5. Iron Line Diagnostics

Iron is the end point of thermonuclear fusion. Heavier elements have to be made in supernova explosions. This makes it the most abundant of the heavy metals with a solar abundance of N_Fe = 3 x 10^-5N_H (Zombeck (1990)). Also, the K fluorescence yield increases with Z (Kortright (1986)) and is 0.34 for neutral iron (Makishima (1986)). This accounts for the prominence of 6.4 keV fluorescent lines in many sources. Spectroscopy of the iron L emission has been used to probe the properties of X-ray binaries (Kallman (1993)). However, in the case of Cen X-3 the iron L emission region (0.8-1 keV; e.g. Kallman (1991)) is seriously attenuated by interstellar absorption. Combined with the lower fluorescence yields (Kallman (1991)) this makes iron L spectroscopy impractical in the present work.

The equivalent width of an emission or absorption feature is defined by

$$\equiv \int_{\rm Line}^{} {\left\vert I(E) - I(E_c)\right\vert \over I(E_c)}$$ (34)

where I is the observed intensity and E_c is the line centroid energy (Léna (1988)). The equivalent width is a particularly useful quantity in astrophysics because it is independent of detector resolution (Thorne (1988)). Makishima (1986) used Monte Carlo calculations to estimate the expected equivalent width of the fluorescent iron line for various configurations of source and scattering material. Thus, the equivalent width can be used to distinguish between different distributions of fluorescing material relative to the source. We can determine the effects of geometry on the equivalent width by separating the X-ray emission into three observed components (Inoue (1985)). These are: the direct emission from the accreting object, the Thomson-scattered continuum, and the fluorescent iron line. The equivalent width of the fluorescent line depends on the relative magnitudes of these components. These are in turn determined by the geometry of the system. Figure 4.5 shows the observed and calculated equivalent width of the K_$\alpha$ line of neutral iron for four different configurations of source and scatterer.

Figure 10: Dependence of observed equivalent width on source geometry (from Makishima (1986)). The spectrum of the central source is assumed to be a power law with photon index $\alpha$ = 0.8.

The energy of the iron line may be used to determine the degree of ionization of the iron in the plasma. This can be used as a diagnostic of the ionization parameter for a photoionized plasma or the temperature of a collisional plasma. Figure 4.5 shows how the Fe K$\alpha$ line energy varies with ionization stage. Electric and magnetic dipole spectra were calculated (Cowan (1981)) with an intrinsic line width of 25 eV. The K$\alpha$ lines were fitted with Gaussian profiles to obtain the centroid energies. The iron line energy is close to 6.4 keV for ionization stages below Fe XVII. Thus when I refer to un-ionized iron in this dissertation I include Fe I-Fe XVII.

Figure 11: Dependence of Fe K$\alpha$ line energy on ionization stage.

Radiation from a luminous HMXB will ionize the stellar wind of its early-type companion. Recombination of Fe XVII to Fe XVI and Fe XVI and Fe XV will produce emission lines at 6.7 and 6.9 keV. The recombination mechanisms are radiative recombination and dielectronic recombination followed by cascading. Radiative recombination is the opposite process to photoionization and dielectronic recombination is the opposite process to autoionization. Photoionization and recombination will balance each other. The state of a photoionized, optically thin plasma may be characterized by the ionization parameter $\xi$ = L/(n_er²) (e.g. Kallman and McCray (1982)) where n_e is the electron density, L is the X-ray luminosity, and r is the distance to the source.

The photoionized plasma surrounding a system similar to Cen X-3 has log₁₀$\xi$ > 10⁴ so it will be transparent to X-rays provided the electron density is not too high. The optical depth for Thomson scattering will be

$$\tau \sigma_{T}^{} \approx$$ (35)

where N₂₂ is the electron column density in units of 10²² cm^-2.