Line Profiles¶

HELIOS-K supports four different line profiles which can be set by the profile parameter.
The supported profiles are:
• 1: Voigt

• 2: Lorentz

(1)$f_L(\nu) = \frac{1}{\pi} \frac{\gamma_L}{(\nu - \nu_0)^2 + \gamma_L^2}$
• 3: Doppler

(2)$f_G(\nu) = \frac{ln(2)}{\pi} \frac{1}{\alpha_D} \exp\left(-\frac{ (\nu - \nu_0)^2 ln(2)}{\alpha_D^2} \right)$
• 4: Binned Gaussian integrated cross section

(3)$f_{BG} = \frac{1}{\Delta \nu} \int_{\nu - \nu/2}^{\nu + \nu/2} f_G(\nu) d \nu = \frac{1}{2 \Delta \nu} \left[ erf(\chi^+) - erf(\chi^-) \right]$

[Yurchenko et al. 2018: (ExoCross : a general program for generating spectra from molecular line lists)]

with the Doppler half-width:

(4)$\alpha_D = \frac{\nu}{c} \sqrt{\frac{2 ln(2) k_B T}{m}}$

and the Lorentz half-width for Hitran like data:

(5)$\gamma_L = \frac{A}{4\pi c} + \left( \frac{T}{T_{ref}}\right)^{-n} \left[ \frac{\alpha_{air} (P-P_{self})}{P_{ref}} + \frac{\alpha_{self} P_{self}}{P_{ref}}\right]$

or the Lorentz half-width for ExoMol like data:

(6)$\gamma_L = \frac{A}{4\pi c} + \left( \frac{T_{ref}}{T} \right)^n \cdot \left( \frac{P}{P_{ref}}\right)$

or the Lorentz half-width for Atomic data:

(7)$\gamma_L = \frac{\Gamma_{nat}}{4\pi c} + \left( \frac{T_{ref}}{T} \right)^n \cdot \left( \frac{P}{P_{ref}}\right)$

In Fig. 2 is shown an example with four different line profiles.

Relevant parameters for this example:
• doStoreFullK = 1

• profile = 1 or 2 or 3 or 4