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vlorabs, zvlorabs: lorentzian absorption line with width in km/s

A lorentzian absorption line with the line width in km/s as a multiplicative model. The zlorabs variant includes redshift as a parameter.

$\displaystyle M(E) = exp(-d*l(E)) $
$\displaystyle l(E) = {\sigma(E_l/c)\over{(\pi-2\arctan(-2E_L/(\sigma(E_l/c))))}}{1\over{(E-E_L)^2 + (\sigma(E_l/c)/2)^2}} $
where:

par1 $E_l$, line energy in keV.
par2 $\sigma$, line width (FWHM) in km/s.
par3 $d$, line depth in keV.

For zlorabs the corresponding formula is:

$\displaystyle M(E) = exp(-d*g(E)) $
$\displaystyle l(E) = {1\over{(1+z)}}{\sigma(E_l/c)\over{(\pi-2\arctan(-2E_L/(\sigma(E_l/c))))}}{1\over{(E(1+z)-E_L)^2 + (\sigma(E_l/c)/2)^2}} $
where:

par1 $E_l$, line energy in keV.
par2 $\sigma$, line width (FWHM) in km/s.
par3 $d$, line depth in keV.
par4 $z$, redshift