"Scaling Relations in 2+1 Dimensional Relativistic Turbulence / Electromagnetic Emission from Magnetized Two-Dipole Neutron Stars"
Relativistic hydrodynamic turbulence has both direct applications, such as in astrophysical jets or accretion scenarios, and indirect ones, such as in the study of gravitational physics through the fluid-gravity correspondence. The latter requires that the fluid under consideration be conformally invariant. In this work, we clarify and extend some recently derived statistical scaling relations in relativistic hydrodynamic turbulence to the case of 2+1 dimensions. Such dimensionality exhibits novel behaviour which can be realized in approximately 2D fluid flows, and is relevant to 3+1 dimensional gravity through the fluid-gravity correspondence. We also perform numerical simulations of steady-state 2+1 dimensional relativistic turbulence of a conformal fluid on a torus, in an effort to numerically measure some of the scaling relations derived in this work. Due to numerical and statistical difficulties, the numerical results are inconclusive thus far.
Electromagnetic counterparts to gravitational wave signals from extreme astrophysical events provide an exciting opportunity to probe physics under conditions not reproducible in terrestrial experiments. Understanding the phenomenology of such electromagnetic counterparts is crucial to developing efficient, inexpensive effective models of these signals. In this work, we take a step in this direction. In an effort to gain insight into the dependence on orbital frequency of the electromagnetic emission from magnetized binary neutron star mergers reported in recent work , we perform simulations in full general relativity of a single rotating neutron star with similar magnetic field structure. Our aim is to identify the strength of an assumed power-law dependence, L ~ Omega^p, i.e. to measure p numerically. We consider two magnetic field structures, both referred to as two-dipole configurations: two dipoles collinear with the rotation axis of the star, placed equidistant from the centre of the star in opposite directions, but either aligned or anti-aligned with respect to each other. We refer to each case as U/U (`Up/Up') and U/D (`Up/Down'). The values of p that we find are p=3.82 +/- 0.10 and $p=4.20 +/- 0.27, respectively, although the latter is subject to notable uncertainty. These values are roughly commensurate with dimensional estimates, but incommensurate with the values reported in previous work on the binary merger case.
Dr. Xiaorong Qin, Chair
Dr. Eric Poisson, Supervisor
Dr. Luis Lehner, Co-Supervisor
Dr. Erik Schnetter, Member