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We establish upper and lower universal bounds for potentials of weighted designs on the sphere $\mathbb{S}^{n-1}$ that depend only on quadrature nodes and weights derived from the design structure. Our bounds hold for a large class of potentials that includes absolutely monotone functions. The classes of spherical designs attaining these bounds are characterized. Additionally, we study the problem of constrained energy minimization for Borel probability measures on $\mathbb{S}^{n-1}$ and apply it to optimal distribution of charge supported at a given number of points on the sphere. In particular, our results apply to $p$-frame energy., Comment: 21 pages

We show that a divergence-free measure on the plane is a continuous sum of unit tangent vector fields on rectifiable Jordan curves. This loop decomposition is more precise than the general decomposition in elementary solenoids given by S.K. Smirnov, when applied to the planar case. The proof involves extending the Fleming-Rishel formula to homogeneous BV functions (in any dimension), and establishing for such functions approximate continuity of measure theoretic connected components of suplevel sets as functions of the level. We apply these results to inverse potential problems whose source term is the divergence of some unknown (vector-valued) measure. A prototypical case is that of inverse magnetization problems when magnetizations are modeled by R3-valued Borel measures. We investigate methods for recovering a magnetization {\mu} by penalizing its measure theoretic total variation norm (TV). In particular, we prove that if a magnetization is supported in a plane, then TV-regularization schemes always have a unique minimizer, even in the presence of noise. It is further shown thatTV-norm minimization (among magnetizations generating the same field) uniquely recovers planar magnetizations in the following cases: when the magnetization is carried by a collection of sufficiently separated line segments and a set that is purely 1-unrectifiable, or when a superset of the support is tree-like. We note that such magnetizations can be recovered via TV-regularization schemes in the zero noise limit, by taking the regularization parameter to zero. This suggests definitions of sparsity in the present infinite dimensional context, that generate results akin to compressed sensing, Comment: 40 pages

Surrogate models for hotspot ignition and growth rates were presented in Part I, where the hotspots were formed by the collapse of single cylindrical voids. Such isolated cylindrical voids are idealizations of the void morphology in real meso-structures. This paper therefore investigates the effect of non-cylindrical void shapes and void-void interactions on hotspot ignition and growth. Surrogate models capturing these effects are constructed using a Bayesian Kriging approach. The training data for machine learning the surrogates are derived from reactive void collapse simulations spanning the parameter space of void aspect ratio (AR), void orientation ($\theta$), and void fraction ($\phi$). The resulting surrogate models portray strong dependence of the ignition and growth rates on void aspect ratio and orientation, particularly when they are oriented at acute angles with respect to the imposed shock. The surrogate models for void interaction effects show significant changes in hotspot ignition and growth rates as the void fraction increases. The paper elucidates the physics of hotspot evolution in void fields due to the creation and interaction of multiple hotspots. The results from this work will be useful not only for constructing meso-informed macro-scale models of HMX, but also for understanding the physics of void-void interactions and sensitivity due to void shape and orientation., Comment: Submitted in Shockwaves

We develop a framework for obtaining linear programming bounds for spherical codes whose inner products belong to a prescribed subinterval $[\ell,s]$ of $[-1,1)$. An intricate relationship between Levenshtein-type upper bounds on cardinality of codes with inner products in $[\ell,s]$ and lower bounds on the potential energy (for absolutely monotone interactions) for codes with inner products in $[\ell,1)$ (when the cardinality of the code is kept fixed) is revealed and explained. Thereby, we obtain a new extension of Levenshtein bounds for such codes. The universality of our bounds is exhibited by a unified derivation and their validity for a wide range of codes and potential functions., Comment: 18 pages, 1 figure

We aim to present 70 spectra of 68 new high-redshift type Ia supernovae (SNeIa) measured at ESO's VLT during the final two years of operation (2006-2008) of the Supernova Legacy Survey (SNLS). We use the full five year SNLS VLT spectral set to investigate a possible spectral evolution of SNeIa populations with redshift and study spectral properties as a function of lightcurve fit parameters and the mass of the host-galaxy. Reduction and extraction are based on both IRAF standard tasks and our own reduction pipeline. Redshifts are estimated from host-galaxy lines whenever possible or alternatively from supernova features. We used the spectrophotometric SNIa model SALT2 combined with a set of galaxy templates that model the host-galaxy contamination to assess the type Ia nature of the candidates. We identify 68 new SNeIa with redshift ranging from z=0.207 to z=0.98 (=0.62). Each spectrum is presented individually along with its best-fit SALT2 model. The five year dataset contains 209 spectra corresponding to 192 SNeIa identified at the VLT. We also publish the redshifts of other candidates (host galaxies or other transients) whose spectra were obtained at the same time as the spectra of live SNe Ia. Using the full VLT SNeIa sample, we build composite spectra around maximum light with cuts in color, lightcurve shape parameter ('stretch'), host-galaxy mass and redshift. We find that high-z SNeIa are bluer, brighter and have weaker intermediate mass element absorption lines than their low-z counterparts at a level consistent with what is expected from selection effects. We also find a flux excess in the range [3000-3400] A for SNeIa in low mass host-galaxies or with locally blue U-V colors, and suggest that the UV flux (or local color) may be used in future cosmological studies as a third standardization parameter in addition to stretch and color., Comment: 55 pages, 159 figures. Associated release: see http://supernovae.in2p3.fr/Snls5VltRelease

