Transonic accretion and winds around Pseudo-Kerr black holes andcomparison with general relativistic solutions

Spectral and timing properties of accretion flows on a black hole depend on their density and temperature distributions, which, in turn come from the underlying dynamics. Thus, an accurate description of the flow which includes hydrodynamics and radiative transfer is a must to interpret the observational results. In the case of non-rotating black holes, Pseudo- Newtonian description of surrounding space-time enables one to make a significant progress in predicting spectral and timing properties. This formalism is lacking for the spinning black holes. In this paper, we show that there exists an exact form of ‘natural’ potential derivable from the general relativistic (GR) radial momentum equation written in the local corotating frame. Use of this potential in an otherwise Newtonian set of equations, allows us to describe transonic flows very accurately as is evidenced by comparing with solutions obtained from the full GR framework. We study the properties of the sonic points and the centrifugal pressure supported shocks in the parameter space spanned by the specific energy and the angular momentum, and compare with the results of GR hydrodynamics. We show that this potential can safely be used for the entire range of Kerr parameter −1 < a < 1 for modeling of observational results around spinning black holes. We assume the flow to be inviscid. Thus, it is non-dissipative with constant energy and angular momentum. These assumptions are valid very close to the black hole horizon as the infall time scale is much shorter as compared to the viscous time scale.

Resolving the Fastest Ejecta from Binary Neutron Star Mergers: Implications for Electromagnetic Counterparts

We examine the effect of spatial resolution on initial mass ejection in grid-based hydrodynamic simulations of binary neutron star mergers. The subset of the dynamical ejecta with velocities greater than ∼0.6c can generate an ultraviolet precursor to the kilonova on approximately hour timescales and contribute to a years long nonthermal afterglow. Previous work has found differing amounts of this fast ejecta, by one to two orders of magnitude, when using particle-based or grid-based hydrodynamic methods. Here, we carry out a numerical experiment that models the merger as an axisymmetric collision in a corotating frame, accounting for Newtonian self-gravity, inertial forces, and gravitational wave losses. The lower computational cost allows us to reach spatial resolutions as high as 4 m, or ∼3 × 10−4 of the stellar radius. We find that fast ejecta production converges to within 10% for a cell size of 20 m. This suggests that fast ejecta quantities found in existing grid-based merger simulations are unlikely to increase to the level needed to match particle-based results upon further resolution increases. The resulting neutron-powered precursors are in principle detectable out to distances ≲200 Mpc with upcoming facilities.We also find that head-on collisions at the freefall speed, relevant for eccentric mergers, yield fast and slow ejecta quantities of order 10−2 M ⊙, with a kilonova signature distinct from that of quasi-circular mergers.

Two-layer geostrophic vortex dynamics. Part 2. Alignment and two-layer V-states

The process of alignment, a new fundamental interaction between vortices in a stratified and rapidly rotating fluid, is defined and studied in detail in the context of the two-layer quasi-geostrophic model. Alignment occurs when two vortices in different density layers coalesce by reducing their horizontal separation. It is found that only vortices whose radii are comparable with or larger than the Rossby deformation radius can align. In the same way as the merger process (in a single two-dimensional layer) is related to the reverse energy cascade of two-dimensional turbulence, geostrophic potential vorticity alignment is related the barotropic-to-baroclinic energy cascade of geostrophic turbulence in two layers. It is also shown how alignment is intimately connected with the existence of two-layer doubly connected geostrophic potential vorticity equilibria (V-states), for which the analysis of the geometry of the stream function in the corotating frame is found to be a crucial diagnostic. The finite-area analogues of the hetons of Hogg & Stommel (1985) are also determined: they consist of a propagating pair of opposite-signed potential vorticity patches located in different layers.

The post - Newtonian rotation of Earth: a first approach

The problems of dynamics of extended bodies in metric theories of gravity are reviewed. In a first approach towards the relativistic description of the Earth's rotational motion the post - Newtonian treatment of the free precession of a pseudo - rigid and axially symmetric model Earth is presented. Definitions of angular momentum, pseudo - rigidity, the corotating frame, tensor of inertia and axial symmetry of the rotating body are based upon the choice of the standard post - Newtonian (PN) coordinates and the full PN energy momentum complex. In this framework, the relation between angular momentum and angular (coordinate) velocity is obtained. Since the PN Euler equations for the angular velocity here formally take their usual Newtonian form it is concluded that apart from PN modifications (renormalizations) of the inertia tensor, the rotational motion of our pseudo - rigid and axially symmetric model Earth essentially is “Newtonian”.

Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation

We consider the evolution of an isolated elliptical vortex in a weakly dissipative fluid. It is shown computationally that a spatially smooth vortex relaxes inviscidly towards axisymmetry on a circulation timescale as the result of filament generation. Heuristically, we derive a simple geometrical formula relating the rate of change of the aspect ratio of a particular vorticity contour to its orientation relative to the streamlines (where the orientation is defined through second-order moments). Computational evidence obtained with diagnostic algorithms validates the formula. By considering streamlines in a corotating frame and applying the new formula, we obtain a detailed kinematic understanding of the vortex's decay to its final state through a primary and a secondary breaking. The circulation transported into the filaments although a small fraction of the total, breaks the symmetry and is the chief cause of axisymmetrization.