Gravitational waves from relativistic rotational core collapse

We present results from simulations of axisymmetric relativistic rotational core collapse. The general relativistic hydrodynamic equations are formulated in flux-conservative form and solved using a high-resolution shock-capturing scheme. The Einstein equations are approximated with a conformally flat 3-metric. We use the quadrupole formula to extract waveforms of the gravitational radiation emitted during the collapse. A comparison of our results with those of Newtonian simulations shows that the wave amplitudes agree within 30%. Surprisingly, in some cases, relativistic effects actually diminish the amplitude of the gravitational wave signal. We further find that the parameter range of models suffering multiple coherent bounces due to centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure

The Spin Periods and Rotational Profiles of Neutron Stars at Birth

We present results from an extensive set of one- and two-dimensional radiation-hydrodynamic simulations of the supernova core collapse, bounce, and postbounce phases, and focus on the protoneutron star (PNS) spin periods and rotational profiles as a function of initial iron core angular velocity, degree of differential rotation, and progenitor mass. For the models considered, we find a roughly linear mapping between initial iron core rotation rate and PNS spin. The results indicate that the magnitude of the precollapse iron core angular velocities is the single most important factor in determining the PNS spin. Differences in progenitor mass and degree of differential rotation lead only to small variations in the PNS rotational period and profile. Based on our calculated PNS spins, at ~ 200-300 milliseconds after bounce, and assuming angular momentum conservation, we estimate final neutron star rotation periods. We find periods of one millisecond and shorter for initial central iron core periods of below ~ 10 s. This is appreciably shorter than what previous studies have predicted and is in disagreement with current observational data from pulsar astronomy. After considering possible spindown mechanisms that could lead to longer periods we conclude that there is no mechanism that can robustly spin down a neutron star from ~ 1 ms periods to the "injection" periods of tens to hundreds of milliseconds observed for young pulsars. Our results indicate that, given current knowledge of the limitations of neutron star spindown mechanisms, precollapse iron cores must rotate with periods around 50-100 seconds to form neutron stars with periods generically near those inferred for the radio pulsar population.Comment: 31 pages, including 20 color figures. High-resolution figures available from the authors upon request. Accepted to Ap

Asymmetric Supernovae from Magneto-Centrifugal Jets

Strong toroidal magnetic fields generated in stellar collapse can generate magneto-centrifugal jets in analogy to those found in simulations of black hole accretion and explain why all core collapse supernovae are found to be substantially asymmetric and predominantly bi-polar. We describe two phases: the initial LeBlanc-Wilson jet and a subsequent protopulsar or toroidal jet that propagates at about the core escape velocity. The jets will produce bow shocks that tend to expel matter, including iron and silicon, into equatorial tori, accounting for observations of the element distribution in Cas A. A magnetic ``switch'' mechanism may apply in instances of low density and large magnetic field with subsequent increase in the speed and collimation of the toroidal jet, depositing relatively little momentum. The result could be enough infall to form a black hole with a third, highly relativistic jet that could catch up to the protopulsar jet after it has emerged from the star. The interaction of these two jets could generate internal shocks and explain the presence of iron lines in the afterglow. Recent estimates that typical gamma-ray burst energy is about 3x10^50 erg imply either a very low efficiency for conversion of rotation into jets, or a rather rapid turnoff of the jet process even though the black hole still rotates rapidly. Magnetars and ``hypernovae'' might arise in an intermediate parameter regime of energetic jets that yield larger magnetic fields and provide more energy than the routine case, but that are not so tightly collimated that they yield failed supernova. (slightly abridged)Comment: AASTeX, 29 pages, 2 postscript figures, accepted by ApJ, November 20, 200

Multi-Dimensional Simulations of the Accretion-Induced Collapse of White Dwarfs to Neutron Stars

