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Simulating image coaddition with the Nancy Grace Roman Space Telescope – I. Simulation methodology and general results

The upcoming Nancy Grace Roman Space Telescope will carry out a wide-area survey in the near-infrared. A key science objective is the measurement of cosmic structure via weak gravitational lensing. Roman data will be undersampled, which introduces new challenges in the measurement of source galaxy shapes; a potential solution is to use linear algebra-based coaddition techniques such as imcom that combine multiple undersampled images to produce a single oversampled output mosaic with a desired ‘target’ point spread function (PSF). We present here an initial application of imcom to 0.64 square degrees of simulated Roman data, based on the Roman branch of the Legacy Survey of Space and Time (LSST) Dark Energy Science Collaboration (DESC) Data Challenge 2 (DC2) simulation. We show that imcom runs successfully on simulated data that includes features such as plate scale distortions, chip gaps, detector defects, and cosmic ray masks. We simultaneously propagate grids of injected sources and simulated noise fields as well as the full simulation. We quantify the residual deviations of the PSF from the target (the ‘leakage’), as well as noise properties of the output images; we discuss how the overall tiling pattern as well as Moiré patterns appear in the final leakage and noise maps. We include appendices on interpolation algorithms and the interaction of undersampling with image processing operations that may be of broader applicability. The companion paper (‘Paper II’) explores the implications for weak lensing analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

Fuzzy dark matter and the Dark Energy Survey Year 1 data

ABSTRACT Gravitational weak lensing by dark matter haloes leads to a measurable imprint in the shear correlation function of galaxies. Fuzzy dark matter (FDM), composed of ultralight axion-like particles of mass m ∼ 10−22 eV, suppresses the matter power spectrum and shear correlation with respect to standard cold dark matter. We model the effect of FDM on cosmic shear using the optimized halo model HMCode, accounting for additional suppression of the mass function and halo concentration in FDM as observed in N-body simulations. We combine Dark Energy Survey Year 1 (DES-Y1) data with the Planck cosmic microwave background anisotropies to search for shear correlation suppression caused by FDM. We find no evidence of suppression compared to the preferred cold dark matter model, and thus set a new lower limit to the FDM particle mass. Using a log-flat prior and marginalizing over uncertainties related to the non-linear model of FDM, we find a new, independent 95 per cent C.L. lower limit log10m > −23 combining Planck and DES-Y1 shear, an improvement of almost two orders of magnitude on the mass bound relative to CMB-only constraints. Our analysis is largely independent of baryonic modelling, and of previous limits to FDM covering this mass range. Our analysis highlights the most important aspects of the FDM non-linear model for future investigation. The limit to FDM from weak lensing could be improved by up to three orders of magnitude with $\mathcal {O}(0.1)$ arcmin cosmic shear angular resolution, if FDM and baryonic feedback can be simultaneously modelled to high precision in the halo model.

79 ASTRONOMY AND ASTROPHYSICS↗

High-resolution Chemical Abundances of the Nyx Stream

Abstract Nyx is a nearby, prograde, and high-eccentricity stellar stream physically contained in the thick disk, but its origin is unknown. Nyx could be the remnant of a disrupted dwarf galaxy, in which case the associated dark matter substructure could affect terrestrial dark matter direct-detection experiments. Alternatively, Nyx could be a signature of the Milky Way’s disk formation and evolution. To determine the origin of Nyx, we obtained high-resolution spectroscopy of 34 Nyx stars using Keck/HIRES and Magellan/MIKE. A differential chemical abundance analysis shows that most Nyx stars reside in a metal-rich ([Fe/H] > −1) high- α component that is chemically indistinguishable from the thick disk. This rules out the originally suggested scenario that Nyx is the remnant of a single massive dwarf galaxy merger. However, we also identify 5 substantially more metal-poor stars ([Fe/H] ∼ −2.0) whose chemical abundances are similar to those of the metal-weak thick disk. It remains unclear how stars that are chemically identical to the thick disk can be on such prograde, high-eccentricity orbits. We suggest two most likely scenarios: that Nyx is the result of an early minor dwarf galaxy merger, or that it is a record of the early spin-up of the Milky Way disk—although neither perfectly reproduces the chemodynamic observations. The most likely formation scenarios suggest that future spectroscopic surveys should find Nyx-like structures outside of the solar neighborhood.

