Rayleigh scattering

References

LMDZ

Hansen (1974) : https://ui.adsabs.harvard.edu/link_gateway/1974SSRv...16..527H/ADS_PDF equations (2.29) to (2.32)

exo_k

Rayleigh routine in exo_k : http://perso.astrophy.u-bordeaux.fr/~jleconte/exo_k-doc/_modules/exo_k/rayleigh.html#Rayleigh.sigma_mol

Exo_k uses formalism from : Caldas (2019) : https://hal.archives-ouvertes.fr/hal-02005332/document equation (12) & appendix D

Formalism

We consider a layer .

DPR(K) is the difference of pressure between the two levels that define the layer.

dm is the mass per m2 of the layer

LMDZ formalism

In LMDZ, in optcv.F90 we have :

TRAY(K,NW) = TAURAY(NW) * DPR(K)

exo_k formalism

TRAY \( \displaystyle = \sigma_{exok} dN \) with \( \displaystyle \sigma_{exok} \) the cross section and dN in molecules/m2

which gives : TRAY \( \displaystyle = \sigma_{exok} \frac{dm}{m_{molecule}} \) with dm in kg/m2

and then : TRAY \( \displaystyle = \frac{\sigma_{exok}}{g * m_{molecule}} dP\)

Relations between LMDZ & Exo_k formalisms

LMDZ & exo_k formalism are linked as following \[ \displaystyle \text{TAURAY} = \frac{\sigma_{exok}}{g * m_{molecule}} \]

Be careful with units !!! (cm-1 for wavenumbers in exo_k, microns for wavelengths in LMDZ, not to forget the scalep factor in LMDZ)

To be noticed

TAURAY(NW) is calculated in calc_rayleigh.F90.

It is in fact TAUVAR which calculated, and then averaged by the black body function for each channel to give TAURAY \[ \text{TAURAY(NW)} = \frac{\int_{\lambda' \in \text{channel}} \text{TAUVAR} (\lambda') B_{\lambda} \, \mathrm{d}\lambda'}{\int B_{\lambda} \, \mathrm{d}\lambda'} \]

TAUVAR is cut into two parts : TAUCONSTI et TAUVARI avec TAUVAR = TAUCONSTI * TAUVARI

The \( \lambda \) dependence is in the TAUVARI