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

We present the results of constraining the angular diameter distance to blazar TXS 0506+056. We used data obtained with the 15 GHz VLBA in MJD 54838-60262 and data from the 15 GHz OVRO 40 m single dish telescope in MJD 54474-59023. We used a variability timescale and a causality argument of a linear size 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 FWHM, 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 $128.0_{-0.3}^{+0.2}$ 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 geometry, equipartition brightness temperature ($5\times10^{10}$ K), and perfect radius. Using the VLBA core sizes obtained near the flare peaks, we found consistent distance measurement results with the $Λ$CDM model within 1$σ$ uncertainties. We suggest that the best distance from the source is $941_{-64}^{+59}$ Mpc, which is comparable with the $Λ$CDM distance of $948.2\pm13.5$ 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 $Λ$CDM. We strongly suggest to decompose light curves when the variability timescales are to be obtained properly.