Revisiting the Polarization of the Emission of the Internal Shock in the Jet of Blazars

Abstract

Recent Imaging X-ray Polarimetry Explorer (IXPE) observations of blazars tend to support the shock model for the X-ray emission, but report a low degree of polarization (Π ∼ 10%) in X-rays compared with the previous theoretical expectations in the shock model. In order to reconcile the theoretical expectations with observations, we revisit the polarization of the shock emission by considering different types of directions in the distribution of the shock-generated magnetic fields (sgMFs). Here, w sg ′ ∝ ( sin θ ′ ) ζ sg ?> with θ ′ = 0 ?> along the shock normal direction is used to describe the direction in the distribution of sgMFs in the shock comoving frame. It is found that the polarization in the X-ray and radio emission for a general jet in blazars can be described as &Pgr; ∼ 44.5 [ 1 − exp ( − ζ sg / 2.6 ) ] % ?> and &Pgr; ∼ 20 [ 1 − exp ( − ζ sg / 2.4 ) ] % ?> , respectively. Correspondingly, one can have ζ sg ∼ 1−1.5 according to IXPE observations. Besides the sgMFs, the magnetic fields generated by the Richtmyer–Meshkov instability (RMI) (rmMFs) are supposed to be present in the jets. The direction of the rmMFs is mainly distributed along the shock normal in the simulations and thus w rm ′ ∝ ( cos θ ′ ) ζ rm ?> is adopted to describe the direction of the distribution in rmMFs. We find that rmMFs are likely to significantly affect the polarization properties at low-frequency emission, especially when the sgMFs decay rapidly. Based on contemporaneous radio and X-ray observations, we find that the emission of electrons in rmMFs makes a significant contribution to the low-frequency emission and the ordered background magnetic fields can be neglected.