  Galactic outflows driven by star formation and active galactic nuclei blow
bubbles into their local environments, causing galactic magnetic fields to be
carried into intergalactic space. We explore the redshift-dependent effect of
these magnetized bubbles on the Faraday Rotation Measure (RM) of extragalactic
radio sources. Using the IllustrisTNG cosmological simulations, we separate the
contribution from magnetic bubbles from that of the volume-filling magnetic
component expected to be due to the seed field originating in the Early
Universe. We use this separation to extract the redshift dependence of each
component and to compare TNG model predictions with observation measurements of
the NRAO VLA Sky Survey (NVSS). We find that magnetized bubbles provide a
sizeable contribution to the extragalactic RM, with redshift-independent
$\langle |{\rm RM}| \rangle \simeq 13$ rad/m$^2$ for sources at redshifts $z\ge
2$. This is close to the mean residual RM of $16$ rad/m$^2$ found from NVSS
data in this redshift range. Using the IllustrisTNG simulations, we also
evaluate a simple model for the contribution to residual RM from individual
host galaxies and show that this contribution is negligible at high-redshift.
While the contribution from magnetic bubbles in the IllustrisTNG model is
currently compatible with observational measurements of residual RM, the
next-generation RM sky surveys, which will be free from the wrapping
uncertainty, have larger statistics and better sensitivity should be able to
observe predicted flat contribution from magnetic bubbles at large redshifts.
This should allow to experimentally probe magnetic bubbles and check models of
galaxy feedback in cosmological simulations.
