Preparing for low surface brightness science with the Vera C. Rubin Observatory: a comparison of observable and simulated intracluster light fractions

MNRAS 528, 771–795 (2024) https://doi.org/10.1093/mnras/stad3810 Advance Access publication 2023 December 12 Preparing for low surface brightness science with the Vera C. Rubin Obser v atory: a comparison of obser v able and simulated intracluster light fractions Sarah Brough , 1 ‹Syeda Lammim Ahad , 2 Yannick M. Bah ´ e , 2 , 3 , 4 Ama ¨ el Ellien, 5 Anthony H. Gonzalez , 6 Yolanda Jim ´ enez-Teja, 7 , 8 Lucas C. Kimmig, 9 Garreth Martin , 10 , 11 Cristina Mart ´ ınez-Lombilla , 1 Mireia Montes , 12 , 13 , 14 Annalisa Pillepich , 15 Rossella Ragusa, 16 , 17 Rhea-Silvia Remus, 9 Chris A. Collins, 18 Johan H. Knapen 12 , 13 and J. Christopher Mihos 19 Affiliations are listed at the end of the paper Accepted 2023 December 5. Received 2023 November 15; in original form 2023 July 28 A B S T R A C T Intracluster light (ICL) provides an important record of the interactions galaxy clusters have undergone. Ho we ver, we are limited in our understanding by our measurement methods. To address this, we measure the fraction of cluster light that is held in the Brightest Cluster Galaxy and ICL (BCG + ICL fraction) and the ICL alone (ICL fraction) using observational methods (surface brightness threshold-SB, non-parametric measure-NP, composite models-CM, and multi-galaxy fitting-MGF) and new approaches under development (wavelet decomposition-WD) applied to mock images of 61 galaxy clusters (14 < log 10 M 200 c /M  < 14.5) from four cosmological hydrodynamical simulations. We compare the BCG + ICL and ICL fractions from observational measures with those using simulated measures (aperture and kinematic separations). The ICL fractions measured by kinematic separation are significantly larger than observed fractions. We find the measurements are related and provide equations to estimate kinematic ICL fractions from observed fractions. The dif ferent observ ational techniques give consistent BCG + ICL and ICL fractions but are biased to underestimating the BCG + ICL and ICL fractions when compared with aperture simulation measures. Comparing the different methods and algorithms, we find that the MGF algorithm is most consistent with the simulations, and CM and SB methods sho w the smallest projection ef fects for the BCG + ICL and ICL fractions, respectively. The Ahad (CM), MGF, and WD algorithms are best set up to process larger samples; ho we ver, the WD algorithm in its current form is susceptible to projection effects. We recommend that new algorithms using these methods are explored to analyse the massive samples that Rubin Observatory’s Le gac y Surv e y of Space and Time will pro vide. Key words: Galaxies: clusters: general – Galaxies: evolution – Galaxies: haloes – Galaxies: photometry. 1 INTRODUCTION A diffuse collection of stars is observed to sprawl across the central regions of galaxy groups and clusters. This is the intracluster light (ICL), an important fossil record of all the interactions these systems have undergone. Therefore, a robust understanding of the ICL serves as a powerful probe of the evolution of cosmic structure and the build-up of the largest bound structures in the Universe. Its physical scale is similar to the scale of the dark matter in clusters, making the ICL an important potential luminous tracer of dark matter in these systems (e.g. Montes & Trujillo 2019 ; Deason et al. 2021 ; Montes & Trujillo 2022 ; Diego et al. 2023 ). The fraction of the cluster light that is held in the ICL (ICL fraction), and its dependence on cluster mass and redshift, are important tools in understanding how galaxies and clusters evolve. Ho we v er, there e xists a crucial problem with the use of ICL for  E-mail: [email protected] this science: the ambiguous observational definition of the ICL. The ICL is observed to be concentrated around the cluster’s massive central galaxy (Brightest Cluster Galaxy or BCG). Deep images of clusters of galaxies show that the transition between the BCG and the ICL happens smoothly with no clear break point. So, without any information about the kinematics of the stars, separating the ICL contribution from that of the BCG is challenging. Clusters also contain satellite galaxies which contribute their own diffuse light to the ICL. As a result, observ ers hav e dev eloped a range of techniques to measure the ICL fraction. These include the following: (i) The surface brightness (SB) threshold method (e.g. Feldmeier et al. 2004 ; Montes & Trujillo 2014 ; Presotto et al. 2014 ; Burke, Hilton & Collins 2015 ; Montes & Trujillo 2018 ; Furnell et al. 2021 ; Montes et al. 2021 ; Mart ´ ınez-Lombilla et al. 2023a ) considers all light below a certain SB threshold to be part of the ICL. While this method is simple to apply and does include light around satellite galaxies, it does not capture the ICL projected o v er the BCG and the satellite galaxies. In addition, observations with different depths lead ©The Author(s) 2023. Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( https:// creativecommons.org/ licenses/ by/ 4.0/ ), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 772 S. Brough et al. MNRAS 528, 771–795 (2024) to different ICL fractions, and observers use different photometric bands (due to the limited availability of deep images, or different redshifts) and different thresholds. Although this method is easy to apply, these caveats make it very difficult to compare results between studies. (ii) Non-parametric measure (NP; e.g. Gonzalez, Zaritsky & Zabludoff 2007 ; DeMaio et al. 2018 ; Mart ´ ınez-Lombilla et al. 2023a ) method measures the BCG + ICL fraction without making any assumption regarding the shape of the BCG or ICL distribution. This method does capture the ICL projected o v er the BCG and can potentially capture the diffuse light associated with satellite galaxies. (iii) The composite model (CM) method combines different empirical models, normally a double S ´ ersic model (Sersic 1968 ) or a S ´ ersic and an exponential (e.g. Gonzalez, Zabludoff & Zaritsky 2005 ; Seigar, Graham & Jerjen 2007 ; Presotto et al. 2014 ; Iodice et al. 2016 ; Spa v one et al. 2017 ; Montes & Trujillo 2018 ; Montes et al. 2021 ; Ragusa et al. 2021 ; Ahad, Bah ´ e & Hoekstra 2023 ; Joo & Jee 2023 ; Ragusa et al. 2023 ; Mart ´ ınez-Lombilla et al. 2023a ) to define and separate the BCG and the ICL. This method does capture the ICL projected o v er the BCG, but the choice of model parameters and the intrinsic difficulty of the problem means that this method can be v ery de generate (Janowiecki et al. 2010 ). It also fails to capture the diffuse light associated with satellite galaxies. (iv) Multi-galaxy fitting (MGF) methods model and remo v e all the galaxies in the image with either traditional analytical profiles (e.g. Giallongo et al. 2014 ; Morishita et al. 2017 ; Poliakov et al. 2021 ) or orthonormal mathematical bases (Jim ´ enez-Teja & Dupke 2016 ; Jim ´ enez-Teja et al. 2018 ). These methods, along with wavelet decomposition (WD), have the advantage of separating galaxies and ICL for the whole image, thereby accounting for all of the ICL present, including that around satellite galaxies and projected o v er all of the cluster galaxies. Additionally, they do not impose a priori assumptions on the physical properties of the ICL (e.g. SB, density, or morphology). (v) The WD method, similar to MGF, separates ICL from all galaxies in the cluster (e.g. Da Rocha & Mendes de Oliveira 2005 ; Guennou et al. 2012 ; Ellien et al. 2019 , 2021 ) using a multiscale approach, where the ICL is usually identified with the lowest frequency component. Similar to the MGF methods, WD also separates galaxies and ICL for the whole image, thereby accounting for all of the ICL present. Other methods to measure the ICL include the kinematic distribution of planetary nebulae or globular clusters (e.g. Arnaboldi et al. 1996 ; Alamo-Mart ´ ınez & Blakeslee 2017 ; Hartke et al. 2017 ; Madrid et al. 2018 ; Powalka et al. 2018 ; Harris et al. 2020 ; Hartke et al. 2022 ; Kluge et al. 2023 ), stacking integral field spectroscopic observations (Edwards et al. 2016 , 2020 ) as well as image stacking (e.g. Zibetti et al. 2005 ; Zhang et al. 2019 ; Sampaio-Santos et al. 2021 ; Chen et al. 2022 ; Golden-Marx et al. 2023 ). Ho we ver, these methods are not considered in this work because kinematic studies are only applicable to a few nearby clusters. Integral field spectroscopic observations are currently limited in sample size, and stacking analyses are only just starting to provide information on the scaling relationships with their host clusters (Zhang et al. 2023 ). Given the difficulty of separating the ICL from the BCG and other satellite galaxies in the cluster, some works instead measure the fraction of light held by the combination of the BCG and the ICL, arguing that it is not possible to accurately separate the two (or more) components (BCG + ICL; e.g. Gonzalez, Zaritsky & Zabludoff 2007 ; Presotto et al. 2014 ; Morishita et al. 2017 ; DeMaio et al. 2018 ; Zhang et al. 2019 ; Spa v one et al. 2020 ; Furnell et al. 2021 ; Kluge et al. 2021 ; Montes et al. 2021 ; Sampaio-Santos et al. 2021 ). When comparing the observed measurements that have been applied to date, they show significant