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S. Kent

Publications and source records attributed to S. Kent.

At least 55 records · Page 3Linked to original sources

First Cosmology Results using Type Ia Supernovae from the Dark Energy Survey: Constraints on Cosmological Parameters

We present the first cosmological parameter constraints using measurements of type Ia supernovae (SNe Ia) from the Dark Energy Survey Supernova Program (DES-SN). The analysis uses a subsample of 207 spectroscopically confirmed SNe Ia from the first three years of DES-SN, combined with a low-redshift sample of 122 SNe from the literature. Our "DES-SN3YR" result from these 329 SNe Ia is based on a series of companion analyses and improvements covering SN Ia discovery, spectroscopic selection, photometry, calibration, distance bias corrections, and evaluation of systematic uncertainties. For a flat LCDM model we find a matter density Omega_m = 0.331 +_ 0.038. For a flat wCDM model, and combining our SN Ia constraints with those from the cosmic microwave background (CMB), we find a dark energy equation of state w = -0.978 +_ 0.059, and Omega_m = 0.321 +_ 0.018. For a flat w0waCDM model, and combining probes from SN Ia, CMB and baryon acoustic oscillations, we find w0 = -0.885 +_ 0.114 and wa = -0.387 +_ 0.430. These results are in agreement with a cosmological constant and with previous constraints using SNe Ia (Pantheon, JLA).

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Cosmological Constraints from Multiple Probes in the Dark Energy Survey

The combination of multiple observational probes has long been advocated as a powerful technique to constrain cosmological parameters, in particular dark energy. The Dark Energy Survey has measured 207 spectroscopically--confirmed Type Ia supernova lightcurves; the baryon acoustic oscillation feature; weak gravitational lensing; and galaxy clustering. Here we present combined results from these probes, deriving constraints on the equation of state, $w$, of dark energy and its energy density in the Universe. Independently of other experiments, such as those that measure the cosmic microwave background, the probes from this single photometric survey rule out a Universe with no dark energy, finding $w=-0.80^{+0.09}_{-0.11}$. The geometry is shown to be consistent with a spatially flat Universe, and we obtain a constraint on the baryon density of $Ω_b=0.069^{+0.009}_{-0.012}$ that is independent of early Universe measurements. These results demonstrate the potential power of large multi-probe photometric surveys and pave the way for order of magnitude advances in our constraints on properties of dark energy and cosmology over the next decade.

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The Dark Energy Survey Data Release 1

We describe the first public data release of the Dark Energy Survey, DES DR1, consisting of reduced single epoch images, coadded images, coadded source catalogs, and associated products and services assembled over the first three years of DES science operations. DES DR1 is based on optical/near-infrared imaging from 345 distinct nights (August 2013 to February 2016) by the Dark Energy Camera mounted on the 4-m Blanco telescope at Cerro Tololo Inter-American Observatory in Chile. We release data from the DES wide-area survey covering ~5,000 sq. deg. of the southern Galactic cap in five broad photometric bands, grizY. DES DR1 has a median delivered point-spread function of g = 1.12, r = 0.96, i = 0.88, z = 0.84, and Y = 0.90 arcsec FWHM, a photometric precision of < 1% in all bands, and an astrometric precision of 151 mas. The median coadded catalog depth for a 1.95" diameter aperture at S/N = 10 is g = 24.33, r = 24.08, i = 23.44, z = 22.69, and Y = 21.44 mag. DES DR1 includes nearly 400M distinct astronomical objects detected in ~10,000 coadd tiles of size 0.534 sq. deg. produced from ~39,000 individual exposures. Benchmark galaxy and stellar samples contain ~310M and ~ 80M objects, respectively, following a basic object quality selection. These data are accessible through a range of interfaces, including query web clients, image cutout servers, jupyter notebooks, and an interactive coadd image visualization tool. DES DR1 constitutes the largest photometric data set to date at the achieved depth and photometric precision.

