Physics in Very Strong Magnetic Fields: Introduction and Overview

This paper provides an introduction to a number of astrophysics problems related to strong magnetic fields. The first part deals with issues related to atoms, condensed matter and high-energy processes in very strong magnetic fields, and how these issues influence various aspects of neutron star astrophysics. The second part deals with classical astrophysical effects of magnetic fields: Even relatively "weak" fields can play a strong role in various astrophysical problems, ranging from stars, accretion disks and outflows, to the formation and merger of compact objects.Comment: 16 pages. To be published in The Strongest Magnetic Fields in the Universe (Space Sciences Series of ISSI, Springer), Space Science Review

Resonant Oscillations and Tidal Heating in Coalescing Binary Neutron Stars

Tidal interaction in a coalescing neutron star binary can resonantly excite the g-mode oscillations of the neutron star when the frequency of the tidal driving force equals the intrinsic g-mode frequencies. We study the g-mode oscillations of cold neutron stars using recent microscopic nuclear equations of state, where we determine self-consistently the sound speed and Brunt-V\"ais\"al\"a frequency in the nuclear liquid core. The properties of the g-modes associated with the stable stratification of the core depend sensitively on the pressure-density relation as well as the symmetry energy of the dense nuclear matter. The frequencies of the first ten g-modes lie approximately in the range of $10-100$ Hz. Resonant excitations of these g-modes during the last few minutes of the binary coalescence result in energy transfer and angular momentum transfer from the binary orbit to the neutron star. The angular momentum transfer is possible because a dynamical tidal lag develops even in the absence of fluid viscosity. However, since the coupling between the g-mode and the tidal potential is rather weak, the amount of energy transfer during a resonance and the induced orbital phase error are very small. Resonant excitations of the g-modes play an important role in tidal heating of binary neutron stars. Without the resonances, viscous dissipation is effective only when the stars are close to contact. The resonant oscillations result in dissipation at much larger orbital separation. The actual amount of tidal heating depends on the viscosity of the neutron star. Using the microscopic viscosity, we find that the binary neutron stars are heated to a temperature $\sim 10^8$ K before they come into contact.Comment: 35 pages, TeX (MNRAS in press). Cornell CRSR-106

DC Circuit Powered by Orbital Motion: Magnetic Interactions in Compact Object Binaries and Exoplanetary Systems

The unipolar induction DC circuit model, originally developed by Goldreich & Lynden-Bell for the Jupiter-Io system, has been applied to different types of binary systems in recent years. We show that there exists an upper limit to the magnetic interaction torque and energy dissipation rate in such model. This arises because when the resistance of the circuit is too small, the large current flow severely twists the magnetic flux tube connecting the two binary components, leading to breakdown of the circuit. Applying this limit, we find that in coalescing neutron star binaries, magnetic interactions produce negligible correction to the phase evolution of the gravitational waveform, even for magnetar-like field strengths. However, energy dissipation in the binary magnetosphere may still give rise to electromagnetic radiation prior to the final merger. For ultra-compact white dwarf binaries, we find that DC circuit does not provide adequate energy dissipation to explain the observed X-ray luminosities of several sources. For exoplanetary systems containing close-in Jupiters or super-Earths, magnetic torque and dissipation are negligible, except possibly during the early T Tauri phase, when the stellar magnetic field is stronger than 10^3G.Comment: 5 pages, one figur

Hydrodynamics of Coalescing Binary Neutron Stars: Ellipsoidal Treatment

We employ an approximate treatment of dissipative hydrodynamics in three dimensions to study the coalescence of binary neutron stars driven by the emission of gravitational waves. The stars are modeled as compressible ellipsoids obeying a polytropic equation of state; all internal fluid velocities are assumed to be linear functions of the coordinates. The hydrodynamic equations then reduce to a set of coupled ordinary differential equations for the evolution of the principal axes of the ellipsoids, the internal velocity parameters and the binary orbital parameters. Gravitational radiation reaction and viscous dissipation are both incorporated. We set up exact initial binary equilibrium configurations and follow the transition from the quasi-static, secular decay of the orbit at large separation to the rapid dynamical evolution of the configurations just prior to contact. A hydrodynamical instability resulting from tidal interactions significantly accelerates the coalescence at small separation, leading to appreciable radial infall velocity and tidal lag angles near contact. This behavior is reflected in the gravitational waveforms and may be observable by gravitational wave detectors under construction.Comment: 14 pages, plain TeX, CRSR-107

Dynamical Tides in Compact White Dwarf Binaries: Influence of Rotation

Tidal interactions play an important role in the evolution and ultimate fate of compact white dwarf (WD) binaries. Not only do tides affect the pre-merger state (such as temperature and rotation rate) of the WDs, but they may also determine which systems merge and which undergo stable mass transfer. In this paper, we attempt to quantify the effects of rotation on tidal angular momentum transport in binary stars, with specific calculations applied to WD stellar models. We incorporate the effect of rotation using the traditional approximation, in which the dynamically excited gravity waves within the WDs are transformed into gravito-inertial Hough waves. The Coriolis force has only a minor effect on prograde gravity waves, and previous results predicting the tidal spin-up and heating of inspiraling WDs are not significantly modified. However, rotation strongly alters retrograde gravity waves and inertial waves, with important consequences for the tidal spin-down of accreting WDs. We identify new dynamical tidal forcing terms that arise from a proper separation of the equilibrium and dynamical tide components; these new forcing terms are very important for systems near synchronous rotation. Additionally, we discuss the impact of Stokes drift currents on the wave angular momentum flux. Finally, we speculate on how tidal interactions will affect super-synchronously rotating WDs in accreting systems.Comment: 18 pages, 7 figure

Dynamical Tides in Compact White Dwarf Binaries: Helium Core White Dwarfs, Tidal Heating, and Observational Signatures

Tidal dissipation in compact white dwarf (WD) binary systems significantly influences the physical conditions (such as surface temperature and rotation rate) of the WDs prior to mass transfer or merger. In these systems, the dominant tidal effects involve the excitation of gravity waves and their dissipation in the outer envelope of the star. We calculate the amplitude of tidally excited gravity waves in low-mass (0.3M_\odot) helium-core (He) WDs as a function of the tidal forcing frequency \omega. Like carbon-oxygen (CO) WDs studied in our previous paper, we find that the dimensionless tidal torque F(\omega) (inversely proportional to the effective tidal quality factor) has an erratic dependence on \omega. On average, F(\omega) scales approximately as \omega^6, and is several orders of magnitude smaller for He WDs than for CO WDs. We find that tidal torques can begin to synchronize the WD rotation when the orbital period is less than about a hour, although a nearly constant asynchronization is maintained even at small periods. We examine where the tidally excited gravity waves experience non-linear breaking or resonant absorption at a critical layer, allowing us to estimate the location and magnitude of tidal heating in the WD envelope. We then incorporate tidal heating in the MESA stellar evolution code, calculating the physical conditions of the WD as a function of orbital period for different WD models. We find that tidal heating makes a significant contribution to the WD luminosity for short-period (~10 min) systems such as SDSS J0651+2844. We also find that for WDs containing a hydrogen envelope, tidal heating can trigger runaway hydrogen shell burning, leading to a nova-like event before the onset of mass transfer.Comment: 23 pages, 12 figures, accepted to MNRA