Hamiltonian variational reconstruction of the 3D magnetic geometry of relativistic jets: accuracy across GRMHD models and the fundamental sign degeneracy

@misc{buffoli2026hamiltonian,
  title = {{Hamiltonian variational reconstruction of the 3D magnetic geometry of relativistic jets: accuracy across GRMHD models and the fundamental sign degeneracy}},
  author = {Fabio Buffoli},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.09569},
  eprint = {2607.09569},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.09569},
}

TY  - UNPB
TI  - Hamiltonian variational reconstruction of the 3D magnetic geometry of relativistic jets: accuracy across GRMHD models and the fundamental sign degeneracy
AU  - Fabio Buffoli
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2607.09569
UR  - https://arxiv.org/abs/2607.09569
AB  - Every resolved image of a relativistic jet encodes its magnetic field, yet no image records which way the field points: synchrotron intensity and linear polarization probe the field only through even combinations of its components. We introduce H-MOG (Hamiltonian Magnetic Optimization of Geometry), a variational method that reconstructs the 3D field from the jet width W(z) and linear polarization p(z), and we determine exactly which properties of the field these observables fix. We validate H-MOG on synthetic jets and apply it to ten GRMHD simulations of magnetically arrested and standard accretion flows at five spins, testing four routes to recover the field sense: a rotation-measure term, full 3D sampling, a spin-based prior, and resolved multi-frequency polarimetry with internal Faraday rotation, including ray-traced GRMHD images. For a side-on jet, W and p are exactly invariant under field reversal and under reflection through the plane of the sky, which reverses the handedness of the helix. Within this four-fold degeneracy the geometry is recovered, with ⟨cos⟩ ≃ 0.94-$1.00$ on synthetic jets and $0.76−0.98$ on the GRMHD library up to the mirror image, which is inherited from the initial guess. The rotation measure fixes the sign of the toroidal field but not that of the poloidal field, at any resolution; the spin prior fails because spin does not set the poloidal sign. Internal Faraday rotation breaks all four images, but in ray-traced GRMHD images it separates them only weakly. From width and polarization alone, field sense and helical handedness are undetermined; for a side-on jet the poloidal sense requires, beyond the rotation measure, the rotation sense of the field lines, a viewing angle away from 90^∘, or circular polarization.
ER  -