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hrefl: reflection model
A simple multiplicative reflection model due to Tahir Yaqoob. This model gives
the reflected X-ray spectrum from a cold, optically thick, circular slab with
inner and outer radii (Ri & Ro, respectively) illuminated by a point source
a height H above the center of the slab. The main difference between this
model and other reflection models is that analytic approximations are used
for the Chandrasekar H functions (and their integrals) and ELASTIC SCATTERING
is assumed (see Basko 1978). The elastic-scattering
approximation means that the model is ONLY VALID UP TO 
15 keV in
the source frame. Future enhancements will include fudge factors that will
allow extension up to 100 keV. The fact that no integration is involved at
any point makes the routine very fast and particularly suitable for
generating error contours, especially when fitting a large number of data
channels. The model is multiplicative, and so can be used with ANY
incident continuum.
Parameters are as follows:
| par1 | minimum angle (degrees) between source photons incident on the slab
and the slab normal
![$[=tan^{-1}(R_i/H)]$](img476.svg) |
| par2 | maximum angle (degrees) between source photons incident on the slab
and the slab normal
![$[=tan^{-1}(R_o/H)]$](img477.svg) |
| par3 | Angle (degrees) between the observer's line of sight and the slab normal. |
| par4 | Iron abundance relative to Solar |
| par5 | Iron K-edge energy |
| par6 | Fraction of the direct flux seen by the observer |
| par7 | Normalization of the reflected continuum |
| par8 | redshift |
Suppose the incident photon spectrum is N(E) photons cm
s
keV and
that the incident continuum is steady in time, and suppose further that the
reflected continuum from the slab is R(E). When you multiply the incident
spectrum with hrefl, what you actually get is the following:
Thus, the actual physical situation described above corresponds to
par6 = 1.0
par7 = 1.0
You may decide to float par6 and/or par7. In that case, you must decide what the best-fitting values of these parameters mean physically for your case. It may imply time-lags between the direct and reflected components, different source and/or disk geometries to those assumed, or something else.