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2.1. Line Production

A substantial amount of the power in AGN is thought to be emitted as X-rays from the accretion disk corona in active or flaring regions. Thermal Comptonization (i.e. multiple inverse Compton scattering by hot thermal electrons; Zdziarski et al. 1994) of soft optical/UV disk photons by the corona naturally gives rise to a power-law X-ray spectrum. The flares irradiate the accretion disk which is relatively cold resulting in the formation of a ``reflection'' component within the X-ray spectrum. A similar component is produced in the Solar spectrum by flares on the solar photosphere (Bai & Ramaty 1978), in X-ray binaries by irradiation of the stellar companion (Basko 1978) and in accreting white dwarfs.

The basic physics of X-ray reflection and iron line fluorescence can be understood by considering a hard X-ray (power-law) continuum illuminating a semi-infinite slab of cold gas. When a hard X-ray photon enters the slab, it is subject to a number of possible interactions: Compton scattering by free or bound electrons (5) photoelectric absorption followed by fluorescent line emission, or photoelectric absorption followed by Auger de-excitation. A given incident photon is either destroyed by Auger de-excitation, scattered out of the slab, or reprocessed into a fluorescent line photon which escapes the slab.

Figure 1 shows the results of a Monte Carlo calculation which includes all of the above processes (Reynolds 1996; based on similar calculations by George & Fabian 1991). Due to the energy dependence of photoelectric absorption, incident soft X-rays are mostly absorbed, whereas hard photons are rarely absorbed and tend to Compton scatter back out of the slab. The reflected continuum is therefore a factor of about sigmaT / sigmape below the incident one. Above energies of several tens of kilovolts, Compton recoil reduces the backscattered photon flux. These effects give the reflection spectrum a broad hump-like shape. In addition, there is an emission line spectrum resulting primarily from fluorescent Kalpha lines of the most abundant metals. The iron Kalpha line at 6.4 keV is the strongest of these lines. For most geometries relevant to this discussion, the observer will see this reflection component superposed on the direct (power-law) primary continuum. Under such circumstances, the main observables of the reflection are a flattening of the spectrum above approximately 10 keV (as the reflection hump starts to emerge) and an iron line at 6.4 keV.

Figure 1

Figure 1. X-ray reflection from an illuminated slab. Dashed line shows the incident continuum and solid line shows the reflected spectrum (integrated over all angles). Monte Carlo simulation from Reynolds (1996).

The fluorescent iron line is produced when one of the 2 K-shell (i.e. n = 1) electrons of an iron atom (or ion) is ejected following photoelectric absorption of an X-ray. The threshold for the absorption by neutral iron is 7.1 keV. Following the photoelectric event, the resulting excited state can decay in one of two ways. An L-shell (n = 2) electron can then drop into the K-shell releasing 6.4 keV of energy either as an emission line photon (34 per cent probability) or an Auger electron (66 per cent probability). (This latter case is equivalent to the photon produced by the n = 2 -> n = 1 transition being internally absorbed by another electron which is consequently ejected from the ion.) In detail there are two components to the Kalpha line, Kalpha1 at 6.404 and Kalpha2 at 6.391 keV, which are not separately distinguished in our discussion here. There is also a Kbeta line at 7.06 keV and a nickel Kalpha line at 7.5 keV is expected.

For ionized iron, the outer electrons are less effective at screening the inner K-shell from the nuclear charge and the energy of both the photoelectric threshold and the Kalpha line are increased. (The line energy is only significantly above 6.4 keV when the M-shell is lost, i.e. FeXVII and higher states.) The fluorescent yield (i.e. the probability that a photoelectric absorption event is followed by fluorescent line emission rather than the Auger effect) is also a weak function of the ionization state from neutral iron (FeI) upto FeXXIII. For Lithium-like iron (FeXXIV) through to Hydrogen-like iron (FeXXVI), the lack of at least 2 electrons in the L-shell means that the Auger effect cannot occur. For He- and H-like iron ions the line is produced by the capture of free electrons, i.e. recombination. The equivalent fluorescent yield is high and depends on the conditions (see Matt, Fabian & Reynolds 1997).

The fluorescent yield for neutral matter varies as the fourth power of atomic number Z4, for example being less than one half per cent for oxygen. Predicted equivalent widths for low Z lines are given in Matt et al (1997). Fluorescent X-ray spectroscopy is a well-known, non-invasive way to determine the surface composition of materials in the laboratory, or even of a planetary surface.

For cosmic abundances the optical depth to bound-free iron absorption is higher than, but close to, the Thomson depth, The iron line production in an X-ray irradiated surface therefore takes place in the outer Thomson depth. This is only a small fraction of the thickness (say 1 to 0.1 per cent) of a typical accretion disk and it is the ionization state of this thin skin which determines the nature of the iron line.

The strength of the iron line is usually measured in terms of its equivalent width with respect to the direct emission. (The equivalent width is the width of the continuum in, say eV, at the position of the line which contains the same flux as the line. Its determination is not entirely straightforward when the line is very broad.) It is a function of the geometry of the accretion disk (primarily the solid angle subtended by the ``reflecting'' matter as seen by the X-ray source), the elemental abundances of the reflecting matter, the inclination angle at which the reflecting surface is viewed, and the ionization state of the surface layers of the disk. We will address the last three of these dependences in turn.

5 Whether the electrons are bound or free is of little consequence for X-rays above 1 keV incident on gas mostly composed of hydrogen (Vainshtein et al 1983). Back.

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