Scaling Relations in 2+1 Dimensional Relativistic Turbulence / Electromagnetic Emission from Magnetized Two-Dipole Neutron Stars
Part I: Relativistic hydrodynamic turbulence has both direct applications, such as in astrophysical jets or accretion, and indirect ones, such as in the fluid-gravity correspondence. We clarify and extend some recently derived scaling relations in relativistic hydrodynamics to 2+1 dimensions. We also perform simulations in an effort to measure the relations we have derived. Due to statistical difficulties, the numerical results are inconclusive. Part II: Electromagnetic counterparts to gravitational wave signals provide an opportunity to probe physics under extreme conditions, but a phenomenological understanding is currently lacking. We simulate a rotating neutron star with the magnetic field of two offset dipoles, similar to dipolar binary merger scenarios, in order to measure the spin-dependence of the luminosity. We find powers of 3.82 and 4.20 for the aligned and anti-aligned cases, respectively. These values are commensurate with dimensional estimates, but incommensurate with the values reported in.