scatter (e.g. Montes 2022 ). It is unclear whether this is physical in origin or due to observational differences (depth, photometric band, and measurement method) that are contributing to the scatter. For example, when using SB to measure the ICL, there is an observed trend of increasing ICL fraction with decreasing redshift (e.g. Burke, Hilton & Collins 2015 ; Montes 2022 ). Ho we ver, the CM method sho ws little e volution at z < 0.6 (Montes 2022 ). Kluge et al. ( 2021 ) compared several ways to separate BCG + ICL in their sample of 170 low redshift clusters: using an SB threshold, a luminosity threshold, a double S ´ ersic decomposition, and the excess light abo v e a de Vaucouleurs profile. They find mean ICL fractions that vary from 10 per cent to 20 per cent depending on the method used and a mean BCG + ICL fraction of 28 per cent. New, deep, wide-field surv e ys that will increase the samples available for the study of ICL by several orders of magnitude are imminent, e.g. The Vera C. Rubin Observatory’s Le gac y Surv e y of Space and Time (LSST; e.g. Montes 2019 ; Robertson et al. 2019 ; Brough et al. 2020 ) and the European Space Agency’s Euclid Wide Surv e y (Euclid Collaboration 2022a , b ). These promise to deliver the large samples needed to explore the ICL as a function of cluster mass, redshift, and dynamical state. Ho we ver, without a detailed analysis of the method by which observers and simulators measure ICL, its interpretation will remain ambiguous. Cosmological hydrodynamical simulations are ideal laboratories to explore and isolate the physical mechanisms that form the ICL. They can access the 6D information of each resolution element in the cluster. Ho we ver, isolating the ICL in simulations is also a complex problem. In simulations, the methods for quantifying the contribution of ICL include: aperture-based measures, identifying the ICL as all star particles in a certain radial range from the cluster centre (Pillepich et al. 2018b ); kinematic-based measures, separating the ICL on the basis of a double-Maxwellian fit to particle velocities (Dolag, Murante & Borgani 2010 ; Remus, Dolag & Hoffmann 2017 ) or Gaussian mixture models (Proctor et al. 2024 ); or using the full distribution of star particles in the 6D phase space (Ca ˜ nas et al. 2019 ). Several attempts have been made to address the issue of how to define the ICL. Rudick, Mihos & McBride ( 2011 ) used a suite of N -body simulations of six galaxy clusters (0.8 < M ×10 14 < 6.5) specifically tailored to studying ICL (Rudick et al. 2006 ) to measure the quantity of ICL found using a number of different methods from the literature (Binding Energy, Willman et al. 2004 ; Murante et al. 2007 ; Dolag et al. 2010 ; Threshold Density, Rudick et al. 2009 and SB threshold, Feldmeier et al. 2004 ; Mihos et al. 2005 ; Rudick et al. 2010 ). They found that techniques that define the ICL solely based on the current position of the cluster luminosity, such as an SB or local density threshold, tend to find less ICL than methods utilizing time or velocity information, including stellar particles’ density history or binding energy. They also found that separating the BCG from the surrounding ICL component was a challenge for all ICL techniques, and the differences in the measured ICL quantity between techniques were largely a consequence of the separation of the ICL light projected o v er the BCG. Rudick et al. ( 2011 ) measured a range of ICL fractions across all the clusters using any definition between 9 per cent and 36 per cent, and within a single cluster different methods changed the measured ICL fraction by up to a factor of 2. Cui et al. ( 2014 ) also compared a dynamical BCG + ICL and ICL fraction separation with an SB threshold in cosmological hydrodynamical simulations of 64 galaxy clusters with (13.5 Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 Measuring intracluster light 773 MNRAS 528, 771–795 (2024) < Log 10 M 500 /M < 15.2). They found that the dynamical method found higher ICL fractions than the SB method (55 per cent compared to 20–30 per cent). Tang et al. ( 2018 ) investigated the limitations of measuring ICL from optical imaging data using hydrodynamical simulations, testing the impact of the limitations optical images are subject to [e.g. image band, pixel size, SB limit, and point-spread function (PSF) size]. Here, we do not investigate the effect of varying these parameters and focus only on the question of measurement method. There have been advances in both simulations and observational techniques since the Rudick et al. ( 2011 ) and Cui et al. ( 2014 ) analyses. F or e xample, the Rudick et al. ( 2011 ) simulations