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B. Flaugher

Publications and source records attributed to B. Flaugher.

At least 199 records · Page 11Linked to original sources

Dynamical Classification of Trans-Neptunian Objects Detected by the Dark Energy Survey

The outer Solar System contains a large number of small bodies (known as trans-Neptunian objects or TNOs) that exhibit diverse types of dynamical behavior. The classification of bodies in this distant region into dynamical classes -- sub-populations that experience similar orbital evolution -- aids in our understanding of the structure and formation of the Solar System. In this work, we propose an updated dynamical classification scheme for the outer Solar System. This approach includes the construction of a new (automated) method for identifying mean-motion resonances. We apply this algorithm to the current dataset of TNOs observed by the Dark Energy Survey (DES) and present a working classification for all of the DES TNOs detected to date. Our classification scheme yields 1 inner centaur, 19 outer centaurs, 21 scattering disk objects, 47 detached TNOs, 48 securely resonant objects, 7 resonant candidates, and 97 classical belt objects. Among the scattering and detached objects, we detect 8 TNOs with semi-major axes greater than 150 AU.

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The STRong lensing Insights into the Dark Energy Survey (STRIDES) 2017/2018 follow-up campaign: Discovery of 10 lensed quasars and 10 quasar pairs

We report the results of the STRong lensing Insights from the Dark Energy Survey (STRIDES) follow-up campaign of the late 2017/early 2018 season. We obtained spectra of 65 lensed quasar candidates either with EFOSC2 on the NTT or ESI on Keck, which confirm 10 new gravitationally lensed quasars and 10 quasar pairs with similar spectra, but which do not show a lensing galaxy in DES images. Eight lensed quasars are doubly imaged with source redshifts between 0.99 and 2.90, one is triply imaged by a group (DESJ0345-2545, $z=1.68$), and one is quadruply imaged (quad: DESJ0053-2012, $z=3.8$). Singular isothermal ellipsoid models for the doubles, based on high-resolution imaging from SAMI on SOAR or NIRC2 on Keck, give total magnifications between 3.2 and 5.6, and Einstein radii between 0.49 and 1.97 arcseconds. After spectroscopic follow-up, we extract multi-epoch $grizY$ photometry of confirmed lensed quasars and contaminant quasar+star pairs from the first 4 years of DES data using parametric multi-band modelling, and compare variability in each system's components. By measuring the reduced $χ^2$ associated with fitting all epochs to the same magnitude, we find a simple cut on the less variable component that retains all confirmed lensed quasars, while removing 94 per cent of contaminant systems with stellar components. Based on our spectroscopic follow-up, this variability information can improve selection of lensed quasars and quasar pairs from 34-45 per cent to 51-70 per cent, with the majority of remaining contaminants being compact star-forming galaxies. Using mock lensed quasar lightcurves we demonstrate that selection based only on variability will over-represent the quad fraction by 10 per cent over a complete DES magnitude-limited sample (excluding microlensing differences), explained by the magnification bias and hence lower luminosity (more variable) sources in quads.

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The SPTpol Extended Cluster Survey

We describe the observations and resultant galaxy cluster catalog from the 2770 deg$^2$ SPTpol Extended Cluster Survey (SPT-ECS). Clusters are identified via the Sunyaev-Zel'dovich (SZ) effect, and confirmed with a combination of archival and targeted follow-up data, making particular use of data from the Dark Energy Survey (DES). With incomplete followup we have confirmed as clusters 244 of 266 candidates at a detection significance $ξ\ge 5$ and an additional 204 systems at $4<ξ<5$. The confirmed sample has a median mass of $M_{500c} \sim {4.4 \times 10^{14} M_\odot h_{70}^{-1}}$, a median redshift of $z=0.49$, and we have identified 44 strong gravitational lenses in the sample thus far. Radio data are used to characterize contamination to the SZ signal; the median contamination for confirmed clusters is predicted to be $\sim$1% of the SZ signal at the $ξ>4$ threshold, and $<4\%$ of clusters have a predicted contamination $>10\% $ of their measured SZ flux. We associate SZ-selected clusters, from both SPT-ECS and the SPT-SZ survey, with clusters from the DES redMaPPer sample, and find an offset distribution between the SZ center and central galaxy in general agreement with previous work, though with a larger fraction of clusters with significant offsets. Adopting a fixed Planck-like cosmology, we measure the optical richness-to-SZ-mass ($λ-M$) relation and find it to be 28% shallower than that from a weak-lensing analysis of the DES data---a difference significant at the 4 $σ$ level---with the relations intersecting at $λ=60$ . The SPT-ECS cluster sample will be particularly useful for studying the evolution of massive clusters and, in combination with DES lensing observations and the SPT-SZ cluster sample, will be an important component of future cosmological analyses.