We study minimum energy problems relative to the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$, $\alpha\in(0,2]$, over signed Radon measures $\mu$ on $\mathbb R^n$, $n\geqslant3$, associated with a generalized condenser $(A_1,A_2)$, where $A_1$ is a relatively closed subset of a domain $D$ and $A_2=\mathbb R^n\setminus D$. We show that, though $A_2\cap\mathrm{Cl}_{\mathbb R^n}A_1$ may have nonzero capacity, this minimum energy problem is uniquely solvable (even in the presence of an external field) if we restrict ourselves to $\mu$ with $\mu^+\leqslant\xi$, where a constraint $\xi$ is properly chosen. We establish the sharpness of the sufficient conditions on the solvability thus obtained, provide descriptions of the weighted $\alpha$-Riesz potentials of the solutions, single out their characteristic properties, and analyze their supports. The approach developed is mainly based on the establishment of an intimate relationship between the constrained minimum $\alpha$-Riesz energy problem over signed measures associated with $(A_1,A_2)$ and the constrained minimum $\alpha$-Green energy problem over positive measures carried by $A_1$. The results are illustrated by examples., Comment: 30 pages

We study the constrained minimum energy problem with an external field relative to the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$ of order $\alpha\in(0,n)$ for a generalized condenser $\mathbf A=(A_i)_{i\in I}$ in $\mathbb R^n$, $n\geqslant 3$, whose oppositely charged plates intersect each other over a set of zero capacity. Conditions sufficient for the existence of minimizers are found, and their uniqueness and vague compactness are studied. Conditions obtained are shown to be sharp. We also analyze continuity of the minimizers in the vague and strong topologies when the condenser and the constraint both vary, describe the weighted equilibrium vector potentials, and single out their characteristic properties. Our arguments are based particularly on the simultaneous use of the vague topology and a suitable semimetric structure on a set of vector measures associated with $\mathbf A$, and the establishment of completeness theorems for proper semimetric spaces. The results remain valid for the logarithmic kernel on $\mathbb R^2$ and $\mathbf A$ with compact $A_i$, $i\in I$. The study is illustrated by several examples., Comment: 3 figures

We investigate separation properties of $N$-point configurations that minimize discrete Riesz $s$-energy on a compact set $A\subset \mathbb{R}^p$. When $A$ is a smooth $(p-1)$-dimensional manifold without boundary and $s\in [p-2, p-1)$, we prove that the order of separation (as $N\to \infty$) is the best possible. The same conclusions hold for the points that are a fixed positive distance from the boundary of $A$ whenever $A$ is any $p$-dimensional set. These estimates extend a result of Dahlberg for certain smooth $(p-1)$-dimensional surfaces when $s=p-2$ (the harmonic case). Furthermore, we obtain the same separation results for `greedy' $s$-energy points. We deduce our results from an upper regularity property of the $s$-equilibrium measure (i.e., the measure that solves the continuous minimal Riesz $s$-energy problem), and we show that this property holds under a local smoothness assumption on the set $A$.

There are many ways to generate a set of nodes on the sphere for use in a variety of problems in numerical analysis. We present a survey of quickly generated point sets on $\mathbb{S}^2$, examine their equidistribution properties, separation, covering, and mesh ratio constants and present a new point set, equal area icosahedral points, with low mesh ratio. We analyze numerically the leading order asymptotics for the Riesz and logarithmic potential energy for these configurations with total points $N<50,000$ and present some new conjectures., Comment: 48 pages, 29 figures

For $s\geqslant d$, we obtain the leading term as $N\to \infty$ of the maximal weighted $N$-point Riesz $s$-polarization (or Chebyshev constant) for a certain class of $d$-rectifiable compact subsets of $\mathbb{R}^p$. This class includes compact subsets of $d$-dimensional $C^1$ manifolds whose boundary relative to the manifold has $\mathcal{H}_d$-measure zero, as well as finite unions of such sets when their pairwise intersections have $\mathcal{H}_d$-measure zero. We also explicitly find the weak$^*$ limit distribution of asymptotically optimal $N$-point polarization configurations as $N\to \infty$.

For a compact $ d $-dimensional rectifiable subset of $ \mathbb{R}^{p} $ we study asymptotic properties as $ N\to\infty $ of $N$-point configurations minimizing the energy arising from a Riesz $ s $-potential $ 1/r^s $ and an external field in the hypersingular case $ s\geq d$. Formulas for the weak$ ^* $ limit of normalized counting measures of such optimal point sets and the first-order asymptotic values of minimal energy are obtained. As an application, we derive a method for generating configurations whose normalized counting measures converge to a given absolutely continuous measure supported on a rectifiable subset of $ \mathbb{R}^{p} $. Results on separation and covering properties of discrete minimizers are given. Our theorems are illustrated with several numerical examples., Comment: Corrected typos; added references

Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds are optimal for absolutely monotone potentials in the sense that for the linear programming technique they cannot be improved by using polynomials of the same or lower degree. When additional information about the structure (upper and lower bounds for the inner products) of the designs is known, improvements on the bounds are obtained. Furthermore, we provide `test functions' for determining when the linear programming lower bounds for energy can be improved utilizing higher degree polynomials. We also provide some asymptotic results for these energy bounds.

Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solvability of these problems in both the unconstrained and the constrained settings, investigate the properties of minimizers, and prove their uniqueness. Furthermore, characterization theorems in terms of variational inequalities for the weighted potentials are established. The results obtained are illustrated by several examples., Comment: 32 pages, 1 figure

We derive and investigate lower bounds for the potential energy of finite spherical point sets (spherical codes). Our bounds are optimal in the following sense -- they cannot be improved by employing polynomials of the same or lower degrees in the Delsarte-Yudin method. However, improvements are sometimes possible and we provide a necessary and sufficient condition for the existence of such better bounds. All our bounds can be obtained in a unified manner that does not depend on the potential function, provided the potential is given by an absolutely monotone function of the inner product between pairs of points, and this is the reason for us to call them universal. We also establish a criterion for a given code of dimension $n$ and cardinality $N$ not to be LP-universally optimal, e.g. we show that two codes conjectured by Ballinger et al to be universally optimal are not LP-universally optimal., Comment: 25 pages, 3 figures, 3 tables

We forecast dark energy constraints that could be obtained from a new large sample of Type Ia supernovae where those at high redshift are acquired with the Euclid space mission. We simulate a three-prong SN survey: a z<0.35 nearby sample (8000 SNe), a 0.2

We consider periodic energy problems in Euclidean space with a special emphasis on long-range potentials that cannot be defined through the usual infinite sum. One of our main results builds on more recent developments of Ewald summation to define the periodic energy corresponding to a large class of long-range potentials. Two particularly interesting examples are the logarithmic potential and the Riesz potential when the Riesz parameter is smaller than the dimension of the space. For these examples, we use analytic continuation methods to provide concise formulas for the periodic kernel in terms of the Epstein Hurwitz Zeta function. We apply our energy definition to deduce several properties of the minimal energy including the asymptotic order of growth and the distribution of points in energy minimizing configurations as the number of points becomes large. We conclude with some detailed calculations in the case of one dimension, which shows the utility of this approach., Comment: 32 pages; Version 2: Minor changes and typos corrected, modified presentation of Theorem 5.4, one additional reference added, to appear in Journal of Mathematical Physics

We present cosmological constraints from a joint analysis of type Ia supernova (SN Ia) observations obtained by the SDSS-II and SNLS collaborations. The data set includes several low-redshift samples (z<0.1), all 3 seasons from the SDSS-II (0.05 < z < 0.4), and 3 years from SNLS (0.2

We present spectra and lightcurves of SNLS 06D4eu and SNLS 07D2bv, two hydrogen-free superluminous supernovae discovered by the Supernova Legacy Survey. At z = 1.588, SNLS 06D4eu is the highest redshift superluminous SN with a spectrum, at M_U = -22.7 is one of the most luminous SNe ever observed, and gives a rare glimpse into the restframe ultraviolet where these supernovae put out their peak energy. SNLS 07D2bv does not have a host galaxy redshift, but based on the supernova spectrum, we estimate it to be at z ~ 1.5. Both supernovae have similar observer-frame griz lightcurves, which map to restframe lightcurves in the U-band and UV, rising in ~ 20 restframe days or longer, and declining over a similar timescale. The lightcurves peak in the shortest wavelengths first, consistent with an expanding blackbody starting near 15,000 K and steadily declining in temperature. We compare the spectra to theoretical models, and identify lines of C II, C III, Fe III, and Mg II in the spectrum of SNLS 06D4eu and SCP 06F6, and find that they are consistent with an expanding explosion of only a few solar masses of carbon, oxygen, and other trace metals. Thus the progenitors appear to be related to those suspected for SNe Ic. A high kinetic energy, 10^52 ergs, is also favored. Normal mechanisms of powering core- collapse or thermonuclear supernovae do not seem to work for these supernovae. We consider models powered by 56Ni decay and interaction with circumstellar material, but find that the creation and spin-down of a magnetar with a period of 2ms, magnetic field of 2 x 10^14 Gauss, and a 3 solar mass progenitor provides the best fit to the data., Comment: ApJ, accepted, 43 pages, 15 figures

Observations suggest that configurations of points on a sphere that are stable with respect to a Riesz potential distribute points uniformly over the sphere. Further, these stable configurations have a local structure that is largely hexagonal. Minimal configurations differ from stable configurations in the arrangement of defects within the hexagonal structure. This paper reports the asymptotic difference between the average energy of stable states and the lowest reported energies. We use this to infer the energy scale at which defects in the hexagonal structure are manifest. We report results for the Riesz potentials for s=0, s=1, s=2 and s=3. Additionally we compare existing theory for the asymptotic expansion in N of the minimal $N$-point energy with experimental results. We report a case of two distinct stable states that have the same Voronoi structure. Finally, we report the observed growth of the number of stable states as a function of N.