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A Search for Optical Emission from Binary-Black-Hole Merger GW170814 with the Dark Energy Camera

Binary black hole (BBH) mergers found by the LIGO and Virgo detectors are of immense scientific interest to the astrophysics community, but are considered unlikely to be sources of electromagnetic emission. To test whether they have rapidly fading optical counterparts, we used the Dark Energy Camera to perform an $i$-band search for the BBH merger GW170814, the first gravitational wave detected by three interferometers. The 87-deg$^2$ localization region (at 90\% confidence) centered in the Dark Energy Survey (DES) footprint enabled us to image 86\% of the probable sky area to a depth of $i\sim 23$ mag and provide the most comprehensive dataset to search for EM emission from BBH mergers. To identify candidates, we perform difference imaging with our search images and with templates from pre-existing DES images. The analysis strategy and selection requirements were designed to remove supernovae and to identify transients that decline in the first two epochs. We find two candidates, each of which is spatially coincident with a star or a high-redshift galaxy in the DES catalogs, and they are thus unlikely to be associated with GW170814. Our search finds no candidates associated with GW170814, disfavoring rapidly declining optical emission from BBH mergers brighter than $i\sim 23$ mag ($L_{\rm optical} \sim 5\times10^{41}$ erg/s) 1-2 days after coalescence. In terms of GW sky map coverage, this is the most complete search for optical counterparts to BBH mergers to date

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Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing

We present cosmological results from a combined analysis of galaxy clustering and weak gravitational lensing, using 1321 deg$^2$ of $griz$ imaging data from the first year of the Dark Energy Survey (DES Y1). We combine three two-point functions: (i) the cosmic shear correlation function of 26 million source galaxies in four redshift bins, (ii) the galaxy angular autocorrelation function of 650,000 luminous red galaxies in five redshift bins, and (iii) the galaxy-shear cross-correlation of luminous red galaxy positions and source galaxy shears. To demonstrate the robustness of these results, we use independent pairs of galaxy shape, photometric redshift estimation and validation, and likelihood analysis pipelines. To prevent confirmation bias, the bulk of the analysis was carried out while blind to the true results; we describe an extensive suite of systematics checks performed and passed during this blinded phase. The data are modeled in flat $Λ$CDM and $w$CDM cosmologies, marginalizing over 20 nuisance parameters, varying 6 (for $Λ$CDM) or 7 (for $w$CDM) cosmological parameters including the neutrino mass density and including the 457 $\times$ 457 element analytic covariance matrix. We find consistent cosmological results from these three two-point functions, and from their combination obtain $S_8 \equiv σ_8 (Ω_m/0.3)^{0.5} = 0.783^{+0.021}_{-0.025}$ and $Ω_m = 0.264^{+0.032}_{-0.019}$ for $Λ$CDM for $w$CDM, we find $S_8 = 0.794^{+0.029}_{-0.027}$, $Ω_m = 0.279^{+0.043}_{-0.022}$, and $w=-0.80^{+0.20}_{-0.22}$ at 68% CL. The precision of these DES Y1 results rivals that from the Planck cosmic microwave background measurements, allowing a comparison of structure in the very early and late Universe on equal terms. Although the DES Y1 best-fit values for $S_8$ and $Ω_m$ are lower than the central values from Planck ...

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Rediscovery of the Sixth Star Cluster in the Fornax Dwarf Spheroidal Galaxy

Since first noticed by Shapley in 1939, a faint object coincident with the Fornax dwarf spheroidal has long been discussed as a possible sixth globular cluster system. However, debate has continued over whether this overdensity is a statistical artifact or a blended galaxy group. In this Letter we demonstrate, using deep DECam imaging data, that this object is well resolved into stars and is a bona fide star cluster. The stellar overdensity of this cluster is statistically significant at the level of ~ 6 - 6.7 sigma in several different photometric catalogs including Gaia. Therefore, it is highly unlikely to be caused by random fluctuation. We show that Fornax 6 is a star cluster with a peculiarly low surface brightness and irregular shape, which may indicate a strong tidal influence from its host galaxy. The Hess diagram of Fornax 6 is largely consistent with that of Fornax field stars, but it appears to be slightly bluer. However, it is still likely more metal-rich than most of the globular clusters in the system. Faint clusters like Fornax 6 that orbit and potentially get disrupted in the centers of dwarf galaxies can prove crucial for constraining the dark matter distribution in Milky Way satellites.

