Quark deconfinement in neutron star cores: The effects of spin-down

We study the role of spin-down in driving quark deconfinement in the high density core of isolated neutron stars. Assuming spin-down to be solely due to magnetic braking, we obtain typical timescales to quark deconfinement for neutron stars that are born with Keplerian frequencies. Employing different equations of state (EOS), we determine the minimum and maximum neutron star masses that will allow for deconfinement via spin-down only. We find that the time to reach deconfinement is strongly dependent on the magnetic field and that this time is least for EOS that support the largest minimum mass at zero spin, unless rotational effects on stellar structure are large. For a fiducial critical density of $5\rho_0$ for the transition to the quark phase ($\rho_0=2.5\times10^{14}$g/cm$^3$ is the saturation density of nuclear matter), we find that neutron stars lighter than $1.5M_{\odot}$ cannot reach a deconfined phase. Depending on the EOS, neutron stars of more than $1.5M_{\odot}$ can enter a quark phase only if they are spinning faster than about 3 milliseconds as observed now, whereas larger spin periods imply that they are either already quark stars or will never become one.Comment: 4 pages, 4 figures, submitted to ApJ

Microscopic Derivation of Non-Markovian Thermalization of a Brownian Particle

In this paper, the first microscopic approach to the Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended Boltzmann equation, which describes correctly the interaction with the fluid, we derive systematicaly via the multiple time-scale analysis a reduced equation controlling the thermalization of the B particle, i.e. the relaxation towards the Maxwell distribution in velocity space. In contradistinction to the Fokker-Planck equation, the derived new evolution equation is non-local both in time and in velocity space, owing to correlated recollision events between the fluid and particle B. In the long-time limit, it describes a non-markovian generalized Ornstein-Uhlenbeck process. However, in spite of this complex dynamical behaviour, the Stokes-Einstein law relating the friction and diffusion coefficients is shown to remain valid. A microscopic expression for the friction coefficient is derived, which acquires the form of the Stokes law in the limit where the mean-free in the gas is small compared to the radius of particle B.Comment: 28 pages, no figure, submitted to Journal of Statistical Physic

Effective slip over superhydrophobic surfaces in thin channels

Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a micro- and nanoscopic texture. Recent work has focused on specific cases, such as striped grooves or arrays of pillars, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g. low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for parallel (or perpendicular) orientation with respect to the mean flow. For isotropic (e.g. chessboard or random) textures, the Hashin-Strikman conditions further constrain the effective slip. These results provide a framework for the rational design of superhydrophobic surfaces.Comment: 4+ page

Diffusion in pores and its dependence on boundary conditions

We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes. Partial slip is shown to significantly influence the diffusion coefficient near a wall. Analytical expressions are derived in the low and high confinement limits, and are in good agreement with numerical results. These calculations indicate that diffusion of tagged particles could be used as a sensitive probe of the solid-liquid boundary conditions.Comment: soumis \`a J.Phys. Cond. Matt. special issue on "Diffusion in Liquids, Polymers, Biophysics and Chemical Dynamics

Magnetically Accreting Isolated Old Neutron Stars

Previous work on the emission from isolated old neutron stars (IONS) accreting the inter-stellar medium (ISM) focussed on gravitational capture - Bondi accretion. We propose a new class of sources which accrete via magnetic interaction with the ISM. While for the Bondi mechanism, the accretion rate decreases with increasing NS velocity, in magnetic accretors (MAGACs="magics") the accretion rate increases with increasing NS velocity. MAGACs will be produced among high velocity (~> 100 km s-1) high magnetic field (B> 1e14 G) radio pulsars - the ``magnetars'' - after they have evolved first through magnetic dipole spin-down, followed by a ``propeller'' phase (when the object sheds angular momentum on a timescale ~< 1e10 yr). The properties of MAGACS may be summarized thus: dipole magnetic fields of B~>1e14 G; minimum velocities relative to the ISM of >25-100 km s-1, depending on B, well below the median in the observed radio-pulsar population; spin-periods of >days to years; accretion luminosities of 1e28- 1e31 ergs s-1 ; and effective temperatures kT=0.3 - 2.5 keV if they accrete onto the magnetic polar cap. We find no examples of MAGACs among previously observed source classes (anomalous X-ray pulsars, soft-gamma-ray repeaters or known IONS). However, MAGACs may be more prevelant in flux-limited X-ray catalogs than their gravitationally accreting counterparts.Comment: ApJ, accepte

WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics

The accurate modelling of astrophysical scenarios involving compact objects and magnetic fields, such as the collapse of rotating magnetized stars to black holes or the phenomenology of gamma-ray bursts, requires the solution of the Einstein equations together with those of general-relativistic magnetohydrodynamics. We present a new numerical code developed to solve the full set of general-relativistic magnetohydrodynamics equations in a dynamical and arbitrary spacetime with high-resolution shock-capturing techniques on domains with adaptive mesh refinements. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code and assess its accuracy. Such tests range from the solution of relativistic Riemann problems in flat spacetime, over to the stationary accretion onto a Schwarzschild black hole and up to the evolution of oscillating magnetized stars in equilibrium and constructed as consistent solutions of the coupled Einstein-Maxwell equations.Comment: minor changes to match the published versio

Violation of Chandrasekhar Mass Limit: The Exciting Potential of Strongly Magnetized White Dwarfs

We consider a relativistic, degenerate, electron gas under the influence of a strong magnetic field, which describes magnetized white dwarfs. Landau quantization changes the density of states available to the electrons, thus modifying the underlying equation of state. In the presence of very strong magnetic fields a maximum of either one, two or three Landau level(s) is/are occupied. We obtain the mass-radius relations for such white dwarfs and their detailed investigation leads us to propose the existence of white dwarfs having a mass ~2.3M_Sun, which overwhelmingly exceeds the Chandrasekhar mass limit.Comment: 10 pages including 4 figures; received Honorable Mention for the Gravity Research Foundation 2012 Awards for Essays on Gravitation; version to appear in IJMP

Cold ideal equation of state for strongly magnetized neutron-star matter: effects on muon production and pion condensationn

Neutron stars with very strong surface magnetic fields have been suggested as the site for the origin of observed soft gamma repeaters (SGRs). In this paper we investigate the influence of such strong magnetic fields on the properties and internal structure of these magnetized neutron stars (magnetars). We study properties of a degenerate equilibrium ideal neutron-proton-electron (npe) gas with and without the effects of the anomalous nucleon magnetic moments in a magnetic field. The presence of a sufficiently strong magnetic field changes the ratio of protons to neutrons as well as the neutron drip density. We also study the appearance of muons as well as pion condensation in strong magnetic fields. We discuss the possibility that boson condensation in the interior of magnetars might be a source of SGRs.Comment: 10 pages included 9 figures, ApJ in pres

On the fluid-fluid phase separation in charged-stabilized colloidal suspensions

We develop a thermodynamic description of particles held at a fixed surface potential. This system is of particular interest in view of the continuing controversy over the possibility of a fluid-fluid phase separation in aqueous colloidal suspensions with monovalent counterions. The condition of fixed surface potential allows in a natural way to account for the colloidal charge renormalization. In a first approach, we assess the importance of the so called ``volume terms'', and find that in the absence of salt, charge renormalization is sufficient to stabilize suspension against a fluid-fluid phase separation. Presence of salt, on the other hand, is found to lead to an instability. A very strong dependence on the approximations used, however, puts the reality of this phase transition in a serious doubt. To further understand the nature of the instability we next study a Jellium-like approximation, which does not lead to a phase separation and produces a relatively accurate analytical equation of state for a deionized suspensions of highly charged colloidal spheres. A critical analysis of various theories of strongly asymmetric electrolytes is presented to asses their reliability as compared to the Monte Carlo simulations

Finite-temperature perturbation theory for quasi-one-dimensional spin-1/2 Heisenberg antiferromagnets

We develop a finite-temperature perturbation theory for quasi-one-dimensional quantum spin systems, in the manner suggested by H.J. Schulz (1996) and use this formalism to study their dynamical response. The corrections to the random-phase approximation formula for the dynamical magnetic susceptibility obtained with this method involve multi-point correlation functions of the one-dimensional theory on which the random-phase approximation expansion is built. This ``anisotropic'' perturbation theory takes the form of a systematic high-temperature expansion. This formalism is first applied to the estimation of the N\'eel temperature of S=1/2 cubic lattice Heisenberg antiferromagnets. It is then applied to the compound Cs$_2$CuCl$_4$, a frustrated S=1/2 antiferromagnet with a Dzyaloshinskii-Moriya anisotropy. Using the next leading order to the random-phase approximation, we determine the improved values for the critical temperature and incommensurability. Despite the non-universal character of these quantities, the calculated values are different by less than a few percent from the experimental values for both compounds.Comment: 11 pages, 6 figure