The population behind X-ray AGN samples

Counting and Characterizing

Ringberg Group Meeting / Oct 2013

Johannes Buchner

in collaboration with A. Georgakakis, K. Nandra, L. Hsu, S. Fotopoulou, C. Rangel, M. Brightman, A. Merloni and M. Salvato

Luminosity function  — 

#/space density of AGN with certain properties

  • How many obscured AGN?
  • — Central engine
  • — LSS assembly

State of the field

  • Maximum likelihood estimators with bins
  • "Bayesian" inference on ad-hoc parametric models
    • Priors can not be motivated for LDDE, LADE with evolving obscured fraction
    • essentially doing maximum likelihood style parameter estimation, but with Monte-Carlo

The right way: a 3D field

  • degrees of freedom
  • but prior: neighboring points should have similar values
  • or similar slope
  • reconstruct continuous field
  • With strong, varying selection bias!

non-parametric parametric reconstruction

  • single parameter maximum
  • weak correlations through priors
  • Best fit with optimization algorithms
  • Parameter estimation with MCMC (probably will not converge)
  • Model selection using AIC: Information loss for going to simpler LADE, LDDE

Requirements for Luminosity function analyses

  • good estimates
  • good uncertainty estimates!
  • handling ambiguities

Ambiguity

Maximum likelihood lottery

  • How can parameters be derived from few counts?
  • How to deal with multiple solutions?
  • How to find the correct sufficient model?

Spectral analysis with Bayesian inference

  • Full probability distribution (uncertainty) on all model parameters
  • Global algorithm (nested sampling, not MCMC or fitting)
  • Model comparison
    Likelihood ratios are problematic:
    • only nested models
    • not on borders
    • when in doubt, remains with simpler model

Model selection on AGN X-ray spectra

Example - Source 179 z=0.605, 2485 counts

powerlaw


Example - Source 179 z=0.605, 2485 counts

wabs


Example - Source 179 z=0.605, 2485 counts

torus+scattering


Example - Source 179 z=0.605, 2485 counts

torus+pexmon+scattering


Example - Source 179 z=0.605, 2485 counts

wabs+pexmon+scattering


Example - Source 179 z=0.605, 2485 counts

torus+pexmon+scattering

X-ray spectral analysis methodology

good ol' times Current Suggested
Statistic with binning C-stat  
Error estimation -stat, Contours of pairs, Fisher matrix, stepping marginal distributions
Model comparison what looks better Likelihood ratio tests Bayesian model comparison
Background handling subtracted bin-wise estimates, continuous background model continuous background model
Goodness-of-Fit & discover model deviation binned, residuals binned, residuals +QQ-plots

Why switch?

  • No fiddling with finding optimum (does not fail)
  • No fiddling with exploring contours
  • Shows multiple solutions
  • Produces estimators, uncertainties and model "evidence" simultaneously
  • Allows comparing arbitrary models
  • Easier!

Conclusions: AGN Model

  1. Obscuring torus is not a sphere, not a disk, something in between
  2. Thomson scattering of intrinsic radiation
  3. Additional compton scattering into LOS from dense region

Have now probability distributions for CDF-S, AEGIS, COSMOS

  • Upcoming: relations between and ,
  • Upcoming: Luminosity function