We constrain X-ray spectral shapes for the ensemble of AGN 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 \langle R \rangle , \langle E _ { cutoff } \rangle and \langle \Gamma \rangle to vary subject to reproducing the CXB .
We report results for \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 can not reproduce the CXB for any XLF .
The marginalized conditional probabilities for the four free parameters are : \langle R \rangle = 0.99 ^ { +0.11 } _ { -0.26 } , \langle E _ { cutoff } \rangle = 118 ^ { +24 } _ { -23 } , \sigma _ { \Gamma } = 0.101 ^ { +0.097 } _ { -0.001 } and \langle \Gamma \rangle = 1.9 ^ { +0.08 } _ { -0.09 } .
We provide an interactive online tool for users to explore any combination of \langle E _ { cutoff } \rangle , \sigma _ { E } , \langle \Gamma \rangle , \sigma _ { \Gamma } , \langle R \rangle and \sigma _ { R } , including different distributions for each absorption bin , subject to the integral CXB constraint .
The distributions observed in many AGN samples can be ruled out by our analysis , meaning these samples can not be representative of the full AGN population .
The few samples that fall within the acceptable parameter space are hard X-ray-selected , commensurate with their having fewer selection biases .