Nuclear Equation of State and Internal Structure of Magnetars

Recently, neutron stars with very strong surface magnetic fields have been suggested as the site for the origin of observed soft gamma repeaters (SGRs). We investigate the influence of a strong magnetic field on the properties and internal structure of such strongly magnetized neutron stars (magnetars). The presence of a sufficiently strong magnetic field changes the ratio of protons to neutrons as well as the neutron appearance density. We also study the pion production and pion condensation in a strong magnetic field. We discuss the pion condensation in the interior of magnetars as a possible source of SGRs.Comment: 5 pages with 3 figures, To appear in the Proceedings of the 5th Huntsville Gamma Ray Burst Symposium, Huntsville, Alabama, USA, Oct. 18-22, 199

Constraining the neutron star equation of state using XMM-Newton

We have identified three possible ways in which future XMM-Newton observations can provide significant constraints on the equation of state of neutron stars. First, using a long observation of the neutron star X-ray transient CenX-4 in quiescence one can use the RGS spectrum to constrain the interstellar extinction to the source. This removes this parameter from the X-ray spectral fitting of the pn and MOS spectra and allows us to investigate whether the variability observed in the quiescent X-ray spectrum of this source is due to variations in the soft thermal spectral component or variations in the power law spectral component coupled with variations in N_H. This will test whether the soft thermal spectral component can indeed be due to the hot thermal glow of the neutron star. Potentially such an observation could also reveal redshifted spectral lines from the neutron star surface. Second, XMM-Newton observations of radius expansion type I X-ray bursts might reveal redshifted absorption lines from the surface of the neutron star. Third, XMM-Newton observations of eclipsing quiescent low-mass X-ray binaries provide the eclipse duration. With this the system inclination can be determined accurately. The inclination determined from the X-ray eclipse duration in quiescence, the rotational velocity of the companion star and the semi-amplitude of the radial velocity curve determined through optical spectroscopy, yield the neutron star mass.Comment: 4 pages, 1 figure, proceedings of the XMM-Newton workshop, June 2007, accepted for publication in A

Detection of a 1258 Hz high-amplitude kilohertz quasi-periodic oscillation in the ultra-compact X-ray binary 1A 1246-588

We have observed the ultra-compact low-mass X-ray binary (LMXB) 1A 1246-588 with the Rossi X-ray Timing Explorer (RXTE). In this manuscript we report the discovery of a kilohertz quasi-periodic oscillation (QPO) in 1A 1246-588. The kilohertz QPO was only detected when the source was in a soft high-flux state reminiscent of the lower banana branch in atoll sources. Only one kilohertz QPO peak is detected at a relatively high frequency of 1258+-2 Hz and at a single trial significance of more than 7 sigma. Kilohertz QPOs with a higher frequency have only been found on two occasions in 4U 0614+09. Furthermore, the frequency is higher than that found for the lower kilohertz QPO in any source, strongly suggesting that the QPO is the upper of the kilohertz QPO pair often found in LMXBs. The full-width at half maximum is 25+-4 Hz, making the coherence the highest found for an upper kilohertz QPO. From a distance estimate of ~6 kpc from a radius expansion burst we derive that 1A 1246-588 is at a persistent flux of ~0.2-0.3 per cent of the Eddington flux, hence 1A 1246-588 is one of the weakest LMXBs for which a kilohertz QPO has been detected. The root-mean-square (rms) amplitude in the 5-60 keV band is 27+-3 per cent, this is the highest for any kilohertz QPO source so far, in line with the general anti-correlation between source luminosity and rms amplitude of the kilohertz QPO peak identified before. Using the X-ray spectral information we produce a colour-colour diagram. The source behaviour in this diagram provides further evidence for the atoll nature of the source.Comment: 4 pages, 3 figures, accepted for publication in MNRA

A coalescence model for freely decaying two-dimensional turbulence

We propose a ballistic coalescence model (punctuated-Hamiltonian approach) mimicking the fusion of vortices in freely decaying two-dimensional turbulence. A temporal scaling behaviour is reached where the vortex density evolves like $t^{-\xi}$. A mean-field analytical argument yielding the approximation $\xi=4/5$ is shown to slightly overestimate the decay exponent $\xi$ whereas Molecular Dynamics simulations give $\xi =0.71\pm 0.01$, in agreement with recent laboratory experiments and simulations of Navier-Stokes equation.Comment: 6 pages, 1 figure, to appear in Europhysics Letter

The Berry-Keating Hamiltonian and the Local Riemann Hypothesis

The local Riemann hypothesis states that the zeros of the Mellin transform of a harmonic-oscillator eigenfunction (on a real or p-adic configuration space) have real part 1/2. For the real case, we show that the imaginary parts of these zeros are the eigenvalues of the Berry-Keating hamiltonian H=(xp+px)/2 projected onto the subspace of oscillator eigenfunctions of lower level. This gives a spectral proof of the local Riemann hypothesis for the reals, in the spirit of the Hilbert-Polya conjecture. The p-adic case is also discussed.Comment: 9 pages, no figures; v2 included more mathematical background, v3 has minor edits for clarit

Commutator Leavitt path algebras

For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras L_K(E) that satisfy L_K(E)=[L_K(E),L_K(E)]. We also show that these Leavitt path algebras have the additional (unusual) property that all their Lie ideals are (ring-theoretic) ideals, and construct examples of such rings with various ideal structures.Comment: 24 page

Mass-Radius Relation for Magnetic White Dwarfs

Recently, several white dwarfs with very strong surface magnetic fields have been observed. In this paper we explore the possibility that such stars could have sufficiently strong internal fields to alter their structure. We obtain a revised white dwarf mass-radius relation in the presence of strong internal magnetic fields. We first derive the equation of state for a fully degenerate ideal electron gas in a magnetic field using an Euler-MacLaurin expansion. We use this to obtain the mass-radius relation for magnetic $^{4}$He, $^{12}$C, and $^{56}$Fe white dwarfs of uniform composition.Comment: 7 pages, 7 figures and 1 table, To appear in Ap

Mean-Field Equations for Spin Models with Orthogonal Interaction Matrices

We study the metastable states in Ising spin models with orthogonal interaction matrices. We focus on three realizations of this model, the random case and two non-random cases, i.e.\ the fully-frustrated model on an infinite dimensional hypercube and the so-called sine-model. We use the mean-field (or {\sc tap}) equations which we derive by resuming the high-temperature expansion of the Gibbs free energy. In some special non-random cases, we can find the absolute minimum of the free energy. For the random case we compute the average number of solutions to the {\sc tap} equations. We find that the configurational entropy (or complexity) is extensive in the range T_{\mbox{\tiny RSB}}. Finally we present an apparently unrelated replica calculation which reproduces the analytical expression for the total number of {\sc tap} solutions.Comment: 22+3 pages, section 5 slightly modified, 1 Ref added, LaTeX and uuencoded figures now independent of each other (easier to print). Postscript available http://chimera.roma1.infn.it/index_papers_complex.htm