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C. To

Publications and source records attributed to C. To.

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Galaxy Morphological Classification Catalogue of the Dark Energy Survey Year 3 data with Convolutional Neural Networks

We present in this paper one of the largest galaxy morphological classification catalogues to date, including over 20 million of galaxies, using the Dark Energy Survey (DES) Year 3 data based on Convolutional Neural Networks (CNN). Monochromatic $i$-band DES images with linear, logarithmic, and gradient scales, matched with debiased visual classifications from the Galaxy Zoo 1 (GZ1) catalogue, are used to train our CNN models. With a training set including bright galaxies ($16\le{i}<18$) at low redshift ($z<0.25$), we furthermore investigate the limit of the accuracy of our predictions applied to galaxies at fainter magnitude and at higher redshifts. Our final catalogue covers magnitudes $16\le{i}<21$, and redshifts $z<1.0$, and provides predicted probabilities to two galaxy types -- Ellipticals and Spirals (disk galaxies). Our CNN classifications reveal an accuracy of over 99\% for bright galaxies when comparing with the GZ1 classifications ($i<18$). For fainter galaxies, the visual classification carried out by three of the co-authors shows that the CNN classifier correctly categorises disky galaxies with rounder and blurred features, which humans often incorrectly visually classify as Ellipticals. As a part of the validation, we carry out one of the largest examination of non-parametric methods, including $\sim$100,000 galaxies with the same coverage of magnitude and redshift as the training set from our catalogue. We find that the Gini coefficient is the best single parameter discriminator between Ellipticals and Spirals for this data set.

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Rates and delay times of type Ia supernovae in the Dark Energy Survey

We use a sample of 809 photometrically classified type Ia supernovae (SNe Ia) discovered by the Dark Energy Survey (DES) along with 40415 field galaxies to calculate the rate of SNe Ia per galaxy in the redshift range $0.2 < z <0.6$. We recover the known correlation between SN Ia rate and galaxy stellar mass across a broad range of scales $8.5 \leq \log(M_*/\mathrm{M}_{\odot}) \leq 11.25$. We find that the SN Ia rate increases with stellar mass as a power-law with index $0.63 \pm 0.02$, which is consistent with previous work. We use an empirical model of stellar mass assembly to estimate the average star-formation histories (SFHs) of galaxies across the stellar mass range of our measurement. Combining the modelled SFHs with the SN Ia rates to estimate constraints on the SN Ia delay time distribution (DTD), we find the data are fit well by a power-law DTD with slope index $β= -1.13 \pm 0.05$ and normalisation $A = 2.11 \pm0.05 \times 10^{-13}~\mathrm{SNe}~{\mathrm{M}_{\odot}}^{-1}~\mathrm{yr}^{-1}$, which corresponds to an overall SN Ia production efficiency $N_{\mathrm{Ia}}/M_* = 0.9~_{-0.7}^{+4.0} \times 10^{-3}~\mathrm{SNe}~\mathrm{M}_{\odot}^{-1}$. Upon splitting the SN sample by properties of the light curves, we find a strong dependence on DTD slope with the SN decline rate, with slower-declining SNe exhibiting a steeper DTD slope. We interpret this as a result of a relationship between intrinsic luminosity and progenitor age, and explore the implications of the result in the context of SN Ia progenitors.

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Spectroscopic Quantification of Projection Effects in the SDSS redMaPPer Galaxy Cluster Catalogue

Projection effects, whereby galaxies along the line-of-sight to a galaxy cluster are mistakenly associated with the cluster halo, present a significant challenge for optical cluster cosmology. We use statistically representative spectral coverage of luminous galaxies to investigate how projection effects impact the low-redshift limit of the Sloan Digital Sky Survey (SDSS) redMaPPer galaxy cluster catalogue. Spectroscopic redshifts enable us to differentiate true cluster members from false positives and determine the fraction of candidate cluster members viewed in projection. Our main results can be summarized as follows: first, we show that a simple double-Gaussian model can be used to describe the distribution of line-of-sight velocities in the redMaPPer sample; second, the incidence of projection effects is substantial, accounting for $\sim 16$ per cent of the weighted richness for the lowest richness objects; third, projection effects are a strong function of richness, with the contribution in the highest richness bin being several times smaller than for low-richness objects; fourth, our measurement has a similar amplitude to state-of-the-art models, but finds a steeper dependence of projection effects on richness than these models; and fifth, the slope of the observed velocity dispersion--richness relation, corrected for projection effects, implies an approximately linear relationship between the true, three-dimensional halo mass and three-dimensional richness. Our results provide a robust, empirical description of the impact of projection effects on the SDSS redMaPPer cluster sample and exemplify the synergies between optical imaging and spectroscopic data for studies of galaxy cluster astrophysics and cosmology.