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Stellar mass as a galaxy cluster mass proxy: application to the Dark Energy Survey redMaPPer clusters

We introduce a galaxy cluster mass observable, $μ_\star$, based on the stellar masses of cluster members, and we present results for the Dark Energy Survey (DES) Year 1 observations. Stellar masses are computed using a Bayesian Model Averaging method, and are validated for DES data using simulations and COSMOS data. We show that $μ_\star$ works as a promising mass proxy by comparing our predictions to X-ray measurements. We measure the X-ray temperature-$μ_\star$ relation for a total of 150 clusters matched between the wide-field DES Year 1 redMaPPer catalogue, and Chandra and XMM archival observations, spanning the redshift range $0.1<z<0.7$. For a scaling relation which is linear in logarithmic space, we find a slope of $α= 0.488\pm0.043$ and a scatter in the X-ray temperature at fixed $μ_\star$ of $σ_{{\rm ln} T_X|μ_\star}=0.266^{+0.019}_{-0.020}$ for the joint sample. By using the halo mass scaling relations of the X-ray temperature from the Weighing the Giants program, we further derive the $μ_\star$-conditioned scatter in mass, finding $σ_{{\rm ln} M|μ_\star}=0.26^{+ 0.15}_{- 0.10}$. These results are competitive with well-established cluster mass proxies used for cosmological analyses, showing that $μ_\star$ can be used as a reliable and physically motivated mass proxy to derive cosmological constraints.

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Dark Energy Survey Year 1 results: The relationship between mass and light around cosmic voids

What are the mass and galaxy profiles of cosmic voids? In this paper we use two methods to extract voids in the Dark Energy Survey (DES) Year 1 redMaGiC galaxy sample to address this question. We use either 2D slices in projection, or the 3D distribution of galaxies based on photometric redshifts to identify voids. For the mass profile, we measure the tangential shear profiles of background galaxies to infer the excess surface mass density. The signal-to-noise ratio for our lensing measurement ranges between 10.7 and 14.0 for the two void samples. We infer their 3D density profiles by fitting models based on N-body simulations and find good agreement for void radii in the range 15-85 Mpc. Comparison with their galaxy profiles then allows us to test the relation between mass and light at the 10%-level, the most stringent test to date. We find very similar shapes for the two profiles, consistent with a linear relationship between mass and light both within and outside the void radius. We validate our analysis with the help of simulated mock catalogues and estimate the impact of photometric redshift uncertainties on the measurement. Our methodology can be used for cosmological applications, including tests of gravity with voids. This is especially promising when the lensing profiles are combined with spectroscopic measurements of void dynamics via redshift-space distortions.

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

We present constraints on extensions of the minimal cosmological models dominated by dark matter and dark energy, $Λ$CDM and $w$CDM, by using a combined analysis of galaxy clustering and weak gravitational lensing from the first-year data of the Dark Energy Survey (DES Y1) in combination with external data. We consider four extensions of the minimal dark energy-dominated scenarios: 1) nonzero curvature $Ω_k$, 2) number of relativistic species $N_{\rm eff}$ different from the standard value of 3.046, 3) time-varying equation-of-state of dark energy described by the parameters $w_0$ and $w_a$ (alternatively quoted by the values at the pivot redshift, $w_p$, and $w_a$), and 4) modified gravity described by the parameters $μ_0$ and $Σ_0$ that modify the metric potentials. We also consider external information from Planck CMB measurements; BAO measurements from SDSS, 6dF, and BOSS; RSD measurements from BOSS; and SNIa information from the Pantheon compilation. Constraints on curvature and the number of relativistic species are dominated by the external data; when these are combined with DES Y1, we find $Ω_k=0.0020^{+0.0037}_{-0.0032}$ at the 68% confidence level, and $N_{\rm eff}<3.28\, (3.55)$ at 68% (95%) confidence. For the time-varying equation-of-state, we find the pivot value $(w_p, w_a)=(-0.91^{+0.19}_{-0.23}, -0.57^{+0.93}_{-1.11})$ at pivot redshift $z_p=0.27$ from DES alone, and $(w_p, w_a)=(-1.01^{+0.04}_{-0.04}, -0.28^{+0.37}_{-0.48})$ at $z_p=0.20$ from DES Y1 combined with external data; in either case we find no evidence for the temporal variation of the equation of state. For modified gravity, we find the present-day value of the relevant parameters to be $Σ_0= 0.43^{+0.28}_{-0.29}$ from DES Y1 alone, and $(Σ_0, μ_0)=(0.06^{+0.08}_{-0.07}, -0.11^{+0.42}_{-0.46})$ from DES Y1 combined with external data, consistent with predictions from GR.

