The fractional Schr\"{o}dinger operator and Toeplitz matrices

Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz matrices. We determine the asymptotic behaviour of the product of eigenvalues for the $\alpha$-stable symmetric laws by employing the Szeg\"o's strong limit theorem. The results of the present work can be applied to a recently proposed model for a particle hopping on a bounded interval in one dimension whose hopping probability is given a discrete representation of the fractional Laplacian.Comment: 10 pages, 2 figure

Fragmentation cross sections of O-16 between 0.9 and 200 GeV/nucleon

Inclusive cross sections for high energy interactions at 0.9, 2.3, 3.6, and 13.5 GeV/nucleon of O-16 with C, CR-39 (C12H18O7), CH2, Al, Cu, Ag, and Pb targets were measured. The total charge-changing cross sections and partial charge-changing cross sections for the production of fragments with charge Z = 6 and Z = 7 are compared to previous experiments at 60 and 200 GeV/nucleon. The contributions of Coulomb dissociation to the total cross sections are calculated. Using factorization rules the partial electromagnetic cross sections are separated from the nuclear components. Energy dependence of both components are investigated and discussed

Three-dimensional Models of Core-collapse Supernovae From Low-mass Progenitors With Implications for Crab

We present 3D full-sphere supernova simulations of non-rotating low-mass (~9 Msun) progenitors, covering the entire evolution from core collapse through bounce and shock revival, through shock breakout from the stellar surface, until fallback is completed several days later. We obtain low-energy explosions [~(0.5-1.0)x 10^{50} erg] of iron-core progenitors at the low-mass end of the core-collapse supernova (LMCCSN) domain and compare to a super-AGB (sAGB) progenitor with an oxygen-neon-magnesium core that collapses and explodes as electron-capture supernova (ECSN). The onset of the explosion in the LMCCSN models is modelled self-consistently using the Vertex-Prometheus code, whereas the ECSN explosion is modelled using parametric neutrino transport in the Prometheus-HOTB code, choosing different explosion energies in the range of previous self-consistent models. The sAGB and LMCCSN progenitors that share structural similarities have almost spherical explosions with little metal mixing into the hydrogen envelope. A LMCCSN with less 2nd dredge-up results in a highly asymmetric explosion. It shows efficient mixing and dramatic shock deceleration in the extended hydrogen envelope. Both properties allow fast nickel plumes to catch up with the shock, leading to extreme shock deformation and aspherical shock breakout. Fallback masses of <~5x10^{-3} Msun have no significant effects on the neutron star (NS) masses and kicks. The anisotropic fallback carries considerable angular momentum, however, and determines the spin of the newly-born NS. The LMCCSNe model with less 2nd dredge-up results in a hydrodynamic and neutrino-induced NS kick of >40 km/s and a NS spin period of ~30 ms, both not largely different from those of the Crab pulsar at birth.Comment: 47 pages, 27 figures, 6 tables; minor revisions, accepted by MNRA

Spectra and Light Curves of GRB Afterglows

We performed accurate numerical calculations of angle-, time-, and frequency-dependent radiative transfer for the relativistic motion of matter in gamma-ray burst (GRB) models. Our technique for solving the transfer equation, which is based on the method of characteristics, can be applied to the motion of matter with a Lorentz factor up to 1000. The effect of synchrotron self-absorption is taken into account. We computed the spectra and light curves from electrons with a power-law energy distribution in an expanding relativistic shock and compare them with available analytic estimates. The behavior of the optical afterglows from GRB 990510 and GRB 000301c is discussed qualitatively.Comment: 8 pages, 7 figure

Three-dimensional models of core-collapse supernovae from low-mass progenitors with implications for Crab

We present 3D full-sphere supernova simulations of non-rotating low-mass (∼9 M_⊙) progenitors, covering the entire evolution from core collapse through bounce and shock revival, through shock breakout from the stellar surface, until fallback is completed several days later. We obtain low-energy explosions (∼0.5–1.0 × 10⁵⁰ erg) of iron-core progenitors at the low-mass end of the core-collapse supernova (LMCCSN) domain and compare to a super-AGB (sAGB) progenitor with an oxygen–neon–magnesium core that collapses and explodes as electron-capture supernova (ECSN). The onset of the explosion in the LMCCSN models is modelled self-consistently using the VERTEX-PROMETHEUS code, whereas the ECSN explosion is modelled using parametric neutrino transport in the PROMETHEUS-HOTB code, choosing different explosion energies in the range of previous self-consistent models. The sAGB and LMCCSN progenitors that share structural similarities have almost spherical explosions with little metal mixing into the hydrogen envelope. A LMCCSN with less second dredge-up results in a highly asymmetric explosion. It shows efficient mixing and dramatic shock deceleration in the extended hydrogen envelope. Both properties allow fast nickel plumes to catch up with the shock, leading to extreme shock deformation and aspherical shock breakout. Fallback masses of ≲ 5×10⁻³ M_⊙ have no significant effects on the neutron star (NS) masses and kicks. The anisotropic fallback carries considerable angular momentum, however, and determines the spin of the newly born NS. The LMCCSN model with less second dredge-up results in a hydrodynamic and neutrino-induced NS kick of >40 km s⁻¹ and a NS spin period of ∼30 ms, both not largely different from those of the Crab pulsar at birth

A surge of light at the birth of a supernova.

It is difficult to establish the properties of massive stars that explode as supernovae. The electromagnetic emission during the first minutes to hours after the emergence of the shock from the stellar surface conveys important information about the final evolution and structure of the exploding star. However, the unpredictable nature of supernova events hinders the detection of this brief initial phase. Here we report the serendipitous discovery of a newly born, normal type IIb supernova (SN 2016gkg), which reveals a rapid brightening at optical wavelengths of about 40 magnitudes per day. The very frequent sampling of the observations allowed us to study in detail the outermost structure of the progenitor of the supernova and the physics of the emergence of the shock. We develop hydrodynamical models of the explosion that naturally account for the complete evolution of the supernova over distinct phases regulated by different physical processes. This result suggests that it is appropriate to decouple the treatment of the shock propagation from the unknown mechanism that triggers the explosion

Spectra of Hydrogen-poor Superluminous Supernovae from the Palomar Transient Factory

Most Type I superluminous supernovae (SLSNe-I) reported to date have been identified by their high peak luminosities and spectra lacking obvious signs of hydrogen. We demonstrate that these events can be distinguished from normal-luminosity SNe (including Type Ic events) solely from their spectra over a wide range of light-curve phases. We use this distinction to select 19 SLSNe-I and four possible SLSNe-I from the Palomar Transient Factory archive (including seven previously published objects). We present 127 new spectra of these objects and combine these with 39 previously published spectra, and we use these to discuss the average spectral properties of SLSNe-I at different spectral phases. We find that Mn II most probably contributes to the ultraviolet spectral features after maximum light, and we give a detailed study of the O II features that often characterize the early-time optical spectra of SLSNe-I. We discuss the velocity distribution of O II, finding that for some SLSNe-I this can be confined to a narrow range compared to relatively large systematic velocity shifts. Mg II and Fe II favor higher velocities than O II and C II, and we briefly discuss how this may constrain power-source models. We tentatively group objects by how well they match either SN 2011ke or PTF12dam and discuss the possibility that physically distinct events may have been previously grouped together under the SLSN-I label