Avoiding spurious breaks in binned luminosity functions

Abstract

We show that using either the method of Page & Carrera or the well-known $1/V_a$ method to construct the binned luminosity function (LF) of a flux limited sample of Active Galactic Nuclei (AGN) can produce an artificial flattening (or steepening in the case of negative evolution) of the binned LF for bins intersected by the flux cutoff of the sample. This effect is more pronounced for samples with steep and strongly evolving parent LFs but is still present even for non-evolving LFs. As a result of this distortion of the true LF, fitting a model LF to binned data may lead to errors in the estimation of the parameters and may even prompt the erroneous use of broken power law functions. We compute the expected positions of apparent breaks in the binned LF. We show that these spurious breaks in the binned LFs can be avoided if the binning is done in the flux--redshift plane instead of the typically used luminosity--redshift plane. Binning in the flux--redshift plane can be used in conjunction with the binning in the luminosity--redshift plane to test for real breaks in the binned LFs and to identify the features that are the result of binning biases. We illustrate this effect for most typical forms of luminosity dependence and redshift evolution and show how the proposed method helps address this problem. We also apply this method to the MOJAVE AGN sample and show that it eliminates an apparent break in the binned LF.

7 pages and 7 figures. Accepted for publication in ApJ

References in corpus (10)

• Unified Schemes for Radio-Loud Active Galactic Nuclei
• MOJAVE: Monitoring of Jets in AGN with VLBA Experiments - I. First-Epoch 15 GHz Linear Polarization Images
• An improved method of constructing binned luminosity functions
• Soft X-ray AGN Luminosity Function from ROSAT Surveys II. Table of the binned Soft X-ray Luminosity Function
• The Deep X-Ray Radio Blazar Survey (DXRBS). III. Radio Number Counts, Evolutionary Properties, and Luminosity Function of Blazars
• The Flat Spectrum Radio Luminosity Function, Gravitational Lensing, Galaxy Ellipticities and Cosmology
• The QSO evolution derived from the HBQS and other complete QSO surveys
• MOJAVE: Monitoring of Jets in AGN with VLBA Experiments. IV. The Parent Luminosity Function of Radio-Loud Blazars
• The radio luminosity function of radio-loud quasars from the 7C Redshift Survey
• Cosmological evolution of compact AGN at 15 GHz

Cited by in corpus (10)

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• MOJAVE: Monitoring of Jets in Active Galactic Nuclei with VLBA Experiments. VI. Kinematics Analysis of a Complete Sample of Blazar Jets
• The Luminosity Function at z~8 from 97 Y-band dropouts: Inferences About Reionization
• The Panchromatic Hubble Andromeda Treasury IV. A Probabilistic Approach to Inferring the High Mass Stellar Initial Mass Function and Other Power-law Functions
• Population statistics of beamed sources. I: A new model for blazars
• A graphical analysis of the systematic error of classical binned methods in constructing luminosity functions
• A flexible method for estimating luminosity functions via Kernel Density Estimation
• The VVDS-VLA Deep Field - IV: Radio-optical properties
• Effect of spectral index distribution on estimating the AGN radio luminosity function
• A New Method to Determine X-ray Luminosity Functions of AGN and their Evolution with Redshift