arXiv subjects

R. L. C. Ogando

Publications and source records attributed to R. L. C. Ogando.

At least 109 records · Page 6Linked to original sources

arXiv2021

Dark Energy Survey Year 3 Results: Photometric Data Set for Cosmology

We describe the Dark Energy Survey (DES) photometric data set assembled from the first three years of science operations to support DES Year 3 cosmology analyses, and provide usage notes aimed at the broad astrophysics community. Y3 Gold improves on previous releases from DES, Y1 Gold and Data Release 1 (DES DR1), presenting an expanded and curated data set that incorporates algorithmic developments in image detrending and processing, photometric calibration, and object classification. Y3 Gold comprises nearly 5000 square degrees of grizY imaging in the south Galactic cap, including nearly 390 million objects, with depth reaching S/N ~ 10 for extended objects up to $i_{AB}\sim 23.0$, and top-of-the-atmosphere photometric uniformity $< 3$ mmag. Compared to DR1, photometric residuals with respect to Gaia are reduced by $50\%$, and per-object chromatic corrections are introduced. Y3 Gold augments DES DR1 with simultaneous fits to multi-epoch photometry for more robust galaxy color measurements and corresponding photometric redshift estimates. Y3 Gold features improved morphological star-galaxy classification with efficiency $>98\%$ and purity $>99\%$ for galaxies with $19 < i_{AB} < 22.5$. Additionally, it includes per-object quality information, and accompanying maps of the footprint coverage, masked regions, imaging depth, survey conditions, and astrophysical foregrounds that are used to select the cosmology analysis samples. This paper will be complemented by online resources.

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arXiv2021

The mass and galaxy distribution around SZ-selected clusters

We present measurements of the radial profiles of the mass and galaxy number density around Sunyaev-Zel'dovich-selected clusters using both weak lensing and galaxy counts. The clusters are selected from the Atacama Cosmology Telescope Data Release 5 and the galaxies from the Dark Energy Survey Year 3 dataset. With signal-to-noise of 62 (43) for galaxy (weak lensing) profiles over scales of about $0.2-20h^{-1}$ Mpc, these are the highest precision measurements for SZ-selected clusters to date. Because SZ selection closely approximates mass selection, these measurements enable several tests of theoretical models of the mass and light distribution around clusters. Our main findings are: 1. The splashback feature is detected at a consistent location in both the mass and galaxy profiles and its location is consistent with predictions of cold dark matter N-body simulations. 2. The full mass profile is also consistent with the simulations; hence it can constrain alternative dark matter models that modify the mass distribution of clusters. 3. The shapes of the galaxy and lensing profiles are remarkably similar for our sample over the entire range of scales, from well inside the cluster halo to the quasilinear regime. This can be used to constrain processes such as quenching and tidal disruption that alter the galaxy distribution inside the halo, and scale-dependent features in the transition regime outside the halo. We measure the dependence of the profile shapes on the galaxy sample, redshift and cluster mass. We extend the Diemer \& Kravtsov model for the cluster profiles to the linear regime using perturbation theory and show that it provides a good match to the measured profiles. We also compare the measured profiles to predictions of the standard halo model and simulations that include hydrodynamics. Applications of these results to cluster mass estimation and cosmology are discussed.

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arXiv2021

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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arXiv2021

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.

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arXiv2021

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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arXiv2021

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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arXiv2021

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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arXiv2021

Is diffuse intracluster light a good tracer of the galaxy cluster matter distribution?

