Equilibrium and stability of charged strange quark stars

Abstract

The hydrostatic equilibrium and the stability against radial perturbation of charged strange quark stars composed of a charged perfect fluid are studied. For this purpose, it is considered that the perfect fluid follows the MIT bag model equation of state and the radial charge distribution follows a power-law. The hydrostatic equilibrium and the stability of charged strange stars are investigated through the numerical solutions of the Tolman-Oppenheimer-Volkoff equation and the Chandrasekhar's pulsation equation, being these equations modified from their original form to include the electrical charge. In order to appreciably affect the stellar structure, it is found that the total charge should be of order 10 20 [C], implying an electric field of around 10 22 [V/m]. We found the electric charge that produces considerable effect on the structure and stability of the object is close to the star's surface. We obtain that for a range of central energy density the stability of the star decreases with the increment of the total charge and for a range of total mass the electric charge helps to grow the stability of the stars under study. We show that the central energy density used to reach the maximum mass value is the same used to determine the zero eigenfrequency of the fundamental mode when the total charge is fixed, thus indicating that the maximum mass point marks the onset of instability. In other words, when fixing the total charge, the conditions dM dρc > 0 and dM dρc < 0 are necessary and sufficient to determine the stable and unstable equilibrium configurations regions against radial oscillations. We also consider another charge distribution, charge density proportional to the energy density, and show that our results do not depend on this choice and the conditions used to determine regions made of the stable and unstable charged equilibrium configurations are maintained.

White dwarfs with a surface electrical charge distribution: equilibrium and stability

“…It is worth mentioning that the electric field found in the charged white dwarfs cases are 10 4 times lower than those found in charged strange stars ones (see, e.g., [30][31][32]). This can be understand since white dwarfs have very larger radii than the strange stars.…”

“…The authors in [32] found that along a sequence of charged stars with increasing central energy density and with fixed total charge, the maximum mass equilibrium configuration states the onset of instability. Thus, likewise, in this section we use the results derived from the equilibrium configurations to determine the maximum mass point which marks the start of the instability.…”

“…Inspired in the study of the turning-point method for axisymmetric stability of uniformly rotating relativistic stars with the angular momentum fixed [51] (see also [52] for a detailed discussion about that theme), in [32] is shown that the stability of charged objects could be investigated using the results obtained from the hydrostatic equilibrium equation. The authors in [32] found that along a sequence of charged stars with increasing central energy density and with fixed total charge, the maximum mass equilibrium configuration states the onset of instability.…”

“…Within them, we found some research where the influence of the electrical charge distribution at the stellar structure of polytropic stars [20][21][22][23][24], incompressible spherical objects [25][26][27][28], anisotropic stars [29] and strange stars [30,31], and in the radial stability against small perturbation [32,33] and in gravitational collapse [34] are investigated. It is important to mention that, although charged stars are anisotropic objects, these maintain their spherical symmetry, since the energy momentum tensor components T 0 0 (r ) and T 1 1 (r ) are equals, being r the radial coordinate (see, e.g., [35][36][37] In this work, we investigate the influence of the surface electric charge in the stellar structure and stability of white dwarfs.…”

Gravitational fields with sources: From compact objects to black holes

“…José Arbañil presented a work 65 in which he studied the hydrostatic equilibrium and the stability against radial perturbations of charged strange quark stars composed by a charged perfect fluid. In his model the perfect fluid follows the MIT bag model equation of state and the charge has a power-law distribution in the radial coordinate.…”