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Dark Energy Survey Year 3 Results: Galaxy clustering and systematics treatment for lens galaxy samples

In this work we present the galaxy clustering measurements of the two DES lens galaxy samples: a magnitude-limited sample optimized for the measurement of cosmological parameters, MagLim, and a sample of luminous red galaxies selected with the redMaGiC algorithm. MagLim / redMaGiC sample contains over 10 million / 2.5 million galaxies and is divided into six / five photometric redshift bins spanning the range $z\in[0.20,1.05]$ / $z\in[0.15,0.90]$. Both samples cover 4143 deg$^2$ over which we perform our analysis blind, measuring the angular correlation function with a S/N $\sim 63$ for both samples. In a companion paper (DES Collaboration et al. 2021)), these measurements of galaxy clustering are combined with the correlation functions of cosmic shear and galaxy-galaxy lensing of each sample to place cosmological constraints with a 3$\times$2pt analysis. We conduct a thorough study of the mitigation of systematic effects caused by the spatially varying survey properties and we correct the measurements to remove artificial clustering signals. We employ several decontamination methods with different configurations to ensure the robustness of our corrections and to determine the systematic uncertainty that needs to be considered for the final cosmology analyses. We validate our fiducial methodology using log-normal mocks, showing that our decontamination procedure induces biases no greater than $0.5σ$ in the $(Ω_m, b)$ plane, where $b$ is galaxy bias. We demonstrate that failure to remove the artificial clustering would introduce strong biases up to $\sim 7 σ$ in $Ω_m$ and of more than $4 σ$ in galaxy bias.

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Identifying RR Lyrae Variable Stars in Six Years of the Dark Energy Survey

We present a search for RR Lyrae stars using the full six-year data set from the Dark Energy Survey (DES) covering ~5,000 sq. deg. of the southern sky. Using a multi-stage multi-variate classification and light curve template-fitting scheme, we identify RR Lyrae candidates with a median of 35 observations per candidate. We detect 6,971 RR Lyrae candidates out to ~335 kpc, and we estimate that our sample is >70% complete at ~150 kpc. We find excellent agreement with other wide-area RR Lyrae catalogs and RR Lyrae studies targeting the Magellanic Clouds and other Milky Way satellite galaxies. We fit the smooth stellar halo density profile using a broken-power-law model with fixed halo flattening (q = 0.7), and we find strong evidence for a break at $R_0 = 32.1^{+1.1}_{-0.9}$ kpc with an inner slope of $n_1 = -2.54^{+0.09}_{-0.09}$ and an outer slope of $n_2 = -5.42^{+0.13}_{-0.14}$. We use our catalog to perform a search for Milky Way satellite galaxies with large sizes and low luminosities. Using a set of simulated satellite galaxies, we find that our RR Lyrae-based search is more sensitive than those using resolved stellar populations in the regime of large ($r_h > 500$ pc), low-surface-brightness dwarf galaxies. A blind search for large, diffuse satellites yields three candidate substructures. The first can be confidently associated with the dwarf galaxy Eridanus II. The second has a similar distance and proper motion to the ultra-faint dwarf galaxy Tucana II but is separated by ~5 deg. The third is close in projection to the globular cluster NGC 1851 but is ~10 kpc more distant and appears to differ in proper motion.

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Consistency of cosmic shear analyses in harmonic and real space

