Polarization Architecture of Steady GRMHD Jets from the Horizon to Infinity

Technical Summary: Polarization Architecture of Steady GRMHD Jets from the Horizon to Infinity

Problem Statement
Relativistic jets originating near spinning black holes are a primary outcome of accretion, yet deciphering their dynamics through Very Long Baseline Interferometry (VLBI) observations remains challenging. While numerical General Relativistic Magnetohydrodynamic (GRMHD) simulations are indispensable for time-dependent formation, they are computationally expensive and ill-suited for isolating individual physical effects or surveying broad parameter spaces. Conversely, existing phenomenological or force-free imaging models often lack strict GRMHD foundations, failing to consistently capture the interplay between plasma inertia, magnetic field geometry, and spacetime curvature. Consequently, there is a lack of a unified, computationally efficient framework that links jet microphysics (specifically plasma mass loading) and spacetime geometry to resolved polarimetric image structures from the event horizon to infinity.

Methodology
The authors develop a semi-analytic framework for stationary, axisymmetric ideal GRMHD jets. The approach combines:

1. Conservation Laws: Utilizing the conserved quantities in ideal GRMHD (mass flux $\eta$, specific energy $E$, angular momentum $L$, field-line angular velocity $\Omega_F$, and stream function $\psi$) to solve the relativistic wind equation algebraically for poloidal flow motion.
2. Boundary Conditions: The model imposes regularity conditions at critical points (Alfvén and fast magnetosonic points) and matches inflow and outflow solutions across a geometrically thin stagnation surface (SS). The outflow adopts a Michel-type solution at infinity, while the inflow is constrained by horizon regularity.
3. Magnetic Geometry: The stream function is specified as $\psi(r, \theta) = Cr^p(1 - |\cos \theta|)$, allowing control over the jet collimation profile via the index $p$.
4. Radiative Transfer: A semi-analytic General Relativistic Radiative Transfer (GRRT) scheme is implemented. Stokes parameters are accumulated linearly along light rays intersecting the emission layer. The model assumes a nonthermal power-law electron distribution function (eDF), with extensions to include beam-like anisotropy.
5. Parameter Space: The framework efficiently generates polarized images across a broad range of black hole spins ($a$), jet collimation indices ($p$), asymptotic Lorentz factors ($\gamma_\infty$, representing plasma loading), and viewing geometries.

Key Contributions and Results
The study identifies a scale-dependent separation in polarimetric diagnostics, revealing distinct physical regimes in the jet's polarization architecture:

1. Acceleration Region (Intermediate Radii):

   • The Electric Vector Position Angle (EVPA) profile is strongly sensitive to plasma mass loading ($\gamma_\infty$).
   • In highly relativistic, low-loading flows (approaching the force-free regime), the EVPA exhibits a "bump" feature near $b \sim 50M$. This arises from the combined emission of forward and counter-jets, where gravitational lensing enhances the counter-jet's pitch angle.
   • As plasma loading increases (lower $\gamma_\infty$), inertia-driven magnetic field winding increases. This suppresses the pitch-angle contrast between the forward and counter-jets, smoothing the EVPA profile and causing the "bump" to disappear.
   • This region provides a diagnostic for constraining jet matter content and mass-loading efficiency.

2. Near-Horizon Region:

   • As the flow approaches the event horizon, frame dragging twists the inflow and magnetic field into toroidal patterns, leading to a radial EVPA structure.
   • The polarization pattern converges to a "Universal Near-Horizon Polarization" (NHP). Differences in velocity and magnetic field structure (governed by $\gamma_\infty$) are erased first, while differences in collimation ($p$) persist to smaller radii before also converging.
   • The leading-order term of the NHP depends solely on the black hole spin ($a$), making this regime a robust probe of spacetime geometry largely independent of jet microphysics.

3. Asymptotic Region (Large Radii):

   • Far outside the light cylinder, the EVPA follows a power-law decay with image-plane radius $b$, specifically $\text{arg}(\beta_2) \propto b^{2/(p-2)}$.
   • The index is determined by the jet collimation profile ($p$).
   • The paper uncovers a fundamental non-commutativity between the force-free limit ($\gamma_\infty \to \infty$) and the large-radius limit ($r \to \infty$). For any MHD flow with finite mass loading, plasma inertia inevitably drives the magnetic field to an asymptotically toroidal configuration, forcing the EVPA to decay as $r^{-1}$ regardless of $p$. This contrasts with force-free electrodynamics (FFE), where the asymptotic EVPA retains a geometry-dependent value.

Significance
The paper establishes a largely achromatic polarimetric diagnostic that connects GRMHD jet dynamics to resolved image structure. By demonstrating that different physical parameters dominate at different scales, the framework enables the disentangling of plasma loading, field-line twisting, jet collimation, and black hole spin.

• Observational Relevance: The results provide direct implications for high-resolution polarimetry (e.g., Event Horizon Telescope and future space-VLBI). The near-horizon convergence offers a clean method to constrain black hole spin, while the acceleration region's sensitivity to loading helps characterize jet matter content.
• Theoretical Insight: The identification of the non-commutativity between the force-free and large-radius limits underscores the absolute necessity of a full GRMHD treatment when tracing jet evolution from the horizon to infinity, challenging the continuous connection between FFE and baryonic outflows at large distances.
• Efficiency: The semi-analytic nature of the framework allows for rapid exploration of parameter spaces that would be prohibitive with full numerical simulations, facilitating the interpretation of upcoming high-resolution polarimetric data.