195 research outputs found
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 -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
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 (ā¼9āM_ā) 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 (ā¼0.5ā1.0 Ć 10āµā° 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 oxygenāneonāmagnesium 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 ā² 5Ć10ā»Ā³ M_ā 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 >40ākmāsā»Ā¹ and a NS spin period of ā¼30āms, both not largely different from those of the Crab pulsar at birth
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