vlorentz, zvlorentz: lorentz line profile with width in velocity

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

$$A(E) = K{\sigma(E_l/c)\over{(\pi-2\arctan(-2E_L/(\sigma(E_l/c))))}}{1\over{(E-E_L)^2 + (\sigma(E_l/c)/2)^2}}$$

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:

$$A(E) = {K\over{(1+z)}}{\sigma(E_l/c)\over{(\pi-2\arctan(-2E_L/(\sigma(E_l/c))))}}{1\over{(E(1+z)-E_L)^2 + (\sigma(E_l/c)/2)^2}}$$

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 truncated at the point that the integrated flux under the line is within a critical value of the total flux. This critical value can be changed using xset LINECRITLEVEL. The default critical value is $1.0\times10^{-6}$. Note also that the normalization is defined as the integral over energies greater than zero since negative energies are unphysical.

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Last modified: Wednesday, 12-Mar-2025 17:05:25 EDT