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Observation and Confirmation of Nine Strong Lensing Systems in Dark Energy Survey Year 1 Data

We describe the observation and confirmation of \nbconfirmtext\ new strong gravitational lenses discovered in Year 1 data from the Dark Energy Survey (DES). We created candidate lists based on a) galaxy group and cluster samples and b) photometrically selected galaxy samples. We selected 46 candidates through visual inspection and then used the Gemini Multi-Object Spectrograph (GMOS) at the Gemini South telescope to acquire spectroscopic follow-up of 21 of these candidates. Through analysis of this spectroscopic follow-up data, we confirmed nine new lensing systems and rejected 2 candidates, but the analysis was inconclusive on 10 candidates. For each of the confirmed systems, we report measured spectroscopic properties, estimated \einsteinradiussub, and estimated enclosed masses. The sources that we targeted have an i-band surface brightness range of iSB ~ 22 - 24 mag arcsec^2 and a spectroscopic redshift range of zspec ~0.8 - 2.6. The lens galaxies have a photometric redshift range of zlens ~ 0.3 - 0.7. The lensing systems range in image-lens separation 2 - 9 arcsec and in enclosed mass 10^12 - 10^13 Msol.

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A Detection of CMB-Cluster Lensing using Polarization Data from SPTpol

We report the first detection of gravitational lensing due to galaxy clusters using only the polarization of the cosmic microwave background (CMB). The lensing signal is obtained using a new estimator that extracts the lensing dipole signature from stacked images formed by rotating the cluster-centered Stokes $Q/U$ map cutouts along the direction of the locally measured background CMB polarization gradient. Using data from the SPTpol 500 deg$^{2}$ survey at the locations of roughly 18,000 clusters with richness $λ\ge 10$ from the Dark Energy Survey (DES) Year-3 full galaxy cluster catalog, we detect lensing at $4.8σ$. The mean stacked mass of the selected sample is found to be $(1.43 \pm 0.4)\ \times 10^{14}\ {\rm M_{\odot}}$ which is in good agreement with optical weak lensing based estimates using DES data and CMB-lensing based estimates using SPTpol temperature data. This measurement is a key first step for cluster cosmology with future low-noise CMB surveys, like CMB-S4, for which CMB polarization will be the primary channel for cluster lensing measurements.

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H0LiCOW X: Spectroscopic/imaging survey and galaxy-group identification around the strong gravitational lens system WFI2033-4723

Galaxies and galaxy groups located along the line of sight towards gravitationally lensed quasars produce high-order perturbations of the gravitational potential at the lens position. When these perturbation are too large, they can induce a systematic error on $H_0$ of a few-percent if the lens system is used for cosmological inference and the perturbers are not explicitly accounted for in the lens model. In this work, we present a detailed characterization of the environment of the lens system WFI2033-4723 ($z_{\rm src} = 1.662$, $z_{\rm lens}$ = 0.6575), one of the core targets of the H0LICOW project for which we present cosmological inferences in a companion paper (Rusu et al. 2019). We use the Gemini and ESO-Very Large telescopes to measure the spectroscopic redshifts of the brightest galaxies towards the lens, and use the ESO-MUSE integral field spectrograph to measure the velocity-dispersion of the lens ($σ_{\rm {los}}= 250^{+15}_{-21}$ km/s) and of several nearby galaxies. In addition, we measure photometric redshifts and stellar masses of all galaxies down to $i < 23$ mag, mainly based on Dark Energy Survey imaging (DR1). Our new catalog, complemented with literature data, more than doubles the number of known galaxy spectroscopic redshifts in the direct vicinity of the lens, expanding to 116 (64) the number of spectroscopic redshifts for galaxies separated by less than 3 arcmin (2 arcmin) from the lens. Using the flexion-shift as a measure of the amplitude of the gravitational perturbation, we identify 2 galaxy groups and 3 galaxies that require specific attention in the lens models. The ESO MUSE data enable us to measure the velocity-dispersions of three of these galaxies. These results are essential for the cosmological inference analysis presented in Rusu et al. (2019).

