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Dong Lai

Publications and source records attributed to Dong Lai.

At least 253 records · Page 14Linked to original sources
arXiv2000

Neutron Star Kicks and Asymmetric Supernovae

Observational advances over the last decade have left little doubt that neutron stars received a large kick velocity (of order a few hundred to a thousand km/s) at birth. The physical origin of the kicks and the related supernova asymmetry is one of the central unsolved mysteries of supernova research. We review the physics of different kick mechanisms, including hydrodynamically driven, neutrino -- magnetic field driven, and electromagnetically driven kicks. The viabilities of the different kick mechanisms are directly related to the other key parameters characterizing nascent neutron stars, such as the initial magnetic field and the initial spin. Recent observational constraints on kick mechanisms are also discussed.

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arXiv2000

Pulsar Jets: Implications for Neutron Star Kicks and Initial Spins

We study implications for the apparent alignment of the spin axes, proper-motions, and polarization vectors of the Crab and Vela pulsars. The spin axes are deduced from recent Chandra X-ray Observatory images that reveal jets and nebular structure having definite symmetry axes. The alignments indicate these pulsars were born either in isolation or with negligible velocity contributions from binary motions. We examine the effects of rotation and the conditions under which spin-kick alignment is produced for various models of neutron star kicks. If the kick is generated when the neutron star first forms by asymmetric mass ejection or/and neutrino emission, then the alignment requires that the protoneutron star possesses an original spin with period $P_s$ much less than the kick timescale, thus spin-averaging the kick forces. The kick timescale ranges from 100 ms to 10 s depending on whether the kick is hydrodynamically driven or neutrino-magnetic field driven. For hydrodynamical models, spin-kick alignment further requires the rotation period of an asymmetry pattern at the radius near shock breakout (>100 km) to be much less than ~100 ms; this is difficult to satisfy unless rotation plays a dynamically important role in the core collapse and explosion ($P_s\lo 1$ ms). Aligned kick and spin vectors are inherent to the slow process of asymmetric electromagnetic radiation from an off-centered magnetic dipole. We reassess the viability of this effect, correcting a factor of 4 error in Harrison and Tademaru's calculation that increases the size of the effect. To produce a kick velocity of order a few hundred km/s requires that the neutron star be born with an initial spin close to 1 ms and that spindown due to r-mode driven gravitational radiation be inefficient compared to standard magnetic braking.

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arXiv2000

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.

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arXiv2000

Global Nonradial Instabilities of Dynamically Collapsing Gas Spheres

Self-similar solutions provide good descriptions for the gravitational collapse of spherical clouds or stars when the gas obeys a polytropic equation of state, $p=Kρ^γ$ (with $γ\le 4/3$). We study the behaviors of nonradial perturbations in the similarity solutions of Larson, Penston and Yahil, which describe the evolution of the collapsing cloud prior to core formation. Our global stability analysis reveals the existence of unstable bar-modes ($l=2$) when $γ\le 1.09$. In particular, for the collapse of isothermal spheres, which applies to the early stages of star formation, the $l=2$ density perturbation relative to the background, $δρ({\bf r},t)/ρ(r,t)$, increases as $(t_0-t)^{-0.352}\propto ρ_c(t)^{0.176}$, where $t_0$ denotes the epoch of core formation, and $ρ_c(t)$ is the cloud central density. Thus, the isothermal cloud tends to evolve into an ellipsoidal shape (prolate bar or oblate disk, depending on initial conditions) as the collapse proceeds. In the context of Type II supernovae, core collapse is described by the $γ\simeq 1.3$ equation of state, and our analysis indicates that there is no growing mode (with density perturbation) in the collapsing core before the proto-neutron star forms, although nonradial perturbations can grow during the subsequent accretion of the outer core and envelope onto the neutron star. We also carry out a global stability analysis for the self-similar expansion-wave solution found by Shu, which describes the post-collapse accretion (``inside-out'' collapse) of isothermal gas onto a protostar. We show that this solution is unstable to perturbations of all $l$'s, although the growth rates are unknown.

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arXiv1999

Physics of Neutron Star Kicks

It is no longer necessary to `sell' the idea of pulsar kicks, the notion that neutron stars receive a large velocity (a few hundred to a thousand km s$^{-1}$) at birth. However, the origin of the kicks remains mysterious. We review the physics of different kick mechanisms, including hydrodynamically driven, neutrino and magnetically driven kicks.

