Pairwise Well-Formed Modes and Transformations

One of the most significant attitudinal shifts in the history of music occurred in the Renaissance, when an emerging triadic consciousness moved musicians towards a new scalar formation that placed major thirds on a par with perfect fifths. In this paper we revisit the confrontation between the two idealized scalar and modal conceptions, that of the ancient and medieval world and that of the early modern world, associated especially with Zarlino. We do this at an abstract level, in the language of algebraic combinatorics on words. In scale theory the juxtaposition is between well-formed and pairwise well-formed scales and modes, expressed in terms of Christoffel words or standard words and their conjugates, and the special Sturmian morphisms that generate them. Pairwise well-formed scales are encoded by words over a three-letter alphabet, and in our generalization we introduce special positive automorphisms of $F3$, the free group over three letters.Comment: 12 pages, 3 figures, paper presented at the MCM2017 at UNAM in Mexico City on June 27, 2017, keywords: pairwise well-formed scales and modes, well-formed scales and modes, well-formed words, Christoffel words, standard words, central words, algebraic combinatorics on words, special Sturmian morphism

Imprint of DES superstructures on the cosmic microwave background

Small temperature anisotropies in the cosmic microwave background (CMB) can be sourced by density perturbations via the late-time integrated Sachs-Wolfe (ISW) effect. Large voids and superclusters are excellent environments to make a localized measurement of this tiny imprint. In some cases excess signals have been reported. We probed these claims with an independent data set, using the first year data of the Dark Energy Survey (DES) in a different footprint, and using a different superstructure finding strategy. We identified 52 large voids and 102 superclusters at redshifts 0.2 < z < 0.65. We used the Jubilee simulation to a priori evaluate the optimal ISW measurement configuration for our compensated top-hat filtering technique, and then performed a stacking measurement of the CMB temperature field based on the DES data. For optimal configurations, we detected a cumulative cold imprint of voids with DeltaTf ≈ -5.0 ± 3.7 muK and a hot imprint of superclusters DeltaTf ≈ 5.1 ± 3.2 muK; this is ˜1.2sigma higher than the expected |DeltaTf| ≈ 0.6 muK imprint of such superstructures in Lambda cold dark matter (LambdaCDM). If we instead use an a posteriori selected filter size (R/Rv = 0.6), we can find a temperature decrement as large as DeltaTf ≈ -9.8 ± 4.7 muK for voids, which is ˜2sigma above LambdaCDM expectations and is comparable to previous measurements made using Sloan Digital Sky Survey superstructure data

Galaxy bias from galaxy–galaxy lensing in the DES science verification data

We present a measurement of galaxy–galaxy lensing around a magnitude-limited (iAB < 22.5) sample of galaxies from the dark energy survey science verification (DES-SV) data. We split these lenses into three photometric-redshift bins from 0.2 to 0.8, and determine the product of the galaxy bias b and cross-correlation coefficient between the galaxy and dark matter overdensity fields r in each bin, using scales above 4 h−1 Mpc comoving, where we find the linear bias model to be valid given our current uncertainties. We compare our galaxy bias results from galaxy–galaxy lensing with those obtained from galaxy clustering and CMB lensing for the same sample of galaxies, and find our measurements to be in good agreement with those in Crocce et al., while, in the lowest redshift bin (z ∼ 0.3), they show some tension with the findings in Giannantonio et al. We measure b· r to be 0.87 ± 0.11, 1.12 ± 0.16 and 1.24 ± 0.23, respectively, for the three redshift bins of width Δz = 0.2 in the range 0.2 < z < 0.8, defined with the photometric-redshift algorithm BPZ. Using a different code to split the lens sample, TPZ, leads to changes in the measured biases at the 10–20 per cent level, but it does not alter the main conclusion of this work: when comparing with Crocce et al. we do not find strong evidence for a cross-correlation parameter significantly below one in this galaxy sample, except possibly at the lowest redshift bin (z ∼ 0.3), where we find r = 0.71 ± 0.11 when using TPZ, and 0.83 ± 0.12 with BPZ

Joint analysis of galaxy-galaxy lensing and galaxy clustering: methodology and forecasts for dark energy survey

