gauss, zgauss: gaussian line profile

A simple gaussian line profile. If the width is $\leq 0$ then it is treated as a delta function. The zgauss variant computes a redshifted gaussian.

$$A(E) = K{2\over{\sigma\sqrt{2\pi}(1-\mathit{erf}(-E_l/(\sqrt{2}\sigma)))}} \exp\left({-(E-E_l)^2\over{2\sigma^2}}\right)$$

where:

par1	$E_l$, line energy in keV
par2	$\sigma$, line width in keV
Norm	$K$, total photons/cm$^2$/s in the line

For zgauss the corresponding formula is:

$$A(E) = K{1\over{(1+z)\sigma\sqrt{2\pi}(1-\mathit{erf}(-E_l/(\sqrt{2}\sigma)))}} \exp\left({-(E(1+z)-E_l)^2\over{2\sigma^2}}\right)$$

and parameter settings are:

par1	$E_l$, source frame line energy in keV
par2	$\sigma$, source frame line width in keV
par3	$z$, redshift
Norm	$K$, source frame total 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 $1.0\times10^{-8}$. 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: Friday, 23-Aug-2024 13:20:40 EDT