We present a technique to measure lightcurves of time-variable point sources on a spatially structured background from imaging data. The technique was developed to measure light curves of SNLS supernovae in order to infer their distances. This photometry technique performs simultaneous PSF photometry at the same sky position on an image series. We describe two implementations of the method: one that resamples images before measuring fluxes, and one which does not. In both instances, we sketch the key algorithms involved and present the validation using semi-artificial sources introduced in real images in order to assess the accuracy of the supernova flux measurements relative to that of surrounding stars. We describe the methods required to anchor these PSF fluxes to calibrated aperture catalogs, in order to derive SN magnitudes. We find a marginally significant bias of 2 mmag of the after-resampling method, and no bias at the mmag accuracy for the non-resampling method. Given surrounding star magnitudes, we determine the systematic uncertainty of SN magnitudes to be less than 1.5 mmag, which represents about one third of the current photometric calibration uncertainty affecting SN measurements. The SN photometry delivers several by-products: bright star PSF flux mea- surements which have a repeatability of about 0.6%, as for aperture measurements; we measure relative astrometric positions with a noise floor of 2.4 mas for a single-image bright star measurement; we show that in all bands of the MegaCam instrument, stars exhibit a profile linearly broadening with flux by about 0.5% over the whole brightness range., Comment: Accepted for publication in A&A. 20 pages

Let $A$ be a compact $d$-rectifiable set embedded in Euclidean space $\RR^p$, $d\le p$. For a given continuous distribution $\sigma(x)$ with respect to $d$-dimensional Hausdorff measure on $A$, our earlier results provided a method for generating $N$-point configurations on $A$ that have asymptotic distribution $\sigma (x)$ as $N\to \infty$; moreover such configurations are "quasi-uniform" in the sense that the ratio of the covering radius to the separation distance is bounded independent of $N$. The method is based upon minimizing the energy of $N$ particles constrained to $A$ interacting via a weighted power law potential $w(x,y)|x-y|^{-s}$, where $s>d$ is a fixed parameter and $w(x,y)=\left(\sigma(x)\sigma(y)\right)^{-({s}/{2d})}$. Here we show that one can generate points on $A$ with the above mentioned properties keeping in the energy sums only those pairs of points that are located at a distance of at most $r_N=C_N N^{-1/d}$ from each other, with $C_N$ being a positive sequence tending to infinity arbitrarily slowly. To do this we minimize the energy with respect to a varying truncated weight $v_N(x,y)=\Phi\(\left|x-y\right|/r_N\)w(x,y)$, where $\Phi:(0,\infty)\to [0,\infty)$ is a bounded function with $\Phi(t)=0$, $t\geq 1$, and $\lim_{t\to 0^+}\Phi(t)=1$. This reduces, under appropriate assumptions, the complexity of generating $N$ point `low energy' discretizations to order $N C_N^d$ computations.

For $N$-point best-packing configurations $\omega_N$ on a compact metric space $(A,\rho)$, we obtain estimates for the mesh-separation ratio $\gamma(\omega_N,A)$, which is the quotient of the covering radius of $\omega_N$ relative to $A$ and the minimum pairwise distance between points in $\omega_N$. For best-packing configurations $\omega_N$ that arise as limits of minimal Riesz $s$-energy configurations as $s\to \infty$, we prove that $\gamma(\omega_N,A)\le 1$ and this bound can be attained even for the sphere. In the particular case when N=5 on $S^2$ with $\rho$ the Euclidean metric, we prove our main result that among the infinitely many 5-point best-packing configurations there is a unique configuration, namely a square-base pyramid $\omega_5^*$, that is the limit (as $s\to \infty$) of 5-point $s$-energy minimizing configurations. Moreover, $\gamma(\omega_5^*,S^2)=1$.

We present a combined photometric calibration of the SNLS and the SDSS supernova survey, which results from a joint effort of the SDSS and the SNLS collaborations. We deliver fluxes calibrated to the HST spectrophotometric star network for large sets of tertiary stars that cover the science fields of both surveys in all photometric bands. We also cross-calibrate directly the two surveys and demonstrate their consistency. For each survey the flat-fielding is revised based on the analysis of dithered star observations. The calibration transfer from the HST spectrophotometric standard stars to the multi-epoch tertiary standard star catalogs in the science fields follows three different paths: observations of primary standard stars with the SDSS PT telescope; observations of Landolt secondary standard stars with SNLS MegaCam instrument at CFHT; and direct observation of faint HST standard stars with MegaCam. In addition, the tertiary stars for the two surveys are cross-calibrated using dedicated MegaCam observations of stripe 82. This overlap enables the comparison of these three calibration paths and justifies using their combination to improve the calibration accuracy. Flat-field corrections have improved the uniformity of each survey as demonstrated by the comparison of photometry in overlapping fields: the rms of the difference between the two surveys is 3 mmag in gri, 4 mmag in z and 8 mmag in u. We also find a remarkable agreement (better than 1%) between the SDSS and the SNLS calibration in griz. The cross-calibration and the introduction of direct calibration observations bring redundancy and strengthen the confidence in the resulting calibration. We conclude that the surveys are calibrated to the HST with a precision of about 0.4% in griz. This precision is comparable to the external uncertainty affecting the color of the HST primary standard stars., Comment: 58 pages, 33 figures, to be published in A&A

We prove a conjecture of Ambrus, Ball and Erd\'{e}lyi that equally spaced points maximize the minimum of discrete potentials on the unit circle whenever the potential is of the form \sum_{k=1}^n f(d(z,z_k)), where $f:[0,\pi]\to [0,\infty]$ is non-increasing and strictly convex and $d(z,w)$ denotes the geodesic distance between $z$ and $w$ on the circle., Comment: 8 pages, 1 figure, to appear Discrete and Computational Geometry

