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)\[f_G(\nu) = \sqrt{\frac{ln(2)}{\pi}} \frac{1}{\alpha_D} \exp\left(-\frac{ (\nu - \nu_0)^2 ln(2)}{\alpha_D^2} \right)\]

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