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We present the first results from SPHINX-MHD, a suite of cosmological radiation-magnetohydrodynamics simulations designed to study the impact of primordial magnetic fields (PMFs) on galaxy formation and the evolution of the intergalactic medium (IGM) during the epoch of reionization. The simulations are among the first to employ multifrequency, on-the-fly radiation transfer and constrained transport ideal MHD in a cosmological context to simultaneously model the inhomogeneous process of reionization as well as the growth of primordial magnetic fields. We run a series of |$(5\, \text{cMpc})^3$| cosmological volumes, varying both the strength of the seed magnetic field and its spectral index. We find that PMFs with a spectral index (nB) and a comoving amplitude (B 0) that have |$\scriptstyle{n_B \gt -0.562\log _{10}\left(\frac{B_0}{1{\rm n}G}\right) - 3.35}$| produce electron optical depths (τe) that are inconsistent with CMB constraints due to the unrealistically early collapse of low-mass dwarf galaxies. For nB ≥ −2.9, our constraints are considerably tighter than the ∼n G constraints from Planck. PMFs that do not satisfy our constraints have little impact on the reionization history or the shape of the UV luminosity function. Likewise, detecting changes in the Ly α forest due to PMFs will be challenging because photoionization and photoheating efficiently smooth the density field. However, we find that the first absorption feature in the global 21-cm signal is a particularly sensitive indicator of the properties of the PMFs, even for those that satisfy our τe constraint. Furthermore, strong PMFs can marginally increase the escape of LyC photons by up to 25 per cent and shrink the effective radii of galaxies by |$\sim 44{{\ \rm per\ cent}}$| which could increase the completeness fraction of galaxy surveys. Finally, our simulations show that surveys with a magnitude limit of |${\rm \mathit{ M}_{UV,1500\,\mathring{\rm A}}=-13}$| can probe the sources that provide the majority of photons for reionization out to z = 12. [ABSTRACT FROM AUTHOR]

We investigate the effect of the Biermann battery during the Epoch of reionization (EoR) using cosmological Adaptive Mesh Refinement simulations within the framework of the sphinx project. We develop a novel numerical technique to solve for the Biermann battery term in the Constrained Transport method, preserving both the zero divergence of the magnetic field and the absence of Biermann battery for isothermal flows. The structure-preserving nature of our numerical method turns out to be very important to minimize numerical errors during validation tests of the propagation of a Str'omgren sphere and of a Sedov blast wave. We then use this new method to model the evolution of a 2.5 and 5 co-moving Mpc cosmological box with a state-of-the-art galaxy formation model within the Ramses code. Contrary to previous findings, we show that three different Biermann battery channels emerge: the first one is associated with linear perturbations before the EoR, the second one is the classical Biermann battery associated with reionization fronts during the EoR, and the third one is associated with strong, supernova-driven outflows. While the two former channels generate spontaneously volume-filling magnetic fields with a strength on the order or below 10−20 G, the latter, owing to the higher plasma temperature and a marginally resolved turbulent dynamo, reaches a field strength as high as 10−18 G in the intergalactic medium around massive haloes. [ABSTRACT FROM AUTHOR]