79 ASTRONOMY AND ASTROPHYSICS↗

HSC-XXL: Baryon budget of the 136 XXL groups and clusters

Abstract We present our determination of the baryon budget for an X-ray-selected XXL sample of 136 galaxy groups and clusters spanning nearly two orders of magnitude in mass (M500 ∼ 1013–1015 M⊙) and the redshift range 0 ≲ z ≲ 1. Our joint analysis is based on the combination of Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) weak-lensing mass measurements, XXL X-ray gas mass measurements, and HSC and Sloan Digital Sky Survey multiband photometry. We carry out a Bayesian analysis of multivariate mass-scaling relations of gas mass, galaxy stellar mass, stellar mass of brightest cluster galaxies (BCGs), and soft-band X-ray luminosity, by taking into account the intrinsic covariance between cluster properties, selection effect, weak-lensing mass calibration, and observational error covariance matrix. The mass-dependent slope of the gas mass–total mass (M500) relation is found to be $1.29_{-0.10}^{+0.16}$, which is steeper than the self-similar prediction of unity, whereas the slope of the stellar mass–total mass relation is shallower than unity; $0.85_{-0.09}^{+0.12}$. The BCG stellar mass weakly depends on cluster mass with a slope of $0.49_{-0.10}^{+0.11}$. The baryon, gas mass, and stellar mass fractions as a function of M500 agree with the results from numerical simulations and previous observations. We successfully constrain the full intrinsic covariance of the baryonic contents. The BCG stellar mass shows the larger intrinsic scatter at a given halo total mass, followed in order by stellar mass and gas mass. We find a significant positive intrinsic correlation coefficient between total (and satellite) stellar mass and BCG stellar mass and no evidence for intrinsic correlation between gas mass and stellar mass. All the baryonic components show no redshift evolution.

Akino, Daichi↗

A composite likelihood approach for inference under photometric redshift uncertainty

ABSTRACT Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.

(cosmology:) large-scale structure of Universe↗

The State of the Molecular Gas in Post-starburst Galaxies

The molecular gas in galaxies traces both the fuel for star formation and the processes that can enhance or suppress star formation. Observations of the molecular gas state can thus point to when and why galaxies stop forming stars. In this study, we present Atacama Large Millimeter/submillimeter Array observations of the molecular gas in galaxies evolving through the post-starburst phase. These galaxies have low current star formation rates (SFRs), regardless of the SFR tracer used, with recent starbursts ending within the last 600 Myr. We present CO (3–2) observations for three post-starburst galaxies, and dense gas HCN/HCO+/HNC (1–0) observations for six (four new) post-starburst galaxies. The post-starbursts have low excitation traced by the CO spectral-line energy distribution up to CO (3–2), more similar to early-type than starburst galaxies. The low excitation indicates that lower density rather than high temperatures may suppress star formation during the post-starburst phase. One galaxy displays a blueshifted outflow traced by CO (3–2). MaNGA observations show that the ionized gas velocity is disturbed relative to the stellar velocity field, with a blueshifted component aligned with the molecular gas outflow, suggestive of a multiphase outflow. Low ratios of HCO + /CO, indicating low fractions of dense molecular gas relative to the total molecular gas, are seen throughout post-starburst phase, except for the youngest post-starburst galaxy considered here. These observations indicate that the impact of any feedback or quenching processes may be limited to low excitation and weak outflows in the cold molecular gas during the post-starburst phase.

79 ASTRONOMY AND ASTROPHYSICS↗

Impact of survey spatial variability on galaxy redshift distributions and the cosmological 3 × 2-point statistics for the Rubin Legacy Survey of Space and Time (LSST)

We investigate the impact of spatial survey non-uniformity on the galaxy redshift distributions for forthcoming data releases of the Rubin Observatory Legacy Survey of Space and Time (LSST). Specifically, we construct a mock photometry data set degraded by the Rubin OpSim observing conditions, and estimate photometric redshifts of the sample using a template-fitting photo-z estimator, BPZ, and a machine learning method, FlexZBoost. We select the Gold sample, defined as $i\lt 25.3$ for 10 yr LSST data, with an adjusted magnitude cut for each year and divide it into five tomographic redshift bins for the weak lensing lens and source samples. We quantify the change in the number of objects, mean redshift, and width of each tomographic bin as a function of the coadd i-band depth for 1-yr (Y1), 3-yr (Y3), and 5-yr (Y5) data. In particular, Y3 and Y5 have large non-uniformity due to the rolling cadence of LSST, hence provide a worst-case scenario of the impact from non-uniformity. We find that these quantities typically increase with depth, and the variation can be $10\!-\!40~{{\rm per\ cent}}$ at extreme depth values. Using Y3 as an example, we propagate the variable depth effect to the weak lensing $3\times 2$ pt analysis, and assess the impact on cosmological parameters via a Fisher forecast. We find that galaxy clustering is most susceptible to variable depth, and non-uniformity needs to be mitigated below 3 per cent to recover unbiased cosmological constraints. There is little impact on galaxy–shear and shear–shear power spectra, given the expected LSST Y3 noise.

