Light echoes reveal an unexpectedly cool Eta Carinae during its 19th-century Great Eruption

Eta Carinae (Eta Car) is one of the most massive binary stars in the Milky Way. It became the second-brightest star in the sky during its mid-19th century "Great Eruption," but then faded from view (with only naked-eye estimates of brightness). Its eruption is unique among known astronomical transients in that it exceeded the Eddington luminosity limit for 10 years. Because it is only 2.3 kpc away, spatially resolved studies of the nebula have constrained the ejected mass and velocity, indicating that in its 19th century eruption, Eta Car ejected more than 10 M_solar in an event that had 10% of the energy of a typical core-collapse supernova without destroying the star. Here we report the discovery of light echoes of Eta Carinae which appear to be from the 1838-1858 Great Eruption. Spectra of these light echoes show only absorption lines, which are blueshifted by -210 km/s, in good agreement with predicted expansion speeds. The light-echo spectra correlate best with those of G2-G5 supergiant spectra, which have effective temperatures of ~5000 K. In contrast to the class of extragalactic outbursts assumed to be analogs of Eta Car's Great Eruption, the effective temperature of its outburst is significantly cooler than allowed by standard opaque wind models. This indicates that other physical mechanisms like an energetic blast wave may have triggered and influenced the eruption.Comment: Accepted for publication by Nature; 4 pages, 4 figures, SI: 6 pages, 3 figures, 5 table

Interacting Supernovae: Types IIn and Ibn

Supernovae (SNe) that show evidence of strong shock interaction between their ejecta and pre-existing, slower circumstellar material (CSM) constitute an interesting, diverse, and still poorly understood category of explosive transients. The chief reason that they are extremely interesting is because they tell us that in a subset of stellar deaths, the progenitor star may become wildly unstable in the years, decades, or centuries before explosion. This is something that has not been included in standard stellar evolution models, but may significantly change the end product and yield of that evolution, and complicates our attempts to map SNe to their progenitors. Another reason they are interesting is because CSM interaction is an efficient engine for making bright transients, allowing super-luminous transients to arise from normal SN explosion energies, and allowing transients of normal SN luminosities to arise from sub-energetic explosions or low radioactivity yield. CSM interaction shrouds the fast ejecta in bright shock emission, obscuring our normal view of the underlying explosion, and the radiation hydrodynamics of the interaction is challenging to model. The CSM interaction may also be highly non-spherical, perhaps linked to binary interaction in the progenitor system. In some cases, these complications make it difficult to definitively tell the difference between a core-collapse or thermonuclear explosion, or to discern between a non-terminal eruption, failed SN, or weak SN. Efforts to uncover the physical parameters of individual events and connections to possible progenitor stars make this a rapidly evolving topic that continues to challenge paradigms of stellar evolution.Comment: Final draft of a chapter in the "SN Handbook". Accepted. 25 pages, 3 fig

Viterbi Training for PCFGs: Hardness Results and Competitiveness of Uniform Initialization

We consider the search for a maximum likelihood assignment of hidden derivations and grammar weights for a probabilistic context-free grammar, the problem approximately solved by “Viterbi training.” We show that solving and even approximating Viterbi training for PCFGs is NP-hard. We motivate the use of uniformat-random initialization for Viterbi EM as an optimal initializer in absence of further information about the correct model parameters, providing an approximate bound on the log-likelihood.

Empirical Risk Minimization for Probabilistic Grammars: Sample Complexity and Hardness of Learning

Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. They are used ubiquitously in computational linguistics. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of probabilistic grammars using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting. By making assumptions about the underlying distribution that are appropriate for natural language scenarios, we are able to derive distribution-dependent sample complexity bounds for probabilistic grammars. We also give simple algorithms for carrying out empirical risk minimization using this framework in both the supervised and unsupervised settings. In the unsupervised case, we show that the problem of minimizing empirical risk is NP-hard. We therefore suggest an approximate algorithm, similar to expectation-maximization, to minimize the empirical risk. Learning from data is central to contemporary computational linguistics. It is in common in such learning to estimate a model in a parametric family using the maximum likelihood principle. This principle applies in the supervised case (i.e., using annotate

Agent-based Simulation of Open Source Software Evolution

We present an agent-based simulation model of open source software (OSS). To our knowledge, this is the first model of OSS evolution that includes four significant factors: productivity limited by the complexity of software modules, the software's fitness for purpose, the motivation of developers, and the role of users in defining requirements. The model was evaluated by comparing the simulated results against four measures of software evolution (system size, proportion of highly complex modules, level of complexity control work, and distribution of changes) for four large OSS systems. The simulated results resembled all the observed data, including alternating periods of growth and stagnation. The fidelity of the model suggests that the factors included here have significant effects on the evolution of OSS systems