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arXiv1999

Magnetically Driven Warping, Precession and Resonances in Accretion Disks

The inner region of the accretion disk onto a rotating magnetized central star (neutron star, white dwarf or T Tauri star) is subjected to magnetic torques which induce warping and precession of the disk. The origin of these torques lies in the interaction between the (induced) surface current on the disk and the horizontal magnetic field (parallel to the disk) produced by the inclined magnetic dipole. Under quite general conditions, there exists a magnetic warping instability in which the magnetic torque drives the disk plane away from the equatorial plane of the star toward a state where the disk normal vector is perpendicular to the spin axis. Viscous stress tends to suppress the warping instability at large radii, but the magnetic torque always dominates as the disk approaches the magnetosphere boundary. The magnetic torque also drives the tilted inner disk into retrograde precession around the stellar spin axis. Moreover, resonant magnetic forcing on the disk can occur which may affect the dynamics of the disk. The magnetically driven warping instability and precession may be related to a number observational puzzles, including: (1) Spin evolution (torque reversal) of accreting X-ray pulsars; (2) Quasi-periodic oscillations in low-mass X-ray binaries; (3) Super-orbital periods in X-ray binaries; (4) Photometric period variations of T Tauri stars.

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arXiv1999

Tidal Interaction between a Fluid Star and a Kerr Black Hole in Circular Orbit

We present a semi-analytic study of the equilibrium models of close binary systems containing a fluid star (mass $m$ and radius $R_0$) and a Kerr black hole (mass $M$) in circular orbit. We consider the limit $M\gg m$ where spacetime is described by the Kerr metric. The tidally deformed star is approximated by an ellipsoid, and satisfies the polytropic equation of state. The models also include fluid motion in the stellar interior, allowing binary models with nonsynchronized stellar spin (as expected for coalescing neutron star-black hole binaries) to be constructed. Tidal disruption occurs at orbital radius $r_{\rm tide}\sim R_0(M/m)^{1/3}$, but the dimensionless ratio $\hat r_{\rm tide}=r_{\rm tide}/[R_0(M/m)^{1/3}]$ depends on the spin parameter of the black hole as well as on the equation of state and the internal rotation of the star. We find that the general relativistic tidal field disrupts the star at a larger $\hat r_{\rm tide}$ than the Newtonian tide; the difference is particularly prominent if the disruption occurs in the vicinity of the black hole's horizon. In general, $\hat r_{\rm tide}$ is smaller for a (prograde rotating) Kerr black hole than for a Schwarzschild black hole. We apply our results to coalescing black hole-neutron star and black hole-white dwarf binaries. The tidal disruption limit is important for characterizing the expected gravitational wave signals and is relevant for determining the energetics of gamma ray bursts which may result from such disruption.

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arXiv1999

Growth of Perturbation in Gravitational Collapse and Accretion

When a self-gravitating spherical gas cloud collapses or accretes onto a central mass, the inner region of the cloud develops a density profile $ρ\propto r^{-3/2}$ and the velocity approaches free-fall. We show that in this region, nonspherical perturbations grow with decreasing radius. In the linear regime, the tangential velocity perturbation increases as $r^{-1}$, while the Lagrangian density perturbation, $Δρ/ρ$, grows as $r^{-1/2}$. Faster growth occurs if the central collapsed object maintains a finite multiple moment, in which case $Δρ/ρ$ increases as $r^{-l}$, where $l$ specifies the angular degree of the perturbation. These scaling relations are different from those obtained for the collapse of a homogeneous cloud. Our numerical calculations indicate that nonspherical perturbations are damped in the subsonic region, and that they grow and approach the asymptotic scalings in the supersonic region. The implications of our results to asymmetric supernova collapse and to black hole accretion are briefly discussed.

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arXiv1999

Kilohertz Quasi-Periodic Oscillations, Magnetic Fields and Mass of Neutron Stars in Low-Mass X-Ray Binaries

It has recently been suggested that the maximum observed quasi-periodic oscillation (QPO) frequencies, $ν_{max}$, for several low-mass X-ray binaries, particularly 4U 1820-30, correspond to the orbital frequency at the inner-most stable orbit of the accretion disk. This would imply that the neutron stars in these systems have masses $\go 2~M_\odot$, considerably larger than any well-measured neutron star mass. We suggest that the levelling off of $ν_{QPO}$ may be also understood in terms of a steepening magnetic field which, although possibly dipolar at the stellar surface, is altered substantially by disk accretion, and presents a ``wall'' to the accretion flow that may be outside the innermost stable orbit. General relativistic effects add to the flattening of the $ν_{QPO}-\mdot$ relation at frequencies below the Kepler frequency at the innermost stable orbit. We offer two other possible ways to reconcile the low value of $ν_{max}$ ($\approx 1060$ Hz for 4U 1820-30) with a moderate neutron star mass, $\approx 1.4\msun$: at sufficiently large $\mdot$, either (i) the disk terminates in a very thin boundary layer near the neutron star surface, or (ii) $ν_{QPO}$ is not the orbital frequency right at the inner edge of the disk, but rather at a somewhat larger radius, where the emissivity of the disk peaks.

