Photoelectric effect

Absorption is an important phenomenon in observing AGN. The presence of an absorber along the line of sight to the X-ray source modifies the intrinsic spectrum, imprinting information about itself. In the X-ray regime the most common interaction of photons with matter is the photoelectric effect because X-ray photons exceed the binding energy of the most populous atoms (H, He). Hence an X-ray interaction will liberate an electron from the innermost K (n=1) shell resulting in ionisation of the atom (this is known as bound–free absorption). However, when the binding energy is not exceeded by the absorbed photon, the electron instead transitions to a higher energy level and not ejected (this is called a bound–bound transition); the atom remains in an excited state until it decays (by either emission or charge exchange). In both, absorption features (such a curvature, edges and/or lines) are imprinted on the intrinsic spectrum as photons are removed from the observer’s line of sight.

1.2.3.1 Bound–free absorption

The amount of photoelectric absorption is defined by the amount of atoms/ions in the line of sight; this gives the optical depth of a species i, defined as:

τi = σ(E)iNi (1.12)

1.2 Physical processes 15

Figure 1.4: Variation of observed spectrum with increasing column density of a neutral absorber. The y-axis is the flux density multiplied by energy squared this is so that power laws with a photon index of two are flat.

density along the line of sight. A simple approximation for a given energy is σ(E) ∝ (E/Eedge)−3 (where Eedge is the energy of the K edge, for example Eedge of hydrogen is

13.6 eV). The total cross section would be the abundance-weighted sum of σi over all species.

The observed modification to the intrinsic spectrum is Fobs(E) = Fsrc(E) ×

X

i

e−σ(E)iNi_{. (1.13)}

The energy of the edge increases with proton number due to the stronger nuclear bonding (Eedge ∼ 0.5 keV for O and Eedge ∼ 7 keV for Fe). Fig. 1.4 shows as the column increases the

weaker edges of heavier elements become visible at increasingly higher energies, until the column density becomes sufficiently large to remove all flux at that energy.

1.2.3.2 Bound–bound absorption & spectral lines

As described earlier, when a photon below the ionisation threshold is absorbed (assuming a valid transition can occur at that energy) the atom/ion enters an excited state. This removes photons from the input spectrum. The energy of this absorption feature is characteristic of the transition and the atom/ion. When the atom/ion returns to the ground state one or more photons are emitted with the total energy emitted equal to that of the original exciting electron. The energy of the outgoing photons is dependent on the element and the charge. This provides an important diagnostic tool; giving information about the ionisation, optical depth and relative abundances of the material observed. The strength of the absorption/emission feature relative to the continuum is the equivalent width (EW) and is defined as: EW = Z E2 E1 f (E) − fc fc dE, (1.14)

where f (E) the flux is the continuum + line and fcis the expected continuum flux. This is a

useful diagnostic tool as lines are reprocessed; they respond to the flux they observe (after a delay for light travel time and recombination). This delay can be used to effectively measure distances between the source and the reprocessing material. This is called reverberation mapping and can be used to test the overall structure of the AGN.

1.2.3.3 photo-ionised absorption

When the rate of photo-ionisation is comparable to the recombination rate (the rate which electrons are captured by ions) – which is likely to be the case when there is a significant X-ray flux – ions can have a large contribution to the overall absorption cross-section. The ionisation state of a gas cloud can be defined as (Tarter & Salpeter 1969):

ξ = Lion nHR2

1.2 Physical processes 17

Figure 1.5: The spectrum of photo-ionised gas under increasing illumination

where Lion is the luminosity of the ionising continuum from 1–1000 Rydberg (a range

covering the ionisation potential of most cosmically abundant elements); nH is the number

density of hydrogen; and R is the distance between the absorbing cloud and the X-ray source. Fig. 1.5, shows the spectrum of a shell of gas ( NH= 1023cm−2) with increasing ionisation

log ξ = 1 to 4. The soft flux increases as the shell becomes more transparent, as atoms/ions are stripped of there outer electrons. At first, more features can be seen between 0.5–2 keV as the electrons have more allowed transitions. However, as the ionisation becomes larger there are less bound electrons and so the continuum becomes comparatively featureless again. This can also be seen around 6 keV, where some absorption features become stronger as the population of He-like Fe increases.

1.2.3.4 Fluorescence

Fluorescence occurs when a high-energy photon interacts with an atom and causes an electron from the inner shell (for example the K-shell in Fe) to be ejected. This leaves a hole which is filled by an electron from a higher shell; this causes the hole to move outwards as

electrons cascade inwards. During this cascade the electrons emit photons as they move to lower energy orbitals. In the case where an emitted fluorescence photon has an energy which overcomes the binding energy of the outer electrons, such as a photon emitted from an L-shell to K-shell transition interacting with an M-shell (or L-Shell) electron, then the outer electron is ejected (therefore no photon is emitted) this process is known as auto-ionisation or the “Auger” effect. The relative probability between these two processes (fluorescence vs auto-ionisation) is given by the fluorescence yield, which varies as α ∝∼ Z3 _(Krause

1979) where Z is the proton number. This strong dependence on atomic number means that heavier elements should have a larger fluorescence yield and therefore produce much stronger fluorescence emission lines.