A distance measurement for blazar TXS 0506+056 using its radio variability and very long baseline interferometry images

Aims. We present the results of constraining the angular diameter distance to blazar TXS 0506+056 (z = 0.3365), a radio-bright active galactic nucleus (AGN) whose jet is aligned with the line of sight. Methods. We used data obtained with the 15 GHz Very Long Baseline Array (VLBA) from MJD 54838 to MJD 60262 (15 years) and data from the 15 GHz Owens Valley Radio Observatory (OVRO) 40 m single dish (SD) telescope from MJD 54474 to MJD 59023 (12 years). We used a variability timescale and a causality argument of a linear size (taking the Doppler factor and a cosmological redshift into account) to measure the angular diameter distance to the source. To constrain the Doppler factor, we applied the relation between the rest-frame brightness temperature of the emission region and the observed brightness temperature. To calculate the observed brightness temperature, the angular size and flux density variation of the emission region are required. The angular size of the emission region (i.e., the VLBA core) was obtained from a full width at half maximum, which is a circular Gaussian model-fitting parameter that ranges from 0.048–0.228 mas, and its uncertainty is determined to be 1.8–13%. Using the OVRO SD light curve, we obtained a variability timescale of $ \tau=128.0_{-0.3}^{+0.2} $ days and a peak flux density of $ 1.750_{-0.104}^{+0.015} $ Jy for the largest flare that peaked on MJD $ 58921.7_{-5.5}^{+2.6} $. We assumed a disk brightness morphology, equipartition brightness temperature (Tb, int = 5 × 1010 K), and perfect radius. Results. By fitting the circular Gaussian model to the VLBA images, we found that the variability in the VLBA core drives the multiple flares. Based on the timescales and peak flux densities for the flares, we calculated the angular diameter distance. Using the VLBA core sizes obtained near the flare peaks, we found consistent distance measurement results with the ΛCDM model within 1σ uncertainties. Conclusions. We suggest that the best distance from the source is $ 941_{-64}^{+59} $ Mpc, which is comparable with the ΛCDM distance of 948.2 ± 13.5 Mpc. The distance measurement should indeed be taken at the peak of a flare. We found that the decomposed timescale allowed us to obtain consistent distances with the ΛCDM. We strongly suggest to decompose light curves when the variability timescales are to be obtained properly.