An MHD Gadget for cosmological simulations

Various radio observations have showed that the hot atmospheres of galaxy clusters are magnetized. However, our understanding of the origin of these magnetic fields, their implications on structure formation and their interplay with the dynamics of the cluster atmosphere, especially in the centers of galaxy clusters is still very limited. In preparation to the upcoming new generation of radio telescopes (like EVLA, LWA, LOFAR and SKA), a huge effort is being made to learn more about cosmological magnetic fields from the observational perspective. Here we present the implementation of magneto hydrodynamics in the cosmological SPH code GADGET. We discuss the details of the implementation and various schemes to suppress numerical instabilities as well as regularization schemes, in the context of cosmological simulations. The performance of the SPH MHD code is demonstrated in various one and two dimensional test problems, which we performed if a fully, three dimensional setup to test the code under realistic circumstances. Comparing with solutions obtained with ATHENA, we find excellent agreement with our SPH MHD implementation. Finally we apply our SPH MHD implementation to forming galaxy clusters within a large, cosmological box. Performing a resolution study we demonstrate the robustness of the predicted shape of the magnetic field profiles in galaxy clusters, which is in good agreement with previous studies.Comment: Updated version, 21 pages, 21 figures, submitted to MNRA

Measuring cosmic magnetic fields by rotation measure-galaxy cross-correlations in cosmological simulations

Using cosmological MHD simulations of the magnetic field in galaxy clusters and filaments we evaluate the possibility to infer the magnetic field strength in filaments by measuring cross-correlation functions between Faraday Rotation Measures (RM) and the galaxy density field. We also test the reliability of recent estimates considering the problem of data quality and Galactic foreground (GF) removal in current datasets. Besides the two self-consistent simulations of cosmological magnetic fields based on primordial seed fields and galactic outflows analyzed here, we also explore a larger range of models scaling up the resulting magnetic fields of one of the simulations. We find that, if an unnormalized estimator for the cross-correlation functions and a GF removal procedure is used, the detectability of the cosmological signal is only possible for future instruments (e.g. SKA and ASKAP). However, mapping of the observed RM signal to the underlying magnetization of the Universe (both in space and time) is an extremely challenging task which is limited by the ambiguities of our model parameters, as well as to the weak response of the RM signal in low density environments. Therefore, we conclude that current data cannot constrain the amplitude and distribution of magnetic fields within the large scale structure and a detailed theoretical understanding of the build up and distribution of magnetic fields within the Universe will be needed for the interpretation of future observations.Comment: 11 pages, 11 figures, comparation between RM data and simulations in fig. 8, submited to MNRAS

Infalling clouds onto super-massive black hole binaries - I. Formation of discs, accretion and gas dynamics

There is compelling evidence that most -if not all- galaxies harbour a super-massive black hole (SMBH) at their nucleus, hence binaries of these massive objects are an inevitable product of the hierarchical evolution of structures in the universe, and represent an important but thus-far elusive phase of galaxy evolution. Gas accretion via a circumbinary disc is thought to be important for the dynamical evolution of SMBH binaries, as well as in producing luminous emission that can be used to infer their properties. One plausible source of the gaseous fuel is clumps of gas formed due to turbulence and gravitational instabilities in the interstellar medium, that later fall toward and interact with the binary. In this context, we model numerically the evolution of turbulent clouds in near-radial infall onto equal-mass SMBH binaries, using a modified version of the SPH code GADGET-3. We present a total of 12 simulations that explore different possible pericentre distances and relative inclinations, and show that the formation of circumbinary discs and discs around each SMBH ('mini-discs') depend on those parameters. We also study the dynamics of the formed discs, and the variability of the feeding rate onto the SMBHs in the different configurations.Comment: Accepted for publication in MNRAS, 17 pages, 13 figures. Animations available at http://www.astro.puc.cl/~fgarrido/animation

Magnetic field structure due to the global velocity field in spiral galaxies

We present a set of global, self-consistent N-body/SPH simulations of the dynamic evolution of galactic discs with gas and including magnetic fields. We have implemented a description to follow the evolution of magnetic fields with the ideal induction equation in the SPH part of the Vine code. Results from a direct implementation of the field equations are compared to a representation by Euler potentials, which pose a div(B)-free description, an constraint not fulfilled for the direct implementation. All simulations are compared to an implementation of magnetic fields in the Gadget code which includes also cleaning methods for div(B). Starting with a homogeneous seed field we find that by differential rotation and spiral structure formation of the disc the field is amplified by one order of magnitude within five rotation periods of the disc. The amplification is stronger for higher numerical resolution. Moreover, we find a tight connection of the magnetic field structure to the density pattern of the galaxy in our simulations, with the magnetic field lines being aligned with the developing spiral pattern of the gas. Our simulations clearly show the importance of non-axisymmetry for the evolution of the magnetic field.Comment: 17 pages, 18 figure

