Accretion Efficiency Evolution of Central Supermassive Black Holes in Quasars

TL;DR

This study investigates the evolution of accretion efficiency in supermassive black holes within quasars across different redshifts, proposing a comprehensive model that accounts for observed variations and their relation to star formation rates.

Contribution

It develops a new model for accretion efficiency that accounts for redshift-dependent variations and removes selection effects using flux- and volume-limited samples.

Findings

Accretion efficiency peaks around redshift 2.708.

Efficiency varies significantly over redshift, increasing above and decreasing below 2.708.

A wider range of efficiency values is observed than previously reported.

Abstract

The ongoing debate regarding the most accurate accretion model for supermassive black holes at the center of quasars has remained a contentious issue in astrophysics. One significant challenge is the variation in calculated accretion efficiency, with values exceeding the standard range of $0.038 < \epsilon < 0.42$. This discrepancy is especially pronounced in high redshift supermassive black holes, necessitating the development of a comprehensive model that can address the accretion efficiency for supermassive black holes in both the low and high redshift ranges. The selection effect was removed from model construction by creating a flux- and volume-limited sample, as the range of values for estimating the accretion efficiency factor varied through different redshifts. In this study, we have focused on low redshift ($z < 0.5$) Palomar-Green quasars (79 quasars) and high redshift ($z \geq 3$) quasars with standard disks from the flux- and volume-limited QUOTAS+QuasarNET dataset (75 quasars) to establish a model for accretion efficiency. By considering the QUOTAS+QuasarNET+DL11 dataset, a peak can be seen around $z \sim 2.708$, and it seems to be related to the peak of the star formation rate ($1 < z_{SFR} < 3$). Consequently, the observed maximum and minimum values of accretion efficiency in standard disks, through the considered bond (3$\sigma$), display a significantly wider range than previously noted and differentiate over time. In redshifts higher than 2.708, the accretion efficiency shows patterns of increase as redshift decreases, while in redshifts lower than 2.708, accretion efficiency is seen to decrease with reducing redshift. This result can potentially lead to a more accurate correlation between the star formation rate in quasars and their relationship with the mass of the central supermassive black holes with a more comprehensive disk model in future studies.