We present a measurement of the volumetric Type Ia supernova (SN Ia) rate (SNR_Ia) as a function of redshift for the first four years of data from the Canada-France-Hawaii Telescope (CFHT) Supernova Legacy Survey (SNLS). This analysis includes 286 spectroscopically confirmed and more than 400 additional photometrically identified SNe Ia within the redshift range 0.1

We use the wide-field capabilities of the 2dF fibre positioner and the AAOmega spectrograph on the Anglo-Australian Telescope (AAT) to obtain redshifts of galaxies that hosted supernovae during the first three years of the Supernova Legacy Survey (SNLS). With exposure times ranging from 10 to 60 ksec per galaxy, we were able to obtain redshifts for 400 host galaxies in two SNLS fields, thereby substantially increasing the total number of SNLS supernovae with host galaxy redshifts. The median redshift of the galaxies in our sample that hosted photometrically classified Type Ia supernovae (SNe Ia) is 0.77, which is 25% higher than the median redshift of spectroscopically confirmed SNe Ia in the three-year sample of the SNLS. Our results demonstrate that one can use wide-field fibre-fed multi-object spectrographs on 4m telescopes to efficiently obtain redshifts for large numbers of supernova host galaxies over the large areas of sky that will be covered by future high-redshift supernova surveys, such as the Dark Energy Survey., Comment: 22 pages, 4 figures, accepted for publication in PASA

In terms of the minimal $N$-point diameter $D_d(N)$ for $R^d,$ we determine, for a class of continuous real-valued functions $f$ on $[0,+\infty],$ the $N$-point $f$-best-packing constant $\min\{f(\|x-y\|)\, :\, x,y\in \R^d\}$, where the minimum is taken over point sets of cardinality $N.$ We also show that $$ N^{1/d}\Delta_d^{-1/d}-2\le D_d(N)\le N^{1/d}\Delta_d^{-1/d}, \quad N\ge 2,$$ where $\Delta_d$ is the maximal sphere packing density in $\R^d$. Further, we provide asymptotic estimates for the $f$-best-packing constants as $N\to\infty$.

We survey known results and present estimates and conjectures for the next-order term in the asymptotics of the optimal logarithmic energy and Riesz $s$-energy of $N$ points on the unit sphere in $\mathbb{R}^{d+1}$, $d\geq 1$. The conjectures are based on analytic continuation assumptions (with respect to $s$) for the coefficients in the asymptotic expansion (as $N\to \infty$) of the optimal $s$-energy.

We calculate the average stretch-corrected rise-time of type Ia supernovae (SNe Ia) in the Supernova Legacy Survey. We use the aggregate lightcurves of spectroscopic and photometrically identified SNe Ia to fit the rising part of the lightcurve with a simple quadratic model. We obtain a lightcurve shape corrected, i .e. stretch-corrected, fiducial rise-time of 17.02^{+0.18}_{-0.28} (stat) days. The measured rise-time differs from an earlier finding by the SNLS (Conley et al. 2006) due to the use of different SN Ia templates. We compare it to nearby samples using the same methods and find no evolution in the early part of the lightcurve of SNe Ia up to z=1. We search for variations among different populations, particularly subluminous objects, by dividing the sample in stretch. Bright and slow decliners (s>1.0) have consistent stretch-corrected rise-times compared to fainter and faster decliners (0.8

We present a sample of 485 photometrically identified Type Ia supernova candidates mined from the first three years of data of the CFHT SuperNova Legacy Survey (SNLS). The images were submitted to a deferred processing independent of the SNLS real-time detection pipeline. Light curves of all transient events were reconstructed in the g_M, r_M, i_M and z_M filters and submitted to automated sequential cuts in order to identify possible supernovae. Pure noise and long-term variable events were rejected by light curve shape criteria. Type Ia supernova identification relied on event characteristics fitted to their light curves assuming the events to be normal SNe Ia. The light curve fitter SALT2 was used for this purpose, assigning host galaxy photometric redshifts to the tested events. The selected sample of 485 candidates is one magnitude deeper than that allowed by the SNLS spectroscopic identification. The contamination by supernovae of other types is estimated to be 4%. Testing Hubble diagram residuals with this enlarged sample allows us to measure the Malmquist bias due to spectroscopic selections directly. The result is fully consistent with the precise Monte Carlo based estimate used to correct SN Ia distance moduli in the SNLS 3-year cosmological analyses. This paper demonstrates the feasibility of a photometric selection of high redshift supernovae with known host galaxy redshifts, opening interesting prospects for cosmological analyses from future large photometric SN Ia surveys., Comment: (The SNLS collaboration) 23 pages, 28 figures, Accepted in A&A

