“Evidence for the alignment of quasar radio polarizations with large quasar group axes” by Pelgins and Hutsemekers.
A number of studies have shown that quasar polarization vectors are not random, but preferentially align with the axes of the large quasar groups (LQGs) to which they belong. These studies have been mostly limited to low redshift (z < 1) as they needed to resolve the shapes of the galaxies. A recent study has shown this to hold for two LQGs at z ~ 1.3.
This study extends this to a large number of LQGs identified by SDSS with z = 1.0 – 1.8. Individual quasar radio polarization measurements were taken from the JVAS/CLASS 8.4GHz surveys. The polarization vector is preferentially perpendicular to the jet axis. They found 185 quasars which satisfied their base criteria.
(Figure 2 on page 3) Position angles of the LQGs are computed in two different ways. While they vary in the number of dimensions considered (2D celestial sphere, 3D comoving positions), they both involve computing the inertia tensor. In the 2D case they use the position angle of the largest eigenvector, and in the 3D case they fit an ellipsoid, and project its major axis onto the celestial sphere. Both methods are roughly equivalent.
To measure the offset in position angle, the position angle from the LQG and an individual quasar are parallel transported to each other, to make the measurements coordinate-independent.
(Figure 3 on page 3) The study ultimately finds that the type of alignment varies with the LQG’s “richness”, m. They find m<10 showing no correlation, 10<m<20 being preferentially parallel, and m>20 being preferentially perpendicular.