Recent cosmic shear studies have reported discrepancies of up to $1σ$ on the parameter ${S_{8}=σ_{8}\sqrt{Ω_{\rm m}/0.3}}$ between the analysis of shear power spectra and two-point correlation functions, derived from the same shear catalogs. It is not a priori clear whether the measured discrepancies are consistent with statistical fluctuations. In this paper, we investigate this issue in the context of the forthcoming analyses from the third year data of the Dark Energy Survey (DES-Y3). We analyze DES-Y3 mock catalogs from Gaussian simulations with a fast and accurate importance sampling pipeline. We show that the methodology for determining matching scale cuts in harmonic and real space is the key factor that contributes to the scatter between constraints derived from the two statistics. We compare the published scales cuts of the KiDS, Subaru-HSC and DES surveys, and find that the correlation coefficients of posterior means range from over 80% for our proposed cuts, down to 10% for cuts used in the literature. We then study the interaction between scale cuts and systematic uncertainties arising from multiple sources: non-linear power spectrum, baryonic feedback, intrinsic alignments, uncertainties in the point-spread function, and redshift distributions. We find that, given DES-Y3 characteristics and proposed cuts, these uncertainties affect the two statistics similarly; the differential biases are below a third of the statistical uncertainty, with the largest biases arising from intrinsic alignment and baryonic feedback. While this work is aimed at DES-Y3, the tools developed can be applied to Stage-IV surveys where statistical errors will be much smaller.

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Galaxy Clustering in Harmonic Space from the Dark Energy Survey Year 1 Data: Compatibility with Real-Space Results

We perform an analysis in harmonic space of the Dark Energy Survey Year 1 Data (DES-Y1) galaxy clustering data using products obtained for the real-space analysis. We test our pipeline with a suite of lognormal simulations, which are used to validate scale cuts in harmonic space as well as to provide a covariance matrix that takes into account the DES-Y1 mask. We then apply this pipeline to DES-Y1 data taking into account survey property maps derived for the real-space analysis. We compare with real-space DES-Y1 results obtained from a similar pipeline. We show that the harmonic space analysis we develop yields results that are compatible with the real-space analysis for the bias parameters. This verification paves the way to performing a harmonic space analysis for the upcoming DES-Y3 data.

astro-ph.CO

Dark Energy Survey internal consistency tests of the joint cosmological probes analysis with posterior predictive distributions

Beyond-$Λ$CDM physics or systematic errors may cause subsets of a cosmological data set to appear inconsistent when analyzed assuming $Λ$CDM. We present an application of internal consistency tests to measurements from the Dark Energy Survey Year 1 (DES Y1) joint probes analysis. Our analysis relies on computing the posterior predictive distribution (PPD) for these data under the assumption of $Λ$CDM. We find that the DES Y1 data have an acceptable goodness of fit to $Λ$CDM, with a probability of finding a worse fit by random chance of ${p = 0.046}$. Using numerical PPD tests, supplemented by graphical checks, we show that most of the data vector appears completely consistent with expectations, although we observe a small tension between large- and small-scale measurements. A small part (roughly 1.5%) of the data vector shows an unusually large departure from expectations; excluding this part of the data has negligible impact on cosmological constraints, but does significantly improve the $p$-value to 0.10. The methodology developed here will be applied to test the consistency of DES Year 3 joint probes data sets.

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Exploring the contamination of the DES-Y1 Cluster Sample with SPT-SZ selected clusters

We perform a cross validation of the cluster catalog selected by the red-sequence Matched-filter Probabilistic Percolation algorithm (redMaPPer) in Dark Energy Survey year 1 (DES-Y1) data by matching it with the Sunyaev-Zel'dovich effect (SZE) selected cluster catalog from the South Pole Telescope SPT-SZ survey. Of the 1005 redMaPPer selected clusters with measured richness $\hatλ>40$ in the joint footprint, 207 are confirmed by SPT-SZ. Using the mass information from the SZE signal, we calibrate the richness--mass relation using a Bayesian cluster population model. We find a mass trend $λ\propto M^{B}$ consistent with a linear relation ($B\sim1$), no significant redshift evolution and an intrinsic scatter in richness of $σ_λ = 0.22\pm0.06$. At low richness SPT-SZ confirms fewer redMaPPer clusters than expected. We interpret this richness dependent deficit in confirmed systems as due to the increased presence at low richness of low mass objects not correctly accounted for by our richness-mass scatter model, which we call contaminants. At a richness $\hat λ=40$, this population makes up $>$12$\%$ (97.5 percentile) of the total population. Extrapolating this to a measured richness $\hat λ=20$ yields $>$22$\%$ (97.5 percentile). With these contamination fractions, the predicted redMaPPer number counts in different plausible cosmologies are compatible with the measured abundance. The presence of such a population is also a plausible explanation for the different mass trends ($B\sim0.75$) obtained from mass calibration using purely optically selected clusters. The mean mass from stacked weak lensing (WL) measurements suggests that these low mass contaminants are galaxy groups with masses $\sim3$-$5\times 10^{13} $ M$_\odot$ which are beyond the sensitivity of current SZE and X-ray surveys but a natural target for SPT-3G and eROSITA.