While it is generally accepted that Type Ia supernovae are the result of the explosion of a carbon-oxygen White Dwarf accreting mass in a binary system, the details of their genesis still elude us, and the nature of the binary companion is uncertain. Kasen (2010) points out that the presence of a non-degenerate companion in the progenitor system could leave an observable trace: a flux excess in the early rise portion of the lightcurve caused by the ejecta impact with the companion itself. This excess would be observable only under favorable viewing angles, and its intensity depends on the nature of the companion. We searched for the signature of a non-degenerate companion in three years of Supernova Legacy Survey data by generating synthetic lightcurves accounting for the effects of shocking and comparing true and synthetic time series with Kolmogorov-Smirnov tests. Our most constraining result comes from noting that the shocking effect is more prominent in rest-frame B than V band: we rule out a contribution from white dwarf-red giant binary systems to Type Ia supernova explosions greater than 10% at 2 sigma, and than 20% at 3 sigma level., Comment: 14 pages, 15 figures, resubmitted to ApJ, figure 15 modified

For a closed subset $K$ of a compact metric space $A$ possessing an $\alpha$-regular measure $\mu$ with $\mu(K)>0$, we prove that whenever $s>\alpha$, any sequence of weighted minimal Riesz $s$-energy configurations $\omega_N=\{x_{i,N}^{(s)}\}_{i=1}^N$ on $K$ (for `nice' weights) is quasi-uniform in the sense that the ratios of its mesh norm to separation distance remain bounded as $N$ grows large. Furthermore, if $K$ is an $\alpha$-rectifiable compact subset of Euclidean space ($\alpha$ an integer) with positive and finite $\alpha$-dimensional Hausdorff measure, it is possible to generate such a quasi-uniform sequence of configurations that also has (as $N\to \infty$) a prescribed positive continuous limit distribution with respect to $\alpha$-dimensional Hausdorff measure. As a consequence of our energy related results for the unweighted case, we deduce that if $A$ is a compact $C^1$ manifold without boundary, then there exists a sequence of $N$-point best-packing configurations on $A$ whose mesh-separation ratios have limit superior (as $N\to \infty$) at most 2.

We combine high redshift Type Ia supernovae from the first 3 years of the Supernova Legacy Survey (SNLS) with other supernova (SN) samples, primarily at lower redshifts, to form a high-quality joint sample of 472 SNe (123 low-$z$, 93 SDSS, 242 SNLS, and 14 {\it Hubble Space Telescope}). SN data alone require cosmic acceleration at >99.9% confidence, including systematic effects. For the dark energy equation of state parameter (assumed constant out to at least $z=1.4$) in a flat universe, we find $w = -0.91^{+0.16}_{-0.20}(\mathrm{stat}) ^{+0.07}_{-0.14} (\mathrm{sys})$ from SNe only, consistent with a cosmological constant. Our fits include a correction for the recently discovered relationship between host-galaxy mass and SN absolute brightness. We pay particular attention to systematic uncertainties, characterizing them using a systematics covariance matrix that incorporates the redshift dependence of these effects, as well as the shape-luminosity and color-luminosity relationships. Unlike previous work, we include the effects of systematic terms on the empirical light-curve models. The total systematic uncertainty is dominated by calibration terms. We describe how the systematic uncertainties can be reduced with soon to be available improved nearby and intermediate-redshift samples, particularly those calibrated onto USNO/SDSS-like systems., Comment: Published in ApJS. Data available from https://tspace.library.utoronto.ca/snls/

We present observational constraints on the nature of dark energy using the Supernova Legacy Survey three year sample (SNLS3) of Guy et al. (2010) and Conley et al. (2011). We use the 472 SNe Ia in this sample, accounting for recently discovered correlations between SN Ia luminosity and host galaxy properties, and include the effects of all identified systematic uncertainties directly in the cosmological fits. Combining the SNLS3 data with the full WMAP7 power spectrum, the Sloan Digital Sky Survey luminous red galaxy power spectrum, and a prior on the Hubble constant H0 from SHOES, in a flat universe we find omega_m=0.269+/-0.015 and w=-1.061+0.069-0.068 -- a 6.5% measure of the dark energy equation-of-state parameter w. The statistical and systematic uncertainties are approximately equal, with the systematic uncertainties dominated by the photometric calibration of the SN Ia fluxes -- without these calibration effects, systematics contribute only a ~2% error in w. When relaxing the assumption of flatness, we find omega_m=0.271+/-0.015, omega_k=-0.002+/-0.006, and w=-1.069+0.091-0.092. Parameterizing the time evolution of w as w(a)=w_0+w_a(1-a), gives w_0=-0.905+/-0.196, w_a=-0.984+1.094-1.097 in a flat universe. All of our results are consistent with a flat, w=-1 universe. The size of the SNLS3 sample allows various tests to be performed with the SNe segregated according to their light curve and host galaxy properties. We find that the cosmological constraints derived from these different sub-samples are consistent. There is evidence that the coefficient, beta, relating SN Ia luminosity and color, varies with host parameters at >4sigma significance (in addition to the known SN luminosity--host relation); however this has only a small effect on the cosmological results and is currently a sub-dominant systematic., Comment: Accepted for publication in ApJ. Data available from https://tspace.library.utoronto.ca/snls

