Results From Core-Collapse Simulations with Multi-Dimensional, Multi-Angle Neutrino Transport

We present new results from the only 2D multi-group, multi-angle calculations of core-collapse supernova evolution. The first set of results from these calculations was published in Ott et al. (2008). We have followed a nonrotating and a rapidly rotating 20 solar mass model for ~400 ms after bounce. We show that the radiation fields vary much less with angle than the matter quantities in the region of net neutrino heating. This obtains because most neutrinos are emitted from inner radiative regions and because the specific intensity is an integral over sources from many angles at depth. The latter effect can only be captured by multi-angle transport. We then compute the phase relationship between dipolar oscillations in the shock radius and in matter and radiation quantities throughout the postshock region. We demonstrate a connection between variations in neutrino flux and the hydrodynamical shock oscillations, and use a variant of the Rayleigh test to estimate the detectability of these neutrino fluctuations in IceCube and Super-K. Neglecting flavor oscillations, fluctuations in our nonrotating model would be detectable to ~10 kpc in IceCube, and a detailed power spectrum could be measured out to ~5 kpc. These distances are considerably lower in our rapidly rotating model or with significant flavor oscillations. Finally, we measure the impact of rapid rotation on detectable neutrino signals. Our rapidly rotating model has strong, species-dependent asymmetries in both its peak neutrino flux and its light curves. The peak flux and decline rate show pole-equator ratios of up to ~3 and ~2, respectively.Comment: 13 pages, 9 figures, ApJ accepted. Replaced with accepted versio

Multi-Dimensional Explorations in Supernova Theory

In this paper, we bring together various of our published and unpublished findings from our recent 2D multi-group, flux-limited radiation hydrodynamic simulations of the collapse and explosion of the cores of massive stars. Aided by 2D and 3D graphical renditions, we motivate the acoustic mechanism of core-collapse supernova explosions and explain, as best we currently can, the phases and phenomena that attend this mechanism. Two major foci of our presentation are the outer shock instability and the inner core g-mode oscillations. The former sets the stage for the latter, which damp by the generation of sound. This sound propagates outward to energize the explosion and is relevant only if the core has not exploded earlier by some other means. Hence, it is a more delayed mechanism than the traditional neutrino mechanism that has been studied for the last twenty years since it was championed by Bethe and Wilson. We discuss protoneutron star convection, accretion-induced-collapse, gravitational wave emissions, pulsar kicks, the angular anisotropy of the neutrino emissions, a subset of numerical issues, and a new code we are designing that should supercede our current supernova code VULCAN/2D. Whatever ideas last from this current generation of numerical results, and whatever the eventual mechanism(s), we conclude that the breaking of spherical symmetry will survive as one of the crucial keys to the supernova puzzle.Comment: To be published in the "Centennial Festschrift for Hans Bethe," Physics Reports (Elsevier: Holland), ed. G.E. Brown, E. van den Heuvel, and V. Kalogera, 200

A Model for Gravitational Wave Emission from Neutrino-Driven Core-Collapse Supernovae

Using a suite of progenitor models, neutrino luminosities, and two-dimensional simulations, we investigate the matter gravitational wave (GW) emission from postbounce phases of neutrino-driven core-collapse supernovae. These phases include prompt and steady-state convection, the standing accretion shock instability (SASI), and asymmetric explosions. For the stages before explosion, we propose a model for the source of GW emission. Downdrafts of the postshock-convection/SASI region strike the protoneutron star "surface" with large speeds and are decelerated by buoyancy forces. We find that the GW amplitude is set by the magnitude of deceleration and, by extension, the downdraft's speed and the vigor of postshock-convective/SASI motions. However, the characteristic frequencies, which evolve from ~100 Hz after bounce to ~300-400 Hz, are practically independent of these speeds (and turnover timescales). Instead, they are set by the deceleration timescale, which is in turn set by the buoyancy frequency at the lower boundary of postshock convection. Consequently, the characteristic GW frequencies are dependent upon a combination of core structure attributes, specifically the dense-matter equation of state (EOS) and details that determine the gradients at the boundary, including the accretion-rate history, the EOS at subnuclear densities, and neutrino transport. During explosion, the high frequency signal wanes and is replaced by a strong low frequency, ~10s of Hz, signal that reveals the general morphology of the explosion (i.e., prolate, oblate, or spherical). However, current and near-future GW detectors are sensitive to GW power at frequencies ≳50 Hz. Therefore, the signature of explosion will be the abrupt reduction of detectable GW emission

