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Two-dimensional models assuming axisymmetry are an economical way to explore the long-term evolution of black hole accretion disks, but they are only realistic if the feedback of the nonaxisymmetric turbulence on the mean momentum and magnetic fields is incorporated. Dynamo terms added to the 2D induction equation should be calibrated to 3D magnetohydrodynamics simulations. For generality, the dynamo tensors should be calibrated as functions of local variables rather than explicit functions of spatial coordinates in a particular basis. In this paper, we study the feedback of nonaxisymmetric features on the 2D mean fields using a global 3D, relativistic, Cartesian simulation from the illinoisgrmhd code. We introduce new methods for estimating overall dynamo alpha and turbulent diffusivity effects, as well as measures of the dominance of nonaxisymmetric components of energies and fluxes within the disk interior. We attempt closure models of the dynamo electromotive force using least-squares fitting, considering both models where coefficient tensors are functions of space and more global, covariant models. None of these models are judged satisfactory, but we are able to draw conclusions on what sorts of generalizations are and are not promising. 

Supermassive black holes (SMBHs) are thought to be located at the centers of most galactic nuclei. When galaxies merge they form supermassive black hole binary (SMBHB) systems and these central SMBHs will also merge at later times, producing gravitational waves (GWs). Because galaxy mergers are likely gas-rich environments, SMBHBs are also potential sources of electromagnetic (EM) radiation. The EM signatures depend on gas dynamics, orbital dynamics, and radiation processes. The gas dynamics are governed by general relativistic magnetohydrodynamics (MHD) in a time-dependent spacetime. Numerically solving the MHD equations for a time-dependent binary spacetime is computationally expensive. Therefore, it is challenging to conduct a full exploration of the parameter space of these systems and the resulting EM signatures. We have developed an analytical accretion disk model for the mini-disks of an SMBHB system and produced images and light curves using a general relativistic ray-tracing code and a superimposed harmonic binary black hole metric. This analytical model greatly reduces the time and computational resources needed to explore these systems, while incorporating some key information from simulations. We present a parameter space exploration of the SMBHB system in which we have studied the dependence of the EM signatures on the spins of the black holes (BHs), the mass ratio, the accretion rate, the viewing angle, and the initial binary separation. Additionally, we study how the commonly used fast-light approximation affects the EM signatures and evaluate its validity in GRMHD simulations. 

Abstract LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the early inspirals of stellar-mass black holes that will ultimately venture into the ground-based detectors’ view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA’s discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This White Paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.