The First Ten Years of Swift Supernovae

The Swift Gamma Ray Burst Explorer has proven to be an incredible platform for studying the multiwavelength properties of supernova explosions. In its first ten years, Swift has observed over three hundred supernovae. The ultraviolet observations reveal a complex diversity of behavior across supernova types and classes. Even amongst the standard candle type Ia supernovae, ultraviolet observations reveal distinct groups. When the UVOT data is combined with higher redshift optical data, the relative populations of these groups appear to change with redshift. Among core-collapse supernovae, Swift discovered the shock breakout of two supernovae and the Swift data show a diversity in the cooling phase of the shock breakout of supernovae discovered from the ground and promptly followed up with Swift. Swift observations have resulted in an incredible dataset of UV and X-ray data for comparison with high-redshift supernova observations and theoretical models. Swift's supernova program has the potential to dramatically improve our understanding of stellar life and death as well as the history of our universe.Comment: Invited review paper accepted into the Journal of High Energy Astrophysics for the dedicated issue: "Swift: Ten Years of Discovery" 8 pages, 4 figure

On the second Tate-Shafarevich group of a 1-motive

We prove finiteness results for Tate--Shafarevich groups in degree 2 associated with 1--motives, rely them to Leopoldt's conjecture, and present an example of a semiabelian variety with an infinite Tate--Shafarevich group in degree 2. We also establish an arithmetic duality theorem for 1--motives over number fields which complements earlier results of Harari and Szamuely in this direction.Comment: 28 page

Theoretical Clues to the Ultraviolet Diversity of Type Ia Supernovae

The effect of metallicity on the observed light of Type Ia supernovae (SNe Ia) could lead to systematic errors as the absolute magnitudes of local and distant SNe Ia are compared to measure luminosity distances and determine cosmological parameters. The UV light may be especially sensitive to metallicity, though different modeling methods disagree as to the magnitude, wavelength dependence, and even the sign of the effect. The outer density structure, ^56 Ni, and to a lesser degree asphericity, also impact the UV. We compute synthetic photometry of various metallicity-dependent models and compare to UV/optical photometry from the Swift Ultra-Violet/Optical Telescope. We find that the scatter in the mid-UV to near-UV colors is larger than predicted by changes in metallicity alone and is not consistent with reddening. We demonstrate that a recently employed method to determine relative abundances using UV spectra can be done using UVOT photometry, but we warn that accurate results require an accurate model of the cause of the variations. The abundance of UV photometry now available should provide constraints on models that typically rely on UV spectroscopy for constraining metallicity, density, and other parameters. Nevertheless, UV spectroscopy for a variety of SN explosions is still needed to guide the creation of accurate models. A better understanding of the influences affecting the UV is important for using SNe Ia as cosmological probes, as the UV light may test whether SNe Ia are significantly affected by evolutionary effects.Comment: 10 pages. Submitted to Ap

The Changing Fractions of Type Ia Supernova NUV-Optical Subclasses with Redshift

UV and optical photometry of Type Ia supernovae (SNe Ia) at low redshift have revealed the existence of two distinct color groups, NUV-red and NUV-blue events. The color curves differ primarily by an offset, with the NUV-blue u- color curves bluer than the NUV-red curves by 0.4 mag. For a sample of 23 low-z SNe~Ia observed with Swift, the NUV-red group dominates by a ratio of 2:1. We compare rest-frame UV/optical spectrophotometry of intermediate and high-z SNe Ia with UVOT photometry and HST spectrophotometry of low-z SNe Ia, finding that the same two color groups exist at higher-z, but with the NUV-blue events as the dominant group. Within each red/blue group, we do not detect any offset in color for different redshifts, providing insight into how SN~Ia UV emission evolves with redshift. Through spectral comparisons of SNe~Ia with similar peak widths and phase, we explore the wavelength range that produces the UV/OPT color differences. We show that the ejecta velocity of NUV-red SNe is larger than that of NUV-blue objects by roughly 12% on average. This velocity difference can explain some of the UV/optical color difference, but differences in the strengths of spectral features seen in meanspectra require additional explanation. Because of the different b-v colors for these groups, NUV-red SNe will have their extinction underestimated using common techniques. This, in turn, leads to under-estimation of the optical luminosity of the NUV-blue SNe~Ia, in particular, for the high-redshift cosmological sample. Not accounting for this effect should thus produce a distance bias that increases with redshift and could significantly bias measurements of cosmological parameters.Comment: submitted to Ap

