Atmospheres and Spectra of Strongly Magnetized Neutron Stars II: Effect of Vacuum Polarization

We study the effect of vacuum polarization on the atmosphere structure and radiation spectra of neutron stars with surface magnetic fields B=10^14-10^15 G, as appropriate for magnetars. Vacuum polarization modifies the dielectric property of the medium and gives rise to a resonance feature in the opacity; this feature is narrow and occurs at a photon energy that depends on the plasma density. Vacuum polarization can also induce resonant conversion of photon modes via a mechanism analogous to the MSW mechanism for neutrino oscillation. We construct atmosphere models in radiative equilibrium with an effective temperature of a few \times 10^6 K by solving the full radiative transfer equations for both polarization modes in a fully ionized hydrogen plasma. We discuss the subtleties in treating the vacuum polarization effects in the atmosphere models and present approximate solutions to the radiative transfer problem which bracket the true answer. We show from both analytic considerations and numerical calculations that vacuum polarization produces a broad depression in the X-ray flux at high energies (a few keV \la E \la a few tens of keV) as compared to models without vacuum polarization; this arises from the density dependence of the vacuum resonance feature and the large density gradient present in the atmosphere. Thus the vacuum polarization effect softens the high energy tail of the thermal spectrum, although the atmospheric emission is still harder than the blackbody spectrum because of the non-grey opacities. We also show that the depression of continuum flux strongly suppresses the equivalent width of the ion cyclotron line and therefore makes the line more difficult to observe.Comment: 21 pages, 21 figures; MNRAS; corrected minor typo

Atmospheres and Spectra of Strongly Magnetized Neutron Stars

We construct atmosphere models for strongly magnetized neutron stars with surface fields $B\sim 10^{12}-10^{15}$ G and effective temperatures $T_{\rm eff}\sim 10^6-10^7$ K. The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars, including radio pulsars, soft gamma-ray repeaters, and anomalous X-ray pulsars. In our models, the atmosphere is composed of pure hydrogen or helium and is assumed to be fully ionized. The radiative opacities include free-free absorption and scattering by both electrons and ions computed for the two photon polarization modes in the magnetized electron-ion plasma. Since the radiation emerges from deep layers in the atmosphere with \rho\ga 10^2 g/cm$^3$, plasma effects can significantly modify the photon opacities by changing the properties of the polarization modes. In the case where the magnetic field and the surface normal are parallel, we solve the full, angle-dependent, coupled radiative transfer equations for both polarization modes. We also construct atmosphere models for general field orientations based on the diffusion approximation of the transport equations and compare the results with models based on full radiative transport. In general, the emergent thermal radiation exhibits significant deviation from blackbody, with harder spectra at high energies. The spectra also show a broad feature (\Delta E/\Ebi\sim 1) around the ion cyclotron resonance \Ebi=0.63 (Z/A)(B/10^{14}{G}) keV, where $Z$ and $A$ are the atomic charge and atomic mass of the ion, respectively; this feature is particularly pronounced when \Ebi\ga 3k\Teff. Detection of the resonance feature would provide a direct measurement of the surface magnetic fields on magnetars.Comment: 29 pages, 11 figures; corrected factor of 2 in He models: minor changes to figs 4 and 9 as a result; other very minor change

Equilibrium spin pulsars unite neutron star populations

Many pulsars are formed with a binary companion from which they can accrete matter. Torque exerted by accreting matter can cause the pulsar spin to increase or decrease, and over long times, an equilibrium spin rate is achieved. Application of accretion theory to these systems provides a probe of the pulsar magnetic field. We compare the large number of recent torque measurements of accreting pulsars with a high-mass companion to the standard model for how accretion affects the pulsar spin period. We find that many long spin period (P > 100 s) pulsars must possess either extremely weak (B < 10^10 G) or extremely strong (B > 10^14 G) magnetic fields. We argue that the strong-field solution is more compelling, in which case these pulsars are near spin equilibrium. Our results provide evidence for a fundamental link between pulsars with the slowest spin periods and strong magnetic fields around high-mass companions and pulsars with the fastest spin periods and weak fields around low-mass companions. The strong magnetic fields also connect our pulsars to magnetars and strong-field isolated radio/X-ray pulsars. The strong field and old age of our sources suggests their magnetic field penetrates into the superconducting core of the neutron star.Comment: 6 pages, 4 figures; to appear in MNRA

New dynamical tide constraints from current and future gravitational wave detections of inspiralling neutron stars

Previous theoretical works using the pre-merger orbital evolution of coalescing neutron stars to constrain properties of dense nuclear matter assume a gravitational wave phase uncertainty of a few radians, or about a half cycle. However, recent studies of the signal from GW170817 and next generation detector sensitivities indicate actual phase uncertainties at least twenty times better. Using these refined estimates, we show that future observations of nearby sources like GW170817 may be able to reveal neutron star properties beyond just radius and tidal deformability, such as the matter composition and/or presence of a superfluid inside neutron stars, via tidal excitation of g-mode oscillations. Data from GW170817 already limits the amount of orbital energy that is transferred to the neutron star to <2x10^47 erg and the g-mode tidal coupling to Qmode<10^-3 at 50 Hz (5x10^48 erg and 4x10^-3 at 200 Hz), and future observations and detectors will greatly improve upon these constraints. In addition, analysis using general parameterization models that have been applied to the so-called p-g instability show that the instability already appears to be restricted to regimes where the mechanism is likely to be inconsequential; in particular, we show that the number of unstable modes is <<100 at <~100 Hz, and next generation detectors will essentially rule out this mechanism (assuming that the instability remains undetected). Finally, we illustrate that measurements of tidal excitation of r-mode oscillations in nearby rapidly rotating neutron stars are within reach of current detectors and note that even non-detections will limit the inferred inspiralling neutron star spin rate to <20 Hz, which will be useful when determining other parameters such as neutron star mass and tidal deformability.Comment: 7 pages, 4 figures; accepted for publication in Physical Review

R-Mode Oscillations and Spindown of Young Rotating Magnetic Neutron Stars

Recent work has shown that a young, rapidly rotating neutron star loses angular momentum to gravitational waves generated by unstable r-mode oscillations. We study the spin evolution of a young, magnetic neutron star including both the effects of gravitational radiation and magnetic braking (modeled as magnetic dipole radiation). Our phenomenological description of nonlinear r-modes is similar to, but distinct from, that of Owen et al. (1998) in that our treatment is consistent with the principle of adiabatic invariance in the limit when direct driving and damping of the mode are absent. We show that, while magnetic braking tends to increase the r-mode amplitude by spinning down the neutron star, it nevertheless reduces the efficiency of gravitational wave emission from the star. For B >= 10^14 (\nus/300 Hz)^2 G, where \nus is the spin frequency, the spindown rate and the gravitational waveforms are significantly modified by the effect of magnetic braking. We also estimate the growth rate of the r-mode due to electromagnetic (fast magnetosonic) wave emission and due to Alfven wave emission in the neutron star magnetosphere. The Alfven wave driving of the r-mode becomes more important than the gravitational radiation driving when B >= 10^13 (\nus/150 Hz)^3 G; the electromagnetic wave driving of the r-mode is much weaker. Finally, we study the properties of local Rossby-Alfven waves inside the neutron star and show that the fractional change of the r-mode frequency due to the magnetic field is of order 0.5 (B/10^16 G)^2 (\nus/100 Hz)^-2.Comment: 18 pages, 4 figures; ApJ, accepted (v544: Nov 20, 2000); added two footnotes and more discussion of mode driving by Alfven wave