Abstract Polarization measurements provide insight into the magnetic field, a critical aspect of the dynamics and emission properties around the compact object. In this paper, we present the polarized magnetic field of the Crab outer torus and the Vela arc utilizing Imaging X-ray Polarimetry Explorer observation data. The polarization angle (PA) measured for the Crab outer torus exhibits two monotonic evolutions along the azimuth angle, which are consistent with the normal line of the elliptical ring. There is a slight increase in PA along the azimuth angle for both the inner arc and the outer arc of the Vela Nebula. The polarized magnetic vector along the outer torus of the Crab Nebula shows the polarized magnetic field aligns with the Crab outer torus structure. The PA variation along the Crab outer torus suggests a bulk flow speed of 0.8 c . Meanwhile, the Vela Nebula polarized magnetic field does not exactly align with the Vela arc structure. We noted that the Crab Nebula possesses a polarized toroidal magnetic field, whereas the Vela Nebula exhibits an incomplete toroidal magnetic field.

Comparison between the Emission Torus and the Measured Toroidal Magnetic Field for the Crab and Vela Nebulae