Abstract

We constrain X-ray spectral shapes for the ensemble of active galactic nuclei (AGNs) based on the shape of the cosmic X-ray background (CXB). Specifically, we rule out regions of X-ray spectral parameter space that do not reproduce the CXB in the energy range 1-100 keV. The key X-ray spectral parameters are the photon index, Gamma; the cutoff energy, E-cutoff; and the reflection scaling factor, R. Assuming each parameter follows a Gaussian distribution, we first explore the parameter space using a Bayesian approach and a fixed X-ray luminosity function (XLF). For sigma(E) = 36 keV and sigma(R) = 0.14, fixed at the observed values from the Swift-BAT 70-month sample, we allow sigma(Gamma) = 0.1-0.5. In an alternative approach, we define the parameter distributions, then forward model to fit the CXB by perturbing the XLF using a neural network. This approach allows us to rule out parameter combinations that cannot reproduce the CXB for any XLF. The marginalized conditional probabilities for the four free parameters are: