[Paper Review] BASS XXX: Distribution Functions of DR2 Eddington-ratios, Black Hole Masses, and X-ray Luminosities

Tonima Tasnim Ananna, Anna K. Weigel+20 more|arXiv (Cornell University)|Jan 14, 2022

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy189 references63 citations

TL;DR

This study presents the first directly observed, bias-corrected black hole mass function (BHMF) and Eddington-ratio distribution function (ERDF) for Type 2 active galactic nuclei (AGN) using the spectroscopically complete BASS DR2 sample. By applying forward modeling to correct for observational biases, it finds that Type 2 AGN have a significantly skewed ERDF toward lower Eddington ratios than Type 1 AGN, supporting the radiation-regulated unification model where radiation pressure shapes the obscuring structure.

ABSTRACT

We determine the low-redshift X-ray luminosity function (XLF), active black hole mass function (BHMF), and Eddington-ratio distribution function (ERDF) for both unobscured (Type 1) and obscured (Type 2) active galactic nuclei (AGN) using the unprecedented spectroscopic completeness of the BAT AGN Spectroscopic Survey (BASS) data release 2. In addition to a straightforward 1/Vmax approach, we also compute the intrinsic distributions, accounting for sample truncation by employing a forward modeling approach to recover the observed BHMF and ERDF. As previous BHMFs and ERDFs have been robustly determined only for samples of bright, broad-line (Type 1) AGNs and/or quasars, ours is the first directly observationally constrained BHMF and ERDF of Type 2 AGN. We find that after accounting for all observational biases, the intrinsic ERDF of Type 2 AGN is significantly skewed towards lower Eddington ratios than the intrinsic ERDF of Type 1 AGN. This result supports the radiation-regulated unification scenario, in which radiation pressure dictates the geometry of the dusty obscuring structure around an AGN. Calculating the ERDFs in two separate mass bins, we verify that the derived shape is consistent, validating the assumption that the ERDF (shape) is mass independent. We report the local AGN duty cycle as a function of mass and Eddington ratio, by comparing the BASS active BHMF with the local mass function for all SMBH. We also present the log N-log S of Swift-BAT 70-month sources.

Motivation & Objective

• To determine the intrinsic distribution functions of X-ray luminosity, black hole mass, and Eddington ratio for low-redshift AGN, correcting for observational biases.
• To provide the first directly observed, bias-corrected black hole mass function (BHMF) and Eddington-ratio distribution function (ERDF) for Type 2 AGN, which have been previously inaccessible due to obscuration.
• To test the radiation-regulated unification model by comparing the intrinsic ERDFs of Type 1 and Type 2 AGN.
• To assess the mass dependence of the ERDF and compute the local AGN duty cycle across different mass and accretion rate regimes.

Proposed method

• Utilizes the spectroscopically complete BASS DR2 sample of 1668 AGN with redshifts 0.01 ≤ z ≤ 0.3 to ensure high completeness in AGN detection.
• Applies a forward modeling approach to correct for sample truncation and observational biases, particularly at low masses and low Eddington ratios.
• Employs a modified Schechter function for the AGN XLF and a double Schechter function for the galaxy stellar mass function to model the data.
• Uses 1/Vmax and forward modeling to compute the intrinsic BHMF and ERDF, with error propagation via Markov Chain Monte Carlo (MCMC) using Emcee.
• Verifies self-consistency by convolving the bias-corrected BHMF and ERDF to reproduce the observed XLF.
• Splits the analysis into Type 1 and Type 2 sub-samples based on X-ray obscuration and spectroscopic classification.

Experimental results

Research questions

• RQ1 What is the intrinsic distribution of Eddington ratios for Type 2 AGN, and how does it compare to Type 1 AGN after correcting for observational biases?
• RQ2 Is the shape of the Eddington-ratio distribution function (ERDF) independent of black hole mass, as assumed in many models?
• RQ3 How do the X-ray luminosity function (XLF), BHMF, and ERDF collectively reproduce the observed AGN population?
• RQ4 What fraction of local supermassive black holes are currently active, and how does this duty cycle vary with mass and accretion rate?

Key findings

• The intrinsic ERDF of Type 2 AGN is significantly skewed toward lower Eddington ratios (log λE ≈ -1.657) compared to Type 1 AGN (log λE ≈ -1.152), with a statistically significant difference in the break point.
• The ERDF shape is consistent across two distinct black hole mass bins (log MBH ≈ 6.5–7.5 and 7.5–8.5), confirming that the ERDF is mass-independent for the BASS DR2 sample.
• The active fraction of AGN, defined as the fraction with log λE > -3 relative to the total black hole mass function, is 10–16% in the local Universe.
• The fraction of mass in active supermassive black holes is 6–10% of the total local SMBH mass, indicating that most SMBHs are currently in a quiescent state.
• The observed trend of decreasing Compton-thin AGN fraction with increasing luminosity and constant Compton-thick fraction supports the radiation-regulated unification model.
• The convolution of the bias-corrected BHMF and ERDF successfully reproduces the observed XLF, validating the self-consistency of the derived distribution functions.