The rate evolution of subluminous Type Ia Supernovae is presented using data from the Supernova Legacy Survey. This sub-sample represents the faint and rapidly-declining light-curves of the observed supernova Ia (SN Ia) population here defined by low stretch values (s<0.8). Up to redshift z=0.6, we find 18 photometrically-identified subluminous SNe Ia, of which six have spectroscopic redshift (and three are spectroscopically-confirmed SNe Ia). The evolution of the subluminous volumetric rate is constant or slightly decreasing with redshift, in contrast to the increasing SN Ia rate found for the normal stretch population, although a rising behaviour is not conclusively ruled out. The subluminous sample is mainly found in early-type galaxies with little or no star formation, so that the rate evolution is consistent with a galactic mass dependent behavior: $r(z)=A\times M_g$, with $A=(1.1\pm0.3)\times10^{-14}$ SNe per year and solar mass., Comment: 19 pages, 27 figures

We present photometric properties and distance measurements of 252 high redshift Type Ia supernovae (0.15 < z < 1.1) discovered during the first three years of the Supernova Legacy Survey (SNLS). These events were detected and their multi-colour light curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshifts. Systematic uncertainties arising from light curve modeling are studied, making use of two techniques to derive the peak magnitude, shape and colour of the supernovae, and taking advantage of a precise calibration of the SNLS fields. A flat LambdaCDM cosmological fit to 231 SNLS high redshift Type Ia supernovae alone gives Omega_M = 0.211 +/- 0.034(stat) +/- 0.069(sys). The dominant systematic uncertainty comes from uncertainties in the photometric calibration. Systematic uncertainties from light curve fitters come next with a total contribution of +/- 0.026 on Omega_M. No clear evidence is found for a possible evolution of the slope (beta) of the colour-luminosity relation with redshift., Comment: (The SNLS Collaboration) 40 pages, 32 figures, Accepted in A&A

GMOS optical long-slit spectroscopy at the Gemini-North telescope was used to classify targets from the Supernova Legacy Survey (SNLS) from July 2005 and May 2006 - May 2008. During this time, 95 objects were observed. Where possible the objects' redshifts (z) were measured from narrow emission or absorption features in the host galaxy spectrum, otherwise they were measured from the broader supernova features. We present spectra of 68 confirmed or probable SNe Ia from SNLS with redshifts in the range 0.17 \leq z \leq 1.02. In combination with earlier SNLS Gemini and VLT spectra, we used these new observations to measure pseudo-equivalent widths (EWs) of three spectral features - CaII H&K, SiII and MgII - in 144 objects and compared them to the EWs of low-redshift SNe Ia from a sample drawn from the literature. No signs of changes with z are seen for the CaII H&K and MgII features. Systematically lower EW SiII is seen at high redshift, but this can be explained by a change in demographics of the SNe Ia population within a two-component model combined with an observed correlation between EW SiII and photometric lightcurve stretch., Comment: 49 pages including 2 online-only appendices, accepted for publication in MNRAS

The Supernova Legacy Survey (SNLS) has produced a high-quality, homogeneous sample of Type Ia supernovae (SNe Ia) out to redshifts greater than z=1. In its first four years of full operation (to June 2007), the SNLS discovered more than 3000 transient candidates, 373 of which have been confirmed spectroscopically as SNe Ia. Use of these SNe Ia in precision cosmology critically depends on an analysis of the observational biases incurred in the SNLS survey due to the incomplete sampling of the underlying SN Ia population. This paper describes our real-time supernova detection and analysis procedures, and uses detailed Monte Carlo simulations to examine the effects of Malmquist bias and spectroscopic sampling. Such sampling effects are found to become apparent at z~0.6, with a significant shift in the average magnitude of the spectroscopically confirmed SN Ia sample towards brighter values for z>0.75. We describe our approach to correct for these selection biases in our three-year SNLS cosmological analysis (SNLS3), and present a breakdown of the systematic uncertainties involved., Comment: Accepted for publication in AJ

(Abridged) Precision cosmology with Type Ia supernovae (SNe Ia) makes use of the fact that SN Ia luminosities depend on their light-curve shapes and colours. Using Supernova Legacy Survey (SNLS) and other data, we show that there is an additional dependence on the global characteristics of their host galaxies: events of the same light-curve shape and colour are, on average, 0.08mag (~4.0sigma) brighter in massive host galaxies (presumably metal-rich) and galaxies with low specific star-formation rates (sSFR). SNe Ia in galaxies with a low sSFR also have a smaller slope ("beta") between their luminosities and colours with ~2.7sigma significance, and a smaller scatter on SN Ia Hubble diagrams (at 95% confidence), though the significance of these effects is dependent on the reddest SNe. SN Ia colours are similar between low-mass and high-mass hosts, leading us to interpret their luminosity differences as an intrinsic property of the SNe and not of some external factor such as dust. If the host stellar mass is interpreted as a metallicity indicator, the luminosity trends are in qualitative agreement with theoretical predictions. We show that the average stellar mass, and therefore the average metallicity, of our SN Ia host galaxies decreases with redshift. The SN Ia luminosity differences consequently introduce a systematic error in cosmological analyses, comparable to the current statistical uncertainties on parameters such as w. We show that the use of two SN Ia absolute magnitudes, one for events in high-mass (metal-rich) galaxies, and one for events in low-mass (metal-poor) galaxies, adequately corrects for the differences. Cosmological fits incorporating these terms give a significant reduction in chi^2 (3.8-4.5sigma). We conclude that future SN Ia cosmological analyses should use a correction of this (or similar) form to control demographic shifts in the galaxy population., Comment: Accepted for publication in MNRAS.