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Dark Energy Survey Year 1 Results: Measurement of the Baryon Acoustic Oscillation scale in the distribution of galaxies to redshift 1

We present angular diameter distance measurements obtained by locating the BAO scale in the distribution of galaxies selected from the first year of Dark Energy Survey data. We consider a sample of over 1.3 million galaxies distributed over a footprint of 1318 deg$^2$ with $0.6 < z_{\rm photo} < 1$ and a typical redshift uncertainty of $0.03(1+z)$. This sample was selected, as fully described in a companion paper, using a color/magnitude selection that optimizes trade-offs between number density and redshift uncertainty. We investigate the BAO signal in the projected clustering using three conventions, the angular separation, the co-moving transverse separation, and spherical harmonics. Further, we compare results obtained from template based and machine learning photometric redshift determinations. We use 1800 simulations that approximate our sample in order to produce covariance matrices and allow us to validate our distance scale measurement methodology. We measure the angular diameter distance, $D_A$, at the effective redshift of our sample divided by the true physical scale of the BAO feature, $r_{\rm d}$. We obtain close to a 4 per cent distance measurement of $D_A(z_{\rm eff}=0.81)/r_{\rm d} = 10.75\pm 0.43 $. These results are consistent with the flat $Λ$CDM concordance cosmological model supported by numerous other recent experimental results. All data products are publicly available here: https://des.ncsa.illinois.edu/releases/y1a1/bao

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First Cosmology Results Using Type Ia Supernovae from the Dark Energy Survey: Effects of Chromatic Corrections to Supernova Photometry on Measurements of Cosmological Parameters

Calibration uncertainties have been the leading systematic uncertainty in recent analyses using type Ia Supernovae (SNe Ia) to measure cosmological parameters. To improve the calibration, we present the application of Spectral Energy Distribution (SED)-dependent "chromatic corrections" to the supernova light-curve photometry from the Dark Energy Survey (DES). These corrections depend on the combined atmospheric and instrumental transmission function for each exposure, and they affect photometry at the 0.01 mag (1%) level, comparable to systematic uncertainties in calibration and photometry. Fitting our combined DES and low-z SN Ia sample with Baryon Acoustic Oscillation (BAO) and Cosmic Microwave Background (CMB) priors for the cosmological parameters $Ω_{\rm m}$ (the fraction of the critical density of the universe comprised of matter) and w (the dark energy equation of state parameter), we compare those parameters before and after applying the corrections. We find the change in w and $Ω_{\rm m}$ due to not including chromatic corrections are -0.002 and 0.000, respectively, for the DES-SN3YR sample with BAO and CMB priors, consistent with a larger DES-SN3YR-like simulation, which has a w-change of 0.0005 with an uncertainty of 0.008 and an $Ω_{\rm m}$ change of 0.000 with an uncertainty of 0.002 . However, when considering samples on individual CCDs we find large redshift-dependent biases (approximately 0.02 in distance modulus) for supernova distances.

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Dark Energy Survey Year 1 Results: Joint Analysis of Galaxy Clustering, Galaxy Lensing, and CMB Lensing Two-point Functions