We explore the relation between diffuse intracluster light (central galaxy included) and the galaxy cluster (baryonic and dark) matter distribution using a sample of 528 clusters at $0.2\leq z \leq 0.35$ found in the Dark Energy Survey (DES) Year 1 data. The surface brightness of the diffuse light shows an increasing dependence on cluster total mass at larger radius, and appears to be self-similar with a universal radial dependence after scaling by cluster radius. We also compare the diffuse light radial profiles to the cluster (baryonic and dark) matter distribution measured through weak lensing and find them to be comparable. The IllustrisTNG galaxy formation simulation, TNG300, offers further insight into the connection between diffuse stellar mass and cluster matter distributions -- the simulation radial profile of the diffuse stellar component does not have a similar slope with the total cluster matter content, although that of the cluster satellite galaxies does. Regardless of the radial trends, the amount of diffuse stellar mass has a low-scatter scaling relation with cluster's total mass in the simulation, out-performing the total stellar mass of cluster satellite galaxies. We conclude that there is no consistent evidence yet on whether or not diffuse light is a faithful radial tracer of the cluster matter distribution. Nevertheless, both observational and simulation results reveal that diffuse light is an excellent indicator of the cluster's total mass.

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arXiv2020

A statistical standard siren measurement of the Hubble constant from the LIGO/Virgo gravitational wave compact object merger GW190814 and Dark Energy Survey galaxies

We present a measurement of the Hubble constant $H_0$ using the gravitational wave (GW) event GW190814, which resulted from the coalescence of a 23 $M_\odot$ black hole with a 2.6 $M_\odot$ compact object, as a standard siren. No compelling electromagnetic counterpart has been identified for this event, thus our analysis accounts for thousands of potential host galaxies within a statistical framework. The redshift information is obtained from the photometric redshift (photo-$z$) catalog from the Dark Energy Survey. The luminosity distance is provided by the LIGO/Virgo gravitational wave sky map. Since this GW event has the second-smallest localization volume after GW170817, GW190814 is likely to provide the best constraint on cosmology from a single standard siren without identifying an electromagnetic counterpart. Our analysis uses photo-$z$ probability distribution functions and corrects for photo-$z$ biases. We also reanalyze the binary-black hole GW170814 within this updated framework. We explore how our findings impact the $H_0$ constraints from GW170817, the only GW merger associated with a unique host galaxy. From a combination of GW190814, GW170814 and GW170817, our analysis yields $H_0 = 72.0^{+ 12}_{- 8.2 }~{\rm km~s^{-1}~Mpc^{-1}}$ (68\% Highest Density Interval, HDI) for a prior in $H_0$ uniform between $[20,140]~{\rm km~s^{-1}~Mpc^{-1}}$. The addition of GW190814 and GW170814 to GW170817 improves the 68\% HDI from GW170817 alone by $\sim 18\%$, showing how well-localized mergers without counterparts can provide a significant contribution to standard siren measurements, provided that a complete galaxy catalog is available at the location of the event.

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arXiv2020

Shadows in the Dark: Low-Surface-Brightness Galaxies Discovered in the Dark Energy Survey

We present a catalog of 23,790 extended low-surface-brightness galaxies (LSBGs) identified in $\sim 5000 °^2$ from the first three years of imaging data from the Dark Energy Survey (DES). Based on a single-component Sérsic model fit, we define extended LSBGs as galaxies with $g$-band effective radii $R_{eff}(g) > 2.5''$ and mean surface brightness $\barμ_{eff}(g) > 24.2 \,mag ȧrcsec^{-2}$. We find that the distribution of LSBGs is strongly bimodal in $(g-r)$ vs.\ $(g-i$) color space. We divide our sample into red ($g-i \geq 0.60$) and blue ($g-i<0.60$) galaxies and study the properties of the two populations. Redder LSBGs are more clustered than their blue counterparts and are correlated with the distribution of nearby ($z < 0.10$) bright galaxies. Red LSBGs constitute $\sim 33\%$ of our LSBG sample, and $\sim 30\%$ of these are located within 1 deg of low-redshift galaxy groups and clusters (compared to $\sim 8\%$ of the blue LSBGs). For nine of the most prominent galaxy groups and clusters, we calculate the physical properties of associated LSBGs assuming a redshift derived from the host system. In these systems, we identify 41 objects that can be classified as ultra-diffuse galaxies, defined as LSBGs with projected physical effective radii $R_{eff} > 1.5 \,kpc$ and central surface brighthness $μ_0(g) > 24.0\, mag \,arcsec^{-2}$. The wide-area sample of LSBGs in DES can be used to test the role of environment on models of LSBG formation and evolution.