Grouping Normal Type Ia Supernovae by UV to Optical Color Differences

Observations of many SNe Ia with the UVOT instrument on the Swift satellite has revealed that there exists order to the differences in the UV-OPT colors of normal SNe. We examine UV-OPT color curves for 25 SNe Ia, dividing them into 4 groups, finding that ~1/3 of these SNe Ia have bluer UV-OPT colors than the larger group, with these "NUV-blue" SNe Ia 0.4 mag bluer than the "NUV-red" SNe Ia in u-v. Another group of events feature colors similar to NUV-red SNe Ia in the u-v to uvw1-v colors, but similar to the NUV-blue SNe Ia in the uvm2-v color. We name these events "MUV-blue". The last group initially has colors similar to NUV-red SNe Ia, but with color curves that feature more modest changes than the larger NUV-red group. These "irregular" events are comprised of all the NUV-red events with the broadest optical peaks, which leads us to consider this minor group a subset of the NUV-red group. When so separated and the accounting is made for the rapid time evolution of the UV-OPT colors, we find that the scatter in two NUV-OPT colors, u-v & uvw1-v, is at the level of the scatter in b-v. This finding is promising for extending the cosmological utilization of SNe Ia into the NUV. We generate spectrophotometry of SNe Ia that have been observed with HST and argue that there is a fundamental spectral difference in the 2900-3500A wavelength range, a range suggested to be dominated by absorption from iron-peak elements. The NUV-blue SNe Ia feature less NUV absorption than the NUV-red SNe Ia. We show that all the NUV-blue SNe Ia in this sample have also featured evidence of unburned carbon in optical spectra, whereas only one NUV-red SN Ia features that absorption line. Every NUV-blue event also exhibits a low gradient of the SiII 6355A absorption feature, but many NUV-red events also exhibit a low gradient, perhaps suggestive that NUV-blue events are a subset of the larger LVG group.Comment: Accepted to the Astrophysical Journal Updated version: Sept 16, 201

A refinement of the Craig-Lyndon Interpolation Theorem for classical first-order logic (with identity)

We refine the interpolation property of classical first-order logic (without identity and without functionsymbols), showing that if G & , & D and G $ D then there is an interpolant c, constructed using onlynon-logical vocabulary common to both members of G and members of D, such that (i) G entails c in thefirst-order version of Kleene's strong three-valued logic, and (ii) c entails D in the first-order version ofPriest's Logic of Paradox. The proof proceeds via a careful analysis of derivations employing semantictableaux. Lyndon's strengthening of the interpolation property falls out of an observation regardingsuch derivations and the steps involved in the construction of interpolants.Through an analysis of tableaux rules for identity, the proof is then extended to classical first-orderlogic with identity (but without function symbols)

A non-classical refinement of the interpolation property for classical propositional logic

We refine the interpolation property of the {^, v, ¬}-fragment of classical propositional logic, showing that if /|= ¬Φ, and /|= Ψ then there is an interpolant Χ constructed using at most atomic formulas occurring in both Φ and Ψ and negation, conjunction and disjunction, such that (i) Φ   entails Χ in Kleene’s strong three-valued logic and (ii) Χ entails Ψ  in Priest’s Logic of Paradox

Classical Logic through the Looking-Glass

In Lewis Carroll’s Through the Looking Glass and What Alice Found There, Alice enters through a mirror into the realm reflected. It is, of course, left-right reversed but this is only the start of the fun and games when Alice explores the world on the other side of the mirror. Borrowing, if only in part, Carroll’s theme of inversion, my aim is to take a look at classical logic in something of an inverted way, or, to be more exact, in three somewhat inverted ways. Firstly, I come at proof of the completeness of classical logic in the Lindenbaum-Henkin style backwards: I take for granted the existence of a set Σ for which it holds, for some formula φ, that ψ !in Σ if, and only if, Σu{ψ} |- φ  then read off the rules of inference governing connectives and quantifiers that most directly yield the desired (classical) semantic properties. We thus obtain general elimination rules and what I have elsewhere called general introduction rules. Secondly, the same approach lets us read off a different set of rules: those of the cut-free sequent calculus S' of (Smullyan, 1968). Smullyan uses this calculus in proving the Craig-Lyndon interpolation theorem for first-order logic (without identity and function symbols). By attending very carefully to the steps in Smullyan’s proof, we obtain a strengthening: if φ |- ψ,  /|- ¬φ and /|- ψ then there is an interpolant χ, a formula employing only the non-logical vocabulary common to φ and ψ, such that φ entails χ in the first-order version of Kleene’s 3-valued logic and χ entails ψ in the first-order version of Graham Priest’s Logic of Paradox. The result, which is hidden from view in natural deduction formulations of classical logic, extends, I believe, to firstorder logic with identity. Thirdly, we look at a contraction-free “approximation” to classical propositional logic. Adding the general introduction rules for negation or the conditional leads to Contraction being a derived rule, apparently blurring the distinction between structural and operational rules

Structures, homomorphisms, and the needs of model theory

When we look closely at textbooks on model theory, we find that there are three different accounts of what a model or structure is. One of these is highly language dependent, so that the same structure cannot be the interpretation of two different languages or signatures. The other two definitions do not fall foul of that dependence but all textbooks tie the notion of homomorphism so closely to language (signature) that only structures interpreting the same language (signature) are isomorphic. Although this follows the practice in universal algebra, it is highly unnatural. The aim here is to present a notion of homomorphism better consonant with intuition and with what the less cautious authors of textbooks say when they speak informally