Optical Observations of Core-Collapse Supernovae

I present an overview of optical observations (mostly spectra) of Type II, Ib, and Ic supernovae (SNe). SNe II are defined by the presence of hydrogen, and exhibit a very wide variety of properties. SNe II-L tend to show evidence of late-time interaction with circumstellar material. SNe IIn are distinguished by relatively narrow emission lines with little or no P-Cygni absorption component and (quite often) slowly declining light curves; they probably have unusually dense circumstellar gas with which the ejecta interact. Some SNe IIn, however, might not be genuine SNe, but rather are ``impostors'' --- specifically, super-outbursts of luminous blue variables. SNe Ib do not exhibit the deep 6150 Angstrom absorption characteristic of ``classical'' SNe Ia; instead, their early-time spectra have He I absorption lines. SNe Ic appear similar to SNe Ib, but lack the helium lines as well. Spectra of SNe IIb initially exhibit hydrogen, yet gradually evolve to resemble those of SNe Ib; their progenitors seem to contain only a low-mass skin of hydrogen. Spectropolarimetry thus far indicates large asymmetries in the ejecta of SNe IIn, but much smaller ones in SNe II-P. As one peers deeper into the ejecta of core-collapse SNe, the asymmetry (indicated by the amount of polarization) seems to increase. There is intriguing, but inconclusive, evidence that some peculiar SNe IIn might be associated with gamma-ray bursts. The rates of different kinds of SNe as a function of Hubble type are still relatively poorly known, although there are good prospects for future improvement.Comment: 19 pages, 10 figures. To appear in "Young Supernova Remnants," ed. S. S. Holt (New York: American Institute of Physics), 200

Non-traditional Calculations of Elementary Mathematical Operations: Part 1. Multiplication and Division

Different computational systems are a set of functional units and processors that can work together and exchange data with each other if required. In most cases, data transmission is organized in such a way that enables for the possibility of connecting each node of the system to the other node of the system. Thus, a computer system consists of components for performing arithmetic operations, and an integrated data communication system, which allows for information interaction between the nodes, and combines them into a single unit. When designing a given type of computer systems, problems might occur if:– computing nodes of the system cannot simultaneously start and finish data processing over a certain time interval;– procedures for processing data in the nodes of the system do not start and do not end at a certain time;– the number of computational nodes of the inputs and outputs of the system is different.This article proposes an unconventional approach to constructing a mathematical model of adaptive-quantum computation of arithmetic operations of multiplication and division using the principle of predetermined random self-organization proposed by Ashby in 1966, as well as the method of the dynamics of averages and of the adaptive system of integration of the system of logical-differential equations for the dynamics of number-average states of particles S1, S2 of sets. This would make it easier to solve some of the problems listed above

Spectropolarimetry of Core-Collapse Supernovae

We briefly review the young field of spectropolarimetry of core-collapse supernovae (SNe). Spectropolarimetry provides the only direct known probe of early-time supernova (SN) geometry. The fundamental result is that asphericity is a ubiquitous feature of young core-collapse SNe. However, the nature and degree of the asphericity vary considerably. The best predictor of core-collapse SN polarization seems to be the mass of the hydrogen envelope that is intact at the time of the explosion: those SNe that arise from progenitors with large, intact envelopes (e.g., Type II-plateau) have very low polarization, while those that result from progenitors that have lost part (SN IIb, SN IIn) or all (SN Ib) of their hydrogen (or even helium; SN Ic) layers prior to the explosion tend to show substantial polarization. Thus, the deeper we probe into core-collapse events, the greater the asphericity seems to be, suggesting a fundamentally asymmetric explosion with the asymmetry damped by the addition of envelope material.Comment: Invited review at Supernovae as Cosmological Lighthouses, 16-19 June, Padua, IT. 6 page

Counterexamples in Scale Calculus

We construct counterexamples to classical calculus facts such as the Inverse and Implicit Function Theorems in Scale Calculus -- a generalization of Multivariable Calculus to infinite dimensional vector spaces in which the reparameterization maps relevant to Symplectic Geometry are smooth. Scale Calculus is a cornerstone of Polyfold Theory, which was introduced by Hofer-Wysocki-Zehnder as a broadly applicable tool for regularizing moduli spaces of pseudoholomorphic curves. We show how the novel nonlinear scale-Fredholm notion in Polyfold Theory overcomes the lack of Implicit Function Theorems, by formally establishing an often implicitly used fact: The differentials of basic germs -- the local models for scale-Fredholm maps -- vary continuously in the space of bounded operators when the base point changes. We moreover demonstrate that this continuity holds only in specific coordinates, by constructing an example of a scale-diffeomorphism and scale-Fredholm map with discontinuous differentials. This justifies the high technical complexity in the foundations of Polyfold Theory.Comment: published in PNAS, final versio

Optical Observations of Type II Supernovae

I present an overview of optical observations (mostly spectra) of Type II supernovae. SNe II are defined by the presence of hydrogen, and exhibit a very wide variety of properties. SNe II-L tend to show evidence of late-time interaction with circumstellar material. SNe IIn are distinguished by relatively narrow emission lines with little or no P-Cygni absorption component and (quite often) slowly declining light curves; they probably have unusually dense circumstellar gas with which the ejecta interact. Some SNe IIn, however, might not be genuine SNe, but rather are super-outbursts of luminous blue variables. The progenitors of SNe IIb contain only a low-mass skin of hydrogen; their spectra gradually evolve to resemble those of SNe Ib. Limited spectropolarimetry thus far indicates large asymmetries in the ejecta of SNe IIn, but much smaller ones in SNe II-P. There is intriguing, but still inconclusive, evidence that some peculiar SNe IIn might be associated with gamma-ray bursts. SNe II-P are useful for cosmological distance determinations with the Expanding Photosphere Method, which is independent of the Cepheid distance scale.Comment: 18 pages, 10 embedded figures, latex with aipproc style file included, to appear in "Cosmic Explosions" -- eds. S. Holt and W. W. Zhang (New York: American Institute of Physics), 200