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Understanding the extreme luminosity of DES14X2fna

We present DES14X2fna, a high-luminosity, fast-declining type IIb supernova (SN IIb) at redshift $z=0.0453$, detected by the Dark Energy Survey (DES). DES14X2fna is an unusual member of its class, with a light curve showing a broad, luminous peak reaching $M_r\simeq-19.3$ mag 20 days after explosion. This object does not show a linear decline tail in the light curve until $\simeq$60 days after explosion, after which it declines very rapidly (4.38$\pm$0.10 mag 100 d$^{-1}$ in $r$-band). By fitting semi-analytic models to the photometry of DES14X2fna, we find that its light curve cannot be explained by a standard $^{56}$Ni decay model as this is unable to fit the peak and fast tail decline observed. Inclusion of either interaction with surrounding circumstellar material or a rapidly-rotating neutron star (magnetar) significantly increases the quality of the model fit. We also investigate the possibility for an object similar to DES14X2fna to act as a contaminant in photometric samples of SNe Ia for cosmology, finding that a similar simulated object is misclassified by a recurrent neural network (RNN)-based photometric classifier as a SN Ia in $\sim$1.1-2.4 per cent of cases in DES, depending on the probability threshold used for a positive classification.

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Pushing automated morphological classifications to their limits with the Dark Energy Survey

We present morphological classifications of $\sim$27 million galaxies from the Dark Energy Survey (DES) Data Release 1 (DR1) using a supervised deep learning algorithm. The classification scheme separates: (a) early-type galaxies (ETGs) from late-types (LTGs); and (b) face-on galaxies from edge-on. Our Convolutional Neural Networks (CNNs) are trained on a small subset of DES objects with previously known classifications. These typically have $\mathrm{m}_r \lesssim 17.7~\mathrm{mag}$; we model fainter objects to $\mathrm{m}_r < 21.5$ mag by simulating what the brighter objects with well determined classifications would look like if they were at higher redshifts. The CNNs reach 97\% accuracy to $\mathrm{m}_r<21.5$ on their training sets, suggesting that they are able to recover features more accurately than the human eye. We then used the trained CNNs to classify the vast majority of the other DES images. The final catalog comprises five independent CNN predictions for each classification scheme, helping to determine if the CNN predictions are robust or not. We obtain secure classifications for $\sim$ 87\% and 73\% of the catalog for the ETG vs. LTG and edge-on vs. face-on models, respectively. Combining the two classifications (a) and (b) helps to increase the purity of the ETG sample and to identify edge-on lenticular galaxies (as ETGs with high ellipticity). Where a comparison is possible, our classifications correlate very well with Sérsic index (\textit{n}), ellipticity ($ε$) and spectral type, even for the fainter galaxies. This is the largest multi-band catalog of automated galaxy morphologies to date.

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The WaZP galaxy cluster sample of the Dark Energy Survey Year 1

We present a new (2+1)D galaxy cluster finder based on photometric redshifts called Wavelet Z Photometric (WaZP) applied to DES first year (Y1A1) data. The results are compared to clusters detected by the South Pole Telescope (SPT) survey and the redMaPPer cluster finder, the latter based on the same photometric data. WaZP searches for clusters in wavelet-based density maps of galaxies selected in photometric redshift space without any assumption on the cluster galaxy populations. The comparison to other cluster samples was performed with a matching algorithm based on angular proximity and redshift difference of the clusters. It led to the development of a new approach to match two optical cluster samples, following an iterative approach to minimize incorrect associations. The WaZP cluster finder applied to DES Y1A1 galaxy survey (1,511 deg2 up to i=23 mag) led to the detection of 60,547 galaxy clusters with redshifts 0.05 5. Considering the overlapping regions and redshift ranges between the DES Y1A1 and SPT cluster surveys, all SZ based SPT clusters are recovered by the WaZP sample.The comparison between WaZP and redMaPPer cluster samples showed an excellent overall agreement for clusters with richness Ngals (λ for redMaPPer) greater than 25 (20), with 95% recovery on both directions. Based on the cluster cross-match we explorethe relative fragmentation of the two cluster samples and investigate the possible signatures of unmatched clusters.

