Time-Domain Radio Loudness of Active Galactic Nuclei: Intermittency, Memory, and Jet Escape

TL;DR

This paper introduces a time-domain framework for radio-loudness in active galactic nuclei, accounting for variability and jet activity, providing new models to interpret radio observations across different timescales.

Contribution

It develops an analytic model for AGN radio response considering intermittency, jet duty cycle, and lobe fading, offering a new perspective on radio-loudness classification.

Findings

The Beta distribution describes the extended-radio response variability.

Short radio memory can explain the radio-loud/quiet boundary.

A core-lobe mismatch index distinguishes jet phases.

Abstract

The classical radio-loudness parameter $R \equiv f_\nu(5\,\mathrm{GHz})/f_\nu(4400\,\text{\AA})$ compares a prompt accretion tracer with a radio numerator that mixes rapidly varying compact-core emission, lobe plasma surviving over millions of years, and host-galaxy synchrotron emission. We introduce a time-domain radio-loudness (TDRL) framework that makes this timescale mismatch explicit. The radio numerator is decomposed into compact-core and extended-lobe contributions, each weighted by a recovered fraction that depends on observing frequency, angular resolution, and surface-brightness sensitivity. For a single intermittently jetted AGN population, a two-state jet duty cycle convolved with exponential lobe fading yields an exact stationary Beta distribution for the normalized extended-radio response, whose mean is $f_{\rm duty}$ and whose variance scales as $(1+\chi_\nu)^{-1}$ with $\chi_\nu\equiv\taunu/t_{\rm switch}$. This result serves as an analytic reference model, while precise inference will require population models matched to specific survey selections. In this minimal reference model, the familiar GHz valley near the classical radio-loud/quiet boundary can in principle arise from short radio memory alone, without invoking two intrinsic engine classes; metre-wave surveys that recover diffuse emission and model the host galaxy contribution should progressively fill that valley. In the $(R^{core}_\nu,R^{lobe}_\nu)$ plane a core--lobe mismatch index distinguishes triggering, sustained, and remnant jet phases. A complementary two-barrier phase diagram in event-horizon-threading magnetic flux and jet-escape parameter provides a heuristic organizing scheme for jet launching and propagation through the nuclear medium. The framework offers testable, frequency-dependent predictions for current and future radio surveys.