Rolf Walder

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 proto-neutron 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 ms after bounce and assuming angular momentum conservation, we estimate final neutron star rotation periods. We find periods of 1 ms and shorter for initial central iron core periods of 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 spin-down 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 spin-down mechanisms, precollapse iron cores must rotate with periods of around 50-100 s to form neutron stars with periods generically near those inferred for the radio pulsar population.

Gravitational Waves from Axisymmetric, Rotating 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 waveforms, 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 first- and second-generation LIGO detectors coming on line. We find that most of our models are detectable by LIGO from anywhere in the Milky Way.

TWO-DIMENSIONAL, TIME-DEPENDENT, MULTIGROUP, MULTIANGLE RADIATION HYDRODYNAMICS TEST SIMULATION IN THE CORE-COLLAPSE SUPERNOVA CONTEXT

We have developed a time-dependent, multi-energy group, multiangle (Sn) Boltzmann transport scheme for radiation hydrodynamics simulations in one and two spatial dimensions. The implicit transport is coupled to both one-dimensional (spherically symmetric) and two-dimensional (axially symmetric) versions of the explicit Newtonian hydrodynamics code VULCAN. The two-dimensional variant, VULCAN/2D, can be operated in general structured or unstructured grids, and although the code can address many problems in astrophysics, it was constructed specifically to study the core-collapse supernova problem. Furthermore, VULCAN/2D can simulate the radiation hydrodynamic evolution of differentially rotating bodies. We summarize the equations solved and methods incorporated into the algorithm and present the results of a time-dependent two-dimensional test calculation. A more complete description of the algorithm is postponed to another paper. We highlight a two-dimensional test run that follows the immediate postbounce evolution of a collapsed core for 22 ms. We present the relationship between the anisotropies of the overturning matter field and the distribution of the corresponding flux vectors as a function of energy group. This is the first two-dimensional multigroup, multiangle, time-dependent radiation hydrodynamics calculation ever performed in core-collapse studies. Although the transport module of the code is not gray and does not use flux limiters (however, there is a flux-limited variant of VULCAN/2D), it still does not include energy redistribution and most velocity-dependent terms.

Anisotropies in the Neutrino Fluxes and Heating Profiles in Two-dimensional, Time-dependent, Multigroup Radiation Hydrodynamics Simulations of Rotating Core-Collapse Supernovae

Using the 2D multi-group, flux-limited diffusion version of the code VULCAN/2D, that also incorporates rotation, we have calculated the collapse, bounce, shock formation, and early post-bounce evolutionary phases of a corecollapse supernova for a variety of initial rotation rates. This is the first series of such multi-group calculations undertaken in supernova theory with fully multi-D tools. We find that though rotation generates pole-to-equator angular anisotropies in the neutrino radiation fields, the magnitude of the asymmetries is not as large as previously estimated. The finite width of the neutrino decoupling surfaces and the significant emissivity above the � = 2/3 surface moderate the angular contrast. Moreover, we find that the radiation field is always more spherically symmetric than the matter distribution, with its plumes and convective eddies. The radiation field at a point is an integral over many sources from the different contributing directions. As such, its distribution is much smoother than that of the matter and has very little power at high spatial frequencies. We present the dependence of the angular anisotropy of the neutrino fields on neutrino species, neutrino energy, and initial rotation rate. Only for our most rapidly rotating model do we start to see qualitatively different hydrodynamics, but for

VLA Observations of ζ Aurigae: Confirmation of the Slow Acceleration Wind Density Structure