cosmology↗

Tracer-field cross-correlations with k -nearest neighbour distributions

ABSTRACT In astronomy and cosmology significant effort is devoted to characterizing and understanding spatial cross-correlations between points – e.g galaxy positions, high energy neutrino arrival directions, X-ray and AGN sources, and continuous fields – e.g. weak lensing meiand Cosmic Microwave Background maps. Recently, we introduced the k-nearest neighbour (kNN) formalism to better characterize the clustering of discrete (point) data sets. Here, we extend it to the point – field cross-correlations analysis. It combines kNN measurements of the point data set with measurements of the field smoothed at many scales. The resulting statistics are sensitive to all orders in the joint clustering of the points and the field. We demonstrate that this approach, unlike the 2-pt cross-correlation, can measure the statistical dependence of two data sets even when there are no linear (Gaussian) correlations between them. We further demonstrate that this framework is far more effective than the two point function in detecting cross-correlations when the continuous field is contaminated by high levels of noise. For a particularly high level of noise, the cross-correlation between haloes and the underlying matter field in a cosmological simulation, between 10 h−1 Mpc and 30 h−1 Mpc, is detected at >5σ significance using the technique presented here, when the two-point cross-correlation significance is ∼1σ. Finally, we show that kNN cross-correlations of haloes and the matter field can be well modelled on quasi-linear scales using the Hybrid Effective Field Theory (HEFT) framework, with the same set of bias parameters as are used for 2-pt cross-correlations. The substantial improvement in the statistical power of detecting cross-correlations using this method makes it a promising tool for various cosmological applications.

79 ASTRONOMY AND ASTROPHYSICS↗

Strong suppression of heat conduction in a laboratory replica of galaxy-cluster turbulent plasmas

In conventional gases and plasmas, it is known that heat fluxes are proportional to temperature gradients, with collisions between particles mediating energy flow from hotter to colder regions and the coefficient of thermal conduction given by Spitzer’s theory. However, this theory breaks down in magnetized, turbulent, weakly collisional plasmas, although modifications are difficult to predict from first principles due to the complex, multiscale nature of the problem. Understanding heat transport is important in astrophysical plasmas such as those in galaxy clusters, where observed temperature profiles are explicable only in the presence of a strong suppression of heat conduction compared to Spitzer’s theory. To address this problem, we have created a replica of such a system in a laser laboratory experiment. Our data show a reduction of heat transport by two orders of magnitude or more, leading to large temperature variations on small spatial scales (as is seen in cluster plasmas).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The Velocity Map Asymmetry of Ionized Gas in MaNGA. I. The Catalog and General Properties

The SDSS-IV MaNGA survey has measured two-dimensional maps of emission-line velocities for a statistically powerful sample of nearby galaxies. The asymmetric features of these kinematics maps reflect the nonrotational component of a galaxy’s internal motion of ionized gas. In this study, we present a catalog of kinematic asymmetry measurements of the H α velocity map of a sample of 5353 MaNGA galaxies. Based on this catalog, we find that “special” galaxies (e.g., merging galaxies, barred galaxies, and active galactic nucleus host galaxies) contain more galaxies with highly asymmetric velocity maps. However, we notice that more than half of galaxies with high kinematic asymmetry in our sample are quite “regular.” For those “regular” galaxies, kinematic asymmetry shows a significant anticorrelation with stellar mass at log M * < 9.7 , while such a trend becomes very weak at log M * > 9.7 . Moreover, at a given stellar mass, the kinematic asymmetry shows weak correlations with photometric morphology, star formation rate, and environment, while it is independent of H i gas content. We also have quantified the observational effects in the kinematic asymmetry measurement. We find that both the signal-to-noise ratio of H α flux and disk inclination angle contribute to the measures of kinematic asymmetry, while the physical spatial resolution is an irrelevant factor inside the MaNGA redshift coverage.