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Dark Energy Survey Year 1 Results: Constraints on Intrinsic Alignments and their Colour Dependence from Galaxy Clustering and Weak Lensing

We perform a joint analysis of intrinsic alignments and cosmology using tomographic weak lensing, galaxy clustering and galaxy-galaxy lensing measurements from Year 1 (Y1) of the Dark Energy Survey. We define early- and late-type subsamples, which are found to pass a series of systematics tests, including for spurious photometric redshift error and point spread function correlations. We analyse these split data alongside the fiducial mixed Y1 sample using a range of intrinsic alignment models. In a fiducial Nonlinear Alignment Model (NLA) analysis, assuming a flat \lcdm~cosmology, we find a significant difference in intrinsic alignment amplitude, with early-type galaxies favouring $A_\mathrm{IA} = 2.38^{+0.32}_{-0.31}$ and late-type galaxies consistent with no intrinsic alignments at $0.05^{+0.10}_{-0.09}$. We find weak evidence of a diminishing alignment amplitude at higher redshifts in the early-type sample. The analysis is repeated using a number of extended model spaces, including a physically motivated model that includes both tidal torquing and tidal alignment mechanisms. In multiprobe likelihood chains in which cosmology, intrinsic alignments in both galaxy samples and all other relevant systematics are varied simultaneously, we find the tidal alignment and tidal torquing parts of the intrinsic alignment signal have amplitudes $A_1 = 2.66 ^{+0.67}_{-0.66}$, $A_2=-2.94^{+1.94}_{-1.83}$, respectively, for early-type galaxies and $A_1 = 0.62 ^{+0.41}_{-0.41}$, $A_2 = -2.26^{+1.30}_{-1.16}$ for late-type galaxies. In the full (mixed) Y1 sample the best constraints are $A_1 = 0.70 ^{+0.41}_{-0.38}$, $A_2 = -1.36 ^{+1.08}_{-1.41}$. For all galaxy splits and IA models considered, we report cosmological parameter constraints that are consistent with the results of Troxel et al. (2017) and Dark Energy Survey Collaboration (2017).

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Phenotypic redshifts with self-organizing maps: A novel method to characterize redshift distributions of source galaxies for weak lensing

Wide-field imaging surveys such as the Dark Energy Survey (DES) rely on coarse measurements of spectral energy distributions in a few filters to estimate the redshift distribution of source galaxies. In this regime, sample variance, shot noise, and selection effects limit the attainable accuracy of redshift calibration and thus of cosmological constraints. We present a new method to combine wide-field, few-filter measurements with catalogs from deep fields with additional filters and sufficiently low photometric noise to break degeneracies in photometric redshifts. The multi-band deep field is used as an intermediary between wide-field observations and accurate redshifts, greatly reducing sample variance, shot noise, and selection effects. Our implementation of the method uses self-organizing maps to group galaxies into phenotypes based on their observed fluxes, and is tested using a mock DES catalog created from N-body simulations. It yields a typical uncertainty on the mean redshift in each of five tomographic bins for an idealized simulation of the DES Year 3 weak-lensing tomographic analysis of $σ_{Δz} = 0.007$, which is a 60% improvement compared to the Year 1 analysis. Although the implementation of the method is tailored to DES, its formalism can be applied to other large photometric surveys with a similar observing strategy.

