Gaus: gaussian line model¶
The Gaussian line model is the simplest model for a broadened emission line.
The spectrum is given by:
where \(E\) is the photon energy in keV, \(F\) the photon flux in units of \(10^{44}\) ph \(\mathrm{s}^{-1}\) \(\mathrm{keV}^{-1}\), \(E_0\) is the average line energy of the spectral line (in keV) and \(A\) is the line normalisation (in units of \(10^{44}\) ph \(\mathrm{s}^{-1}\)). The total line flux is simply given by \(A\). Further \(\sigma\) is the Gaussian width, which is related to the full width at half maximum \(FWHM\) by \(FWHM=\sigma \sqrt{\ln 256}\) or approximately \(FWHM = 2.3548\sigma\).
To ease the use for dispersive spectrometers (gratings) there is an option to define the wavelength instead of the energy as the basic parameter. The parameter type determines which case applies: type=0 (default) corresponding to energy, type=1 corresponding to wavelength units.
Warning
Do not confuse \(\sigma\) with \(FWHM\) when interpreting your fit results with other data.
Warning
When changing from energy to wavelength units, take care about the frozen/thawn status of the line centroid and FWHM.
Warning
You need to do a calc or fit command to get an update
of the wavelength (for type=0) or energy (type=1).
The parameters of the model are:
norm : Normalisation \(A\), in units of
\(10^{44}\) ph \(\mathrm{s}^{-1}\). Default value: 1.e : The line energy \(E_0\) in keV. Default value: 6.4 keV.fwhm : The line \(FWHM\), in keV.type : The type: 0 for energy units, 1 for wavelength units.w : The line wavelength \(\lambda\) in Å. Default value: 20 Å.awid : The line \(FWHM\), in Å.Recommended citation: Gauss (1809).