We present 2.5D radiation-hydrodynamics simulations of the accretion-induced collapse (AIC) of white dwarfs, starting from 2D rotational equilibrium configurations of a 1.46-Msun and a 1.92-Msun model. Electron capture leads to the collapse to nuclear densities of these cores within a few tens of milliseconds. The shock generated at bounce moves slowly, but steadily, outwards. Within 50-100ms, the stalled shock breaks out of the white dwarf along the poles. The blast is followed by a neutrino-driven wind that develops within the white dwarf, in a cone of ~40deg opening angle about the poles, with a mass loss rate of 5-8 x 10^{-3} Msun/yr. The ejecta have an entropy on the order of 20-50 k_B/baryon, and an electron fraction distribution that is bimodal. By the end of the simulations, at >600ms after bounce, the explosion energy has reached 3-4 x 10^{49}erg and the total ejecta mass has reached a few times 0.001Msun. We estimate the asymptotic explosion energies to be lower than 10^{50}erg, significantly lower than those inferred for standard core collapse. The AIC of white dwarfs thus represents one instance where a neutrino mechanism leads undoubtedly to a successful, albeit weak, explosion. We document in detail the numerous effects of the fast rotation of the progenitors: The neutron stars are aspherical; the ``nu_mu'' and anti-nu_e neutrino luminosities are reduced compared to the nu_e neutrino luminosity; the deleptonized region has a butterfly shape; the neutrino flux and electron fraction depend strongly upon latitude (a la von Zeipel); and a quasi-Keplerian 0.1-0.5-Msun accretion disk is formed.Comment: 25 pages, 19 figures, accpeted to ApJ, high resolution of the paper and movies available at http://hermes.as.arizona.edu/~luc/aic/aic.htm

Explosive Nucleosynthesis in Axisymmetrically Deformed Type II Supernovae

Explosive nucleosynthesis under the axisymmetric explosion in Type II supernova has been performed by means of two dimensional hydrodynamical calculations. We have compared the results with the observations of SN 1987A. Our chief findings are as follows: (1) $^{44}Ti$ is synthesized so much as to explain the tail of the bolometric light curve of SN 1987A. We think this is because the alpha-rich freezeout takes place more actively under the axisymmetric explosion. (2) $^{57}Ni$ and $^{58}Ni$ tend to be overproduced compared with the observations. However, this tendency relies strongly on the progenitor's model. We have also compared the abundance of each element in the mass number range $A= 16-73$ with the solar values. We have found three outstanding features. (1) For the nuclei in the range $A=16-40$, their abundances are insensitive to the initial form of the shock wave. This insensitivity is favored since the spherical calculations thus far can explain the solar system abundances in this mass range. (2) There is an enhancement around A=45 in the axisymmetric explosion compared with the spherical explosion fairly well. In particular, $^{44}Ca$, which is underproduced in the present spherical calculations, is enhanced significantly. (3) In addition, there is an enhancement around A=65. This tendency does not rely on the form of the mass cut but of the initial shock wave. This enhancement may be the problem of the overproduction in this mass range, although this effect would be relatively small since Type I supernovae are chiefly responsible for this mass number range.Comment: 32 pages, 12 figures, LaTe

Gravitational Radiation from Standing Accretion Shock Instability in Core-Collapse Supernovae

We present the results of numerical experiments, in which we study how the asphericities induced by the growth of the standing accretion shock instability (SASI) produce the gravitational waveforms in the postbounce phase of core-collapse supernovae. To obtain the neutrino-driven explosions, we parameterize the neutrino fluxes emitted from the central protoneutron star and approximate the neutrino transfer by a light-bulb scheme. We find that the waveforms due to the anisotropic neutrino emissions show the monotonic increase with time, whose amplitudes are up to two order-of-magnitudes larger than the ones from the convective matter motions outside the protoneutron stars. We point out that the amplitudes begin to become larger when the growth of the SASI enters the nonlinear phase, in which the deformation of the shocks and the neutrino anisotropy become large. From the spectrum analysis of the waveforms, we find that the amplitudes from the neutrinos are dominant over the ones from the matter motions at the frequency below $\sim 100$ Hz, which are suggested to be within the detection limits of the detectors in the next generation such as LCGT and the advanced LIGO for a supernova at 10 kpc. As a contribution to the gravitational wave background, we show that the amplitudes from this source could be larger at the frequency above $\sim$ 1 Hz than the primordial gravitational wave backgrounds, but unfortunately, invisible to the proposed space-based detectors.Comment: 22 pages, 10 figures, revised version including referee's comments and with a new high-resolution simulation, accepted by Ap