have a large luminous particle mass of 1.4 ×10 6 M and did not include hydrodynamic evolution and so neglected certain aspects of galaxy and cluster evolution which may play a role in determining the spatial distribution of luminous material in the cluster. This included not being able to resolve galactic cores, and so they did not attempt to test CMs on their simulations. On the observational side, new methods based on theoretical data analysis considerations are being developed to provide new flexible approaches to ICL measurements, with more evolved MGF and WD techniques like the CICLE (MGF) and DAWIS (WD) algorithms applied here. To better facilitate future ICL investigations with the nextgeneration of facilities, we have assembled a cross-section of theorists and observers working on this topic to test the robustness and biases associated with different ICL measurement methods. These include theorists working with different simulations and observers who span the range of techniques currently employed for ICL analyses. The aim of the work presented here is to assess the different definitions of ICL in both observations and simulations, to determine their fidelity and enable robust comparisons between observations and simulations. We apply eight currently used observational BCG + ICL and ICL techniques to mock images of 61 galaxy clusters from four of the most widely used cosmological hydrodynamical simulations (Horizon-AGN, Dubois et al. 2014 ; Hydrangea, Bah ´ e et al. 2017 ; Magneticum, Dolag, Mevius & Remus 2017 ; and Illustris-TNG, Nelson et al. 2019 ). We then compare the results obtained with the observational methods with the amount of ICL predicted in the simulations. The layout of the paper is as follows: Section 2 describes the four simulations used in this analysis, the method used to create mock images for the observational analyses and the simulation-based measures of BCG and ICL applied to these simulations. Section 3 describes the eight different observation-based measures of BCG and ICL applied to the mock images. Section 4 presents our comparison of these different measures. We discuss our results in the context of recent research in Section 5 and draw our conclusions in Section 6 . Throughout this work, we assume the native cosmology of each of the simulations as described in Section 2 . 2 SIMULATIONS AND THEORETICAL QUANTITIES 2.1 Galaxy clusters from cosmological simulations In this study, we compare the outcome of a diverse range of methods intended to extract ICL properties from observed and simulated clusters of galaxies. We hence apply these methods to simulated clusters from a range of cosmological  CDM hydrodynamical simulations. By using simulated objects, instead of observed images, we can access all of the information content provided by the underlying simulation data and extract ICL properties as typically measured within the numerical and theoretical community. We aimed to target relaxed clusters with mass  10 14 M , namely haloes that are massive enough to have significant amounts of ICL, but not so massive that too few would be present in currently available cosmological simulations. For these, we require sufficiently good numerical resolution so that the diffuse stellar component of the ICL is properly sampled, i.e. with large numbers of stellar particles. We choose and analyse galaxy clusters from four different stateof-the-art hydrodynamical cosmological simulation suites: Magneticum, Horizon-AGN, Hydrangea, and Next-Generation Illustris (IllustrisTNG). These allow us to perform our ICL-focused comparisons by marginalizing o v er the possible effects of (1) different numerical methods to solve for the coupled equations of gravity and hydrodynamics, (2) different numerical mass and spatial resolutions, (3) different adopted cosmology assumptions, (4) different halo finders, and, chiefly, (5) different choices and implementations of the underlying galaxy-formation astrophysical models, such as feedback processes. The four different simulation suites have been described and used e xtensiv ely in the literature o v er the past few years: we summarize salient aspects of each of them in the following and in Table A1 . 