We perform a joint analysis of the auto and cross-correlations between three cosmic fields: the galaxy density field, the galaxy weak lensing shear field, and the cosmic microwave background (CMB) weak lensing convergence field. These three fields are measured using roughly 1300 sq. deg. of overlapping optical imaging data from first year observations of the Dark Energy Survey and millimeter-wave observations of the CMB from both the South Pole Telescope Sunyaev-Zel'dovich survey and Planck. We present cosmological constraints from the joint analysis of the two-point correlation functions between galaxy density and galaxy shear with CMB lensing. We test for consistency between these measurements and the DES-only two-point function measurements, finding no evidence for inconsistency in the context of flat $Λ$CDM cosmological models. Performing a joint analysis of five of the possible correlation functions between these fields (excluding only the CMB lensing autospectrum) yields $S_{8}\equiv σ_8\sqrt{Ω_{\rm m}/0.3} = 0.782^{+0.019}_{-0.025}$ and $Ω_{\rm m}=0.260^{+0.029}_{-0.019}$. We test for consistency between these five correlation function measurements and the Planck-only measurement of the CMB lensing autospectrum, again finding no evidence for inconsistency in the context of flat $Λ$CDM models. Combining constraints from all six two-point functions yields $S_{8}=0.776^{+0.014}_{-0.021}$ and $Ω_{\rm m}= 0.271^{+0.022}_{-0.016}$. These results provide a powerful test and confirmation of the results from the first year DES joint-probes analysis.

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Dark Energy Survey Year 1 Results: Methodology and Projections for Joint Analysis of Galaxy Clustering, Galaxy Lensing, and CMB Lensing Two-point Functions

Optical imaging surveys measure both the galaxy density and the gravitational lensing-induced shear fields across the sky. Recently, the Dark Energy Survey (DES) collaboration used a joint fit to two-point correlations between these observables to place tight constraints on cosmology (DES Collaboration et al. 2017). In this work, we develop the methodology to extend the DES year one joint probes analysis to include cross-correlations of the optical survey observables with gravitational lensing of the cosmic microwave background (CMB) as measured by the South Pole Telescope (SPT) and Planck. Using simulated analyses, we show how the resulting set of five two-point functions increases the robustness of the cosmological constraints to systematic errors in galaxy lensing shear calibration. Additionally, we show that contamination of the SPT+Planck CMB lensing map by the thermal Sunyaev-Zel'dovich effect is a potentially large source of systematic error for two-point function analyses, but show that it can be reduced to acceptable levels in our analysis by masking clusters of galaxies and imposing angular scale cuts on the two-point functions. The methodology developed here will be applied to the analysis of data from the DES, the SPT, and Planck in a companion work.

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Dark Energy Survey Year 1 Results: Measurement of the Galaxy Angular Power Spectrum

We use data from the first-year (Y1) observations of the DES collaboration to measure the galaxy angular power spectrum (APS), and search for its BAO feature using a template-fitting method. We test our methodology in a sample of 1800 DES Y1-like mock catalogs. The APS is measured with the pseudo-$C_\ell$ method, using pixelized maps constructed from the mock catalogs and the DES mask. The covariance matrix of the $C_\ell$'s in these tests are also obtained from the mock catalogs. We use templates to model the measured spectra and estimate template parameters firstly from the $C_\ell$'s of the mocks using two different methods, a maximum likelihood estimator and a MCMC, finding consistent results with a good reduced $χ^2$. Robustness tests are performed to estimate the impact of different choices of settings used in our analysis. After these tests on mocks, we apply our method to a galaxy sample constructed from DES Y1 data specifically for LSS studies. This catalog comprises galaxies within an effective area of 1318 deg$^2$ and $0.6<z<1.0$. We fit the observed spectra with our optimized templates, considering models with and without BAO features. We find that the DES Y1 data favors a model with BAO at the $2.6\,σ$ C.L. with a best-fit shift parameter of $α=1.023\pm 0.047$. However, the goodness-of-fit is somewhat poor, with $χ^2/$(dof) = 1.49. We identify a possible cause of this issue and show that using a theoretical covariance matrix obtained from $C_\ell$'s that are better adjusted to data results in an improved value of $χ^2/$(dof) = 1.36 which is similar to the value obtained with the real-space analysis. Our results correspond to a distance measurement of $D_A(z_{\rm eff} = 0.81)/r_d = 10.65 \pm 0.49$, consistent with the main DES BAO findings. This is a companion paper to the main DES BAO article showing the details of the harmonic space analysis.

