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gabs, zgabs: gaussian absorption line

A gaussian absorption line as a multiplicative model. The zgabs variant includes redshift as a parameter.

$\displaystyle M(E) = exp(-d*g(E)) $
$\displaystyle g(E) = {2\over{\sigma\sqrt{2\pi}(1-\mathit{erf}(-E_l/(\sigma\sqrt{2})))}} \exp\left({-(E-E_l)^2\over{2\sigma^2}}\right) $
where:

par1 $E_l$, line energy in keV.
par2 $\sigma$, line width (sigma) in keV.
par3 $d$, line depth in keV. The optical depth at line center is par3/par2/$\sqrt{2\pi}$.

For zgabs the corresponding formula is:

$\displaystyle M(E) = exp(-d*g(E)) $
$\displaystyle g(E) = {2\over{\sigma*\sqrt{2\pi}(1-\mathit{erf}(-E_l/(\sigma\sqrt{2})))}} \exp\left({-(E(1+z)-E_l)^2\over{2\sigma^2}}\right) $
where:

par1 $E_l$, line energy in keV.
par2 $\sigma$, line width (sigma) in keV.
par3 $d$, line depth in keV. The optical depth at line center is par3/par2/$\sqrt{2\pi}$.
par4 $z$, redshift

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Last modified: Friday, 23-Aug-2024 13:20:40 EDT