Revision of Faraday rotation measure constraints on the primordial magnetic field using the IllustrisTNG simulation

Previously derived Faraday rotation constraints on the volume-filling intergalactic magnetic field (IGMF) have used analytic models that made a range of simplifying assumptions about magnetic field evolution in the intergalactic medium and did not consider the effect of baryonic feedback on large-scale structures. In this work we revise existing Faraday rotation constraints on the IGMF using a numerical model of the intergalactic medium from the IllustrisTNG cosmological simulation that includes a sophisticated model of the baryonic feedback. We use the IllustrisTNG model to calculate the rotation measure and compare the resulting mean and median of the absolute value of the rotation measure with data from the NRAO VLA Sky Survey (NVSS). The numerical model of the intergalactic medium includes a full magneto-hydrodynamic model of the compressed primordial magnetic field as well as a model of the regions where the magnetic field is not primordial, but is rather produced by the process of baryonic feedback. Separating these two types of regions, we are able to assess the influence of the primordial magnetic field on the Faraday rotation signal. We find that by correcting for regions of compressed primordial field and accounting for the fact that part of the intergalactic medium is occupied by magnetic fields spread by baryonic feedback processes rather than by the primordial field relaxes the Faraday rotation bound by a factor of $\simeq 3$. This results in $B_0<1.8\times10^{-9}$ G for large correlation length IGMFs.