Warm: continuous photoionised absorption model¶
The warm model is a multi-component version of the xabs model. In the warm model, we construct a model for a continuous distribution of column density \(N_{\mathrm H}\) as a function of \(\xi\). It is in some sense comparable to the differential emission measure models used to model the emission from multi-temperature gas. Here we have absorption from multi-ionization gas. Depending upon the physics of the source, this may be a better approximation than just the sum of a few xabs components. A disadvantage of the model may be (but this also depends upon the physics of the source), that all dynamical parameters for each value of \(\xi\) are the same, like the outflow velocity and turbulent broadening. If this appears to be the case in a given source, one may of course avoid this problem by taking multiple, non-overlapping warm components.
The model assumes a logarithmic grid of \(n\) equidistant values of \(\log\xi\), between a lower limit \(\xi_1\) and an upper limit \(\xi_2\). For each of the grid points \(\xi_i\), a value of \(f_i\) can be adjusted; here \(f_i\) is given as \(f_i={\mathrm d}N_{\mathrm H}/{\mathrm d}\ln\xi\) evaluated at \(\xi_i\), where the differential column density is assumed to be a continuous function of \(\xi\). At each intermediate point, the value of \({\mathrm d}N_{\mathrm H}/{\mathrm d}\ln\xi\) is then determined by doing cubic spline interpolation in the \(\ln f\) – \(\ln\xi\) space. In order not to consume too much computer time, the step size for numerical integration \(\Delta\log\xi\) can be set. A typical, recommended value for this (the default) is 0.2.
For more information on this model, the atomic data and parameters we refer to Different types of absorption models.
The parameters of the model are:
xil1 : \(\log\xi_1\) of the lower limit of the ionisation
parameter range in units of \(10^{-9}\) W m. Default value: -4.xil2 : \(\log\xi_2\) of the upper limit of the ionisation
parameter range in units of \(10^{-9}\) W m. Default value: 5.npol : The number of grid points for the \(\log\xi\) grid,
including the end points for \(\xi_1\). Default value: 19; lower
values are generally recommended; minimum value is 2.dxi : step size for numerical integration \(\Delta\log\xi\).
Default value: 0.2.f01...f19 : Values of
\(f_i={\mathrm d}N_{\mathrm H}/{\mathrm
d}\ln\xi\) at the grid points. Default values \(10^{-6}\). When
npol\(<19\), the remaining values of \(f_i\) are simply
ignored.The following parameters are common to all our absorption models:
fcov : The covering factor of the absorber. Default value: 1 (full
covering)v : Root mean square velocity \(\sigma_{\mathrm v}\)rms : Rms velocity \(\sigma_{\mathrm b}\) of line blend
componentsdv : Velocity distance \(\Delta v\) between different blend
componentszv : Average systematic velocity \(v\) of the absorber (using relativistic Doppler shift)col : File name for the photoionisation
balance parametersRecommended citation: Steenbrugge et al. (2005)