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arXiv2020

Dark Energy Survey Year 3 Results: Clustering Redshifts -- Calibration of the Weak Lensing Source Redshift Distributions with redMaGiC and BOSS/eBOSS

We present the calibration of the Dark Energy Survey Year 3 (DES Y3) weak lensing source galaxy redshift distributions $n(z)$ from clustering measurements. In particular, we cross-correlate the weak lensing (WL) source galaxies sample with redMaGiC galaxies (luminous red galaxies with secure photometric redshifts) and a spectroscopic sample from BOSS/eBOSS to estimate the redshift distribution of the DES sources sample. Two distinct methods for using the clustering statistics are described. The first uses the clustering information independently to estimate the mean redshift of the source galaxies within a redshift window, as done in the DES Y1 analysis. The second method establishes a likelihood of the clustering data as a function of $n(z)$, which can be incorporated into schemes for generating samples of $n(z)$ subject to combined clustering and photometric constraints. Both methods incorporate marginalisation over various astrophysical systematics, including magnification and redshift-dependent galaxy-matter bias. We characterise the uncertainties of the methods in simulations; the first method recovers the mean $z$ of tomographic bins to RMS (precision) of $\sim 0.014$. Use of the second method is shown to vastly improve the accuracy of the shape of $n(z)$ derived from photometric data. The two methods are then applied to the DES Y3 data.

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arXiv2020

Machine Learning for Searching the Dark Energy Survey for Trans-Neptunian Objects

In this paper we investigate how implementing machine learning could improve the efficiency of the search for Trans-Neptunian Objects (TNOs) within Dark Energy Survey (DES) data when used alongside orbit fitting. The discovery of multiple TNOs that appear to show a similarity in their orbital parameters has led to the suggestion that one or more undetected planets, an as yet undiscovered "Planet 9", may be present in the outer Solar System. DES is well placed to detect such a planet and has already been used to discover many other TNOs. Here, we perform tests on eight different supervised machine learning algorithms, using a dataset consisting of simulated TNOs buried within real DES noise data. We found that the best performing classifier was the Random Forest which, when optimised, performed well at detecting the rare objects. We achieve an area under the receiver operating characteristic (ROC) curve, (AUC) $= 0.996 \pm 0.001$. After optimizing the decision threshold of the Random Forest, we achieve a recall of 0.96 while maintaining a precision of 0.80. Finally, by using the optimized classifier to pre-select objects, we are able to run the orbit-fitting stage of our detection pipeline five times faster.

astro-ph.EP↗

arXiv2020

Reducing ground-based astrometric errors with Gaia and Gaussian processes

Stochastic field distortions caused by atmospheric turbulence are a fundamental limitation to the astrometric accuracy of ground-based imaging. This distortion field is measurable at the locations of stars with accurate positions provided by the Gaia DR2 catalog; we develop the use of Gaussian process regression (GPR) to interpolate the distortion field to arbitrary locations in each exposure. We introduce an extension to standard GPR techniques that exploits the knowledge that the 2-dimensional distortion field is curl-free. Applied to several hundred 90-second exposures from the Dark Energy Survey as a testbed, we find that the GPR correction reduces the variance of the turbulent distortions $\approx12\times$, on average, with better performance in denser regions of the Gaia catalog. The RMS per-coordinate distortion in the $riz$ bands is typically $\approx7$ mas before any correction, and $\approx2$ mas after application of the GPR model. The GPR astrometric corrections are validated by the observation that their use reduces, from 10 to 5 mas RMS, the residuals to an orbit fit to $riz$-band observations over 5 years of the $r=18.5$ trans-Neptunian object Eris. We also propose a GPR method, not yet implemented, for simultaneously estimating the turbulence fields and the 5-dimensional stellar solutions in a stack of overlapping exposures, which should yield further turbulence reductions in future deep surveys.

