Merging black hole binaries in gaseous environments: simulations in general-relativistic magnetohydrodynamics

Merging supermassive black hole-black hole (BHBH) binaries produced in galaxy mergers are promising sources of detectable gravitational waves. If such a merger takes place in a gaseous environment, there is a possibility of a simultaneous detection of electromagnetic and gravitational radiation, as the stirring, shock heating and accretion of the gas may produce variability and enhancements in the electromagnetic flux. This can provide a wealth of opportunities to study gravitational physics, accretion physics, and cosmology. We investigate this scenario by performing fully general relativistic, (magneto)hydrodynamic simulations of merging, equal-mass, nonspinning BHBH binaries embedded in gaseous environments. We evolve the metric using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation with standard moving puncture gauge conditions and handle the magnetohydrodynamics via a high-resolution shock-capturing (HRSC) scheme. In the limit of negligible gas angular momentum, we consider both “binary Bondi accretion” in which the binary is at rest relative to the ambient gas cloud, as well as “binary Bondi-Hoyle-Lyttleton accretion” in which the binary moves relative to the gas cloud. The gas cloud is assumed to be homogeneous far from the binary and governed by a Γ-law equation of state. During the binary inspiral, we find evidence for significant enhancements in both the accretion rate and luminosity over values for a single black hole of the same mass as the binary. We also consider disk-like accretion flows with significant gas angular momentum. In this case, we track the inspiral starting from a binary separation of 10M, where M is the total binary mass. Disks are allowed to relax in the “early inspiral” epoch to provide quasistationary initial data. We then evolve the spacetime metric and matter during the “late inspiral and merger” epochs. The later simulations are designed to track BHBH inspiral following disk-binary decoupling, through merger and ringdown. Finally, we present results from the first fully general relativistic magnetohydrodynamic (MHD) simulations of an equal-mass BHBH embedded in a magnetized circumbinary accretion disk. Prior to decoupling, we find that the competition between the binary tidal torques and the effective viscous torque due to MHD turbulence depletes the disk interior to the binary orbit but induces a two-stream accretion flow onto the BHs and a mildly relativistic polar outflow. Following decoupling we find that the accretion rate is reduced, while the electromagnetic luminosity peaks near merger due to shock heating

Using Multiple-Stimulus Without Replacement Preference Assessments to Increase Student Engagement and Performance

Multiple-stimulus without replacement preference assessment is a research-based method for identifying appropriate rewards for students with emotional and behavioral disorders. This article presents a brief history of how this technology evolved and describes a step-by-step approach for conducting the procedure. A discussion of necessary materials and data sheets is included. Finally, a case study is presented to illustrate how the procedure can be used to improve behavioral and academic outcomes