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The association of the high-energy neutrino event IceCube-170922A with theflaring blazar TXS~0506+056 indicates that hadronic processes may operate in ablazar jet. We perform semi-analytical spectral fitting of the multi-wavelengthemission to obtain estimates of the jet physical parameters, and find that themulti-wavelength emission can be explained by either a proton synchrotronscenario or an electron inverse Compton scattering scenario. In the protonsynchrotron scenario, a strong magnetic field of $10-100$~G is required,implying that the particle acceleration is likely driven by magnetic energydissipation such as magnetic reconnection events. The inverse Compton scenarioimplies a magnetic field of $0.1-1$~G. Thus the particle acceleration is likelydriven by the kinetic energy dissipation such as shocks. We also discuss theneutrino production in the context of single-zone and multi-zone models basedon the above two scenarios. We demonstrate that the variability and opticalpolarization signatures can be used to distinguish the two scenarios due totheir drastically different magnetic field. Specifically, the protonsynchrotron scenario may show orphan fast variability in the low-energyspectral component on top of the active state, with an optical polarizationdegree $\lesssim 10\%$ throughout the active state. The inverse Comptonscattering scenario instead predicts co-variability of the low- and high-energycomponents on both short and long time scales, as well as a strongly variableoptical polarization degree that can reach $\gtrsim 20\%$. Our results suggestthat optical polarization measurements and well-resolved multi-wavelength lightcurves can be used to understand the electromagnetic and high-energy neutrinoemissions by TXS~0506+056 and similar events in the future.

Variability and Optical Polarization Can Probe the Neutrino and Electromagnetic Emission Mechanisms of TXS~0506+056