The joint analysis of galaxy-galaxy lensing and galaxy clustering is a promising method for inferring the growth function of large-scale structure. Anticipating a near future application of this analysis to Dark Energy Survey (DES) measurements of galaxy positions and shapes, we develop a practical approach to modeling the assumptions and systematic effects affecting the joint analysis of small-scale galaxy-galaxy lensing and large-scale galaxy clustering. Introducing parameters that characterize the halo occupation distribution (HOD), photometric redshift uncertainties, and shear measurement errors, we study how external priors on different subsets of these parameters affect our growth constraints. Degeneracies within the HOD model, as well as between the HOD and the growth function, are identified as the dominant source of complication, with other systematic effects being subdominant. The impact of HOD parameters and their degeneracies necessitate the detailed joint modeling of the galaxy sample that we employ. We conclude that DES data will provide powerful constraints on the evolution of structure growth in the Universe, conservatively/optimistically constraining the growth function to 7.9%/4.8% with its first-year data that cover over 1000 square degrees, and to 3.9%/2.3% with its full five-year data that will survey 5000 square degrees, including both statistical and systematic uncertainties

Cosmology from large scale galaxy clustering and galaxy-galaxy lensing with Dark Energy Survey Science Verification data

We present cosmological constraints from the Dark Energy Survey (DES) using a combined analysis of angular clustering of red galaxies and their cross-correlation with weak gravitational lensing of background galaxies. We use a 139 square degree contiguous patch of DES data from the Science Verification (SV) period of observations. Using large scale measurements, we constrain the matter density of the Universe as Omega_m = 0.31 +/- 0.09 and the clustering amplitude of the matter power spectrum as sigma_8 = 0.74 +/- 0.13 after marginalizing over seven nuisance parameters and three additional cosmological parameters. This translates into S_8 = sigma_8(Omega_m/0.3)^{0.16} = 0.74 +/- 0.12 for our fiducial lens redshift bin at 0.35 <z< 0.5, while S_8 = 0.78 +/- 0.09 using two bins over the range 0.2 <z< 0.5. We study the robustness of the results under changes in the data vectors, modelling and systematics treatment, including photometric redshift and shear calibration uncertainties, and find consistency in the derived cosmological parameters. We show that our results are consistent with previous cosmological analyses from DES and other data sets and conclude with a joint analysis of DES angular clustering and galaxy-galaxy lensing with Planck CMB data, Baryon Accoustic Oscillations and Supernova type Ia measurements

Galaxy-galaxy lensing in the Dark Energy Survey Science Verification data

We present galaxy-galaxy lensing results from 139 deg2 of Dark Energy Survey (DES) Science Verification (SV) data. Our lens sample consists of red galaxies, known as redMaGiC, which are specifically selected to have a low photometric redshift error and outlier rate. The lensing measurement has a total signal-to-noise ratio of 29 over scales 0.09 < R < 15 Mpc h-1, including all lenses over a wide redshift range 0.2 < z < 0.8. Dividing the lenses into three redshift bins for this constant moving number density sample, we find no evidence for evolution in the halo mass with redshift. We obtain consistent results for the lensing measurement with two independent shear pipelines, NGMIX and IM3SHAPE. We perform a number of null tests on the shear and photometric redshift catalogues and quantify resulting systematic uncertainties. Covariances from jackknife subsamples of the data are validated with a suite of 50 mock surveys. The result and systematic checks in this work provide a critical input for future cosmological and galaxy evolution studies with the DES data and redMaGiC galaxy samples. We fit a halo occupation distribution (HOD) model, and demonstrate that our data constrain the mean halo mass of the lens galaxies, despite strong degeneracies between individual HOD parameters

Weak-lensing mass calibration of redMaPPer galaxy clusters in Dark Energy Survey Science Verification data

We use weak-lensing shear measurements to determine the mean mass of optically selected galaxy clusters in Dark Energy Survey Science Verification data. In a blinded analysis, we split the sample of more than 8000 redMaPPer clusters into 15 subsets, spanning ranges in the richness parameter 5 ≤ λ ≤ 180 and redshift 0.2 ≤ z ≤ 0.8, and fit the averaged mass density contrast profiles with a model that accounts for seven distinct sources of systematic uncertainty: shear measurement and photometric redshift errors; clustermember contamination; miscentring; deviations from the NFW halo profile; halo triaxiality and line-of-sight projections. We combine the inferred cluster masses to estimate the joint scaling relation between mass, richness and redshift, M(λ, z) ∝ M0λF (1 + z) G. We find M0 ≡ (M200m | λ = 30, z = 0.5) = [2.35 ± 0.22 (stat) ± 0.12 (sys)] × 1014 M., with F = 1.12 ± 0.20 (stat) ± 0.06 (sys) and G = 0.18 ± 0.75 (stat) ± 0.24 (sys). The amplitude of the mass–richness relation is in excellent agreement with the weak-lensing calibration of redMaPPer clusters in SDSS by Simet et al. and with the Saro et al. calibration based on abundance matching of SPT-detected clusters. Our results extend the redshift range over which the mass–richness relation of redMaPPer clusters has been calibrated with weak lensing from z ≤ 0.3 to z ≤ 0.8. Calibration uncertainties of shear measurements and photometric redshift estimates dominate our systematic error budget and require substantial improvements for forthcoming studies

