Letter to the Editor

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

¹ University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea
² Korea Astronomy and Space Science Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon 34055, Republic of Korea
³ Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul, Republic of Korea

^⋆ Corresponding authors: wheeyeon@kasi.re.kr; sslee@kasi.re.kr

Received: 17 July 2025
Accepted: 14 October 2025

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_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_cos ≪ 1) to high (z_cos > 4) redshifts. Previous studies have found T_int ≈ 10¹⁰–10¹¹ K, with a potential frequency dependence.

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_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_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_int constrain upper limits of log₁₀T_int [K] < 11.56 at 15 GHz and log₁₀T_int [K] < 11.65 at 43 GHz under a certain set of geometric assumptions. The population analysis suggests lower limits of log₁₀T_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_int appear to be cadence-limited.

Conclusions. Methods used to constrain T_int are more uncertain than previously thought. However, with improved datasets, the estimates should converge.