79 ASTRONOMY AND ASTROPHYSICS↗

The Southern Stellar Stream Spectroscopic Survey (S{sup 5}): Chemical Abundances of Seven Stellar Streams

We present high-resolution Magellan/MIKE spectroscopy of 42 red giant stars in seven stellar streams confirmed by the Southern Stellar Stream Spectroscopic Survey (S {sup 5}): ATLAS, Aliqa Uma, Chenab, Elqui, Indus, Jhelum, and Phoenix. Abundances of 30 elements have been derived from over 10,000 individual line measurements or upper limits using photometric stellar parameters and a standard LTE analysis. This is currently the most extensive set of element abundances for stars in stellar streams. Three streams (ATLAS, Aliqa Uma, and Phoenix) are disrupted metal-poor globular clusters, although only weak evidence is seen for the light-element anticorrelations commonly observed in globular clusters. Four streams (Chenab, Elqui, Indus, and Jhelum) are disrupted dwarf galaxies, and their stars display abundance signatures that suggest progenitors with stellar masses ranging from 10{sup 6} to 10{sup 7} M {sub ⊙}. Extensive description is provided for the analysis methods, including the derivation of a new method for including the effect of stellar parameter correlations on each star’s abundance and uncertainty. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile.

79 ASTRONOMY AND ASTROPHYSICS↗

Effects of overlapping sources on cosmic shear estimation: Statistical sensitivity and pixel-noise bias

The next generation of dark-energy imaging surveys — so called “Stage-IV” surveys, such as that of the Rubin Observatory Legacy Survey of Space and Time (LSST) — will cross a threshold in the number density of detected sources on the sky that requires qualitatively different image analysis and measurement techniques compared to the current generation of Stage-III surveys. In Stage-IV surveys, a significant amount of the cosmologically useful information is due to sources whose images overlap with those of other sources on the sky. Here, we focus on the weak gravitational lensing probe, for which we expect the largest impact since the cosmic shear signal is primarily encoded in the estimated shapes of observed galaxies and thus directly impacted by overlaps. We introduce a framework based on the Fisher formalism to analyze the effect of the overlapping sources (“blending”) on the estimation of cosmic shear. This method gives concrete predictions for the minimum loss of information due to noise and blending for any choice of “deblending” scheme and shape-measurement algorithm. Our studies account for undetected sources but do not address their full effects and biases they may introduce. We use simulated images and predict this impact of blending for three surveys: the Dark Energy Survey (DES), the Hyper-Suprime Cam Subaru Strategic Program (HSC-SSP), and the Rubin LSST. Our methodology successfully estimates the statistical sensitivity to weak lensing for DES and HSC early results. For LSST, we present the expected loss in statistical sensitivity for the ten-year survey due to blending. We find that for approximately 62% of galaxies that are likely to be detected in full-depth LSST images, at least 1% of the flux in their pixels is from overlapping sources. We also find that the statistical correlations between measures of overlapping galaxies and, to a much lesser extent (0.2%) the higher shot noise level due to their presence, decrease the effective number density of galaxies, N eff , by ~ 18%. We calculate an upper limit on N eff of 39.4 galaxies per arcmin 2 in r band. We study the impact of stars on as a function of stellar density and illustrate the diminishing returns of extending the survey into lower Galactic latitudes. We extend the simulation-based Fisher formalism to predict the expected increase in pixel-noise bias due to blending for maximum-likelihood (ML) shape estimators. We find that noise bias depends sensitively on the particular shape estimator and measure of ensemble-average shape that is used, and properties of the galaxy that include redshift-dependent quantities such as size and luminosity. The source code for these studies is available online.[The documented software developed for the catalog-level studies are available in the open-source LSST DESC github repository https://github.com/LSSTDESC/WeakLensingDeblending. The software for analyzing one or two galaxies with user-defined parameters is in the open-source github repository https://github.com/ismael-mendoza/ShapeMeasurementFisherFormalism.]

79 ASTRONOMY AND ASTROPHYSICS↗

The SRG/eROSITA All-Sky Survey: Constraints on ultralight axion dark matter through galaxy cluster number counts

