Time-dependent, compositionally driven convection in the oceans of accreting neutron stars

We discuss the effect of chemical separation as matter freezes at the base of the ocean of an accreting neutron star, and the subsequent enrichment of the ocean in light elements and inward transport of heat through convective mixing. We extend the steady-state results of Medin & Cumming 2011 to transiently accreting neutron stars, by considering the time-dependent cases of heating during accretion outbursts and cooling during quiescence. Convective mixing is extremely efficient, flattening the composition profile in about one convective turnover time (weeks to months at the base of the ocean). During accretion outbursts, inward heat transport has only a small effect on the temperature profile in the outer layers until the ocean is strongly enriched in light elements, a process that takes hundreds of years to complete. During quiescence, however, inward heat transport rapidly cools the outer layers of the ocean while keeping the inner layers hot. We find that this leads to a sharp drop in surface emission at around a week followed by a gradual recovery as cooling becomes dominated by the crust. Such a dip should be observable in the light curves of these neutron star transients, if enough data is taken at a few days to a month after the end of accretion. If such a dip is definitively observed, it will provide strong constraints on the chemical composition of the ocean and outer crust.Comment: 22 pages, 11 figures, submitted to Ap

Model Atmospheres for X-ray Bursting Neutron Stars

The hydrogen and helium accreted by X-ray bursting neutron stars is periodically consumed in runaway thermonuclear reactions that cause the entire surface to glow brightly in X-rays for a few seconds. With models of the emission, the mass and radius of the neutron star can be inferred from the observations. By simultaneously probing neutron star masses and radii, X-ray bursts are one of the strongest diagnostics of the nature of matter at extremely high densities. Accurate determinations of these parameters are difficult, however, due to the highly non-ideal nature of the atmospheres where X-ray bursts occur. Observations from X-ray telescopes such as RXTE and NuStar can potentially place strong constraints on nuclear matter once uncertainties in atmosphere models have been reduced. Here we discuss current progress on modeling atmospheres of X-ray bursting neutron stars and some of the challenges still to be overcome.Comment: 25 pages, 14 figure

Crystallization of classical multi-component plasmas

We develop a method for calculating the equilibrium properties of the liquid-solid phase transition in a classical, ideal, multi-component plasma. Our method is a semi-analytic calculation that relies on extending the accurate fitting formulae available for the one-, two-, and three-component plasmas to the case of a plasma with an arbitrary number of components. We compare our results to those of Horowitz, Berry, & Brown (Phys. Rev. E, 75, 066101, 2007), who use a molecular dynamics simulation to study the chemical properties of a 17-species mixture relevant to the ocean-crust boundary of an accreting neutron star, at the point where half the mixture has solidified. Given the same initial composition as Horowitz et al., we are able to reproduce to good accuracy both the liquid and solid compositions at the half-freezing point; we find abundances for most species within 10% of the simulation values. Our method allows the phase diagram of complex mixtures to be explored more thoroughly than possible with numerical simulations. We briefly discuss the implications for the nature of the liquid-solid boundary in accreting neutron stars.Comment: 14 pages, 5 figures, submitted to Phys. Rev.

Pair cascades in the magnetospheres of strongly-magnetized neutron stars

We present numerical simulations of electron-positron pair cascades in the magnetospheres of magnetic neutron stars for a wide range of surface fields (B_p = 10^{12}--10^{15} G), rotation periods (0.1--10 s), and field geometries. This has been motivated by the discovery in recent years of a number of radio pulsars with inferred magnetic fields comparable to those of magnetars. Evolving the cascade generated by a primary electron or positron after it has been accelerated in the inner gap of the magnetosphere, we follow the spatial development of the cascade until the secondary photons and pairs leave the magnetosphere, and we obtain the pair multiplicity and the energy spectra of the cascade pairs and photons under various conditions. Going beyond previous works, which were restricted to weaker fields (B < a few x 10^{12} G), we have incorporated in our simulations detailed treatments of physical processes that are potentially important (especially in the high field regime) but were either neglected or crudely treated before, including photon splitting with the correct selection rules for photon polarization modes, one-photon pair production into low Landau levels for the e^+e^-, and resonant inverse Compton scattering from polar cap hot spots. We discuss the implications of our results for the radio pulsar death line and for the hard X-ray emission from magnetized neutron stars.Comment: 28 pages, 18 figures, submitted to MNRA

Density-Functional-Theory Calculations of Matter in Strong Magnetic Fields: II. Infinite Chains and Condensed Matter

We present new, ab initio calculations of the electronic structure of one-dimensional infinite chains and three-dimensional condensed matter in strong magnetic fields ranging from B=10^12 G to 2x10^15 G, appropriate for observed magnetic neutron stars. At these field strengths, the magnetic forces on the electrons dominate over the Coulomb forces, and to a good approximation the electrons are confined to the ground Landau level. Our calculations are based on the density functional theory, and use a local magnetic exchange-correlation function appropriate in the strong field regime. The band structures of electrons in different Landau orbitals are computed self-consistently. Numerical results of the ground-state energies and electron work functions are given for one-dimensional chains of H, He, C, and Fe. Fitting formulae for the B-dependence of the energies are also provided. For all the field strengths considered in this paper, hydrogen, helium, and carbon chains are found to be bound relative to individual atoms (although for B less than a few x 10^12 G, the relative binding between C and C_infinity is small). Iron chains are significantly bound for B>10^14 G and are weakly bound if at all at B<10^13 G. We also study the cohesive property of three-dimensional condensed matter of H, He, C, and Fe at zero pressure, constructed from interacting chains in a body-centered tetragonal lattice. Such three-dimensional condensed matter is found to be bound relative to individual atoms, with the cohesive energy increasing rapidly with increasing B.Comment: 32 pages, 18 figures. Minor changes, figure omissions. Phys. Rev. A in pres