Magnetic Fields in Core Collapse Supernovae: Possibilities and Gaps

Spectropolarimetry of core collapse supernovae has shown that they are asymmetric and often, but not universally, bi-polar. The Type IIb SN1993J and similar events showed large scatter in the Stokes parameter plane. Observational programs clearly have much more to teach us about the complexity of asymmetric supernovae and the physics involved in the asymmetry. Jet-induced supernova models give a typical jet/torus structure that is reminiscent of some objects like the Crab nebula, SN1987A and perhaps Cas A. Jets, in turn, may arise from the intrinsic rotation and magnetic fields that are expected to accompany core collapse. We summarize the potential importance of the magneto-rotational instability for the core collapse problem and sketch some of the effects that large magnetic fields, ~10^{15} G, may have on the physics of the supernova explosion. Open issues in the problem of multi-dimensional magnetic core collapse are summarized and a critique is given of some recent MHD collapse calculations.Comment: 20 pages, 2 figures, to appear in the proceedings of the INT workshop "Open Issues in Understanding Core Collapse Supernovae," Seattle, 2004, ed. T. Mezzacappa (World Scientific

The Non-Monotonic Dependence of Supernova and Remnant Formation on Progenitor Rotation

Traditional models of core collapse suggest the issue of successful versus failed supernova explosions and neutron star versus black hole formation depends monotonically on the mass (and metallicity) of the progenitor star. Here we argue that the issue of success or failure of the explosion or other possible outcomes may depend non--monotonically on the rotation of the progenitor star even at fixed progenitor mass and composition. We have computed "shellular" models of core collapse for a star of 15 M_solar with initial central angular velocity, Omega_0, in the range 0.1 -- 8 rad/s until a few hundred ms after bounce to explore qualitative trends. The non--monotonic behavior will be manifested in the rotation of the proto--neutron star and hence in the strength of the associated magnetic field that will be generated by shear in that rotating environment. We estimate that our maximally rotating and shearing models generate toroidal fields approaching or exceeding 10^17G, strengths nearing dynamical significance.Comment: 20 pages, 6 figures, accepted for publication in The Astrophysical Journal. Few typos are correcte

Supernova Asymmetries

All core collapse supernovae are strongly aspherical. The "Bochum event," with velocity components displaced symmetrically about the principal H$\alpha$ line, strongly suggests that SN 1987A was a bi-polar rather than a uni-polar explosion. While there is a general tendency to display a single prominant axis in images and spectropolarimetry, there is also growing evidence for frequent departures from axisymmetry. There are various mechanisms that might contribute to large scale departures from spherical symmetry: jet-induced processes, the spherical shock accretion instability (SASI) and associated phenomena, and non-axisymmetric instabilities (NAXI). The MRI gives inevitable production of large toroidal magnetic fields. In sum: no $\Omega$ without B. The role of magnetic fields, non-axisymmetric instabilities, and of the de-leptonization phase are discussed.Comment: 8 pages, 3 figures, to be published in the proceedings of the conference "Supernova 1987A: 20 Years After" Aspen, 200

Inapproximability of maximal strip recovery

In comparative genomic, the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes. For the reliable recovery of syntenic blocks, noise and ambiguities in the genomic maps need to be removed first. Maximal Strip Recovery (MSR) is an optimization problem proposed by Zheng, Zhu, and Sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities. Given $d$ genomic maps as sequences of gene markers, the objective of \msr{d} is to find $d$ subsequences, one subsequence of each genomic map, such that the total length of syntenic blocks in these subsequences is maximized. For any constant $d \ge 2$, a polynomial-time 2d-approximation for \msr{d} was previously known. In this paper, we show that for any $d \ge 2$, \msr{d} is APX-hard, even for the most basic version of the problem in which all gene markers are distinct and appear in positive orientation in each genomic map. Moreover, we provide the first explicit lower bounds on approximating \msr{d} for all $d \ge 2$. In particular, we show that \msr{d} is NP-hard to approximate within $\Omega(d/\log d)$. From the other direction, we show that the previous 2d-approximation for \msr{d} can be optimized into a polynomial-time algorithm even if $d$ is not a constant but is part of the input. We then extend our inapproximability results to several related problems including \cmsr{d}, \gapmsr{\delta}{d}, and \gapcmsr{\delta}{d}.Comment: A preliminary version of this paper appeared in two parts in the Proceedings of the 20th International Symposium on Algorithms and Computation (ISAAC 2009) and the Proceedings of the 4th International Frontiers of Algorithmics Workshop (FAW 2010

The First Ground Level Enhancement Event of Solar Cycle 24: Direct Observation of Shock Formation and Particle Release Heights

We report on the 2012 May 17 Ground Level Enhancement (GLE) event, which is the first of its kind in Solar Cycle 24. This is the first GLE event to be fully observed close to the surface by the Solar Terrestrial Relations Observatory (STEREO) mission. We determine the coronal mass ejection (CME) height at the start of the associated metric type II radio burst (i.e., shock formation height) as 1.38 Rs (from the Sun center). The CME height at the time of GLE particle release was directly measured from a STEREO image as 2.32 Rs, which agrees well with the estimation from CME kinematics. These heights are consistent with those obtained for cycle-23 GLEs using back-extrapolation. By contrasting the 2012 May 17 GLE with six other non-GLE eruptions from well-connected regions with similar or larger flare size and CME speed, we find that the latitudinal distance from the ecliptic is rather large for the non-GLE events due to a combination of non-radial CME motion and unfavorable solar B0 angle, making the connectivity to Earth poorer. We also find that the coronal environment may play a role in deciding the shock strength.Comment: 16 pages, 4 figures, 1 tabl

Determining All Universal Tilers

A universal tiler is a convex polyhedron whose every cross-section tiles the plane. In this paper, we introduce a certain slight-rotating operation for cross-sections of pentahedra. Based on a selected initial cross-section and by applying the slight-rotating operation suitably, we prove that a convex polyhedron is a universal tiler if and only if it is a tetrahedron or a triangular prism.Comment: 18 pages, 12 figure

Ground Level Enhancement in the 2014 January 6 Solar Energetic Particle Event

We present a study of the 2014 January 6 solar energetic particle (SEP) event, which produced a small ground level enhancement (GLE), making it the second GLE of this unusual solar cycle 24. This event was primarily observed by the South Pole neutron monitors (increase of ~2.5%) whereas a few other neutron monitors recorded smaller increases. The associated coronal mass ejection (CME) originated behind the western limb and had the speed of 1960 km/s. The height of the CME at the start of the associated metric type II radio burst, which indicates the formation of a strong shock, was measured to be 1.61 Rs using a direct image from STEREO-A/EUVI. The CME height at the time of GLE particle release (determined using the South Pole neutron monitor data) was directly measured as 2.96 Rs, from the STEREO-A/COR1 white-light observations. These CME heights are consistent with those obtained for the GLE71, the only other GLE of the current cycle as well as cycle-23 GLEs derived using back-extrapolation. GLE72 is of special interest because it is one of the only two GLEs of cycle 24, one of the two behind-the-limb GLEs and one of the two smallest GLEs of cycles 23 and 24