A discontinuous Galerkin (DG) method suitable for large-scale astrophysical simulations on Cartesian meshes as well as arbitrary static and moving Voronoi meshes is presented. Most major astrophysical fluid dynamics codes use a finite volume (FV) app
roach. We demonstrate that the DG technique offers distinct advantages over FV formulations on both static and moving meshes. The DG method is also easily generalized to higher than second-order accuracy without requiring the use of extended stencils to estimate derivatives (thereby making the scheme highly parallelizable). We implement the technique in the AREPO code for solving the fluid and the magnetohydrodynamic (MHD) equations. By examining various test problems, we show that our new formulation provides improved accuracy over FV approaches of the same order, and reduces post-shock oscillations and artificial diffusion of angular momentum. In addition, the DG method makes it possible to represent magnetic fields in a locally divergence-free way, improving the stability of MHD simulations and moderating global divergence errors, and is a viable alternative for solving the MHD equations on meshes where Constrained-Transport (CT) cannot be applied. We find that the DG procedure on a moving mesh is more sensitive to the choice of slope limiter than is its FV method counterpart. Therefore, future work to improve the performance of the DG scheme even further will likely involve the design of optimal slope limiters. As presently constructed, our technique offers the potential of improved accuracy in astrophysical simulations using the moving mesh AREPO code as well as those employing adaptive mesh refinement (AMR).
We develop a simple evolutionary scenario for the growth of supermassive black holes (BHs), assuming growth due to accretion only, to learn about the evolution of the BH mass function from $z=3$ to 0 and from it calculate the energy budgets of differ
ent modes of feedback. We tune the parameters of the model by matching the derived X-ray luminosity function (XLF) with the observed XLF of active galactic nuclei. We then calculate the amount of comoving kinetic and bolometric feedback as a function of redshift, derive a kinetic luminosity function and estimate the amount of kinetic feedback and $PdV$ work done by classical double Fanaroff-Riley II (FR II) radio sources. We also derive the radio luminosity function for FR IIs from our synthesized population and set constraints on jet duty cycles. Around 1/6 of the jet power from FR II sources goes into $PdV$ work done in the expanding lobes during the time the jet is on. Anti hierarchical growth of BHs is seen in our model due to addition of an amount of mass being accreted on to all BHs independent of the BH mass. The contribution to the total kinetic feedback by active galaxies in a low accretion, kinetically efficient mode is found to be the most significant at $z<1.5$. FR II feedback is found to be a significant mode of feedback above redshifts $zsim 1.5$, which has not been highlighted by previous studies.
We present new GMRT observations of HDF 130, an inverse-Compton (IC) ghost of a giant radio source that is no longer being powered by jets. We compare the properties of HDF 130 with the new and important constraint of the upper limit of the radio flu
x density at 240 MHz to an analytic model. We learn what values of physical parameters in the model for the dynamics and evolution of the radio luminosity and X-ray luminosity (due to IC scattering of the cosmic microwave background (CMB)) of a Fanaroff-Riley II (FR II) source are able to describe a source with features (lobe length, axial ratio, X-ray luminosity, photon index and upper limit of radio luminosity) similar to the observations. HDF 130 is found to agree with the interpretation that it is an IC ghost of a powerful double-lobed radio source, and we are observing it at least a few Myr after jet activity (which lasted 5--100 Myr) has ceased. The minimum Lorentz factor of injected particles into the lobes from the hotspot is preferred to be $gammasim10^3$ for the model to describe the observed quantities well, assuming that the magnetic energy density, electron energy density, and lobe pressure at time of injection into the lobe are linked by constant factors according to a minimum energy argument, so that the minimum Lorentz factor is constrained by the lobe pressure. We also apply the model to match the features of 6C 0905+3955, a classical double FR II galaxy thought to have a low-energy cutoff of $gammasim10^4$ in the hotspot due to a lack of hotspot inverse-Compton X-ray emission. The models suggest that the low-energy cutoff in the hotspots of 6C 0905+3955 is $gammagtrsim 10^3$, just slightly above the particles required for X-ray emission.