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arXiv2020

The impact of spectroscopic incompleteness in direct calibration of redshift distributions for weak lensing surveys

Obtaining accurate distributions of galaxy redshifts is a critical aspect of weak lensing cosmology experiments. One of the methods used to estimate and validate redshift distributions is apply weights to a spectroscopic sample so that their weighted photometry distribution matches the target sample. In this work we estimate the \textit{selection bias} in redshift that is introduced in this procedure. We do so by simulating the process of assembling a spectroscopic sample (including observer-assigned confidence flags) and highlight the impacts of spectroscopic target selection and redshift failures. We use the first year (Y1) weak lensing analysis in DES as an example data set but the implications generalise to all similar weak lensing surveys. We find that using colour cuts that are not available to the weak lensing galaxies can introduce biases of $Δ~z\sim0.015$ in the weighted mean redshift of different redshift intervals. To assess the impact of incompleteness in spectroscopic samples, we select only objects with high observer-defined confidence flags and compare the weighted mean redshift with the true mean. We find that the mean redshift of the DES Y1 weak lensing sample is typically biased at the $Δ~z=0.005-0.05$ level after the weighting is applied. The bias we uncover can have either sign, depending on the samples and redshift interval considered. For the highest redshift bin, the bias is larger than the uncertainties in the other DES Y1 redshift calibration methods, justifying the decision of not using this method for the redshift estimations. We discuss several methods to mitigate this bias.

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arXiv2020

Constraining Radio Mode Feedback in Galaxy Clusters with the Cluster Radio AGN Properties to z$\sim$1

We study the properties of the Sydney University Molonglo Sky Survey (SUMSS) 843~MHz radio AGN population in galaxy clusters from two large catalogs created using the Dark Energy Survey (DES): $\sim$11,800 optically selected RM-Y3 and $\sim$1,000 X-ray selected MARD-Y3 clusters. We show that cluster radio loud AGN are highly concentrated around cluster centers to $z\sim1$. We measure the halo occupation number for cluster radio AGN above a threshold luminosity, finding that the number of radio AGN per cluster increases with cluster halo mass as $N\propto M^{1.2\pm0.1}$ ($N\propto M^{0.68\pm0.34}$) for the RM-Y3 (MARD-Y3) sample. Together, these results indicate that radio mode feedback is favoured in more massive galaxy clusters. Using optical counterparts for these sources, we demonstrate weak redshift evolution in the host broad band colors and the radio luminosity at fixed host galaxy stellar mass. We use the redshift evolution in radio luminosity to break the degeneracy between density and luminosity evolution scenarios in the redshift trend of the radio AGN luminosity function (LF). The LF exhibits a redshift trend of the form $(1+z)^γ$ in density and luminosity, respectively, of $γ_{\rm D}=3.0\pm0.4$ and $γ_{\rm P}=0.21\pm0.15$ in the RM-Y3 sample, and $γ_{\rm D}=2.6\pm0.7$ and $γ_{\rm P}=0.31\pm0.15$ in MARD-Y3. We discuss the physical drivers of radio mode feedback in cluster AGN, and we use the cluster radio galaxy LF to estimate the average radio-mode feedback energy as a function of cluster mass and redshift and compare it to the core ($<0.1R_{500}$) X-ray radiative losses for clusters at $z<1$.

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arXiv2020

Testing the isotropy of the Dark Energy Survey's extreme trans-Neptunian objects

We test whether the population of "extreme" trans-Neptunian objects (eTNOs) detected in the Y4 Dark Energy Survey (DES) data exhibit azimuthal asymmetries which might be evidence of gravitational perturbations from an unseen super-Earth in a distant orbit. By rotating the orbits of the detected eTNOs, we construct a synthetic population which, when subject to the DES selection function, reproduces the detected distribution of eTNOs in the orbital elements $a,e,$ and $i$ as well as absolute magnitude $H$, but has uniform distributions in mean anomaly $M$, longitude of ascending node $Ω,$ and argument of perihelion $ω.$ We then compare the detected distributions in each of $Ω, ω,$ and $\varpi\equivΩ+ω$ to those expected from the isotropic population, using Kuiper's variant of the Kolmogorov-Smirnov test. The three angles are tested for each of 4 definitions of the eTNO population, choosing among $a>(150,250)$ AU and perihelion $q>(30,37)$ AU. These choices yield 3--7 eTNOs in the DES Y4 sample. Among the twelve total tests, two have the likelihood of drawing the observed angles from the isotropic population at $p<0.05.$ The 3 detections at $a>250, q>37$ AU, and the 4 detections at $a>250, q>30$ AU, have $Ω$ distribution with $p=0.03$ of coming from the isotropic construction, but this is not strong evidence of anisotropy given the 12 different tests. The DES data taken on their own are thus consistent with azimuthal isotropy and do not require a "Planet 9" hypothesis. The limited sky coverage and object count mean, however, that the DES data by no means falsify this hypothesis.

