arXiv subjects

Charalampos Markakis

Publications and source records attributed to Charalampos Markakis.

24 records · Page 2Linked to original sources

arXiv2011

Magnetohydrodynamics in stationary and axisymmetric spacetimes: a fully covariant approach

A fully geometrical treatment of general relativistic magnetohydrodynamics (GRMHD) is developed under the hypotheses of perfect conductivity, stationarity and axisymmetry. The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in GRMHD. Expressing the electromagnetic field tensor solely in terms of three scalar fields related to the spacetime symmetries, we generalize previously obtained results in various directions. In particular, we present the first relativistic version of the Soloviev transfield equation, subcases of which lead to fully covariant versions of the Grad-Shafranov equation and of the Stokes equation in the hydrodynamical limit. We have also derived, as another subcase of the relativistic Soloviev equation, the equation governing magnetohydrodynamical equilibria with purely toroidal magnetic fields in stationary and axisymmetric spacetimes.

gr-qc↗

arXiv2010

Thermodynamics of magnetized binary compact objects

Binary systems of compact objects with electromagnetic field are modeled by helically symmetric Einstein-Maxwell spacetimes with charged and magnetized perfect fluids. Previously derived thermodynamic laws for helically-symmetric perfect-fluid spacetimes are extended to include the electromagnetic fields, and electric currents and charges; the first law is written as a relation between the change in the asymptotic Noether charge $\dl Q$ and the changes in the area and electric charge of black holes, and in the vorticity, baryon rest mass, entropy, charge and magnetic flux of the magnetized fluid. Using the conservation laws of the circulation of magnetized flow found by Bekenstein and Oron for the ideal magnetohydrodynamic (MHD) fluid, and also for the flow with zero conducting current, we show that, for nearby equilibria that conserve the quantities mentioned above, the relation $\dl Q=0$ is satisfied. We also discuss a formulation for computing numerical solutions of magnetized binary compact objects in equilibrium with emphasis on a first integral of the ideal MHD-Euler equation.

gr-qc↗

arXiv2010

Inferring the neutron star equation of state from binary inspiral waveforms

The properties of neutron star matter above nuclear density are not precisely known. Gravitational waves emitted from binary neutron stars during their late stages of inspiral and merger contain imprints of the neutron-star equation of state. Measuring departures from the point-particle limit of the late inspiral waveform allows one to measure properties of the equation of state via gravitational wave observations. This and a companion talk by J. S. Read reports a comparison of numerical waveforms from simulations of inspiraling neutron-star binaries, computed for equations of state with varying stiffness. We calculate the signal strength of the difference between waveforms for various commissioned and proposed interferometric gravitational wave detectors and show that observations at frequencies around 1 kHz will be able to measure a compactness parameter and constrain the possible neutron-star equations of state.

gr-qc↗

arXiv2009

Iteration Stability for Simple Newtonian Stellar Systems

For an equation of state in which pressure is a function only of density, the analysis of Newtonian stellar structure is simple in principle if the system is axisymmetric, or consists of a corotating binary. It is then required only to solve two equations: one stating that the "injection energy", $κ$, a potential, is constant throughout the stellar fluid, and the other being the integral over the stellar fluid to give the gravitational potential. An iterative solution of these equations generally diverges if $κ$ is held fixed, but converges with other choices. We investigate the mathematical reason for this convergence/divergence by starting the iteration from an approximation that is perturbatively different from the actual solution. A cycle of iteration is then treated as a linear "updating" operator, and the properties of the linear operator, especially its spectrum, determine the convergence properties. For simplicity, we confine ourselves to spherically symmetric models in which we analyze updating operators both in the finite dimensional space corresponding to a finite difference representation of the problem, and in the continuum, and we find that the fixed-$κ$ operator is self-adjoint and generally has an eigenvalue greater than unity; in the particularly important case of a polytropic equation of state with index greater than unity, we prove that there must be such an eigenvalue. For fixed central density, on the other hand, we find that the updating operator has only a single eigenvector, with zero eigenvalue, and is nilpotent in finite dimension, thereby giving a convergent solution.

astro-ph.SR↗

arXiv2009

Measuring the neutron star equation of state with gravitational wave observations

We report the results of a first study that uses numerical simulations to estimate the accuracy with which one can use gravitational wave observations of double neutron star inspiral to measure parameters of the neutron-star equation of state. The simulations use the evolution and initial-data codes of Shibata and Uryu to compute the last several orbits and the merger of neutron stars, with matter described by a parametrized equation of state. Previous work suggested the use of an effective cutoff frequency to place constraints on the equation of state. We find, however, that greater accuracy is obtained by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly for smaller values of the neutron star compactness (the ratio of the mass of the neutron star to its radius). We estimate that realistic equations of state will lead to gravitational waveforms that are distinguishable from point particle inspirals at an effective distance (the distance to an optimally oriented and located system that would produce an equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash observed, neutron-star radius is closely tied to the pressure at density not far above nuclear. Our results suggest that broadband gravitational wave observations at frequencies between 500 and 1000 Hz will constrain this pressure, and we estimate the accuracy with which it can be measured. Related first estimates of radius measurability show that the radius can be determined to an accuracy of ~1 km at 100 Mpc.

gr-qc↗

arXiv2008

Quasi-equilibrium models for triaxially deformed rotating compact stars

Quasi-equilibrium models of rapidly rotating triaxially deformed stars are computed in general relativistic gravity, assuming a conformally flat spatial geometry (Isenberg-Wilson-Mathews formulation) and a polytropic equation of state. Highly deformed solutions are calculated on the initial slice covered by spherical coordinate grids, centered at the source, in all angular directions up to a large truncation radius. Constant rest mass sequences are calculated from nearly axisymmetric to maximally deformed triaxial configurations. Selected parameters are to model (proto-) neutron stars; the compactness is M/R = 0.001, 0.1, 0.14, 0.2 for polytropic index n = 0.3 and M/R = 0.001, 0.1, 0.12, 0.14 for n = 0.5. We confirmed that the triaxial solutions exist for these parameters as in the case of Newtonian polytropes. However, it is also found that the triaxial sequences become shorter for higher compactness, and those may disappear at a certain large compactness for the n = 0.5 case. In the scenario of the contraction of proto-neutron stars being subject to strong viscosity and rapid cooling, it is plausible that, once the viscosity driven secular instability sets in during the contraction, the proto-neutron stars are always maximally deformed triaxial configurations, as long as the compactness and the equation of state parameters allow such triaxial sequences. Detection of gravitational waves from such sources may be used as another probe for the nuclear equation of state.

astro-ph↗