McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions

Evidence is presented to suggest that, in three dimensions, spherical 6-designs with N points exist for N=24, 26, >= 28; 7-designs for N=24, 30, 32, 34, >= 36; 8-designs for N=36, 40, 42, >= 44; 9-designs for N=48, 50, 52, >= 54; 10-designs for N=60, 62, >= 64; 11-designs for N=70, 72, >= 74; and 12-designs for N=84, >= 86. The existence of some of these designs is established analytically, while others are given by very accurate numerical coordinates. The 24-point 7-design was first found by McLaren in 1963, and -- although not identified as such by McLaren -- consists of the vertices of an "improved" snub cube, obtained from Archimedes' regular snub cube (which is only a 3-design) by slightly shrinking each square face and expanding each triangular face. 5-designs with 23 and 25 points are presented which, taken together with earlier work of Reznick, show that 5-designs exist for N=12, 16, 18, 20, >= 22. It is conjectured, albeit with decreasing confidence for t >= 9, that these lists of t-designs are complete and that no others exist. One of the constructions gives a sequence of putative spherical t-designs with N= 12m points (m >= 2) where N = t^2/2 (1+o(1)) as t -> infinity.Comment: 16 pages, 1 figur

Photometry of supernovae in an image series : methods and application to the Supernova Legacy Survey (SNLS)

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 page

Measuring Baryon Acoustic Oscillations with Millions of Supernovae

Since type Ia Supernovae (SNe) explode in galaxies, they can, in principle, be used as the same tracer of the large-scale structure as their hosts to measure baryon acoustic oscillations (BAOs). To realize this, one must obtain a dense integrated sampling of SNe over a large fraction of the sky, which may only be achievable photometrically with future projects such as the Large Synoptic Survey Telescope. The advantage of SN BAOs is that SNe have more uniform luminosities and more accurate photometric redshifts than galaxies, but the disadvantage is that they are transitory and hard to obtain in large number at high redshift. We find that a half-sky photometric SN survey to redshift z = 0.8 is able to measure the baryon signature in the SN spatial power spectrum. Although dark energy constraints from SN BAOs are weak, they can significantly improve the results from SN luminosity distances of the same data, and the combination of the two is no longer sensitive to cosmic microwave background priors.Comment: 4 pages, 3 figures, ApJL accepte

Two superluminous supernovae from the early universe discovered by the Supernova Legacy Survey

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 figure

Dark energy constraints and correlations with systematics from CFHTLS weak lensing, SNLS supernovae Ia and WMAP5

We combine measurements of weak gravitational lensing from the CFHTLS-Wide survey, supernovae Ia from CFHT SNLS and CMB anisotropies from WMAP5 to obtain joint constraints on cosmological parameters, in particular, the dark energy equation of state parameter w. We assess the influence of systematics in the data on the results and look for possible correlations with cosmological parameters. We implement an MCMC algorithm to sample the parameter space of a flat CDM model with a dark-energy component of constant w. Systematics in the data are parametrised and included in the analysis. We determine the influence of photometric calibration of SNIa data on cosmological results by calculating the response of the distance modulus to photometric zero-point variations. The weak lensing data set is tested for anomalous field-to-field variations and a systematic shape measurement bias for high-z galaxies. Ignoring photometric uncertainties for SNLS biases cosmological parameters by at most 20% of the statistical errors, using supernovae only; the parameter uncertainties are underestimated by 10%. The weak lensing field-to-field variance pointings is 5%-15% higher than that predicted from N-body simulations. We find no bias of the lensing signal at high redshift, within the framework of a simple model. Assuming a systematic underestimation of the lensing signal at high redshift, the normalisation sigma_8 increases by up to 8%. Combining all three probes we obtain -0.10<1+w<0.06 at 68% confidence (-0.18<1+w<0.12 at 95%), including systematic errors. Systematics in the data increase the error bars by up to 35%; the best-fit values change by less than 0.15sigma. [Abridged]Comment: 14 pages, 10 figures. Revised version, matches the one to be published in A&A. Modifications have been made corresponding to the referee's suggestions, including reordering of some section