Simulating magnetic fields in the Antennae galaxies

We present self-consistent high-resolution simulations of NGC4038/4039 (the "Antennae galaxies") including star formation, supernova feedback and magnetic fields performed with the N-body/SPH code Gadget, in which magnetohydrodynamics are followed with the SPH method. We vary the initial magnetic field in the progenitor disks from 1 nG to 100 muG. At the time of the best match with the central region of the Antennae system the magnetic field has been amplified by compression and shear flows to an equilibrium field of approximately 10 muG, independent of the initial seed field. These simulations are a proof of the principle that galaxy mergers are efficient drivers for the cosmic evolution of magnetic fields. We present a detailed analysis of the magnetic field structure in the central overlap region. Simulated radio and polarization maps are in good morphological and quantitative agreement with the observations. In particular, the two cores with the highest synchrotron intensity and ridges of regular magnetic fields between the cores and at the root of the southern tidal arm develop naturally in our simulations. This indicates that the simulations are capable of realistically following the evolution of the magnetic fields in a highly non-linear environment. We also discuss the relevance of the amplification effect for present day magnetic fields in the context of hierarchical structure formation.Comment: 18 pages, 14 figures, accepte

A divergence-cleaning scheme for cosmological SPMHD simulations

In magnetohydrodynamics (MHD), the magnetic field is evolved by the induction equation and coupled to the gas dynamics by the Lorentz force. We perform numerical smoothed particle magnetohydrodynamics (Spmhd) simulations and study the influence of a numerical magnetic divergence. For instabilities arising from divergence B related errors, we find the hyperbolic/parabolic cleaning scheme suggested by Dedner et al. 2002 to give good results and prevent numerical artifacts from growing. Additionally, we demonstrate that certain current Spmhd implementations of magnetic field regularizations give rise to unphysical instabilities in long-time simulations. We also find this effect when employing Euler potentials (divergenceless by definition), which are not able to follow the winding-up process of magnetic field lines properly. Furthermore, we present cosmological simulations of galaxy cluster formation at extremely high resolution including the evolution of magnetic fields. We show synthetic Faraday rotation maps and derive structure functions to compare them with observations. Comparing all the simulations with and without divergence cleaning, we are able to confirm the results of previous simulations performed with the standard implementation of MHD in Spmhd at normal resolution. However, at extremely high resolution, a cleaning scheme is needed to prevent the growth of numerical errors at small scales.Comment: 15 pages, 19 figures, submitted to MNRA

Magnetic Field Amplification in Galaxy Clusters and its Simulation

We review the present theoretical and numerical understanding of magnetic field amplification in cosmic large-scale structure, on length scales of galaxy clusters and beyond. Structure formation drives compression and turbulence, which amplify tiny magnetic seed fields to the microGauss values that are observed in the intracluster medium. This process is intimately connected to the properties of turbulence and the microphysics of the intra-cluster medium. Additional roles are played by merger induced shocks that sweep through the intra-cluster medium and motions induced by sloshing cool cores. The accurate simulation of magnetic field amplification in clusters still poses a serious challenge for simulations of cosmological structure formation. We review the current literature on cosmological simulations that include magnetic fields and outline theoretical as well as numerical challenges.Comment: 60 pages, 19 Figure

A non-ideal MHD Gadget: Simulating massive galaxy clusters

Magnetic fields in the intra-cluster medium of galaxy clusters have been studied in the past years through different methods. In the next years the up-coming generation of radio telescopes is going to provide new data that have the potential of setting constraints on the properties of magnetic fields in galaxy clusters. Here we present zoomed-in simulations for a set of massive galaxy clusters (M_v > 10^15 M_sun/h). This is an ideal sample to study the evolution of magnetic field during the process of structure formation in detail. Turbulent motions of the gas within the ICM will manifest themselves in a macroscopic magnetic resistivity eta_m, which has to be taken explicitly into account, especially at scales below the resolution limit. We have adapted the MHD GADGET code by Dolag & Stasyszyn (2009) to include the treatment of the magnetic resistivity and for the first time we have included non-ideal MHD equations to better follow the evolution of the magnetic field within galaxy clusters. We investigate which value of the magnetic resistivity eta_m is required to match the magnetic field profile derived from radio observations. We find that a value of eta_m ~ 6 10^27 cm^2/s is necessary to recover the shape of the magnetic field profile inferred from radio observations of the Coma cluster. This value agrees well with the expected level of turbulent motions within the ICM at our resolution limit. The magnetic field profiles can be fitted by a beta-model like profile (Cavaliere & Fusco-Femiano 1976), with small dispersion of the parameters. We find also that that the temperature, density and entropy profiles of the clusters depend on the magnetic resistivity constant, having flatter profiles in the inner regions when the magnetic resistivity increases.Comment: 19 pages, 11 figures. Resubmitted to MNRAS after referee repor