Abstract
Collecting and analyzing X-ray photons over either spatial or temporal scales encompassing varying optical depth values requires knowledge about the optical depth distribution. For a sufficiently broad optical depth distribution, assuming a single column density value leads to a misleading interpretation of the source emission properties, nominally its spectral model. We present a model description for the interstellar medium absorption in X-ray spectra at moderate energy resolution, extracted over spatial or temporal regions encompassing a set of independent column densities. The absorption model (called disnht) approximates the distribution with a lognormal distribution and is presented in table format. The solution table and source code are made available and can be further generalized or tailored for arbitrary optical depth distributions encompassed by the extraction region. The disnht absorption model and its generalized solution are expected to be relevant for current and upcoming large angular scale analyses of diffuse X-ray emission, such as those from the extended ROentgen Survey with an Imaging Telescope Array (eROSITA) and the future Athena missions.
Highlights
For a sufficiently broad optical depth distribution, assuming a single column density value leads to a misleading interpretation of the source emission properties, nominally its spectral model
We have demonstrated that (i) there are several cases of significantly broad column density distributions, produced by averaging over a large enough sky area; (ii) in many of these cases, the distribution of column densities can be approximated with a lognormal distribution; and (iii) this approximation leads to a more precise characterization of the absorption spectrum in terms of statistical power and accuracy of the best-fit values
The assumption of an absorption spectrum described by a single column density value breaks
Summary
Neutral and partially ionized material can efficiently absorb ultraviolet light and X-rays (Wilms et al 2000). If the light collected into an instrument and summed into a spectrum encompasses several independent NH elements (in space or time), an appropriate description of the absorption necessarily requires a description of the NH distribution of values, such as a single column density value describing the absorption within a given (and satisfactory) accuracy, may not exist This fact follows from the mathematical evidence that a sum over exponential functions can be approximated by a single exponential function only in the case of a strongly peaked distribution of exponents around one value. Modeling of the spectral absorption through distribution of column densities has already been successfully performed in the past using a powerlaw column density distribution (pwab model, presented in Done & Magdziarz 1998) and more recently using a lognormal distribution (Cheng et al 2021; Wang et al 2021) These examples show the increasing need in the X-ray community of a careful and systematic treatment of the absorption when its properties change in a non-negligible way across space or time. For these and all the other cases mentioned above, in this work we aim to provide the community with a method and precomputed tables
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