The analytical and numerical solutions of the free precession of triaxial NS

The dynamics under the near-field torque

The figures in the paper

The effective parameters under the effectively free precession problem (absorb the near-field torque into the MoI)

The evolution of magnetic inclination angle in precession (numerical solution, the analytical solution is the same)

The dynamics under the far-field torque

The figures in the paper

A simple derivation of the RVM model

The timing model of precession

The figures in the paper

gaunt factors to calculate the opacity

free-free and scattering opacity of the magnetized plasma

The vacuum birefringence effects

Solving the radiative transfer equation

The phase resolved polarization for precessing magnetars

The phase averaged polarization for precessing magnetars

The modulations of PA