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arXiv1999

Secular Instability of g-Modes in Rotating Neutron Stars

Gravitational radiation tends to drive gravity modes in rotating neutron stars unstable. For an inviscid star, the instability sets in when the rotation frequency is about 0.7 times the corresponding mode frequency of the nonrotating star. Neutron stars with spin frequencies $\go 100$ Hz are susceptible to this instability, with growth time of order years. However, it is likely that viscous dissipation suppresses the instability except for a narrow range of temperatures around $10^9$ K. We also show that the viscosity driven instability of g-modes is absent.

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arXiv1999

Resonant Tidal Excitations of Rotating Neutron Stars in Coalescing Binaries

In a coalescing neutron star-neutron star (NS-NS) or neutron star-black hole (NS-BH) binary, oscillation modes of the NS can be resonantly excited by the companion during the final minutes of the inspiral. The resonant energy transfer between the orbit and NS speeds up or slows down the inspiral and induces a phase change in the emitted gravitational waves from the binary. A tidal resonance, (jk,m), occurs when the mode frequency equals m times the orbital frequency. For f-mode resonance to occur before coalescence, the NS must have rapid rotation, with spin frequency nu_s>710Hz for (22,2)-resonance and nu_s>570Hz for (33,3)-resonance (M=1.4Mo and R=10km; however, for R=15km, these spin frequencies become 330Hz and 250Hz). Because of strong tidal coupling, f-mode resonances induce a large change in the number of orbital cycles, N_orb, with maximum N_orb~10-1000 for (22,2)-resonance and N_orb~1 for (33,3)- resonance. Such resonant effects, if present, must be included in constructing waveform templates used in searching for gravitational wave signals. Higher order f-mode resonances can occur at slower rotation rates, but N_orb<0.1. For the dominant g-mode (22,2)-resonance, even modest rotation (nu_s<100Hz) can enhance the resonant effect on the orbit by shifting resonance to a smaller orbital frequency. However, because of the weak coupling, N_orb lies in the range 10^-3-10^-2 (depending on the NS EOS) and is probably negligible for the purpose of detecting gravitational waves. R-mode resonances require misaligned spin-orbit inclinations, and the dominant resonances correspond to (22,3) and (22,1). Since tidal coupling depends strongly on rotation rate, N_orb<10^-2(R/10km)^(10)(M/1.4Mo)^(-20/3) is negligible for canonical NS parameters but can be appreciable if the NS radius is larger.

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arXiv1998

Neutrino-Nucleon Interactions in Magnetized Neutron-Star Matter: The Effects of Parity Violation

We study neutrino-nucleon scattering and absorption in a dense, magnetized nuclear medium. These are the most important sources of neutrino opacity governing the cooling of a proto-neutron star in the first tens of seconds after its formation. Because the weak interaction is parity violating, the absorption and scattering cross-sections depend asymmetrically on the directions of the neutrino momenta with respect to the magnetic field. We develop the moment formalism of neutrino transport in the presence of such asymmetric opacities and derive explicit expressions for the neutrino flux and other angular moments of the Boltzmann transport equation. For a given neutrino species, there is a drift flux of neutrinos along the magnetic field in addition to the usual diffusive flux. This drift flux depends on the deviation of the neutrino distribution function from thermal equilibrium. Hence, despite the fact that the neutrino cross-sections are asymmetric throughout the star, asymmetric neutrino flux can be generated only in the outer region of the proto-neutron star where the neutrino distribution deviates significantly from thermal equilibrium. In addition to the asymmetric absorption opacity arising from nucleon polarization, we find the contribution of the electron (or positron) ground state Landau level. For neutrinos of energy less than a few times the temperature, this is the dominant source of asymmetric opacity. Lastly, we discuss the implication of our result to the origin of pulsar kicks: in order to generate kick velocity of a few hundred km/s from asymmetric neutrino emission using the parity violation effect, the proto-neutron star must have a dipole magnetic field of at least $10^{15}-10^{16}$ G.

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arXiv1998

Neutrino Transport in Strongly Magnetized Proto-Neutron Stars and the Origin of Pulsar Kicks: I. The Effect of Parity Violation in Weak Interactions

The original paper describes neutrino cooling calculations in the presence of asymmetric neutrino opacities due to parity violation in strong magnetic fields. In early April, through the work of P. Arras and D. Lai at Cornell (see astro-ph/9806285) we became aware that the paper contains a serious flaw: although the neutrino scattering opacities depend asymmetrically on the initial and final neutrino momenta, detailed balance requires that there be no cumulative effect from multiple scatterings in the bulk interior of the proto-neutron star where local thermodynamic equilibrium applies to a good approximation. This paper was therefore withdrawn from ApJ in April. Also in April, we submitted an erratum to ApJ Lett. pointing out this error. (The erratum will appear in the July 1, 1998 issue of ApJ Lett.)

