Probing magnetic fields in high-redshift galactic systems is crucial to investigate galactic dynamics and evolution. Utilizing the rotation measure of the background quasars, we have developed a radial profile of the magnetic field in a typical high-$z$ galaxy. We have compiled a catalog of 59 confirmed quasar sightlines, having one intervening Mg \rom{ 2} absorber in the redshift range $0.372\leq z_{ \text{ abs}} \leq 0.8$. The presence of the foreground galaxy is ensured by comparing the photometric and spectroscopic redshifts within $3 \sigma_{ z-\text{ photo}}$ and visual checks. These quasar line-of-sights (LoS) pass through various impact parameters (D) up to $160$ kpc, covering the circumgalactic medium of a typical Milky-Way type galaxy. Utilizing the residual rotation measure (RRM) of these sightlines, we estimated the excess in RRM dispersion, $\sigma_{ \text{ ex}}^{ \text{ RRM}}$. We found $\sigma_{ \text{ ex}}^{ \text{ RRM}}$ decreases with increasing D. We translated $\sigma_{ \text{ ex}}^{ \text{ RRM}}$ to average LoS magnetic field strength, $\langle B_{ \|}\rangle$ by considering a typical electron column density. Consequently, the decreasing trend is sustained in the magnetic field. In particular for sightlines with $\text{ D} \leq 50$ kpc and $\text{ D} > 50$ kpc, $\langle B_{ \|}\rangle$ is found to be $2.39 \pm 0.7 \ \mu$G and $1.67 \pm 0.38 \ \mu$G, respectively. This suggests a clear indication of varying magnetic field from the disk to the circumgalactic medium. This work provides a methodology that, when applied to ongoing and future radio polarisation surveys such as LOFAR and SKA, promises to significantly enhance our understanding of magnetic field mapping in galactic systems.
Categories: astro-ph.GA astro-ph.CO