The variability angular diameter distance and the intrinsic brightness temperature of active galactic nuclei

TL;DR

This work assesses whether variability-based estimates of the intrinsic brightness temperature $T_{ m int}$ for AGN cores converge to a common value and whether $T_{ m int}$ depends on frequency, enabling a Doppler-factor–free derivation of the angular diameter distance. It refines the theoretical framework to account for source geometry, yielding $T_{ m int}$ values that are roughly a factor of two lower than previous estimates and highlighting substantial current uncertainties due to cadence and modeling. Through two complementary approaches—a variability-based method and a population-based envelope involving $T_{ m vlb}$ and $\beta_{ m app}$—the study establishes upper limits at 15 and 43 GHz and lower limits at 24, 43, and 86 GHz, while revealing notable offsets between methods. The results underscore the need for regular, high-cadence, multifrequency VLBI on complete samples to robustly determine any frequency dependence of $T_{ m int}$ and to achieve convergence across redshifts for cosmological applications.

Abstract

Context. It has recently been suggested that angular diameter distances derived from comparing the variability timescales of blazars to angular size measurements with very long baseline interferometry (VLBI) may provide an alternative method to study the cosmological evolution of the Universe. Once the intrinsic brightness temperature ($T_{\rm int}$) is known, the angular diameter distance may be found without knowledge of the relativistic Doppler factor, opening up the possibility of a single rung distance measurement method from low $(z_{\rm cos}\ll1)$ to high $(z_{\rm cos}>4)$ redshifts. Aims. We aim to verify whether the variability-based estimates of the intrinsic brightness temperature of multiple active galactic nuclei (AGNs) converges to a common value. We also investigate whether the intrinsic brightness temperature changes as a function of frequency. Methods. We estimated the $T_{\rm int}$ of AGNs based on the flux variability of the radio cores of their jets. We utilized radio core light curves and size measurements of 75 sources at 15 GHz and of 37 sources at 43 GHz. We also derived $T_{\rm int}$ from a population study of the brightness temperatures of VLBI cores using VLBI survey data of more than $100$ sources at 24, 43, and 86 GHz. Results. Radio core variability-based estimates of $T_{\rm int}$ constrain upper limits of $\log_{10}T_{\rm int}$ [K]$<11.56$ at 15~GHz and $\log_{10}T_{\rm int}$ [K]$<11.65$ at 43 GHz under a certain set of geometric assumptions. The population analysis suggests lower limits of $\log_{10}T_{\rm int}$ [K]$>9.7$, $9.1$, and $9.3$ respectively at 24, 43, and 86 GHz. Even with monthly observations, variability-based estimates of $T_{\rm int}$ appear to be cadence-limited. Conclusions. Methods used to constrain $T_{\rm int}$ are more uncertain than previously thought. However, with improved datasets, the estimates should converge.

Figures (3)

• Figure 1: Intrinsic brightness temperature, $T_{\rm int}$, of AGNs obtained at different $\nu^{\rm o}$. Values with the label "pop" were obtained from a population analysis of $T_{\rm vlb}$ and $\beta_{\rm app}$. Values with the label "var" were obtained utilizing flux density variability. All values were scaled to correspond to a disk source geometry. The dashed horizontal line corresponds to the $T_{\rm eq}\approx5\times10^{10}$ K of 1994ApJ...426...51R. The values of Lee2014 are from 2014JKAS...47..303L, Nair2019 from 2019AA...622A..92N, Homan2021 from 2021ApJ...923...67H, and Liodakis2018 from 2018ApJ...866..137L, and they have been adjusted for the source geometry.
• Figure 2: Estimated $T_{\rm int}$ at 15 GHz (upper row) and at 43 GHz (lower row).
• Figure 3: Estimated $T_{\rm int}$ at 24 GHz (left), 43 GHz (center), and 86 GHz (right) using a population study (see Section \ref{['sec:app_estimation_of_Tint']} for details).