A Provably Positive, Divergence-free Constrained Transport Scheme for the Simulation of Solar Wind

In this paper, we present a provably positive, divergence-free constrained transport (CT) scheme to simulate the steady-state solar wind ambient with the three-dimensional magnetohydrodynamics numerical model. The positivity can be lost in two ways: one way is in the reconstruction process, and the other is in the updating process when the variables are advanced to the next time step. We adopt a self-adjusting strategy to bring the density and pressure into the permitted range in the reconstruction process, and use modified wave speeds in the Harten–Lax–van Leer flux to ensure the positivity in the updating process. The CT method can keep the magnetic fields divergence-free if the magnetic fields are divergence-free initially. Thus, we combine the least-squares reconstruction of the magnetic fields with the divergence-free constraints to make the magnetic fields globally solenoidal initially. Furthermore, we adopt a radial basis function method to interpolate variables at boundaries that can keep the magnetic field locally divergence-free. To verify the capability of the model in producing structured solar wind, the modeled results are compared with Parker Solar Probe (PSP) in situ observations during its first two encounters, as well as Wind observations at 1 au. Additionally, a solar maximum solar wind background is simulated to show the property of the model’s ability to preserve the positivity. The results show that the model can provide a relatively satisfactory comparison with PSP or Wind observations, and the divergence error is about 10−10 for all of the tests in this paper.

Cosmological Magnetogenesis: The Biermann battery during the Epoch of Reionization

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.

How primordial magnetic fields shrink galaxies

ABSTRACT As one of the prime contributors to the interstellar medium energy budget, magnetic fields naturally play a part in shaping the evolution of galaxies. Galactic magnetic fields can originate from strong primordial magnetic fields provided these latter remain below current observational upper limits. To understand how such magnetic fields would affect the global morphological and dynamical properties of galaxies, we use a suite of high-resolution constrained transport magnetohydrodynamic cosmological zoom simulations where we vary the initial magnetic field strength and configuration along with the prescription for stellar feedback. We find that strong primordial magnetic fields delay the onset of star formation and drain the rotational support of the galaxy, diminishing the radial size of the galactic disc and driving a higher amount of gas towards the centre. This is also reflected in mock UVJ observations by an increase in the light profile concentration of the galaxy. We explore the possible mechanisms behind such a reduction in angular momentum, focusing on magnetic braking. Finally, noticing that the effects of primordial magnetic fields are amplified in the presence of stellar feedback, we briefly discuss whether the changes we measure would also be expected for galactic magnetic fields of non-primordial origin.

Constrained transport and adaptive mesh refinement in the Black Hole Accretion Code

Context. Worldwide very long baseline radio interferometry (VLBI) arrays are expected to obtain horizon-scale images of supermassive black hole candidates and of relativistic jets in several nearby active galactic nuclei. This, together with the expected detection of electromagnetic counterparts of gravitational-wave signals, motivates the development of models for magnetohydrodynamic flows in strong gravitational fields. Aims. The Black Hole Accretion Code (BHAC) is a publicliy available code intended to aid with the modeling of such sources by performing general relativistic magnetohydrodynamical simulations in arbitrary stationary spacetimes. New additions to the code are required in order to guarantee an accurate evolution of the magnetic field when small and large scales are captured simultaneously. Methods. We discuss the adaptive mesh refinement (AMR) techniques employed in BHAC, which are essential to keep several problems computationally tractable, as well as staggered-mesh-based constrained transport (CT) algorithms to preserve the divergence-free constraint of the magnetic field. We also present a general class of prolongation operators for face-allocated variables compatible with them. Results. After presenting several standard tests for the new implementation, we show that the choice of the divergence-control method can produce qualitative differences in the simulation results for scientifically relevant accretion problems. We demonstrate the ability of AMR to decrease the computational costs of black hole accretion simulations while sufficiently resolving turbulence arising from the magnetorotational instability. In particular, we describe a simulation of an accreting Kerr black hole in Cartesian coordinates using AMR to follow the propagation of a relativistic jet while self-consistently including the jet engine, a problem set up for which the new AMR implementation is particularly advantageous. Conclusions. The CT methods and AMR strategies discussed here are currently being used in the simulations performed with BHAC for the generation of theoretical models for the Event Horizon Telescope collaboration.