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Abstract Binary black holes are the most abundant source of gravitational-wave observations. Gravitational-wave observatories in the next decade will require tremendous increases in the accuracy of numerical waveforms modeling binary black holes, compared to today’s state of the art. One approach to achieving the required accuracy is using spectral-type methods that scale to many processors. Using theSpECTREnumerical-relativity (NR) code, we present the first simulations of a binary black hole inspiral, merger, and ringdown using discontinuous Galerkin (DG) methods. The efficiency of DG methods allows us to evolve the binary through ∼ 18 orbits at reasonable computational cost. We then useSpECTRE’s Cauchy Characteristic Evolution (CCE) code to extract the gravitational waves at future null infinity. The open-source nature ofSpECTREmeans this is the first time a spectral-type method for simulating binary black hole evolutions is available to the entire NR community. 

Abstract Short γ -ray burst (sGRB) jets form in the aftermath of a neutron star merger, drill through disk winds and dynamical ejecta, and extend over four to five orders of magnitude in distance before breaking out of the ejecta. We present the first 3D general-relativistic magnetohydrodynamic sGRB simulations to span this enormous scale separation. They feature three possible outcomes: jet+cocoon, cocoon, and neither. Typical sGRB jets break out of the dynamical ejecta if (i) the bound ejecta’s isotropic equivalent mass along the pole at the time of the BH formation is ≲10 −4 M ⊙ , setting a limit on the delay time between the merger and BH formation, otherwise, the jets perish inside the ejecta and leave the jet-inflated cocoon to power a low-luminosity sGRB; (ii) the postmerger remnant disk contains a strong large-scale vertical magnetic field, ≳10 15 G; and (iii) if the jets are weak (≲10 50 erg), the ejecta’s isotropic equivalent mass along the pole must be small (≲10 −2 M ⊙ ). Generally, the jet structure is shaped by the early interaction with disk winds rather than the dynamical ejecta. As long as our jets break out of the ejecta, they retain a significant magnetization (≲1), suggesting that magnetic reconnection is a fundamental property of sGRB emission. The angular structure of the outflow isotropic equivalent energy after breakout consistently features a flat core followed by a steep power-law distribution (slope ≳3), similar to hydrodynamic jets. In the cocoon-only outcome, the dynamical ejecta broadens the outflow angular distribution and flattens it (slope ∼1.5).