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Dark Energy Survey Year 1 Results: Cosmological Constraints from Cosmic Shear

We use 26 million galaxies from the Dark Energy Survey (DES) Year 1 shape catalogs over 1321 deg$^2$ of the sky to produce the most significant measurement of cosmic shear in a galaxy survey to date. We constrain cosmological parameters in both the flat $Λ$CDM and $w$CDM models, while also varying the neutrino mass density. These results are shown to be robust using two independent shape catalogs, two independent \photoz\ calibration methods, and two independent analysis pipelines in a blind analysis. We find a 3.5\% fractional uncertainty on $σ_8(Ω_m/0.3)^{0.5} = 0.782^{+0.027}_{-0.027}$ at 68\% CL, which is a factor of 2.5 improvement over the fractional constraining power of our DES Science Verification results. In $w$CDM, we find a 4.8\% fractional uncertainty on $σ_8(Ω_m/0.3)^{0.5} = 0.777^{+0.036}_{-0.038}$ and a dark energy equation-of-state $w=-0.95^{+0.33}_{-0.39}$. We find results that are consistent with previous cosmic shear constraints in $σ_8$ -- $Ω_m$, and see no evidence for disagreement of our weak lensing data with data from the CMB. Finally, we find no evidence preferring a $w$CDM model allowing $w\ne -1$. We expect further significant improvements with subsequent years of DES data, which will more than triple the sky coverage of our shape catalogs and double the effective integrated exposure time per galaxy.

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Dark Energy Survey Year 1 Results: Curved-Sky Weak Lensing Mass Map

We construct the largest curved-sky galaxy weak lensing mass map to date from the DES first-year (DES Y1) data. The map, about 10 times larger than previous work, is constructed over a contiguous $\approx1,500 $deg$^2$, covering a comoving volume of $\approx10 $Gpc$^3$. The effects of masking, sampling, and noise are tested using simulations. We generate weak lensing maps from two DES Y1 shear catalogs, Metacalibration and Im3shape, with sources at redshift $0.2<z<1.3,$ and in each of four bins in this range. In the highest signal-to-noise map, the ratio between the mean signal-to-noise in the E-mode and the B-mode map is $\sim$1.5 ($\sim$2) when smoothed with a Gaussian filter of $σ_{G}=30$ (80) arcminutes. The second and third moments of the convergence $κ$ in the maps are in agreement with simulations. We also find no significant correlation of $κ$ with maps of potential systematic contaminants. Finally, we demonstrate two applications of the mass maps: (1) cross-correlation with different foreground tracers of mass and (2) exploration of the largest peaks and voids in the maps.

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Forward Global Photometric Calibration of the Dark Energy Survey

Many scientific goals for the Dark Energy Survey (DES) require calibration of optical/NIR broadband $b = grizY$ photometry that is stable in time and uniform over the celestial sky to one percent or better. It is also necessary to limit to similar accuracy systematic uncertainty in the calibrated broadband magnitudes due to uncertainty in the spectrum of the source. Here we present a "Forward Global Calibration Method (FGCM)" for photometric calibration of the DES, and we present results of its application to the first three years of the survey (Y3A1). The FGCM combines data taken with auxiliary instrumentation at the observatory with data from the broad-band survey imaging itself and models of the instrument and atmosphere to estimate the spatial- and time-dependence of the passbands of individual DES survey exposures. "Standard" passbands are chosen that are typical of the passbands encountered during the survey. The passband of any individual observation is combined with an estimate of the source spectral shape to yield a magnitude $m_b^{\mathrm{std}}$ in the standard system. This "chromatic correction" to the standard system is necessary to achieve sub-percent calibrations. The FGCM achieves reproducible and stable photometric calibration of standard magnitudes $m_b^{\mathrm{std}}$ of stellar sources over the multi-year Y3A1 data sample with residual random calibration errors of $σ=5-6\,\mathrm{mmag}$ per exposure. The accuracy of the calibration is uniform across the $5000\,\mathrm{deg}^2$ DES footprint to within $σ=7\,\mathrm{mmag}$. The systematic uncertainties of magnitudes in the standard system due to the spectra of sources are less than $5\,\mathrm{mmag}$ for main sequence stars with $0.5<g-i<3.0$.

