Modeling and statistical characterization of synchrotron multi-zone polarization in blazars

Multiwavelength polarimetric observations of blazars reveal complex energy-dependent polarization behavior, with a decrease in the polarization fraction from X-ray to millimeter bands and significant variability in the electric vector position angle (EVPA). These trends challenge simple single-zone synchrotron models and suggest a more intricate turbulent jet structure with multiple emission zones. This work aims to develop a statistical framework to model the energy-dependent polarization patterns observed in blazars, particularly focusing on the behavior captured by IXPE in the X-ray and RoboPol in the optical. The goal is to determine the statistical characterization of multi-zone models, in terms of the cell size distribution, and of the distribution of the physical parameters of the electron energy distribution (EED). A Monte Carlo simulation approach was employed to generate synthetic multi-zone synchrotron emission, using the code, from a spherical region populated by turbulent cells with randomly distributed physical properties. Simulations were run across various scenarios: from identical cells to power-law-distributed cell sizes and EEDs with different cutoff and low-energy slope distributions. The simulation results were compared with the observed IXPE and RoboPol polarization trends. Our analysis demonstrates that a purely turbulent, multi-zone model can explain the observed energy-dependent polarization patterns without requiring a correlation between the cell size and the EED parameters. The key determinant of polarization is the effective number (flux-weighted) of emitting cells, which is significantly modulated by the dispersion in cell properties, especially the EED cutoff energy, at higher frequencies, and the dispersion in the EED low-energy spectral index, at lower frequencies. Using a fractional dispersion on the EED cutoff on the order of 90%, and a dispersion of the EED low-energy spectral index between ≈ 0.5 and ≈ 1.5, our model reproduces both the chromaticity of the millimiter-to-X-ray polarization trends observed in IXPE multiwavelength campaigns for high synchrotron-peaked blazars, and the optical polarization limiting envelope, observed in the RoboPol dataset.