Ultralight axions are hypothetical scalar particles that influence the evolution of large-scale structures of the Universe. Depending on their mass, they can potentially be part of the dark matter component of the Universe as candidates commonly referred to as fuzzy dark matter. While strong constraints have been established for pure fuzzy dark matter models, the more general scenario where ultralight axions constitute only a fraction of the dark matter has been limited to only a few observational probes. In this work, we use the galaxy cluster number counts obtained from the first All-Sky Survey (eRASS1) of the SRG/eROSITA mission together with gravitational weak lensing data from the Dark Energy Survey, the Kilo-Degree Survey, and the Hyper Suprime-Cam to constrain the fraction of ultralight axions in the mass range 10 −32 eV to 10 −24 eV. We put upper bounds on the ultralight axion relic density Ω a in independent logarithmic axion mass bins by performing a full cosmological parameter inference. We find an exclusion region in the intermediate ultralight axion mass regime with the tightest bounds reported so far in the mass bins around m a = 10 −27 eV with Ω a < 0.0035 and m a = 10 −26 eV with Ω a < 0.0079; both are at a 95% confidence level. When combined with cosmic microwave background probes, these bounds are tightened to Ω a < 0.0030 in the m a = 10 −27 eV mass bin and Ω a < 0.0058 in the m a = 10 −26 eV mass bin, with both at a 95% confidence level. This is the first time that constraints on ultralight axions have been obtained using the growth of structure measured by galaxy cluster number counts. These results pave the way for large surveys, which can be utilized to obtain tight constraints on the mass and relic density of ultralight axions with better theoretical modeling of the abundance of halos.

cosmological parameters↗

Milky Way and M31 rotation curves: Λ CDM versus MOND

We analyze the existing rotation-curve data of the Milky Way and M31 galaxies that extend to very large distances and low accelerations. We find a systematic downward trend in the weak acceleration (large distances) segment of the radial acceleration. A similar downward trend has been noticed in the ΛCDM EAGLE simulation [Phys. Rev. D 96, 124016 (2017).], while the deviation from the generic MOND prediction would need to be ascribed to an external field effect, or possibly a post facto selected acceleration function μ(x).

79 ASTRONOMY AND ASTROPHYSICS↗

Lorentz Symmetry Group, Retardation, Intergalactic Mass Depletion and Mechanisms Leading to Galactic Rotation Curves

The general theory of relativity (GR) is symmetric under smooth coordinate transformations, also known as diffeomorphisms. The general coordinate transformation group has a linear subgroup denoted as the Lorentz group of symmetry, which is also maintained in the weak field approximation to GR. The dominant operator in the weak field equation of GR is thus the d’Alembert (wave) operator, which has a retarded potential solution. Galaxies are huge physical systems with dimensions of many tens of thousands of light years. Thus, any change at the galactic center will be noticed at the rim only tens of thousands of years later. Those retardation effects are neglected in the present day galactic modelling used to calculate rotational velocities of matter in the rims of the galaxy and surrounding gas. The significant differences between the predictions of Newtonian instantaneous action at a distance and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND). In this paper, we will show that, by taking general relativity seriously without neglecting retardation effects, one can explain the radial velocities of galactic matter in the M33 galaxy without postulating dark matter. It should be stressed that the current approach does not require that velocities v are high; in fact, the vast majority of galactic bodies (stars, gas) are substantially subluminal—in other words, the ratio of $\frac{v}{c} \ll 1$. Typical velocities in galaxies are 100 km/s, which makes this ratio 0.001 or smaller. However, one should consider the fact that every gravitational system, even if it is made of subluminal bodies, has a retardation distance, beyond which the retardation effect cannot be neglected. Every natural system, such as stars and galaxies and even galactic clusters, exchanges mass with its environment, for example, the sun loses mass through solar wind and galaxies accrete gas from the intergalactic medium. This means that all natural gravitational systems have a finite retardation distance. The question is thus quantitative: how large is the retardation distance? For the M33 galaxy, the velocity curve indicates that the retardation effects cannot be neglected beyond a certain distance, which was calculated to be roughly 14,000 light years; similar analysis for other galaxies of different types has shown similar results. We demonstrate, using a detailed model, that this does not require a high velocity of gas or stars in or out of the galaxy and is perfectly consistent with the current observational knowledge of galactic and extra galactic material content and dynamics