Gravitational Waves from Axisymmetric, Rotational Stellar Core Collapse

We have carried out an extensive set of two-dimensional, axisymmetric, purely-hydrodynamic calculations of rotational stellar core collapse with a realistic, finite-temperature nuclear equation of state and realistic massive star progenitor models. For each of the total number of 72 different simulations we performed, the gravitational wave signature was extracted via the quadrupole formula in the slow-motion, weak-field approximation. We investigate the consequences of variation in the initial ratio of rotational kinetic energy to gravitational potential energy and in the initial degree of differential rotation. Furthermore, we include in our model suite progenitors from recent evolutionary calculations that take into account the effects of rotation and magnetic torques. For each model, we calculate gravitational radiation wave forms, characteristic wave strain spectra, energy spectra, final rotational profiles, and total radiated energy. In addition, we compare our model signals with the anticipated sensitivities of the 1st- and 2nd-generation LIGO detectors coming on line. We find that most of our models are detectable by LIGO from anywhere in the Milky Way.Comment: 13 pages, 22 figures, accepted for publication in ApJ (v600, Jan. 2004). Revised version: Corrected typos and minor mistakes in text and references. Minor additions to the text according to the referee's suggestions, conclusions unchange

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.Comment: Small changes/additions; final version to be published in ApJ, Vol.549 (March 10, 2001

Core-Collapse Simulations of Rotating Stars

We present the results from a series of two-dimensional core-collapse simulations using a rotating progenitor star. We find that the convection in these simulations is less vigorous because a) rotation weakens the core bounce which seeds the neutrino-driven convection and b) the angular momentum profile in the rotating core stabilizes against convection. The limited convection leads to explosions which occur later and are weaker than the explosions produced from the collapse of non-rotating cores. However, because the convection is constrained to the polar regions, when the explosion occurs, it is stronger along the polar axis. This asymmetric explosion can explain the polarization measurements of core-collapse supernovae. These asymmetries also provide a natural mechanism to mix the products of nucleosynthesis out into the helium and hydrogen layers of the star. We also discuss the role the collapse of these rotating stars play on the generation of magnetic fields and neutron star kicks. Given a range of progenitor rotation periods, we predict a range of supernova energies for the same progenitor mass. The critical mass for black hole formation also depends upon the rotation speed of the progenitor.Comment: 16 pages text + 13 figures, submitted to Ap

Towards Gravitational Wave Signals from Realistic Core Collapse Supernova Models

We have computed the gravitational wave signal from supernova core collapse using the presently most realistic input physics available. We start from state-of-the-art progenitor models of rotating and non-rotating massive stars, and simulate the dynamics of their core collapse by integrating the equations of axisymmetric hydrodynamics together with the Boltzmann equation for the neutrino transport including an elaborate description of neutrino interactions, and a realistic equation of state. We compute the quadrupole wave amplitudes, the Fourier wave spectra, the amount of energy radiated in form of gravitational waves, and the S/N ratios for the LIGO and the tuned Advanced LIGO interferometers resulting both from non-radial mass motion and anisotropic neutrino emission. The simulations demonstrate that the dominant contribution to the gravitational wave signal is produced by neutrino-driven convection behind the supernova shock. For stellar cores rotating at the extreme of current stellar evolution predictions, the core-bounce signal is detectable with advanced LIGO up to a distance of 5kpc, whereas the signal from post-shock convection is observable up to a distance of about 100kpc. If the core is non-rotating its gravitational wave emission can be measured up to a distance of 15kpc, while the signal from the Ledoux convection in the deleptonizing, nascent neutron star can be detected up to a distance of 10kpc. Both kinds of signals are generically produced by convection in any core collapse supernova.Comment: 9 pages, 13 figures, Latex, submitted to ApJ, error in ps-file fixed; figures in full resolution are available upon reques