Can Primordial Magnetic Fields Seeded by Electroweak Strings Cause an Alignment of Quasar Axes on Cosmological Scales?

The decay of nontopological electroweak strings may leave an observable imprint in the Universe today in the form of primordial magnetic fields. Protogalaxies preferentially tend to form with their axis of rotation parallel to an external magnetic field, and, moreover, an external magnetic field produces torque which tends to align the galaxy axis with the magnetic field. We demonstrate that the shape of a magnetic field left over from two looped electroweak strings can explain the observed nontrivial alignment of quasar polarization vectors and make predictions for future observations.

Figure 1

The configuration of the magnetic from Eq. (1). The locations of the $A1\mathrm{\text{−}}A3$ axis (straight thick line) and Earth (dot on the $A1\mathrm{\text{−}}A3$ axis) are drawn in. Today each loop of the magnetic field has a characteristic scale on the order of Gpc. The strongest alignment effect is predicted at the intersection of the line of sight with linked loops, i.e., four peaks in the data (see Fig. 2 for predictions and Fig. 3 for the actual data).

Figure 2

The magnitude of the magnetic field described by Eq. (4). Compare this figure to Fig. 3, which shows the degree of alignment along the $A1\mathrm{\text{−}}A3$ axis from Ref. 1. For this plot we chose $B=1$, $R=1.29$, $d=1.8$, and $s=-0.7$.

Figure 3

A plot of the local statistics along the $A1\mathrm{\text{−}}A3$ axis as described in Ref. 1. The local statistics is a measure of the degree by which the quasar polarization vectors are preferentially aligned with other nearby quasars. A high local statistic value indicates a greater degree of alignment. Bins of size $\Delta r=0.4h^{-1}\mathrm{Gpc}$ are used. Instead of redshift, comoving distances of $r=6[1-(1+z{)}^{-1/2}]h^{-1}\mathrm{Gpc}$ are used, where $h$ is the Hubble constant in units of $100\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. Objects in the direction of the NGP (SGP) are assigned positive (negative) distances. The histogram below the graph gives the number of quasars in each bin. This figure was taken directly from Ref. 1.

Figure 4

Polarization angle vectorially averaged for 183 quasars along the $A1\mathrm{\text{−}}A3$ axis from Ref. 1. The objects are divided into bins of $\Delta z=0.5$. Error bars show the 68% angular confidence interval [21]. The straight line is the best fit from Ref. 1 given by $\overline{\theta }=268-42z$. The curvy line is our best fit described by Eq. (5). As in Fig. 13 from Ref. 1, each data point is replicated 3 times: at $\overline{\theta }$, $\overline{\theta }+180$, and $\overline{\theta }+360$.