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

TL;DR

This work tests whether a Doppler-boosted blazar can serve as a direct distance indicator by linking variability timescales, observed flux changes, and VLBI core sizes to the angular diameter distance, under an intrinsic brightness-temperature constraint $T_{b,int}$ and a Doppler factor $\delta$. By combining 32 epochs of 15 GHz VLBA data with long-term OVRO monitoring and performing flare decomposition, the authors extract robust flare timescales and peak fluxes, and relate them to core sizes near flare peaks via the causality framework $R\!=\!g\,c\,\delta\tau^{rec}/(1+z)$ and $\theta_R^{rec}=R/D_A$. They derive a distance $D_A = 941_{-64}^{+59}$ Mpc for TXS 0506+056, in good agreement with the $\Lambda$CDM value $948.2\pm13.5$ Mpc, and show that distances are most reliable when based on core sizes at flare peaks and when light curves are decomposed to isolate individual flares. This demonstrates the feasibility of using highly Doppler-boosted blazars to extend the cosmic distance ladder, provided high-cadence, high-resolution data to accurately measure core sizes and flare parameters. The study highlights the importance of decomposition to mitigate flare overlap and the potential of blazars to contribute additional, higher-redshift distance anchors.

Abstract

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.

Figures (9)

• Figure 1: Panel (a): Flux density curves for each VLBA circular Gaussian model component (colored dashed lines), VLBA total clean (dashed black line), and OVRO SD (gray dots). Panels (b), (c), and (d): FWHM curves for VLBA C0, J2, and J3. The VLBA model components are defined by their positions as in Fig. \ref{['fig:positions']}.
• Figure 2: Clean map of TXS 0506+056 on MJD 60126 (July 1, 2023) from MOJAVE overlapped with multiepoch positions of Gaussian model components (VLBA C0, J1, J2, and J3). The major and minor FWHMs of the elliptical clean beam are plotted in the lower left corner. The contours are given at $\log_{2}$ level from three times the root mean square to the peak intensity.
• Figure 3: Flare decomposition plots of the VLBA C0 (a), J2 (b), and J3 (c), respectively. For a purpose of comparison, the flare model components in panels (a)--(c) overlap the OVRO SD+VLBA TC light curve in panel (d). A flare decomposition plot (e) of the OVRO SD+VLBA TC light curve using the initial sample shown in panel (d). The solid lines are the single flare model components. The dashed line in each panel describes the sum of all flare model components and the quiescent flux density. All panels note the number of components $N$, log-likelihood $\log \mathcal{L}$, $\chi^{2}$, and reduced $\chi^{2}_{d}$ ($d$ is the degrees of freedom) in the upper left corner. The quiescent flux density ($F_{\rm qs}$) is noted in the lower left corner (as well as by the horizontal dotted lines).
• Figure 4: Posterior distributions, point estimates, and credible intervals of the cross-identified flare decomposition parameters $t_{0}$, $\tau$, $F_{0}$, and $s$ for flares C0a, C0c, C0d, and C0e (color plots from panels (a) to (d)) and SD4 (C0a), SD14 (C0c), SD19 (C0d), and SD24 (C0e) (gray and black plots from panels (a) to (d)). The bar plots illustrate the posterior distributions. The solid and dashed line plots note the point estimates and interval estimates, respectively.
• Figure 5: Distance estimates of VLBA C0, J2, J3, and OVRO SD+VLBA TC (from panels (a) to (d)). The solid colored lines show decomposed flares, the colored symbols show the distance estimates using timescales and peak flux densities from the individual flares in corresponding colors, and the black circles show the data (VLBA and OVRO) light curves. The horizontal dashed gray lines note the $\Lambda$CDM distance ($948.2\pm13.5$ Mpc) with 1$\sigma$ uncertainty. The color symbols of the distance estimates are opaque when the distance measurements are consistent with the $\Lambda$CDM distance within 1$\sigma$ uncertainties, and they are transparent when the distances are not.