2.1.1 Horizon-AGN Horizon-AGN (Dubois et al. 2014 ) is a cosmological-volume hydrodynamical simulation performed using RAMSES (Teyssier 2002 ), an adaptive-mesh refinement-based Eulerian hydrodynamics code. An initial 142 comoving Mpc-length box contains 1024 3 dark matter particles each with a mass of 8 ×10 7 M . An initially uniform 1024 3 cell gas grid is refined according to a quasi-Lagrangian criterion, with the smallest cell sizes fixed at 1 physical kpc. The implemented subgrid physics include the following processes: gas cooling via Hydrogen and Helium cooling with a contribution from metals down to 10 4 K (Sutherland & Dopita 1993 ); the star formation is modelled via a Schmidt law with standard 2 per cent ef ficiency (K ennicutt 1998 ) and feedback from Type II, Type Ia supernovae, and stellar winds. Black holes include a high-efficiency quasar mode with isotropic injection of thermal energy and a lowefficienc y r adio mode with c ylindrical bipolar outflows and jet velocity of 10 4 km s −1 following Omma et al. ( 2004 ). The stellar particles, i.e. the resolution elements that constitute the ICL, have a mass resolution of about 2 ×10 6 M . 2.1.2 Hydrangea Hydrangea (Bah ´ e et al. 2017 , see also Barnes et al. 2017 ) is a suite of 24 cosmological hydrodynamical zoom-in simulations of massive galaxy clusters using a variant of the EAGLE simulation mode (Schaye et al. 2015 ). Similar to Magneticum, the simulations are based on the SPH code GADGET-3 (Springel 2005 ). Sub-grid models are used for gas cooling, star formation, the associated mass and energy feedback, as well as the growth of and feedback from supermassive black holes (SMBHs). For details on their implementation, we refer the interested reader to Schaye et al. ( 2015 ) and Bah ´ e et al. ( 2017 ), but note here that particular care w as tak en to calibrate the efficienc y of superno va and black hole feedback to observations of stellar masses and sizes, as well as the gas content of group-scale haloes. As demonstrated by Bah ´ e et al. ( 2017 ) and Ahad et al. ( 2021 ), the predicted stellar mass function of satellite galaxies matches Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 774 S. Brough et al. MNRAS 528, 771–795 (2024) observations closely both in the local Universe and out to at least z ≈1.5. The total stellar mass within z ≈0 clusters is also realistic, although the BCGs are too massive by a factor of 2–3 compared to observations (Bah ´ e et al. 2017 ). The latter is not unique to Hydrangea; it is likely that it reflects shortcomings in the AGN feedback model that also lead to o v erly high gas fractions and central entropy cores as discussed by Barnes et al. ( 2017 , see also Oppenheimer et al. 2021 ). We note that the substructure identification used in Hydrangea includes an additional step that remo v es stars bound to satellites more rigorously than the standard SUBFIND algorithm (Bah ´ e et al., in preparation) and therefore tends to lead to a lower mass of stars associated with the BCG and ICL. 2.1.3 IllustrisTNG The IllustrisTNG 1 is a suite of cosmological magnetohydrodynamical (MHD) simulations of galaxies of three different comoving volumes each performed at varying resolution levels. The flagship runs of the series are called TNG100, TNG300, and TNG50, and in this paper, we make e xclusiv e use of the TNG100 run (Marinacci et al. 2018 ; Naiman et al. 2018 ; Nelson et al. 2018 ; Springel et al. 2018 ; Pillepich et al. 2018b ; Nelson et al. 2019 ). Tens of thousands of galaxies are therein evolved across a period-boundary box of 110 comoving Mpc aside and with stellar/gas particle resolution of 1 . 4 ×10 6 M , i.e. mass resolution similar to that of Hydrangea and Horizon-AGN (Table A1 ). In contrast to the other simulation suites of this paper, IllustrisTNG includes MHD. It is based on a moving-mesh code, AREPO (Springel 2010 ), which combines the benefits of both grid (as in Horizon-AGN) and lagrangian (as in Magneticum and Hydrangea) codes. Similar to the other simulation models, the IllustrisTNG simulations, and hence TNG100, are the results of a rich ensemble of coupled astrophysical processes acting across spatial and time-scales, including star formation, gas cooling and heating, stellar evolution and metal enrichment, feedback from stars and seeding, and growth and feedback from SMBHs. The details of the IllustrisTNG model are described by Weinberger et al. ( 2017 ) and Pillepich et al. ( 2018a ), and succinctly summarized and compared to the other suites in Table A1 . There are 280, 14, and 2 clusters more massive than 10 14 M in the TNG300, TNG100, and TNG50 volumes at z = 0, respectively. Their stellar mass content and their BCG and satellite populations have been extensively characterized and compared to observations by Pillepich et al. ( 2018b ) and by Joshi et al. ( 2020 ) in terms of morphological transformations, Pulsoni et al. ( 2020 , 2021 ) for their stellar kinematics, Donnari et al. ( 2021 ) in terms of quenched fractions. Of particular rele v ance for this work, Ardila et al. ( 2021 ) had shown, with an apples-to-apples comparison to deep Hyper Suprime-Cam (HSC) observations, that the outer stellar masses of TNG100 galaxies in ∼10 14 M haloes are consistent with weaklensing inferences to better than 0.12 dex. 2.1.4 Magneticum Magneticum Pathfinder 2 is a suite of fully hydrodynamical cosmological simulations co v ering a large range in simulation volumes and resolutions. All simulations were performed with an updated version of the TreePM-smoothed-particle hydrodynamics (SPH) 1 www.tng-project.org 2 www.magneticum.org code GADGET-3 based on GADGET-2 (Springel 2005 ). They also include updates to the SPH formulation with respect to the treatment of viscosity (Dolag et al. 2005 ; Beck et al. 2016 ), the SPH kernels (Donnert et al. 2013 ; Beck et al. 2016 ), and the thermal conductivity (Dolag et al. 2004 ). The implemented subgrid physics contains SMBH treatment and active galactic nuclei (AGNs) feedback (Fabjan et al. 2010 ; Hirschmann et al. 2014 ), star formation and metal enrichment from Supernovae Ia, Supernovae II and Asymptotic Giant Branch stars according to Tornatore et al. ( 2004 , 2007 ), as well as cooling processes coupled to the local metallicity following Wiersma, Schaye & Smith ( 2009 ); Dolag et al. ( 2017 ). Kinetic feedback from stellar winds is included according to Springel & Hernquist ( 2003 ). In this paper, we include galaxy clusters from two of the simulation volumes of the Magneticum suite: Box2b at the high resolution (HR) level, and Box4 at the ultra-high resolution (UHR) level. Box4 is a volume of (68 comoving Mpc ) 3 , with initially 2 ×576 3 particles at the UHR resolution level. The individual mass resolution is ∼ 2 . 6 ×10 6 M for stellar particles, with their gravitational softening being ∼1 kpc. Box2b has a volume of (909 comoving Mpc ) 3 , with 2 ×2880 3 particles at the HR resolution level: this corresponds to a mass resolution of ∼5 ×10 7 M for stellar particles and gravitational softening for the stellar component of ∼2.8 kpc. See papers abo v e for more details on the numerical resolution of all matter components. Note that for the Magneticum simulations, one gas particle can spawn up to four stellar particles, and thus the stellar particle mass quoted here is just the average stellar mass and can be substantially smaller than the initial gas particle mass. Both box v olumes ha ve been used to study galaxy and galaxy cluster properties in prior works, most notably for the study presented here are those on the ICL and BCG properties (Remus et al. 2017 ), early cluster and BCG formation (Remus, Dolag & Dannerbauer 2023 ), stellar halo properties (Remus & Forbes 2022 ), galaxy populations in galaxy clusters (Lotz et al. 2019 ), and substructure properties (Kimmig et al. 2023 ), as well as the general introductory papers on halo-to-stellar mass properties (Teklu et al. 2017 ) and AGN properties (e.g. Hirschmann et al. 2014 ). 2.2 Selection of simulated clusters From the simulations described abo v e, we select galaxy clusters at z = 0 in the halo mass range log 10 ( M 200c / M ) = [14 . 0 , 14 . 5], whereby M 200c denotes the mass enclosed within a spherical o v erdensity of 200 times the critical density. As the Magneticum Box4 simulation co v ers a small volume, it harbours only three galaxy clusters with masses larger than M crit ≥ 1 ×10 14 M , of which only one is relaxed as preferred for this study. The much larger Box2b , on the other hand, realizes more than 1000 clusters, from which we select 13 clusters with low total substructure masses, as this is a good indicator for relaxed galaxy clusters (e.g. Kimmig et al. 2023 ). We only explicitly apply a relaxedness criterion to the Magneticum systems and discuss the effects of this choice in Section 5.5 . We have indicated the Box4 cluster separately in the figures introducing the different simulations, to show that its properties are consistent with those of the other simulations which have a similar box size (Table A1 ). These cuts resulted in a final sample of 61 simulated clusters, with 9, 27, 11, and 14 clusters from Horizon-AGN, Hydrangea, TNG100, and the two boxes of Magneticum, respectively. Of the 61 clusters, 29 are relaxed by visual inspection. We analyse this sample throughout the following sections. Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 Measuring intracluster light 775 MNRAS 528, 771–795 (2024) 2.3 Finding structures and substructures To identify galaxies and satellite galaxies within the large cosmological simulated volumes, and thus to isolate the BCG and the ICL, haloes and subhaloes need to be located. For the Magneticum, Hydrangea, and IllustrisTNG runs, we use the output of the simulations based on the baryonic version of the SUBFIND halo finder (Dolag et al. 2009 , see also Springel, Yoshida & White 2001 ) to identify gravitationally bound (sub)structures. The versions of these halo finders used on the three aforementioned projects are not identical but are very similar. In contrast, Horizon-AGN uses the ADAPTAHOP halo finder (Tweed et al. 2009 ). The SUBFIND and ADAPTAHOP codes differ in terms of how they define particle membership to (sub)haloes: SUBFIND identifies substructures that are both locally o v erdense and gravitationally bound. In the initial step, haloes are identified through a Friends-of-Friends (FoF) algorithm. This is run on the dark matter particles only, with baryon particles assigned to the FoF halo (if any) of their nearest DM neighbour. Within each FoF halo, substructures are then identified by searching for local density peaks, now considering all types of resolution elements and particles. Different subhaloes are separated by saddle points in the density field, with each subhalo limited to particles within the isodensity contour passing through its limiting saddle point. An iterative unbinding procedure is then applied to each subhalo to remo v e an y particle/cell that is not gravitationally bound to it. Finally, all resolution elements not assigned to a substructure are considered as members of the central subhalo, after applying the same iterative unbinding process. This procedure is based on the kinetic (and for gas, internal) energy of each particle, and as such is not directly comparable to observationally feasible approaches. A noteworthy limitation of this approach is that by design any resolution element that lies beyond the limiting isodensity contour is ignored, even if it is in fact gravitationally bound to the subhalo (e.g. Muldrew, Pearce & Power 2011 ; Ca ˜ nas et al. 2019 ). ADAPTAHOP is a fully topological code that does not feature an unbinding procedure. Particles are first sorted into groups around peaks in the density field that are linked to other groups at saddle points. Each structure is then hierarchically divided into smaller groups in steps of increasing density. Haloes are defined as a groupof-groups linked by saddle points that exceed 160 times the mean dark matter density and groups within each halo are hierarchically regrouped so that each substructure has a smaller mass than the host (sub)structure. The absence of an unbinding procedure implies that different numbers of particles and resolution elements are associated to structures and substructures by ADAPTAHOP in comparison to SUBFIND , and hence to haloes versus subhaloes and galaxies versus satellites. These differences between (sub)halo finders are non-trivial. For example, different subhalo finders will clearly leave an impact on what it means to ‘excise’ the contribution of satellite galaxies from the mass of the BCG and of the ICL (e.g. Knebe et al. 2011 ). Ho we ver, they encompass what is typically done in the field by different research groups and thus provide us with yet another opportunity to account for possible systematic differences. Moreo v er, the remo val of the light/mass from satellites is also performed in a variety of ways observationally (Section 3 ). We hence proceed as is and comment on possible differences below. Finally, in the case of the Magneticum, Hydrangea, and IllustrisTNG simulations, the total cluster masses, defined throughout this paper based on M 200, crit , do not depend on the functioning of the SUBFIND and FoF algorithms. Namely, once an FoF halo and its centre are identified, the latter being the deepest point of the potential well, spherical-o v erdensity masses are measured accounting for all particles and resolution elements in the volume, irrespective of whether they belong to the FoF or SUBFIND structure. In the case of Horizon-AGN, the M 200, crit masses are based on the particles and resolution elements that are deemed by ADAPTAHOP to belong to a given halo. Based on the cluster centres found as described abo v e, we extract cubes around each halo with a side length of 4 Mpc that are used to generate the mock observations (Section 2.5 ). 