Polarization Movies

Here, we discuss additional steps necessary for making polarization movies. Proceed with steps 1 & 2 from section 2.1.1, this time using all three Stokes ($I$, $Q$, and $U$) images. Stokes $V$ (circular polarization) images can be treated identically to $I$ images as described in section 2.1.1. After aligning the $I$ images, the corresponding $Q$ and $U$ (and $V$) images must be shifted by the same amount.

1. If rotations to the tick-marks that illustrate the orientation of the electric field vectors need to be made⁴ (e.g. accounting for Faraday rotation by adding a correction angle, $\theta$, or changing the tick-marks to show the orientation of the magnetic field vectors⁵), the total polarized intensity ( $p=\sqrt{Q^{2}+U^{2}}$) and electric field vector orientation ( $\chi'=\frac{1}{2}\arctan{\frac{U}{Q}} + \theta$) images at each epoch are made first from the restored and aligned $Q$ and $U$ images with the task COMB. This is done in order to avoid the problem of having tick-marks rotating improperly later.

2. The resultant $p$ and $\chi'$ images are used to make new $Q$ and $U$ images⁶(eqns 1 & 2) using the task COMB, via:

   
   

   $$Q'=p*\cos{2\chi'},$$ (1)

   
   

   
   

   $$U'=p*\sin{2\chi'}.$$ (2)

   
   

3. Lastly, the $I$, $Q'$, and $U'$ images are linearly interpolated separately with the task COMB. These images are then used to make the $I$, $p$, and fractional polarization ($m=p/I$) movie frames. The length of the tick-marks on the $p$ frames can be made uniform or proportional to the magnitude of $m$ or $p$.

Our AIPS script, BAMM, will implement all of these steps (section 3) after the user specifies the epochs of observations and the positions of a stationary feature. The individual movie frames are ready for inspection with standard AIPS tools, or the procedure may be repeated with different parameters if the user is not satisfied with the output.