Reconstructing AGN X-ray spectral parameter distributions with Bayesian methods II: Population inference. (arXiv:2111.15235v2 [astro-ph.HE] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Ge_L/0/1/0/all/0/1">Lingsong Ge</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Paltani_S/0/1/0/all/0/1">Stéphane Paltani</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Eckert_D/0/1/0/all/0/1">Dominique Eckert</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Salvato_M/0/1/0/all/0/1">Mara Salvato</a>
We present a new Bayesian method for reconstructing the parent distributions
of X-ray spectral parameters of active galactic nuclei (AGN) in large surveys.
The method uses the probability distribution function (PDF) of posteriors
obtained by fitting a consistent physical model to each object with a Bayesian
method. The PDFs are often broadly distributed and may present systematic
biases, such that naive point estimators or even some standard parametric
modeling are not sufficient to reconstruct the parent population without
obvious bias. Our method uses a transfer function computed from a large
realistic simulation with the same selection as in the actual sample to
redistribute the stacked PDF and then forward-fit a nonparametric model to it
in a Bayesian way, so that the biases in the PDFs are properly taken into
account. In this way, we are able to accurately reconstruct the parent
distributions. We apply our spectral fitting and population inference methods
to the XMM-COSMOS survey as a pilot study. For the 819 AGN detected in the
COSMOS field, 663 (8%) of which have spectroscopic redshifts (spec-z) and the
others high-quality photometric redshifts (photo-z), we find prominent
bi-modality with widely separated peaks in the distribution of the absorbing
hydrogen column density (N_H) and an indication that absorbed AGN have harder
photon indices. A clear decreasing trend of the absorbed AGN fraction versus
the intrinsic 2-10keV luminosity is observed, but there is no clear evolution
in the absorbed fraction with redshift. Our method is designed to be readily
applicable to large AGN samples such as the XXL survey, and eventually eROSITA.
We present a new Bayesian method for reconstructing the parent distributions
of X-ray spectral parameters of active galactic nuclei (AGN) in large surveys.
The method uses the probability distribution function (PDF) of posteriors
obtained by fitting a consistent physical model to each object with a Bayesian
method. The PDFs are often broadly distributed and may present systematic
biases, such that naive point estimators or even some standard parametric
modeling are not sufficient to reconstruct the parent population without
obvious bias. Our method uses a transfer function computed from a large
realistic simulation with the same selection as in the actual sample to
redistribute the stacked PDF and then forward-fit a nonparametric model to it
in a Bayesian way, so that the biases in the PDFs are properly taken into
account. In this way, we are able to accurately reconstruct the parent
distributions. We apply our spectral fitting and population inference methods
to the XMM-COSMOS survey as a pilot study. For the 819 AGN detected in the
COSMOS field, 663 (8%) of which have spectroscopic redshifts (spec-z) and the
others high-quality photometric redshifts (photo-z), we find prominent
bi-modality with widely separated peaks in the distribution of the absorbing
hydrogen column density (N_H) and an indication that absorbed AGN have harder
photon indices. A clear decreasing trend of the absorbed AGN fraction versus
the intrinsic 2-10keV luminosity is observed, but there is no clear evolution
in the absorbed fraction with redshift. Our method is designed to be readily
applicable to large AGN samples such as the XXL survey, and eventually eROSITA.
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