Rosenkranz) line-mixing coefficient Y_LM, they fold it in automatically as the asymmetric Y·Im(W) term. Line mixing matters where neighboring lines overlap strongly (CO₂ Q-branches, O₂ A-band), redistributing intensity between the lines and reshaping the band envelope. You do not enable it separately — the fold is built into the collisional profiles and switches on for exactly those lines whose Y_LM is non-zero.

Y_LM is filled from HITRAN's line-mixing parameters (Y_HT_air_296 / Y_SDV_air_296) through the authenticated non-Voigt endpoint (see Data sources §3) — currently provided by HITRAN for CO₂, O₂, and a few others. A basic Voigt .par load leaves Y_LM at zero, so no mixing is applied there. Doppler(), being the zero-pressure limit, carries no line mixing.

The effect is dramatic across the CO₂ 4.3 µm band: mixing redistributes intensity between the densely-overlapping lines and makes the band wings fall off far faster than a plain Voigt sum (the well-known sub-Lorentzian behavior). For CO₂, HITRAN supplies the speed-dependent-Voigt line-mixing coefficient (no γ₂), so the Hartmann-Tran curve below coincides with "Voigt + line mixing".

Swapping profiles on the same line list

Because the profile is just a keyword, you can hold the line list, partition function, grid, pressure, and temperature fixed and swap only the broadening physics:

using AtmosphericAbsorption

# Authenticated load so the advanced (HT) columns are populated
activate_hitran!("your-key")
lines     = load_hitran_nonvoigt("H2O"; numin=3700, numax=3850, FT=Float64)
partition = TIPS2021PF()

grid = collect(3700.0:0.01:3850.0)   # cm⁻¹
p, T = 1013.25, 296.0                 # hPa, K

# Same line list, three different physics models
σ_voigt = compute_cross_section(
    LineByLineModel(lines, partition; profile=Voigt()),               grid, p, T)
σ_sdv   = compute_cross_section(
    LineByLineModel(lines, partition; profile=SpeedDependentVoigt()), grid, p, T)
σ_ht    = compute_cross_section(
    LineByLineModel(lines, partition; profile=HartmannTran()),        grid, p, T)

Each σ is a Vector in cm²/molecule on the model's device. The differences between σ_voigt, σ_sdv, and σ_ht are exactly the speed-dependence and Dicke-narrowing effects described above.

CPF strategy (advanced)

The Voigt-family profiles are all evaluated through a complex probability function (the Faddeeva function w(z)). The CPF strategy is selectable but rarely needs changing:

• HumlicekWeideman32() — default. A 32-term rational approximation that is fast and GPU-safe.

• ErfcxCPF() — a CPU reference implementation using erfcx, useful for cross-checking accuracy.

model = LineByLineModel(lines, partition; profile=Voigt(), cpf=ErfcxCPF())

Low-level shape functions (teaching)

For plots and pedagogy you can call the bare shape functions directly, without building a model. They take detunings Δν = ν − ν₀ and the relevant widths (all in cm⁻¹):

using AtmosphericAbsorption

Δν = -0.5:0.001:0.5

g_doppler = doppler.(Δν, 0.05)            # Gaussian, half-width γ_d
g_lorentz = lorentz.(Δν, 0.05)            # Lorentzian, half-width γ_l

cpf = HumlicekWeideman32()
y   = 0.6                                  # γ_l / γ_d (the Voigt y parameter)
g_voigt = voigt.(Ref(cpf), Δν, 0.05, y)   # Voigt via the CPF

# Full pCqSDHC kernel (returns complex; the real part is the profile)
z = pcqsdhc.(Ref(cpf), 0.0, 0.05, 0.01, 0.0, 0.0, 0.0, 0.0, Δν)
g_ht = real.(z)

pcqsdhc(cpf, ν0, Γ0, Γ2, Δ0, Δ2, νVC, η, ν) is the single kernel underneath both SpeedDependentVoigt() (set νVC = η = 0) and HartmannTran() (full arguments). Setting Γ₂ = Δ₂ = νVC = η = 0 reduces it to a plain Voigt, which is a good way to see how the family nests.

Validation

The line-shape implementations are validated against HAPI, the HITRAN reference Python interface:

• Voigt cross-sections on real CO₂/H₂O match HAPI to ≤ 5×10⁻³.

• Hartmann-Tran and speed-dependent Voigt match HAPI's pcqsdhc to ~1×10⁻⁶.

• GPU results equal CPU results to machine precision, and the Float32 pipeline matches Float64 to machine precision.

So you can move up the profile family — Voigt → speed-dependent Voigt → Hartmann-Tran — purely on physical-accuracy grounds, confident that each shape reproduces the HITRAN reference.