K. M. Shahabasyan

Gravitational Radiation from Pulsating White Dwarfs

Rotating white dwarfs undergoing quasi-radial oscillations can emit gravitational radiation in a frequency range from 0.1 to 0.3 Hz. Assuming that the energy source for the gravitational radiation comes from the oblateness of the white dwarf induced by the rotation, the strain amplitude is found to be ~10-27 for a white dwarf at ~50 pc. The Galactic population of these sources is estimated to be ~107 and may produce a confusion-limited foreground for proposed advanced detectors in the frequency band between space-based and ground-based interferometers. Nearby oscillating white dwarfs may provide a clear enough signal to investigate white dwarf interiors through gravitational wave asteroseismology.

Vortex structure of neutron stars with CFL quark cores

The Ginzburg-Landau equations are derived for the magnetic and gluomagnetic gauge fields of nonabelian semi-superfluid vortex filaments in color superconducting cores of neutron stars containing a diquark CFL condensate. The interaction of the diquark CFL condensate with the magnetic and gluomagnetic gauge fields is taken into account. The asymptotic values of the energies of these filaments are determined from the quantization conditions. It is shown that a lattice of semi-superfluid vortex filaments with a minimal quantum of circulation develops in the quark superconducting core during rotation of the star. The magnetic field in the core of this vortex is on the order of 1018 G. A cluster of proton vortices, which develops in the hadron phase surrounding every superfluid neutron vortex owing to an entrainment effect, creates new semi-superfluid vortex filaments with a minimal quantum of circulation in the quark superconducting core.

Meissner Effect for “Color” Superconducting Quark Matter

The behavior of the magnetic field inside the superconducting quark matter core of a neutron star is investigated in the framework of the Ginzburg-Landau theory. We take into account the simultaneous coupling of the diquark condensate field to the usual magnetic and to the gluomagnetic gauge fields. We solve the problem for three different physical situations: a semi-infinite region with a planar boundary, a spherical region, and a cylindrical region. We show that Meissner currents near the quark core boundary effectively screen the external static magnetic field.

Gravitational radiation from differentially rotating white dwarfs

We examine the possibility of gravitational radiation from white dwarfs undergoing self-similar oscillations which are fed by the energy of the differential rotation of the white dwarf. We consider two typical cases of angular momentum distribution. Assuming the energy of the self-similar oscillations causing gravitational wave emission is about 1% of the energy dissipated in the differentially rotating white dwarf, the strain amplitudes are found to be less than 10−27 for a white dwarf at ~50 pc. Combined with the mechanism of gravitational radiation based on deformation energy from magnetic white dwarfs, the gravitational radiation from differentially rotating white dwarfs may produce a confusion limited foreground above the stochastic cosmological background for proposed advanced detectors in the decihertz frequency band.

MAGNETIC FIELDS OF COMPACT STARS WITH SUPERCONDUCTING QUARK CORES

The behavior of the magnetic field of a rotating neutron star with a superconducting color-flavor-locked (CFL) quark matter core is investigated in the framework of the Ginzburg-Landau theory. We take into account the simultaneous coupling of the diquark condensate field to the magnetic and gluomagnetic gauge fields. We solve the Ginzburg-Landau equations by properly taking into account the boundary conditions, in particular the gluon confinement condition. The rotation of the CFL condensate produces neutral vortices with normal cores. We find the distribution of the magnetic field in both the quark and the hadronic phases and show that a magnetic field penetrates into quark phase through normal cores of the rotational vortices. As a result, equivalent ”magnetic vortices” are formed due to the induced Meissner currents.

Magnetic field of pulsars with superconducting quark core

Within recent nonperturbative approaches to the effective quark interaction the diquark condensate forms a superconductor of second kind. Therefore the magnetic field will not be expelled from the superconducting quark core in accordance with observational data which indicate that life times of pulsar magnetic fields exceed 10 years. The physical properties of pulsars can constrain our hypotheses about the state of matter at high densities. For example, Bailin and Love (1984) have suggested that the magnetic field of pulsars should be expelled from the superconducting interior of the star due to the Meissner effect and decay subsequently within ≈ 10 years. If their arguments would hold in general, the observation of lifetimes as large as 10 years (Makashima 1992) would exclude the occurence of an extended superconducting quark matter phase in pulsars. For their estimate, they assumed a homogeneous magnetic field and used a perturbative quark interaction which results in a very small pairing gap. Since both assumptions seem not to be valid in general, we perform a reinvestigation of this question. Recently there has been excitement (Wilczek 1999) about the observation that in chiral quark models with nonperturbative 4-point interactions the anomalous quark pair amplitudes in the color antitriplet channel can be very large of the order ≈ 100 MeV. In Fig. 1 (a) we show the solution of the corresponding diquark gap equation for a BCS-type quark-quark interaction model (Berges & Rajagopal 1999) and the corresponding Ginzburg-Landau Parameter κ. Quark matter with a diquark condensate appears as a superconductor of second kind into which the magnetic field H can penetrate by forming quantized vortex lines provided Hc1 < H < Hc2 where Hc1 = 1.8 · 10 16 G (Blaschke, Sedrakian & Shahabasyan 1999). It is generally accepted that neutrons and protons in the “npe”-phase are superfluid. While the neutrons take part in the rotation, forming a lattice of quantized vortex lines, the superconducting protons will be entrained by the neutrons (Sedrakian & Shahabasian 1980) and form inside the neutron vortex a magnetic field strengthH(r) which acts as an external field for the non-entrained protons. This entails the formation of a cluster of proton vortices with fluxes Φ0 in a region with the radius δn = 10 −5 cm around the axis of the neutron vortex. The mean magnetic induction within the cluster reaches values of 4 · 10 G