astro-ph.EP↗

arXiv2020

A DESGW Search for the Electromagnetic Counterpart to the LIGO/Virgo Gravitational Wave Binary Neutron Star Merger Candidate S190510g

We present the results from a search for the electromagnetic counterpart of the LIGO/Virgo event S190510g using the Dark Energy Camera (DECam). S190510g is a binary neutron star (BNS) merger candidate of moderate significance detected at a distance of 227$\pm$92 Mpc and localized within an area of 31 (1166) square degrees at 50\% (90\%) confidence. While this event was later classified as likely non-astrophysical in nature within 30 hours of the event, our short latency search and discovery pipeline identified 11 counterpart candidates, all of which appear consistent with supernovae following offline analysis and spectroscopy by other instruments. Later reprocessing of the images enabled the recovery of 6 more candidates. Additionally, we implement our candidate selection procedure on simulated kilonovae and supernovae under DECam observing conditions (e.g., seeing, exposure time) with the intent of quantifying our search efficiency and making informed decisions on observing strategy for future similar events. This is the first BNS counterpart search to employ a comprehensive simulation-based efficiency study. We find that using the current follow-up strategy, there would need to be 19 events similar to S190510g for us to have a 99\% chance of detecting an optical counterpart, assuming a GW170817-like kilonova. We further conclude that optimization of observing plans, which should include preference for deeper images over multiple color information, could result in up to a factor of 1.5 reduction in the total number of followups needed for discovery.

astro-ph.HE↗

arXiv2020

$μ_{\star}$ Masses: Weak Lensing Calibration of the Dark Energy Survey Year 1 redMaPPer Clusters using Stellar Masses

We present the weak lensing mass calibration of the stellar mass based $μ_{\star}$ mass proxy for redMaPPer galaxy clusters in the Dark Energy Survey Year 1. For the first time we are able to perform a calibration of $μ_{\star}$ at high redshifts, $z>0.33$. In a blinded analysis, we use $\sim 6,000$ clusters split into 12 subsets spanning the ranges $0.1 \leqslant z<0.65$ and $μ_{\star}$ up to $\sim 5.5 \times 10^{13} M_{\odot}$, and infer the average masses of these subsets through modelling of their stacked weak lensing signal. In our model we account for the following sources of systematic uncertainty: shear measurement and photometric redshift errors, miscentring, cluster-member contamination of the source sample, deviations from the NFW halo profile, halo triaxiality and projection effects. We use the inferred masses to estimate the joint mass--$μ_{\star}$--$z$ scaling relation given by $\langle M_{200c} | μ_{\star},z \rangle = M_0 (μ_{\star}/5.16\times 10^{12} \mathrm{M_{\odot}})^{F_{μ_{\star}}} ((1+z)/1.35)^{G_z}$. We find $M_0= (1.14 \pm 0.07) \times 10^{14} \mathrm{M_{\odot}}$ with $F_{μ_{\star}}= 0.76 \pm 0.06$ and $G_z= -1.14 \pm 0.37$. We discuss the use of $μ_{\star}$ as a complementary mass proxy to the well-studied richness $λ$ for: $i)$ exploring the regimes of low $z$, $λ<20$ and high $λ$, $z \sim 1$; $ii)$ testing systematics such as projection effects for applications in cluster cosmology.

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