The DES Science Verification weak lensing shear catalogues

We present weak lensing shear catalogues for 139 square degrees of data taken during the Science Verification (SV) time for the new Dark Energy Camera (DECam) being used for the Dark Energy Survey (DES). We describe our object selection, point spread function estimation and shear measurement procedures using two independent shear pipelines, IM3SHAPE and NGMIX, which produce catalogues of 2.12 million and 3.44 million galaxies, respectively. We detail a set of null tests for the shear measurements and find that they pass the requirements for systematic errors at the level necessary for weak lensing science applications using the SV data. We also discuss some of the planned algorithmic improvements that will be necessary to produce sufficiently accurate shear catalogues for the full 5-yr DES, which is expected to cover 5000 square degrees

Cosmic Voids and Void Lensing in the Dark Energy Survey Science Verification Data

Galaxies and their dark matter halos populate a complicated filamentary network around large, nearly empty regions known as cosmic voids. Cosmic voids are usually identified in spectroscopic galaxy surveys, where 3D information about the large-scale structure of the Universe is available. Although an increasing amount of photometric data is being produced, its potential for void studies is limited since photometric redshifts induce line-of-sight position errors of $\sim50$ Mpc/$h$ or more that can render many voids undetectable. In this paper we present a new void finder designed for photometric surveys, validate it using simulations, and apply it to the high-quality photo-$z$ redMaGiC galaxy sample of the Dark Energy Survey Science Verification (DES-SV) data. The algorithm works by projecting galaxies into 2D slices and finding voids in the smoothed 2D galaxy density field of the slice. Fixing the line-of-sight size of the slices to be at least twice the photo-$z$ scatter, the number of voids found in these projected slices of simulated spectroscopic and photometric galaxy catalogs is within 20% for all transverse void sizes, and indistinguishable for the largest voids of radius $\sim 70$ Mpc/$h$ and larger. The positions, radii, and projected galaxy profiles of photometric voids also accurately match the spectroscopic void sample. Applying the algorithm to the DES-SV data in the redshift range $0.2<z<0.8$, we identify 87 voids with comoving radii spanning the range 18-120 Mpc/$h$, and carry out a stacked weak lensing measurement. With a significance of $4.4\sigma$, the lensing measurement confirms the voids are truly underdense in the matter field and hence not a product of Poisson noise, tracer density effects or systematics in the data. It also demonstrates, for the first time in real data, the viability of void lensing studies in photometric surveys

Cosmology from cosmic shear with Dark Energy Survey science verification data

We present the first constraints on cosmology from the Dark Energy Survey (DES), using weak lensing measurements from the preliminary Science Verification (SV) data. We use 139 square degrees of SV data, which is less than 3% of the full DES survey area. Using cosmic shear 2-point measurements over three redshift bins we find sigma8(Omegam/0.3 )0.5=0.81 ±0.06 (68% confidence), after marginalizing over 7 systematics parameters and 3 other cosmological parameters. We examine the robustness of our results to the choice of data vector and systematics assumed, and find them to be stable. About 20% of our error bar comes from marginalizing over shear and photometric redshift calibration uncertainties. The current state-of-the-art cosmic shear measurements from CFHTLenS are mildly discrepant with the cosmological constraints from Planck CMB data; our results are consistent with both data sets. Our uncertainties are ˜30 % larger than those from CFHTLenS when we carry out a comparable analysis of the two data sets, which we attribute largely to the lower number density of our shear catalogue. We investigate constraints on dark energy and find that, with this small fraction of the full survey, the DES SV constraints make negligible impact on the Planck constraints. The moderate disagreement between the CFHTLenS and Planck values of sigma8(Omegam/0.3 )0.5 is present regardless of the value of w