The observed brightness of Type Ia supernovae is affected by gravitational lensing caused by the mass distribution along the line of sight, which introduces an additional dispersion into the Hubble diagram. We look for evidence of lensing in the SuperNova Legacy Survey 3-year data set. We investigate the correlation between the residuals from the Hubble diagram and the gravitational magnification based on a modeling of the mass distribution of foreground galaxies. A deep photometric catalog, photometric redshifts, and well established mass luminosity relations are used. We find evidence of a lensing signal with a 2.3 sigma significance. The current result is limited by the number of SNe, their redshift distribution, and the other sources of scatter in the Hubble diagram. Separating the galaxy population into a red and a blue sample has a positive impact on the significance of the signal detection. On the other hand, increasing the depth of the galaxy catalog, the precision of photometric redshifts or reducing the scatter in the mass luminosity relations have little effect. We show that for the full SuperNova Legacy Survey sample (~400 spectroscopically confirmed Type Ia SNe and ~200 photometrically identified Type Ia SNe), there is an 80% probability of detecting the lensing signal with a 3 sigma significance., Comment: 13 pages, 17 figures, 1 table. Accepted for publication in AA

We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\Gamma$ in ${\mathbb R}^p$, $p\geq2$, as $N \to \infty$. For $f$ decreasing and convex, such a point configuration minimizes the $f$-energy $\sum_{j\neq k}f(d(\mathbf{x}_j, \mathbf{x}_k))$, where $d$ is the geodesic distance (with respect to $\Gamma$) between points on $\Gamma$. Completely monotonic functions, analytic kernel functions, Laurent series, and weighted kernel functions $f$ are studied. % Of particular interest are the geodesic Riesz potential $1/d^s$ ($s \neq 0$) and the geodesic logarithmic potential $\log(1/d)$. By analytic continuation we deduce the expansion for all complex values of $s$.

We have combined the large SN Ia database of the Canada-France-Hawaii Telescope Supernova Legacy Survey and catalogs of galaxies with photometric redshifts, VLA 1.4 GHz radio sources, and Spitzer infrared sources. We present eight SNe Ia in early-type host galaxies which have counterparts in the radio and infrared source catalogs. We find the SN Ia rate in subsets of radio and infrared early-type galaxies is ~1-5 times the rate in all early-type galaxies, and that any enhancement is always <~ 2 sigma. Rates in these subsets are consistent with predictions of the two component "A+B" SN Ia rate model. Since infrared properties of radio SN Ia hosts indicate dust obscured star formation, we incorporate infrared star formation rates into the "A+B" model. We also show the properties of SNe Ia in radio and infrared galaxies suggest the hosts contain dust and support a continuum of delay time distributions for SNe Ia, although other delay time distributions cannot be ruled out based on our data., Comment: 14 pages, 6 figures, 7 tables, accepted for publication in AJ

We present a method using the SALT2 light curve fitter to determine the redshift of Type Ia supernovae in the Supernova Legacy Survey (SNLS) based on their photometry in g', r', i' and z'. On 289 supernovae of the first three years of SNLS data, we obtain a precision $\sigma_{\Delta z/(1+z)} = 0.022$ on average up to a redshift of 1.0, with a higher precision of 0.016 for z<0.45 and a lower one of 0.025 for z>0.45. The rate of events with $|\Delta z|/(1+z)>0.15$ (catastrophic errors) is 1.4%. Both the precision and the rate of catastrophic errors are better than what can be currently obtained using host galaxy photometric redshifts. Photometric redshifts of this precision may be useful for future experiments which aim to discover up to millions of supernovae Ia but without spectroscopy for most of them., Comment: 7 pages, 9 figures, published in Astronomy and Astrophysics

We present 139 spectra of 124 Type Ia supernovae (SNeIa) that were observed at the ESO/VLT during the first three years of the Canada-France-Hawai Telescope (CFHT) Supernova Legacy Survey (SNLS). This homogeneous data set is used to test for redshift evolution of SNeIa spectra, and will be used in the SNLS 3rd year cosmological analyses. Spectra have been reduced and extracted with a dedicated pipeline that uses photometric information from deep CFHT Legacy Survey (CFHT-LS) reference images to trace, at sub-pixel accuracy, the position of the supernova on the spectrogram as a function of wavelength. It also separates the supernova and its host light in 60% of cases. The identification of the supernova candidates is performed using a spectrophotometric SNIa model. A total of 124 SNeIa, roughly 50% of the overall SNLS spectroscopic sample, have been identified using the ESO/VLT during the first three years of the survey. Their redshifts range from z=0.149 to z=1.031. The average redshift of the sample is z=0.63+/-0.02. This constitutes the largest SNIa spectral set to date in this redshift range. The spectra are presented along with their best-fit spectral SNIa model and a host model where relevant. In the latter case, a host subtracted spectrum is also presented. We produce average spectra for pre-maximum, maximum and post-maximum epochs for both z<0.5 and z>=0.5 SNeIa. We find that z<0.5 spectra have deeper intermediate mass element absorptions than z>= 0.5 spectra. The differences with redshift are consistent with the selection of brighter and bluer supernovae at higher redshift., Comment: Accepted for publication in Astronomy and Astrophysics, 103 pages, 11 main figures (+139 figures of VLT spectra)