Computationally Tractable Pairwise Complexity Profile

Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the information to describe a system as a function of the scale at which it is observed. We present a new formulation of the complexity profile, which expands its possible application to high-dimensional real-world and mathematically defined systems. The new method is constructed from the pairwise dependencies between components of the system. The pairwise approach may serve as both a formulation in its own right and a computationally feasible approximation to the original complexity profile. We compare it to the original complexity profile by giving cases where they are equivalent, proving properties common to both methods, and demonstrating where they differ. Both formulations satisfy linear superposition for unrelated systems and conservation of total degrees of freedom (sum rule). The new pairwise formulation is also a monotonically non-increasing function of scale. Furthermore, we show that the new formulation defines a class of related complexity profile functions for a given system, demonstrating the generality of the formalism.Comment: 18 pages, 3 figure

Luminous Supernovae

Supernovae (SNe), the luminous explosions of stars, were observed since antiquity, with typical peak luminosity not exceeding 1.2x10^{43} erg/s (absolute magnitude >-19.5 mag). It is only in the last dozen years that numerous examples of SNe that are substantially super-luminous (>7x10^{43} erg/s; <-21 mag absolute) were well-documented. Reviewing the accumulated evidence, we define three broad classes of super-luminous SN events (SLSNe). Hydrogen-rich events (SLSN-II) radiate photons diffusing out from thick hydrogen layers where they have been deposited by strong shocks, and often show signs of interaction with circumstellar material. SLSN-R, a rare class of hydrogen-poor events, are powered by very large amounts of radioactive 56Ni and arguably result from explosions of very massive stars due to the pair instability. A third, distinct group of hydrogen-poor events emits photons from rapidly-expanding hydrogen-poor material distributed over large radii, and are not powered by radioactivity (SLSN-I). These may be the hydrogen-poor analogs of SLSN-II.Comment: This manuscript has been accepted for publication in Science (to appear August 24). This version has not undergone final editing. Please refer to the complete version of record at http://www.sciencemag.org/. The manuscript may not be reproduced or used in any manner that does not fall within the fair use provisions of the Copyright Act without the prior, written permission of AAA

Caltech Core-Collapse Project (CCCP) Observations of Type II Supernovae: Evidence for Three Distinct Photometric Subtypes

We present R-Band light curves of Type II supernovae (SNe) from the Caltech Core Collapse Project (CCCP). With the exception of interacting (Type IIn) SNe and rare events with long rise times, we find that most light curve shapes belong to one of three distinct classes: plateau, slowly declining and rapidly declining events. The last class is composed solely of Type IIb SNe which present similar light curve shapes to those of SNe Ib, suggesting, perhaps, similar progenitor channels. We do not find any intermediate light curves, implying that these subclasses are unlikely to reflect variance of continuous parameters, but rather might result from physically distinct progenitor systems, strengthening the suggestion of a binary origin for at least some stripped SNe. We find a large plateau luminosity range for SNe IIP, while the plateau lengths seem rather uniform at approximately 100 days. As analysis of additional CCCP data goes on and larger samples are collected, demographic studies of core collapse SNe will likely continue to provide new constraints on progenitor scenarios.Comment: Submitted to ApJ