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A machine learning approach to galaxy properties: joint redshift-stellar mass probability distributions with Random Forest

We demonstrate that highly accurate joint redshift-stellar mass probability distribution functions (PDFs) can be obtained using the Random Forest (RF) machine learning (ML) algorithm, even with few photometric bands available. As an example, we use the Dark Energy Survey (DES), combined with the COSMOS2015 catalogue for redshifts and stellar masses. We build two ML models: one containing deep photometry in the $griz$ bands, and the second reflecting the photometric scatter present in the main DES survey, with carefully constructed representative training data in each case. We validate our joint PDFs for $10,699$ test galaxies by utilizing the copula probability integral transform and the Kendall distribution function, and their univariate counterparts to validate the marginals. Benchmarked against a basic set-up of the template-fitting code BAGPIPES, our ML-based method outperforms template fitting on all of our predefined performance metrics. In addition to accuracy, the RF is extremely fast, able to compute joint PDFs for a million galaxies in just under $6$ min with consumer computer hardware. Such speed enables PDFs to be derived in real time within analysis codes, solving potential storage issues. As part of this work we have developed GALPRO, a highly intuitive and efficient Python package to rapidly generate multivariate PDFs on-the-fly. GALPRO is documented and available for researchers to use in their cosmology and galaxy evolution studies.

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No Evidence for Orbital Clustering in the Extreme Trans-Neptunian Objects

The apparent clustering in longitude of perihelion $\varpi$ and ascending node $Ω$ of extreme trans-Neptunian objects (ETNOs) has been attributed to the gravitational effects of an unseen 5-10 Earth-mass planet in the outer solar system. To investigate how selection bias may contribute to this clustering, we consider 14 ETNOs discovered by the Dark Energy Survey, the Outer Solar System Origins Survey, and the survey of Sheppard and Trujillo. Using each survey's published pointing history, depth, and TNO tracking selections, we calculate the joint probability that these objects are consistent with an underlying parent population with uniform distributions in $\varpi$ and $Ω$. We find that the mean scaled longitude of perihelion and orbital poles of the detected ETNOs are consistent with a uniform population at a level between $17\%$ and $94\%$, and thus conclude that this sample provides no evidence for angular clustering.

astro-ph.EP

Dark Energy Survey Year 3 Results: Optimizing the Lens Sample in Combined Galaxy Clustering and Galaxy-Galaxy Lensing Analysis

We investigate potential gains in cosmological constraints from the combination of galaxy clustering and galaxy-galaxy lensing by optimizing the lens galaxy sample selection using information from Dark Energy Survey (DES) Year 3 data and assuming the DES Year 1 Metacalibration sample for the sources. We explore easily reproducible selections based on magnitude cuts in $i$-band as a function of (photometric) redshift, $z_{\rm phot}$, and benchmark the potential gains against those using the well established redMaGiC sample. We focus on the balance between density and photometric redshift accuracy, while marginalizing over a realistic set of cosmological and systematic parameters. Our optimal selection, the MagLim sample, satisfies $i < 4 \, z_{\rm phot} + 18$ and has $\sim 30\%$ wider redshift distributions but $\sim 3.5$ times more galaxies than redMaGiC. Assuming a wCDM model and equivalent scale cuts to mitigate nonlinear effects, this leads to $40\%$ increase in the figure of merit for the pair combinations of $Ω_m$, $w$, and $σ_8$, and gains of $16\%$ in $σ_8$, $10\%$ in $Ω_m$, and $12\%$ in $w$. Similarly, in LCDM we find an improvement of $19\%$ and $27\%$ on $σ_8$ and $Ω_m$, respectively. We also explore flux-limited samples with a flat magnitude cut finding that the optimal selection, $i < 22.2$, has $\sim 7$ times more galaxies and $\sim 20\%$ wider redshift distributions compared to MagLim, but slightly worse constraints. We show that our results are robust with respect to the assumed galaxy bias and photometric redshift uncertainties with only moderate further gains from increased number of tomographic bins or the inclusion of bin cross-correlations, except in the case of the flux-limited sample, for which these gains are more significant.