Conflict-Free Coloring of Planar Graphs

A conflict-free k-coloring of a graph assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and v's neighbors. Such colorings have applications in wireless networking, robotics, and geometry, and are well-studied in graph theory. Here we study the natural problem of the conflict-free chromatic number chi_CF(G) (the smallest k for which conflict-free k-colorings exist). We provide results both for closed neighborhoods N[v], for which a vertex v is a member of its neighborhood, and for open neighborhoods N(v), for which vertex v is not a member of its neighborhood. For closed neighborhoods, we prove the conflict-free variant of the famous Hadwiger Conjecture: If an arbitrary graph G does not contain K_{k+1} as a minor, then chi_CF(G) <= k. For planar graphs, we obtain a tight worst-case bound: three colors are sometimes necessary and always sufficient. We also give a complete characterization of the computational complexity of conflict-free coloring. Deciding whether chi_CF(G)<= 1 is NP-complete for planar graphs G, but polynomial for outerplanar graphs. Furthermore, deciding whether chi_CF(G)<= 2 is NP-complete for planar graphs G, but always true for outerplanar graphs. For the bicriteria problem of minimizing the number of colored vertices subject to a given bound k on the number of colors, we give a full algorithmic characterization in terms of complexity and approximation for outerplanar and planar graphs. For open neighborhoods, we show that every planar bipartite graph has a conflict-free coloring with at most four colors; on the other hand, we prove that for k in {1,2,3}, it is NP-complete to decide whether a planar bipartite graph has a conflict-free k-coloring. Moreover, we establish that any general} planar graph has a conflict-free coloring with at most eight colors.Comment: 30 pages, 17 figures; full version (to appear in SIAM Journal on Discrete Mathematics) of extended abstract that appears in Proceeedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), pp. 1951-196

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

2D Multi-Angle, Multi-Group Neutrino Radiation-Hydrodynamic Simulations of Postbounce Supernova Cores

We perform axisymmetric (2D) multi-angle, multi-group neutrino radiation-hydrodynamic calculations of the postbounce phase of core-collapse supernovae using a genuinely 2D discrete-ordinate (S_n) method. We follow the long-term postbounce evolution of the cores of one nonrotating and one rapidly-rotating 20-solar-mass stellar model for ~400 milliseconds from 160 ms to ~550 ms after bounce. We present a multi-D analysis of the multi-angle neutrino radiation fields and compare in detail with counterpart simulations carried out in the 2D multi-group flux-limited diffusion (MGFLD) approximation to neutrino transport. We find that 2D multi-angle transport is superior in capturing the global and local radiation-field variations associated with rotation-induced and SASI-induced aspherical hydrodynamic configurations. In the rotating model, multi-angle transport predicts much larger asymptotic neutrino flux asymmetries with pole to equator ratios of up to ~2.5, while MGFLD tends to sphericize the radiation fields already in the optically semi-transparent postshock regions. Along the poles, the multi-angle calculation predicts a dramatic enhancement of the neutrino heating by up to a factor of 3, which alters the postbounce evolution and results in greater polar shock radii and an earlier onset of the initially rotationally weakened SASI. In the nonrotating model, differences between multi-angle and MGFLD calculations remain small at early times when the postshock region does not depart significantly from spherical symmetry. At later times, however, the growing SASI leads to large-scale asymmetries and the multi-angle calculation predicts up to 30% higher average integral neutrino energy deposition rates than MGFLD.Comment: 20 pages, 21 figures. Minor revisions. Accepted for publication in ApJ. A version with high-resolution figures may be obtained from http://www.stellarcollapse.org/papers/Ott_et_al2008_multi_angle.pd

One-armed Spiral Instability in a Low T/|W| Postbounce Supernova Core

A three-dimensional, Newtonian hydrodynamic technique is used to follow the postbounce phase of a stellar core collapse event. For realistic initial data we have employed post core-bounce snapshots of the iron core of a 20 solar mass star. The models exhibit strong differential rotation but have centrally condensed density stratifications. We demonstrate for the first time that such postbounce cores are subject to a so-called low-T/|W| nonaxisymmetric instability and, in particular, can become dynamically unstable to an m=1 - dominated spiral mode at T/|W| ~ 0.08. We calculate the gravitational wave emission by the instability and find that the emitted waves may be detectable by current and future GW observatories from anywhere in the Milky Way.Comment: 4 pages, 4 figures, final, accepted (ApJL) versio

Spatial Patterns and Sequential Sampling Plans for Estimating Densities of Stink Bugs (Hemiptera: Pentatomidae) in Soybean in the North Central Region of the United States

Stink bugs are an emerging threat to soybean (Fabales: Fabaceae) in the North Central Region of the United States. Consequently, region-specific scouting recommendations for stink bugs are needed. The aim of this study was to characterize the spatial pattern and to develop sampling plans to estimate stink bug population density in soybean fields. In 2016 and 2017, 125 fields distributed across nine states were sampled using sweep nets. Regression analyses were used to determine the effects of stink bug species [Chinavia hilaris (Say) (Hemiptera: Pentatomidae) and Euschistus spp. (Hemiptera: Pentatomidae)], life stages (nymphs and adults), and field locations (edge and interior) on spatial pattern as represented by variance–mean relationships. Results showed that stink bugs were aggregated. Sequential sampling plans were developed for each combination of species, life stage, and location and for all the data combined. Results for required sample size showed that an average of 40–42 sample units (sets of 25 sweeps) would be necessary to achieve a precision of 0.25 for stink bug densities commonly encountered across the region. However, based on the observed geographic gradient of stink bug densities, more practical sample sizes (5–10 sample units) may be sufficient in states in the southeastern part of the region, whereas impractical sample sizes (\u3e100 sample units) may be required in the northwestern part of the region. Our findings provide research-based sampling recommendations for estimating densities of these emerging pests in soybean