X-ray Transmission Through Photoionized Gas with Moderate Thomson Optical Depth

Abstract

We model the absorption of X-rays by gas obscuring the source and photoionized by it. We consider a broad range of column densities, including both Thomson-thin and Thomson-thick media. For the Thomson thin regime, we derive a simple criterion based on the source luminosity and spectrum, as well as the medium radius and column density, that distinguishes between the following cases: (i) The absorption can be modeled well by a neutral medium; (ii) The radiation ionizes its way through the medium, and no absorption is expected; and (iii) A detailed model is required because the column density inferred from modeling the absorption with a neutral gas is much lower than the actual column density, or because the absorption features cannot be fitted by a neutral absorber. We derive the criterion analytically using a toy model of hydrogen and oxygen and calibrate it for realistic compositions with metallicities in the range $Z/Z_{\odot}=0.01-50$, using \textsc{Cloudy}. We generalize the model to the Thomson-thick regime, where we consider, alongside photoabsorption, electron scattering, Compton heating, Comptonization, and photon degradation. In this case, the emergent spectrum depends on the boundary condition experienced by photons scattered back towards the source. We discuss the effect of a reflective boundary and a reprocessing boundary. We provide simple criteria for the expected absorption state and discuss additional effects that alter the spectrum. The main motivation for our modeling is X-ray emission from supernovae interacting with the circumstellar medium; however, we expect it to be useful for many other applications.

Figures (7)

• Figure 1: The ionization profile (left panels) and transmitted spectrum (right panels) of simulations with $1-y_{\rm in} \sim 1$ (composition of hydrogen and oxygen only). The column density grows from top to bottom, while the rest of the parameters are held constant (i.e., constant $\xi$ and composition). Note that in such a setup, the ionization profile is independent of where the matter is truncated. On the left, the three panels show the ionization fraction of oxygen $O^{5+}$ to $O^{8+}$. At the illuminated face of the matter, the $O^{8+}$ fraction is set by the ionization-recombination equilibrium. This value then decreases on a scale $\tau_\text{abs}\simeq1$. On the right, the corresponding transmitted spectra are shown, with the incident spectra given for reference. In the top simulation, there is nearly no absorption, the middle one corresponds to marginal absorption, and the bottom one shows significant absorption. The gray dashed line marks the absorption by neutral matter of the same composition and column density.
• Figure 2: For each of the simulations we ran, we plot the ratio between the best-fit column density obtained under the assumption of fully neutral gas, $\Sigma_\text{fit,nt}$, and the actual column density $\Sigma$, as a function of $W$ (Eq. \ref{['eq:W_val']}). Every simulation corresponds to a single dot. Grey dots: simulations in which $\xi\le\xi_c$. For these, the neutral column density is fit only above 1 keV, because below it, non-neutral features appear. An example of such a spectrum can be seen in the second panel of figure \ref{['fig:example']}. Cases in which $\xi\ge \xi_c$ are marked in various colors, according to the fit to neutral column density. Blue dots: cases in which the neutral column density that fits the spectrum is approximately half the actual column density. An example is given in the top panel of figure \ref{['fig:example']}. Orange dots: cases in which a good fit can be found for absorption by neutral column density, but the fit results in a value much lower than the actual column density (example in the third panel of figure \ref{['fig:example']}). Green triangles: simulations for which there is no significant absorption, and only an upper limit on the neutral column density can be found. For readability, all these simulations are plotted at the same value, although each results in a different upper limit (example in the bottom panel of figure \ref{['fig:example']}). Black hollow circles: simulations for which no neutral column density can provide a good fit; the value of $\Sigma_\text{fit,nt}/\Sigma$ is meaningless and is arbitrarily set to 0.1 in the figure for clarity. An example of such a case is given in the fourth panel of figure \ref{['fig:example']}.
• Figure 3: Example spectra from our simulations, showing the incident spectrum, the transmitted spectrum, and the best-fit neutral absorption spectrum. Top panel: approximately neutral column density, corresponding to orange dots in figure \ref{['fig:Sigma_fit']}. Second panel: spectrum with $\xi<\xi_c$, where the neutral cross-section is a good approximation only above 1 keV, corresponding to the gray markers in figure \ref{['fig:Sigma_fit']}. Third and fourth panels: spectra from the transition region; the third panel shows a spectrum where the best-fit cross-section is significantly below the actual cross-section, and the fourth panel shows a spectrum where absorption features are not well-described by a neutral fit. In figure \ref{['fig:Sigma_fit']}, these are marked in orange and hollow circles, accordingly. Fifth panel: negligible absorption, where all elements up to oxygen are fully ionized. Such simulations are marked in green triangles in figure \ref{['fig:Sigma_fit']}.
• Figure 4: The matter temperature at the illuminated side of the medium is given as a function of $\xi$, for each of our simulations (all Thomson thin). The color bar shows the temperature relative to the Compton temperature (equation \ref{['eq:Tc']}). Note that for Thomson thick matter, scattering increases the effective local value of $\xi$ by a factor of $\sim \tau_\text{T}$, and to read the expected temperature from this graph, one must compare the X-axis of this plot to the value of $\tau_\text{T}\cdot \xi$for a reflective boundary and to $\xi \frac{\tau_\text{T}}{\tau_\text{T}(r_{\rm in})}$ for a reprocessing boundary, assuming negligible absorption.
• Figure 5: This figure shows the absorption cross-section at $h\nu=1~{\rm keV}$ and $h\nu=0.5~{\rm keV}$ at the illuminated side of the slab, as a function of the fraction of $O^{7+}$ - $\frac{n_{O^{7+}}}{n_ O}$, for our complete set of simulations.