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DES Y1 results: Splitting growth and geometry to test $Λ$CDM

We analyze Dark Energy Survey (DES) data to constrain a cosmological model where a subset of parameters -- focusing on $Ω_m$ -- are split into versions associated with structure growth (e.g. $Ω_m^{\rm grow}$) and expansion history (e.g. $Ω_m^{\rm geo}$). Once the parameters have been specified for the $Λ$CDM cosmological model, which includes general relativity as a theory of gravity, it uniquely predicts the evolution of both geometry (distances) and the growth of structure over cosmic time. Any inconsistency between measurements of geometry and growth could therefore indicate a breakdown of that model. Our growth-geometry split approach therefore serves as both a (largely) model-independent test for beyond-$Λ$CDM physics, and as a means to characterize how DES observables provide cosmological information. We analyze the same multi-probe DES data as arXiv:1811.02375 : DES Year 1 (Y1) galaxy clustering and weak lensing, which are sensitive to both growth and geometry, as well as Y1 BAO and Y3 supernovae, which probe geometry. We additionally include external geometric information from BOSS DR12 BAO and a compressed Planck 2015 likelihood, and external growth information from BOSS DR12 RSD. We find no significant disagreement with $Ω_m^{\rm grow}=Ω_m^{\rm geo}$. When DES and external data are analyzed separately, degeneracies with neutrino mass and intrinsic alignments limit our ability to measure $Ω_m^{\rm grow}$, but combining DES with external data allows us to constrain both growth and geometric quantities. We also consider a parameterization where we split both $Ω_m$ and $w$, but find that even our most constraining data combination is unable to separately constrain $Ω_m^{\rm grow}$ and $w^{\rm grow}$. Relative to $Λ$CDM, splitting growth and geometry weakens bounds on $σ_8$ but does not alter constraints on $h$.

astro-ph.CO

Combination of cluster number counts and two-point correlations: Validation on Mock Dark Energy Survey

We present a method of combining cluster abundances and large-scale two-point correlations, namely galaxy clustering, galaxy--cluster cross-correlations, cluster auto-correlations, and cluster lensing. This data vector yields comparable cosmological constraints to traditional analyses that rely on small-scale cluster lensing for mass calibration. We use cosmological survey simulations designed to resemble the Dark Energy Survey Year One (DES-Y1) data to validate the analytical covariance matrix and the parameter inferences. The posterior distribution from the analysis of simulations is statistically consistent with the absence of systematic biases detectable at the precision of the DES Y1 experiment. We compare the $χ^2$ values in simulations to their expectation and find no significant difference. The robustness of our results against a variety of systematic effects is verified using a simulated likelihood analysis of a Dark Energy Survey Year 1-like data vectors. This work presents the first-ever end-to-end validation of a cluster abundance cosmological analysis on galaxy catalog-level simulations.

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The Effect of Environment on Type Ia Supernovae in the Dark Energy Survey Three-Year Cosmological Sample

Analyses of type Ia supernovae (SNe Ia) have found puzzling correlations between their standardised luminosities and host galaxy properties: SNe Ia in high-mass, passive hosts appear brighter than those in lower-mass, star-forming hosts. We examine the host galaxies of SNe Ia in the Dark Energy Survey three-year spectroscopically-confirmed cosmological sample, obtaining photometry in a series of "local" apertures centred on the SN, and for the global host galaxy. We study the differences in these host galaxy properties, such as stellar mass and rest-frame $U-R$ colours, and their correlations with SN Ia parameters including Hubble residuals. We find all Hubble residual steps to be $>3σ$ in significance, both for splitting at the traditional environmental property sample median and for the step of maximum significance. For stellar mass, we find a maximal local step of $0.098\pm0.018$ mag; $\sim 0.03$ mag greater than the largest global stellar mass step in our sample ($0.070 \pm 0.017$ mag). When splitting at the sample median, differences between local and global $U-R$ steps are small, both $\sim 0.08$ mag, but are more significant than the global stellar mass step ($0.057\pm0.017$ mag). We split the data into sub-samples based on SN Ia light curve parameters: stretch ($x_1$) and colour ($c$), finding that redder objects ($c > 0$) have larger Hubble residual steps, for both stellar mass and $U-R$, for both local and global measurements, of $\sim0.14$ mag. Additionally, the bluer (star-forming) local environments host a more homogeneous SN Ia sample, with local $U-R$ r.m.s. scatter as low as $0.084 \pm 0.017$ mag for blue ($c < 0$) SNe Ia in locally blue $U-R$ environments.

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