X-ray Absorption by the ISM

In Uncategorized on March 1, 2011 at 3:58 am

When interpreting data from X-ray satellites like Chandra and XMM-Newton, it is necessary to understand how the X-ray spectrum is modified as it passes through the interstellar medium, i.e. how high-energy photons (0.1-10 keV) interact with the ISM (and IGM). Essentially answering this boils down to calculating the (energy-dependent) photo-ionization cross-section of the ISM, $\sigma_{ISM}$ . (If you want more detail than what is described here, a good starting point is Wilms, J et al., 2000 and citations.)

Typically, the cross-section is normalized to the total hydrogen column density, $N_H$ (in atoms cm $^{-2}$ ), so that the observed X-ray spectrum is given by

$I_{obs}(E) = I_{source}(E) \times e^{-\sigma_{ISM}(E) \times N_H}.$

The cross-section itself can be written as the sum of three different contributions: from atomic gas, molecular gas, and dust grains. Formally,

$\sigma_{\mathrm{ISM}} = \sigma_{\mathrm{gas}} + \sigma_{\mathrm{molecules}} + \sigma_{\mathrm{grains}}$ .

(A plot showing the combined cross-section at X-ray energies is shown in Fig. 1 of Wilms et al.)

Absorption by gas

In principle, the gas cross section is simply a sum over the cross-sections of all available species and ionization states, weighted by their abundance. In practice, the atomic physics is still fairly uncertain and in many cases, the exact cross-sections are not known. Nevertheless, it’s worth noting a few points.

For hydrogenic atoms, one can write down an analytic expression for the cross-section (eqn. 13.1 in Draine). As $h \nu >> Z^2 I_H$ , this asymptotes to $\sigma(\nu) \sim (h\nu/Z^2I_H)^{-3.5}$ . Here $Z$ is the atomic number, and $I_H$ is the ionization energy of hydrogen. With more electrons present, the energy dependence is more complicated due to the many different states available.
The cross-section of heavier elements show an “absorption edge” at the energy necessary to remove electrons from the K-shell; beyond this edge the cross-section from heavier elements can be 3-4 orders of magnitude higher than that of hydrogen. This means that these elements can dominate the cross-section, even if their abundances are only $10^{-3}$ that of hydrogen. (Some examples of cross-sections including contributions from different subshells are shown here.) Also note that the total cross-section can depend quite sensitively on the abundances assumed for the gas.
Rather than being absorbed photo-electrically, X-ray photons can also interact with electrons in gas via Compton Scattering. For hydrogen, the Compton scattering cross-section becomes equal to the photo-ionization cross-section at about 2.5 keV.
As electrons are removed from the K-shell of an atom, rather than it relaxing from this excited state radiatively, it can also happen that one electron drops down to the K-shell, while another is excited further (and often ejected). This is known as the Auger effect, and plays an important role in the ionization of heavy elements by X-rays. Alternatively, electrons from the L or M shell can drop down to the K-shell, emitting a K $\alpha$ or K $\beta$ photon – this is thought to be an important source for emission from gas near X-ray sources.

Absorption by Molecules

Typically only the contribution from H $_2$ is considered due to its large abundance, but in principle one should again sum over the different species present. Like most atoms, the cross-sections cannot be calculated analytically, though fits to experimental data are available. For H $_2$ , note that $\sigma_{H_{2, bf}} > 2 \sigma_{H_{bf}}$ , so ignoring the fact that some of the gas is molecular will lead to an under-estimation of the total cross-section. Molecular hydrogen contributes significantly to the total cross-section at energies below 1 keV.

Absorption by Dust Grains

X-rays, as high-energy photons, are thought to mainly be absorbed at the surface of dust grains. This means that material “within” the grain is not really seen by the photon, and so, somewhat non-intuitively, if abundances stay the same but more of the heavy elements are in the form of dust, the cross-section will be lower at X-ray energies than if they were in the form of gas. Calculating the actual cross-section due to dust requires knowing the size distribution and composition of the dust grains, which again in general is uncertain. In fact, since X-rays will penetrate material over a large range of densities and temperatures, it has been suggested to use X-rays as a probe to study interstellar gas and dust. (This white paper by Julia Lee and Randall Smith, and references, is a good place to start if you are interested in how this can be done.)

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