Electromagnetic signals from bare strange stars

Abstract

The crystalline color superconducting phase is believed to be the ground state of deconfined quark matter for sufficiently large values of the strange quark mass. This phase has the remarkable property of being more rigid than any known material. It can therefore sustain large shear stresses, supporting torsional oscillations of large amplitude. The torsional oscillations could lead to observable electromagnetic signals if strange stars have a crystalline color superconducting crust. Indeed, considering a simple model of strange star with a bare quark matter surface, it turns out that a positive charge is localized in a narrow shell about ten Fermi thick beneath the star surface. The electrons needed to neutralize the positive charge of quarks spill in the star exterior forming an electromagnetically bounded atmosphere hundreds of Fermi thick. When a torsional oscillation is excited, for example by a stellar glitch, the positive charge oscillates with typical kHz frequencies, for a crust thickness of about one-tenth of the stellar radius, to hundreds of Hz, for a crust thickness of about nine-tenths of the stellar radius. Higher frequencies, of the order of few GHz, can be reached if the star crust is of the order of few centimeters thick. We estimate the emitted power considering emission by an oscillating magnetic dipole, finding that it can be quite large, of the order of 10 45 erg/s for a thin crust. The associated relaxation times are very uncertain, with values ranging between microseconds and minutes, depending on the crust thickness. The radiated photons will be in part absorbed by the electronic atmosphere, but a sizable fraction of them should be emitted by the star.

Torsional oscillations of strange stars

“…(7). The detailed analysis of [13] and sketched below shows that this is indeed the case. Our interest in the torsional oscillations is clearly due to the fact that in the CCSC phase the shear modulus is extremely large and can therefore sustain oscillations of large amplitude and high frequency.…”

“…Indeed, there is a big electric dipole moment close to the star surface which turns out to be a powerful source of electromagnetic (EM) radiation [13]. In particular, we studied the EM emission associated with the torsional oscillations of the crust.…”

“…In order to take into account the impact of the uncertainty of these coefficients on our results, we consider two extreme situations, namely A (a 4 = 0.7, a 2 = (200 MeV) 2 and B eff = (165 MeV) 4 ) and B (a 4 = 0.7, a 2 = 0 and B eff = (145 MeV) 4 ). Solving the TOV equations using the above EoS one obtains a sequence of stable configurations, see [13] for more details. Our reference models are -Model A, with mass of M = 1.27M , R 7.1 km and -Model B, with M 2.0M , R 10.9 km.…”

“…Solving the Poisson's equation with the appropriate boundary conditions (see [13] for more details), one can determine the potential φ(z) and feeding it in Eq. (6) one determines the space dependent effective chemical potential and therefore the number densities.…”

“…In the following we report on the results obtained in [13] studying the torsional oscillations of strange stars having no nuclear matter crust (so-called bare strange stars [1]), with a color-flavor locked (CFL) [14] core and a crystalline color superconducting (CCSC) crust, see [12] for a review.…”