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Dark Energy Survey Year 1 Results: The effect of intracluster light on photometric redshifts for weak gravitational lensing

We study the effect of diffuse intracluster light on the critical surface mass density estimated from photometric redshifts of lensing source galaxies, and the resulting bias in a weak lensing measurement of galaxy cluster mass. Under conservative assumptions, we find the bias to be negligible for imaging surveys like the Dark Energy Survey (DES) with a recommended scale cut of >=200 kpc distance from cluster centers. For significantly deeper source catalogs from present and future surveys like the Large Synoptic Survey Telescope (LSST) program, more conservative scale and source magnitude cuts or a correction of the effect may be necessary to achieve per-cent level lensing measurement accuracy, especially at the massive end of the cluster population.

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Cosmological lensing ratios with DES Y1, SPT and Planck

Correlations between tracers of the matter density field and gravitational lensing are sensitive to the evolution of the matter power spectrum and the expansion rate across cosmic time. Appropriately defined ratios of such correlation functions, on the other hand, depend only on the angular diameter distances to the tracer objects and to the gravitational lensing source planes. Because of their simple cosmological dependence, such ratios can exploit available signal-to-noise down to small angular scales, even where directly modeling the correlation functions is difficult. We present a measurement of lensing ratios using galaxy position and lensing data from the Dark Energy Survey, and CMB lensing data from the South Pole Telescope and Planck, obtaining the highest precision lensing ratio measurements to date. Relative to the concordance $Λ$CDM model, we find a best fit lensing ratio amplitude of $A = 1.1 \pm 0.1$. We use the ratio measurements to generate cosmological constraints, focusing on the curvature parameter. We demonstrate that photometrically selected galaxies can be used to measure lensing ratios, and argue that future lensing ratio measurements with data from a combination of LSST and Stage-4 CMB experiments can be used to place interesting cosmological constraints, even after considering the systematic uncertainties associated with photometric redshift and galaxy shear estimation.

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Chemical Abundance Analysis of Tucana III, the Second $r$-process Enhanced Ultra-Faint Dwarf Galaxy

We present a chemical abundance analysis of four additional confirmed member stars of Tucana III, a Milky Way satellite galaxy candidate in the process of being tidally disrupted as it is accreted by the Galaxy. Two of these stars are centrally located in the core of the galaxy while the other two stars are located in the eastern and western tidal tails. The four stars have chemical abundance patterns consistent with the one previously studied star in Tucana III: they are moderately enhanced in $r$-process elements, i.e. they have $<$[Eu/Fe]$> \approx +$0.4 dex. The non-neutron-capture elements generally follow trends seen in other dwarf galaxies, including a metallicity range of 0.44 dex and the expected trend in $α$-elements, i.e., the lower metallicity stars have higher Ca and Ti abundance. Overall, the chemical abundance patterns of these stars suggest that Tucana III was an ultra-faint dwarf galaxy, and not a globular cluster, before being tidally disturbed. As is the case for the one other galaxy dominated by $r$-process enhanced stars, Reticulum II, Tucana III's stellar chemical abundances are consistent with pollution from ejecta produced by a binary neutron star merger, although a different $r$-process element or dilution gas mass is required to explain the abundances in these two galaxies if a neutron star merger is the sole source of $r$-process enhancement.

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Galaxies in X-ray Selected Clusters and Groups in Dark Energy Survey Data II: Hierarchical Bayesian Modeling of the Red-Sequence Galaxy Luminosity Function

Using $\sim 100$ X-ray selected clusters in the Dark Energy Survey Science Verification data, we constrain the luminosity function (LF) of cluster red sequence galaxies as a function of redshift. This is the first homogeneous optical/X-ray sample large enough to constrain the evolution of the luminosity function simultaneously in redshift ($0.1<z<1.05$) and cluster mass ($13.5 \le \rm{log_{10}}(M_{200crit}) \sim< 15.0$). We pay particular attention to completeness issues and the detection limit of the galaxy sample. We then apply a hierarchical Bayesian model to fit the cluster galaxy LFs via a Schecter function, including its characteristic break ($m^*$) to a faint end power-law slope ($α$). Our method enables us to avoid known issues in similar analyses based on stacking or binning the clusters. We find weak and statistically insignificant ($\sim 1.9 σ$) evolution in the faint end slope $α$ versus redshift. We also find no dependence in $α$ or $m^*$ with the X-ray inferred cluster masses. However, the amplitude of the LF as a function of cluster mass is constrained to $\sim 20\%$ precision. As a by-product of our algorithm, we utilize the correlation between the LF and cluster mass to provide an improved estimate of the individual cluster masses as well as the scatter in true mass given the X-ray inferred masses. This technique can be applied to a larger sample of X-ray or optically selected clusters from the Dark Energy Survey, significantly improving the sensitivity of the analysis.

