Magnetic field evolution and equilibrium configurations in neutron star cores: the effect of ambipolar diffusion

As another step towards understanding the long-term evolution of the magnetic field in neutron stars, we provide the first simulations of ambipolar diffusion in a spherical star. Restricting ourselves to axial symmetry, we consider a charged-particle fluid of protons and electrons carrying the magnetic flux through a motionless, uniform background of neutrons that exerts a collisional drag force on the former. We also ignore the possible impact of beta decays, proton superconductivity, and neutron superfluidity. All initial magnetic field configurations considered are found to evolve on the analytically expected time-scales towards "barotropic equilibria" satisfying the "Grad-Shafranov equation", in which the magnetic force is balanced by the degeneracy pressure gradient, so ambipolar diffusion is choked. These equilibria are so-called "twisted torus" configurations, which include poloidal and toroidal components, the latter restricted to the toroidal volumes in which the poloidal field lines close inside the star. In axial symmetry, they appear to be stable, although they are likely to undergo non-axially symmetric instabilities.Comment: MNRAS, accepte

A Hamiltonian functional for the linearized Einstein vacuum field equations

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie

Local continuity laws on the phase space of Einstein equations with sources

Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the adjoint of a differential operator. Such covariant conservation laws are generated by means of decoupled equations and their adjoints in such a way that the corresponding covariantly conserved currents possess some gauge-invariant properties and are expressed in terms of Debye potentials. These continuity laws lead to both a covariant description of bilinear forms on the phase space and the existence of conserved quantities. Differences and similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page

OH+ in astrophysical media: state-to-state formation rates, Einstein coefficients and inelastic collision rates with He

The rate constants required to model the OH$^+$ observations in different regions of the interstellar medium have been determined using state of the art quantum methods. First, state-to-state rate constants for the H$_2(v=0,J=0,1)$+ O$^+$($^4S$) $\rightarrow$ H + OH$^+(X ^3\Sigma^-, v', N)$ reaction have been obtained using a quantum wave packet method. The calculations have been compared with time-independent results to asses the accuracy of reaction probabilities at collision energies of about 1 meV. The good agreement between the simulations and the existing experimental cross sections in the $0.01-$1 eV energy range shows the quality of the results. The calculated state-to-state rate constants have been fitted to an analytical form. Second, the Einstein coefficients of OH$^+$ have been obtained for all astronomically significant ro-vibrational bands involving the $X^3\Sigma^-$ and/or $A^3\Pi$ electronic states. For this purpose the potential energy curves and electric dipole transition moments for seven electronic states of OH$^+$ are calculated with {\it ab initio} methods at the highest level and including spin-orbit terms, and the rovibrational levels have been calculated including the empirical spin-rotation and spin-spin terms. Third, the state-to-state rate constants for inelastic collisions between He and OH$^+(X ^3\Sigma^-)$ have been calculated using a time-independent close coupling method on a new potential energy surface. All these rates have been implemented in detailed chemical and radiative transfer models. Applications of these models to various astronomical sources show that inelastic collisions dominate the excitation of the rotational levels of OH$^+$. In the models considered the excitation resulting from the chemical formation of OH$^+$ increases the line fluxes by about 10 % or less depending on the density of the gas

Truncation effects in superdiffusive front propagation with L\'evy flights

A numerical and analytical study of the role of exponentially truncated L\'evy flights in the superdiffusive propagation of fronts in reaction-diffusion systems is presented. The study is based on a variation of the Fisher-Kolmogorov equation where the diffusion operator is replaced by a $\lambda$-truncated fractional derivative of order $\alpha$ where $1/\lambda$ is the characteristic truncation length scale. For $\lambda=0$ there is no truncation and fronts exhibit exponential acceleration and algebraic decaying tails. It is shown that for $\lambda \neq 0$ this phenomenology prevails in the intermediate asymptotic regime $(\chi t)^{1/\alpha} \ll x \ll 1/\lambda$ where $\chi$ is the diffusion constant. Outside the intermediate asymptotic regime, i.e. for $x > 1/\lambda$, the tail of the front exhibits the tempered decay $\phi \sim e^{-\lambda x}/x^{(1+\alpha)}$, the acceleration is transient, and the front velocity, $v_L$, approaches the terminal speed $v_* = (\gamma - \lambda^\alpha \chi)/\lambda$ as $t\to \infty$, where it is assumed that $\gamma > \lambda^\alpha \chi$ with $\gamma$ denoting the growth rate of the reaction kinetics. However, the convergence of this process is algebraic, $v_L \sim v_* - \alpha /(\lambda t)$, which is very slow compared to the exponential convergence observed in the diffusive (Gaussian) case. An over-truncated regime in which the characteristic truncation length scale is shorter than the length scale of the decay of the initial condition, $1/\nu$, is also identified. In this extreme regime, fronts exhibit exponential tails, $\phi \sim e^{-\nu x}$, and move at the constant velocity, $v=(\gamma - \lambda^\alpha \chi)/\nu$.Comment: Accepted for publication in Phys. Rev. E (Feb. 2009