4.1.17. Etau: simple transmission model

This model calculates the transmission T(E) between energies E1 and E_2 for a simple (often unphysical!) case:

T(E) = e^{-\tau(E)},

with the optical depth \tau(E) given by:

\tau(E) = \tau_0 E^a.

In addition, we put here T\equiv 1 for E<E_1 and E>E_2, where E_1 and E_2 are adjustable parameters. This allows the user for example to mimick an edge. Note however, that in most circumstances there are more physical models present in SPEX that contain realistic transmissions of edges! If you do not want or need edges, simply keep E_1 and E_2 at their default values.

Note that \tau_0 should be non-negative. For a>0 the spectrum has a high-energy cut-off, for a<0 it has a low-energy cut-off, and for a=0 the transmission is flat. The larger the value of a, the sharper the cut-off is.

The model can be used as a basis for more complicated continuum absorption models. For example, if the optical depth is given as a polynomial in the photon energy E, say for example \tau = 2 + 3E + 4E^2, one may define three etau components, with \tau_0 values of 2, 3, and 4, and indices a of 0, 1 and 2. This is because of the mathematical identity e^{-(\tau_1+\tau_2)} = e^{-\tau1}\times e^{-\tau2}.

The parameters of the model are:

tau0:

Optical depth \tau_0 at E=1 keV. Default value: 1.

a:

The index a defined above. Default value: 1.

e1:

Lower energy E_1 (keV). Default value: 10^{-20}.

e2:

Upper energy E_2 (keV). Default value: 10^{20}.

icov:

Type of the covering fraction. Default value: 2 (constant, set by fcov). If icov=1, full covering is applied. If icov=3, covering fraction follows a tangent function that increases with energy. If icov=4, covering fraction follows an inverse tangent function that decreases with energy. See description in pion.

fcov:

The covering factor of the absorber if icov=2. Default value: 1 (full covering). If icov=3 or 4, it sets the covering factor at the high energy end.

lcov:

The covering factor of the absorber at the low energy end. Default value: 1. lcov is applied only when icov=3 or 4. See description in pion.

ecov:

The energy when the covering factor changes from lcov to fcov. Only applied if icov=3 or 4.

acov:

The width of the transit on covering factor. Only applied if icov=3 or 4.