[Paper Review] AGN Broad Line Regions Scale with Bolometric Luminosity

Sascha Trippe|arXiv (Cornell University)|Jun 15, 2015

Galaxies: Formation, Evolution, Phenomena16 references3 citations

TL;DR

This paper proposes that the size of active galactic nucleus (AGN) broad line regions scales with bolometric luminosity rather than monochromatic luminosity ($\lambda L_\lambda$), challenging the standard assumption in virial mass estimators. Using cross-comparisons of mass estimates from different emission lines (H$\beta$, H$\alpha$, C IV) in a sample of lensed quasars, the study demonstrates that mass ratios derived from $\lambda L_\lambda$ proxies deviate systematically unless bolometric corrections are applied, revealing that $\lambda L_\lambda$ is an inadequate proxy due to AGN color variations.

ABSTRACT

The masses of supermassive black holes in active galactic nuclei (AGN) can be derived spectroscopically via virial mass estimators based on selected broad optical/ultraviolet emission lines. These estimates commonly use the line width as a proxy for the gas speed and the monochromatic continuum luminosity as a proxy for the radius of the broad line region. However, if the size of the broad line region scales with bolometric rather than monochromatic AGN luminosity, mass estimates based on different emission lines will show a systematic discrepancy which is a function of the color of the AGN continuum. This has actually been observed in mass estimates based on H-alpha / H-beta and C IV lines, indicating that AGN broad line regions indeed scale with bolometric luminosity. Given that this effect seems to have been overlooked as yet, currently used single-epoch mass estimates are likely to be biased.

Motivation & Objective

• To test whether the radius of the broad line region in AGN scales with bolometric luminosity rather than monochromatic luminosity ($\lambda L_\lambda$), challenging a long-standing assumption in virial mass estimators.
• To address the systematic bias in black hole mass estimates arising from the use of $\lambda L_\lambda$ as a proxy for broad line region radius, which neglects AGN continuum color variations.
• To demonstrate that cross-comparisons of mass estimates from different emission lines (e.g., H$\beta$, C IV) reveal systematic discrepancies unless bolometric corrections are applied.
• To show that the observed scatter in mass estimator relations is not random but driven by hidden parameters—specifically, the AGN spectral energy distribution and bolometric corrections.
• To advocate for source-specific bolometric corrections in virial mass estimation to reduce systematic bias in large AGN surveys.

Proposed method

• Uses a cross-comparison of virial mass estimates derived from different emission lines (H$\beta$, H$\alpha$, C IV) in 12 lensed high-redshift quasars from Assef et al. (2011).
• Applies the virial mass estimator $M = \kappa v^2 L^\alpha$, where $L$ is bolometric luminosity, and $\alpha \approx 0.5$, to test consistency across lines.
• Derives the expected mass ratio $M'_a/M'_b = \xi_{ab} (L_a/L_b)^\alpha$ when using $\lambda L_\lambda$ as a proxy, with $\xi_{ab}$ accounting for color effects.
• Compares observed mass ratios from different lines to the theoretical expectation under the assumption of consistent $M$ values, revealing deviations unless $\xi_{ab}$ is calibrated.
• Uses the ensemble average of $M'_a/M'_b$ to infer $\xi_{ab} = \langle (L_a/L_b)^\alpha \rangle^{-1}$, showing that $\lambda L_\lambda$ alone cannot account for the full luminosity dependence.
• Analyzes the impact of AGN variability and bolometric corrections on mass estimator consistency, concluding that variability increases error but not systematic bias.

Experimental results

Research questions

• RQ1 Does the radius of the broad line region in AGN scale with bolometric luminosity or with monochromatic luminosity ($\lambda L_\lambda$)?
• RQ2 Why do mass estimates from different emission lines (e.g., H$\beta$ vs. C IV) systematically differ when using standard $\lambda L_\lambda$-based estimators?
• RQ3 To what extent do AGN continuum colors introduce systematic biases in virial mass estimators based on $\lambda L_\lambda$?
• RQ4 Can the observed scatter in cross-comparisons of mass estimators from different lines be explained by bolometric corrections and spectral energy distribution variations?
• RQ5 What are the implications for large-scale AGN surveys if mass estimators are not corrected for source-specific bolometric luminosity?

Key findings

• The broad line region radius scales with bolometric luminosity rather than monochromatic luminosity $\lambda L_\lambda$, as evidenced by systematic deviations in mass estimates from different emission lines.
• When using $\lambda L_\lambda$ as a proxy, mass estimates from C IV and Balmer lines (H$\alpha$, H$\beta$) differ by up to a factor of four unless bolometric corrections are applied.
• The ratio of mass estimates from different lines depends on the luminosity ratio and the color factor $\xi_{ab}$, which must be calibrated per source to avoid bias.
• The ensemble average of mass ratios $\langle M'_a/M'_b \rangle = 1$ only if $\xi_{ab}$ is properly accounted for, validating the need for source-specific bolometric corrections.
• AGN variability does not introduce systematic trends but increases measurement error; variations of up to a factor of five in luminosity are within typical 0.3 dex errors of mass estimates.
• The Baldwin effect and ionization stratification in the broad line region support the physical plausibility of a bolometric scaling, as higher-ionization lines form closer to the central source.