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arXiv1998

Neutrino Transport in Strongly Magnetized Proto-Neutron Stars and the Origin of Pulsar Kicks: The Effect of Asymmetric Magnetic Field Topology

In proto-neutron stars with strong magnetic fields, the cross section for $ν_e$ ($\barν_e$) absorption on neutrons (protons) depends on the local magnetic field strength due to the quantization of energy levels for the $e^-$ ($e^+$) produced in the final state. If the neutron star possesses an asymmetric magnetic field topology in the sense that the magnitude of magnetic field in the north pole is different from that in the south pole, then asymmetric neutrino emission may be generated. We calculate the absorption cross sections of $\nue$ and $\bnue$ in strong magnetic fields as a function of the neutrino energy. These cross sections exhibit oscillatory behaviors which occur because new Landau levels for the $e^-$ ($e^+$) become accessible as the neutrino energy increases. By evaluating the appropriately averaged neutrino opacities, we demonstrate that the change in the local neutrino flux due to the modified opacities is rather small. To generate appreciable kick velocity ($\sim 300$ km~s$^{-1}$) to the newly-formed neutron star, the difference in the field strengths at the two opposite poles of the star must be at least $10^{16}$~G. We also consider the magnetic field effect on the spectral neutrino energy fluxes. The oscillatory features in the absorption opacities give rise to modulations in the emergent spectra of $ν_e$ and $\barν_e$.

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arXiv1998

Can Parity Violation in Neutrino Transport Lead to Pulsar Kicks?

In magnetized proto-neutron stars, neutrino cross sections depend asymmetrically on the neutrino momenta due to parity violation. However, these asymmetric opacities do not induce any asymmetric flux in the bulk interior of the star where neutrinos are nearly in thermal equilibrium. Consequently, parity violation in neutrino absorption and scattering can only give rise to asymmetric neutrino flux above the neutrino-matter decoupling layer. The kick velocity is substantially reduced from previous estimates, requiring a dipole field $B \sim 10^{16}$~G to get $v_{kick}$ of order a few hundred km~s$^{-1}$.

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arXiv1998

Transonic Magnetic Slim Accretion Disks and kilo-Hertz Quasi-Periodic Oscillations in Low-Mass X-Ray Binaries

The inner regions of accretion disks of weakly magnetized neutron stars are affected by general relativity and stellar magnetic fields. Even for field strengths sufficiently small so that there is no well-defined magnetosphere surrounding the neutron star, there is still a region in the disk where magnetic field stress plays an important dynamical role. We construct magnetic slim disk models appropriate for neutron stars in low-mass X-ray binaries (LMXBs) which incorporate both effects (GR and magnetic fields). The B-field--disk interaction is treated in a phenomenological manner, allowing for both closed and open field configurations. We show that even for surface magnetic fields as weak as $10^7-10^8$ G, the sonic point of the accretion flow can be significantly modified from the pure GR value (near $6M$). We derive an approximate analytical expression for the sonic radius and show that it mainly depends on the surface field strength $B_0$ and mass accretion rate $\dot M$ through the ratio $b^2\propto B_0^2/\dot M$. The sonic radius thus obtained approaches the usual Alfven radius for high $b^2$, and asymptotes to $6M$ as $b^2\to 0$. We therefore suggest that for neutron stars in LMXBs, the distinction between the disk sonic radius and the magnetospheric radius may not exist. We apply our theoretical results to the kHz QPOs observed in the X-ray fluxes of LMXBs. If these QPOs are associated with the orbital frequency at the inner radius of the disk, then the QPO frequencies and their correlation with mass accretion rate can provide useful constraints on the nature of the magnetic field -- disk interactions as well as on the structure of magnetic fields in LMXBs. Current observational data may suggest that the magnetic fields in LMXBs have complex topology.

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arXiv1998

Parity Violation in Neutrino Transport and the Origin of Pulsar Kicks

In proto-neutron stars with strong magnetic fields, the neutrino-nucleon scattering/absorption cross sections depend on the direction of neutrino momentum with respect to the magnetic field axis, a manifestation of parity violation in weak interactions. We study the deleptonization and thermal cooling (via neutrino emission) of proto-neutron stars in the presence of such asymmetric neutrino opacities. Significant asymmetry in neutrino emission is obtained due to multiple neutrino-nucleon scatterings. For an ordered magnetic field threading the neutron star interior, the fractional asymmetry in neutrino emission is about $0.006 (B/10^{14}G)$, corresponding to a pulsar kick velocity of about $200 (B/10^{14}G)$ km/s for a total radiated neutrino energy of $3\times 10^{53}$ erg.

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