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Cosmology from Cosmic Shear with DES 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 $σ_8 (Ω_{\rm m}/0.3)^{0.5} = 0.81 \pm 0.06$ (68\% confidence), after marginalising 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 marginalising 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 datasets. Our uncertainties are $\sim$30\% larger than those from CFHTLenS when we carry out a comparable analysis of the two datasets, 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 $σ_8 (Ω_{\rm m}/0.3)^{0.5}$ is present regardless of the value of $w$.

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Astrometric calibration and performance of the Dark Energy Camera

We characterize the ability of the Dark Energy Camera (DECam) to perform relative astrometry across its 500~Mpix, 3 deg^2 science field of view, and across 4 years of operation. This is done using internal comparisons of ~4x10^7 measurements of high-S/N stellar images obtained in repeat visits to fields of moderate stellar density, with the telescope dithered to move the sources around the array. An empirical astrometric model includes terms for: optical distortions; stray electric fields in the CCD detectors; chromatic terms in the instrumental and atmospheric optics; shifts in CCD relative positions of up to ~10 um when the DECam temperature cycles; and low-order distortions to each exposure from changes in atmospheric refraction and telescope alignment. Errors in this astrometric model are dominated by stochastic variations with typical amplitudes of 10-30 mas (in a 30 s exposure) and 5-10 arcmin coherence length, plausibly attributed to Kolmogorov-spectrum atmospheric turbulence. The size of these atmospheric distortions is not closely related to the seeing. Given an astrometric reference catalog at density ~0.7 arcmin^{-2}, e.g. from Gaia, the typical atmospheric distortions can be interpolated to 7 mas RMS accuracy (for 30 s exposures) with 1 arcmin coherence length for residual errors. Remaining detectable error contributors are 2-4 mas RMS from unmodelled stray electric fields in the devices, and another 2-4 mas RMS from focal plane shifts between camera thermal cycles. Thus the astrometric solution for a single DECam exposure is accurate to 3-6 mas (0.02 pixels, or 300 nm) on the focal plane, plus the stochastic atmospheric distortion.

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Searching for Dark Matter Annihilation in Recently Discovered Milky Way Satellites with Fermi-LAT

We search for excess gamma-ray emission coincident with the positions of confirmed and candidate Milky Way satellite galaxies using 6 years of data from the Fermi Large Area Telescope (LAT). Our sample of 45 stellar systems includes 28 kinematically confirmed dark-matter-dominated dwarf spheroidal galaxies (dSphs) and 17 recently discovered systems that have photometric characteristics consistent with the population of known dSphs. For each of these targets, the relative predicted gamma-ray flux due to dark matter annihilation is taken from kinematic analysis if available, and estimated from a distance-based scaling relation otherwise, assuming that the stellar systems are dark-matter-dominated dSphs. LAT data coincident with four of the newly discovered targets show a slight preference (each ~$2 σ$ local) for gamma-ray emission in excess of the background. However, the ensemble of derived gamma-ray flux upper limits for individual targets is consistent with the expectation from analyzing random blank-sky regions, and a combined analysis of the population of stellar systems yields no globally significant excess (global significance $<1 σ$). Our analysis has increased sensitivity compared to the analysis of 15 confirmed dSphs by Ackermann et al. 2015. The observed constraints on the dark matter annihilation cross section are statistically consistent with the background expectation, improving by a factor of ~2 for large dark matter masses ($m_{{\rm DM},b \bar b} \gtrsim 1$ TeV and $m_{{\rm DM},τ^{+}τ^{-}} \gtrsim 70$ GeV) and weakening by a factor of ~1.5 at lower masses relative to previously observed limits.

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Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (kappa_WL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the Counts in Cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey (DES) Science Verification data over 139 deg^2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirm that the galaxy density contrast distribution is well modeled by a lognormal PDF convolved with Poisson noise at angular scales from 10-40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as kappa_WL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the kappa_WL distribution is well modeled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fit chi^2/DOF of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07 respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.

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