79 ASTRONOMY AND ASTROPHYSICS↗

Improving galaxy cluster selection with the outskirt stellar mass of galaxies

The number density and redshift evolution of optically selected galaxy clusters offer an independent measurement of the amplitude of matter fluctuations, 𝑆 8 . However, recent results have shown that clusters chosen by the redMaPPer algorithm show richness-dependent biases that affect the weak lensing signals and number densities of clusters, increasing uncertainty in the cluster mass calibration and reducing their constraining power. Here, in this work, we evaluate an alternative cluster proxy, outskirt stellar mass, 𝑀 out , defined as the total stellar mass within a [50, 100] kpc envelope centered on a massive galaxy. This proxy exhibits scatter comparable to redMaPPer richness, 𝜆, but is less likely to be subject to projection effects. We compare the Dark Energy Survey Year 3 redMaPPer cluster catalog with a 𝑀 out selected cluster sample from the Hyper-Suprime Camera survey. We use weak lensing measurements to quantify and compare the scatter of 𝑀 out and 𝜆 with halo mass. Our results show 𝑀 out has a scatter consistent with 𝜆, with a similar halo mass dependence, and that both proxies contain unique information about the underlying halo mass. We find 𝜆-selected samples introduce features into the measured Δ⁢Σ signal that are not well fit by a log-normal scatter only model, absent in 𝑀 out selected samples. Our findings suggest that 𝑀 out offers an alternative for cluster selection with more easily calibrated selection biases, at least at the generally lower richnesses probed here. Combining both proxies may yield a mass proxy with a lower scatter and more tractable selection biases, enabling the use of lower mass clusters in cosmology. Finally, we find the scatter and slope in the 𝜆 −𝑀 out scaling relation to be 0.49 ±0.02 and 0.38 ±0.09.

79 ASTRONOMY AND ASTROPHYSICS↗

Probing gravity with the DES-CMASS sample and BOSS spectroscopy

ABSTRACT The DES-CMASS sample (DMASS) is designed to optimally combine the weak lensing measurements from the Dark Energy Survey (DES) and redshift-space distortions (RSD) probed by the CMASS galaxy sample from the Baryonic Oscillation Spectroscopic Survey. In this paper, we demonstrate the feasibility of adopting DMASS as the equivalent of CMASS for a joint analysis of DES and BOSS in the framework of modified gravity. We utilize the angular clustering of the DMASS galaxies, cosmic shear of the DES metacalibration sources, and cross-correlation of the two as data vectors. By jointly fitting the combination of the data with the RSD measurements from the CMASS sample and Planck data, we obtain the constraints on modified gravity parameters $\mu _0=-0.37^{+0.47}_{-0.45}$ and $\Sigma _0=0.078^{+0.078}_{-0.082}$. Our constraints of modified gravity with DMASS are tighter than those with the DES Year 1 redMaGiC sample with the same external data sets by 29 per cent for μ0 and 21 per cent for Σ0, and comparable to the published results of the DES Year 1 modified gravity analysis despite this work using fewer external data sets. This improvement is mainly because the galaxy bias parameter is shared and more tightly constrained by both CMASS and DMASS, effectively breaking the degeneracy between the galaxy bias and other cosmological parameters. Such an approach to optimally combine photometric and spectroscopic surveys using a photometric sample equivalent to a spectroscopic sample can be applied to combining future surveys having a limited overlap such as DESI and LSST.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

CODEX weak lensing mass catalogue and implications on the mass–richness relation

The COnstrain Dark Energy with X-ray clusters (CODEX) sample contains the largest flux limited sample of X-ray clusters at 0.35 < z < 0.65. It was selected from ROSAT data in the 10 000 square degrees of overlap with BOSS, mapping a total number of 2770 high-z galaxy clusters. We present here the full results of the CFHT CODEX programme on cluster mass measurement, including a reanalysis of CFHTLS Wide data, with 25 individual lensing-constrained cluster masses. We employ lensfit shape measurement and perform a conservative colour–space selection and weighting of background galaxies. Using the combination of shape noise and an analytic covariance for intrinsic variations of cluster profiles at fixed mass due to large-scale structure, miscentring, and variations in concentration and ellipticity, we determine the likelihood of the observed shear signal as a function of true mass for each cluster. We combine 25 individual cluster mass likelihoods in a Bayesian hierarchical scheme with the inclusion of optical and X-ray selection functions to derive constraints on the slope α, normalization β, and scatter σln λ|μ of our richness–mass scaling relation model in log-space: ${\langle {\rm In}\,\, \lambda\!\!\mid\!\!\mu\rangle = \alpha\mu + \beta,} $ with μ = ln (M 200c /M piv ), and M piv = 10 14.81 M ⊙ . We find a slope $\alpha = 0.49^{+0.20}_{-0.15}$, normalization $\exp (\beta) = 84.0^{+9.2}_{-14.8}$, and $\sigma _{\ln \lambda | \mu } = 0.17^{+0.13}_{-0.09}$ using CFHT richness estimates. In comparison to other weak lensing richness–mass relations, we find the normalization of the richness statistically agreeing with the normalization of other scaling relations from a broad redshift range (0.0 < z < 0.65) and with different cluster selection (X-ray, Sunyaev–Zeldovich, and optical).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