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vlorentz, zvlorentz: lorentz line profile with width in velocity

A Lorentzian line profile with the line width in km/s.

$\displaystyle A(E) = K{\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 $\sigma$, FWHM line width in km/s
norm $K$, photons/cm$^2$/s in the line

For zvlorentz the corresponding formula is:

$\displaystyle A(E) = {K\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}} $

and the parameters are:

par1 $E_L$, line energy in keV
par2 $\sigma$, FWHM line width in km/s
par3 $z$, redshift
norm $K$, photons/cm$^2$/s in the line

The line is calculated out to fifty sigma. Note also that the normalization is defined as the integral over energies greater than zero since negative energies are unphysical.