What can the 2008/10 broadband flare of PKS 1502+106 tell us? Nuclear opacity, magnetic fields, and the location of gamma rays

Context. The origin of blazar variability, seen from radio up to gamma rays, is still a heavily debated matter and broadband flares offer a unique testbed towards a better understanding of these extreme objects. Such an energetic outburst was detected by Fermi/LAT in 2008 from the blazar PKS 1502+106. The outburst was observed from gamma rays down to radio frequencies. Aims. Through the delay between flare maxima at different radio frequencies, we study the frequency-dependent position of the unit-opacity surface and infer its absolute position with respect to the jet base. This nuclear opacity profile enables the magnetic field tomography of the jet. We also localize the gamma-ray emission region and explore the mechanism producing the flare. Methods. The radio flare of PKS 1502+106 is studied through single-dish flux density measurements at 12 frequencies in the range 2.64 to 226.5 GHz. To quantify it, we employ both a Gaussian process regression and a discrete cross-correlation function analysis. Results. We find that the light curve parameters (flare amplitude and cross-band delays) show a power-law dependence on frequency. Delays decrease with frequency, and the flare amplitudes increase up to about 43 GHz and then decay. This behavior is consistent with a shock propagating downstream the jet. The self-absorbed radio cores are located between about 10 and 4 pc from the jet base and their magnetic field strengths range between 14 and 176 mG, at the frequencies 2.64 to 86.24 GHz. Finally, the gamma-ray active region is located at (1.9 +/- 1.1) pc away from the jet base.