Studies of the winds from single K and early M evolved stars indicate that these flows typically reach a significant fraction of their terminal velocity within the first couple of stellar radii. The most detailed spatially resolved information of the extended atmospheres of these spectral types comes from the ζ Aur eclipsing binaries. However, the wind acceleration inferred for the evolved primaries in these systems appears significantly slower than for stars of similar spectral type. Since there are no successful theories for mass loss from K and early M evolved stars, it is important to place strong empirical constraints on potential models and determine whether this difference in acceleration is real or an artifact of the analyses. We have undertaken a radio continuum monitoring study of ζ Aurigae (K4 Ib + B5 V) using the Very Large Array to test the wind density model of Baade et al. that is based on Hubble Space Telescope (HST) Goddard High Resolution Spectrograph ultraviolet spectra. ζ Aur was monitored at centimeter wavelengths over a complete orbital cycle, and flux variations during the orbit are found to be of similar magnitude to variations at similar orbital phases in the adjacent orbit. During eclipse, the flux does not decrease, showing that the radio emission originates from a volume substantially larger than R ~ (150 R⊙)3 surrounding the B star. Using the one-dimensional density model of the K4 Ib primarys wind derived from HST spectral line profile modeling and electron temperature estimates from previous optical and new HST studies, we find that the predicted radio fluxes are consistent with those observed. Three-dimensional hydrodynamic simulations indicate that the accretion flow perturbations near the B star do not contribute significantly to the total radio flux from the system, consistent with the radio eclipse observations. Our radio observations confirm the slow wind acceleration for the evolved K4 Ib component. ζ Aurs velocity structure does not appear to be typical of single stars with similar spectral types. This highlights the need for more comprehensive multiwavelength studies for both single stars, which have been sadly neglected, and other ζ Aur systems to determine if its wind properties are typical.

Structuring and support by Alfvén waves around prestellar cores

Observations of molecular clouds show the existence of starless, dense cores, threaded by magnetic fields. Observed line widths indicate these dense condensates to be embedded in a supersonically turbulent environment. Under these conditions, the generation of magnetic waves is inevitable. In this paper, we study the structure and support of a 1D plane-parallel, self-gravitating slab, as a monochromatic, circularly polarized Alfven wave is injected in its central plane. Dimensional analysis shows that the solution must depend on three dimensionless parameters. To study the nonlinear, turbulent evolution of such a slab, we use 1D high resolution numerical simulations. For a parameter range inspired by molecular cloud observations, we find the following. 1) A single source of energy injection is sufficient to force persistent supersonic turbulence over several hydrostatic scale heights. 2) The time averaged spatial extension of the slab is comparable to the extension of the stationary, analytical WKB solution. Deviations, as well as the density substructure of the slab, depend on the wave-length of the injected wave. 3) Energy losses are dominated by loss of Poynting-flux and increase with increasing plasma beta. 4) Good spatial resolution is mandatory, making similar simulations in 3D currently prohibitively expensive.

3D Radiative Transfer Under Conditions of Non-local Thermodynamic Equilibrium: A Contribution to the Numerical Solution

A new approach to the solution of the 3D NLTE optically thick radiative transfer problem for moving media is presented. The radiative transfer problem basically consists of determining consistent values for the radiation field and the state of the matter. A first task, therefore, is the solution of the radiative transfer equation, which describes the propagation of radiation in the presence of matter. The second task is the determination of the state of the matter in the presence of a radiation field. These two parts are then coupled iteratively. We present the first application of the generalized mean intensity approach, suggested by Turek [9], [10] for the solution of the radiative transfer equation, to NLTE problems. The resulting linear system is solved using BiCGStab. The corresponding code has successfully been applied to some first test problems.

Colliding winds in Wolf-Rayet binaries: further developments within a complicated story

We present large scale 3D simulations of colliding winds in the WR binary v Velorum (WR 11). The a-star wind is confined by cold, high density shells and forms a spirally shaped region within the WR-wind. As a consequence of the elliptic orbit, the opening angle and the curvature of the spiral as well as the ratio of the volumes occupied by the WRand the a-wind are functions of the orbital phase. Our model qualitatively reproduces the observed X-ray lightcurve. The impact of magnetic fields and heat conduction on the physics of colliding winds is briefly discussed and some remarks on the important question of stability are made! .