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Superluminous Supernovae from the Dark Energy Survey

We present a sample of 21 hydrogen-free superluminous supernovae (SLSNe-I), and one hydrogen-rich SLSN (SLSN-II) detected during the five-year Dark Energy Survey (DES). These SNe, located in the redshift range 0.220<z<1.998, represent the largest homogeneously-selected sample of SLSN events at high redshift. We present the observed g,r, i, z light curves for these SNe, which we interpolate using Gaussian Processes. The resulting light curves are analysed to determine the luminosity function of SLSN-I, and their evolutionary timescales. The DES SLSN-I sample significantly broadens the distribution of SLSN-I light curve properties when combined with existing samples from the literature. We fit a magnetar model to our SLSNe, and find that this model alone is unable to replicate the behaviour of many of the bolometric light curves. We search the DES SLSN-I light curves for the presence of initial peaks prior to the main light-curve peak. Using a shock breakout model, our Monte Carlo search finds that 3 of our 14 events with pre-max data display such initial peaks. However, 10 events show no evidence for such peaks, in some cases down to an absolute magnitude of <-16, suggesting that such features are not ubiquitous to all SLSN-I events. We also identify a red pre-peak feature within the light curve of one SLSN, which is comparable to that observed within SN2018bsz.

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Producing a BOSS-CMASS sample with DES imaging

We present a sample of galaxies with the Dark Energy Survey (DES) photometry that replicates the properties of the BOSS CMASS sample. The CMASS galaxy sample has been well characterized by the Sloan Digital Sky Survey (SDSS) collaboration and was used to obtain the most powerful redshift-space galaxy clustering measurements to date. A joint analysis of redshift-space distortions (such as those probed by CMASS from SDSS) and a galaxy-galaxy lensing measurement for an equivalent sample from DES can provide powerful cosmological constraints. Unfortunately, the DES and SDSS-BOSS footprints have only minimal overlap, primarily on the celestial equator near the SDSS Stripe 82 region. Using this overlap, we build a robust Bayesian model to select CMASS-like galaxies in the remainder of the DES footprint. The newly defined DES-CMASS (DMASS) sample consists of 117,293 effective galaxies covering $1,244 {\rm deg}^2$. Through various validation tests, we show that the DMASS sample selected by this model matches well with the BOSS CMASS sample, specifically in the South Galactic cap (SGC) region that includes Stripe 82. Combining measurements of the angular correlation function and the clustering-z distribution of DMASS, we constrain the difference in mean galaxy bias and mean redshift between the BOSS CMASS and DMASS samples to be $Δb = 0.010^{+0.045}_{-0.052}$ and $Δz = \left( 3.46^{+5.48}_{-5.55} \right) \times 10^{-3}$ for the SGC portion of CMASS, and $Δb = 0.044^{+0.044}_{-0.043} $ and $Δz= ( 3.51^{+4.93}_{-5.91}) \times 10^{-3}$ for the full CMASS sample. These values indicate that the mean bias of galaxies and mean redshift in the DMASS sample is consistent with both CMASS samples within $1σ$.

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Dark Energy Survey Year 1 Results: Calibration of Cluster Mis-centering in the redMaPPer Catalogs

The center determination of a galaxy cluster from an optical cluster finding algorithm can be offset from theoretical prescriptions or $N$-body definitions of its host halo center. These offsets impact the recovered cluster statistics, affecting both richness measurements and the weak lensing shear profile around the clusters. This paper models the centering performance of the \RM~cluster finding algorithm using archival X-ray observations of \RM-selected clusters. Assuming the X-ray emission peaks as the fiducial halo centers, and through analyzing their offsets to the \RM~centers, we find that $\sim 75\pm 8 \%$ of the \RM~clusters are well centered and the mis-centered offset follows a Gamma distribution in normalized, projected distance. These mis-centering offsets cause a systematic underestimation of cluster richness relative to the well-centered clusters, for which we propose a descriptive model. Our results enable the DES Y1 cluster cosmology analysis by characterizing the necessary corrections to both the weak lensing and richness abundance functions of the DES Y1 redMaPPer cluster catalog.

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