2.4 Idealized, simulation-based measures of BCG and ICL For all galaxy clusters, we define a radius of 1 Mpc around the central galaxy (the BCG), comparable to the cluster virial radius at these cluster masses. The true total stellar mass within this sphere, including all satellite galaxies, is denoted M ∗, Tot . Furthermore, the stellar mass within this sphere that is not allocated to a satellite galaxy comprises both the BCG and the ICL, and we refer to this component as M BCG + ICL . We calculate the mass fraction of the BCG + ICL with respect to the whole stellar mass within this sphere as f BCG + ICL = M BCG + ICL / M ∗, Tot . The (simulated) mass fraction is different from the (observed) luminosity fraction and depends on how the mass-tolight ratio differs between the ICL and the galaxy populations. We explore this further in Section 5.1 . Separating the ICL from the BCG is more complicated than separating the substructures from the main body in simulations (as well as in observations), as a simple binding criterion is not sufficient to achieve this. Therefore, in this work, we compare two different methods which are applied to separate those components in simulations. These are described in the following. 2.4.1 Apertur e-based measur es A simple and robust method to define the ICL in simulations is to consider all star particles in a certain radial range from the cluster centre. In this approach, the (fixed) inner cut is used to separate the ICL from the BCG. As discussed by Pillepich et al. ( 2018b ), the choice of this radius ( r inner ) is somewhat ad-hoc, although commonly used observational definitions of the BCG extent (e.g. Petrosian or Kron radii) typically correspond to around 30–100 kpc. We therefore separately calculate ICL fractions with r inner = 30, 50, and 100 kpc in this study. These are 3D radii, i.e. spheres so the simulated ICL measurements are not made in projection. In each case, we only consider star particles associated with the main halo of the cluster, i.e. with all satellites excised. 3 2.4.2 Kinematic-based measures The stellar light of a galaxy cluster, after subtracting the substructures, has been shown to consist of two kinematically distinct components (e.g. Dressler 1979 ; Nelson et al. 2002 ; Bender et al. 2015 ; Longobardi et al. 2015 ). These two components have been found in simulated galaxy clusters as well, and have been associated to the inner BCG and the outer diffuse stellar component, or ICL (Dolag et al. 2010 ; Remus et al. 2017 ). The velocity component of a galaxy cluster can be described by a double-Maxwellian 3 This definition excludes ‘fuzz’ particles that are completely unbound from the cluster, but we have verified that such particles contribute 1 per cent to the ICL. Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 776 S. Brough et al. MNRAS 528, 771–795 (2024) distribution in 3D space, which in projection resembles a doubleGaussian distribution (see Remus et al. 2017 , for more details). Unfortunately, separating the ICL and BCG through this kinematic measure often does not resemble the radial separation found if a double-S ´ ersic profile is fit to the radial density distribution of the ICL and BGC component (Remus et al. 2017 ), indicating that the kinematic and spatial measures trace different aspects of the ICL and BCG and highlighting the need to define these two components self-consistently. 2.5 Mock images of simulated clusters One of the most robust methods for the comparison of simulations with observational data is through the analysis of synthetic ‘mock’ observations (e.g. Jonsson 2006 ; Naab et al. 2014 ; Choi et al. 2018 ; Camps & Baes 2020 ; Olsen et al. 2021 ), which enable us to measure quantities in the same way as we would observationally. In making these synthetic observations, we consider future idealized LSST-like images created using the method described in Martin et al. ( 2022 ). We summarize how we produce mock images for each of the clusters in our sample below. Mock images are produced for each cluster by extracting all star particles in a (4 Mpc) 3 cube centred around each BCG. The spectral energy distribution (SED) for each star particle is then calculated, based on its age and metallicity, from a grid of Bruzual & Charlot ( 2003 ) simple stellar population models assuming a Chabrier ( 2003 ) IMF. 4 Unlike Martin et al. ( 2022 ), we choose to neglect the effect of dust attenuation on the SED of each particle due to the different stellar evolution recipes, feedback schemes, and hydrodynamics codes employed by each simulation. This can have a strong effect on the diffusion and distribution of metals or dust and therefore the amount of attenuation. Additionally, since we focus on the ICL where very little dust should be present, modelling dust attenuation is only rele v ant for observational predictions for the flux of the member galaxies. The luminosity of each star particle is calculated by first summing the resultant luminosity of the attenuated SEDs once they have been redshifted to z = 0.05 and convolved with the LSST r -band transmission functions (Olivier, Seppala & Gilmore 2008 ). We employ an adaptive smoothing scheme in order to better represent the distribution of stellar mass in phase space and remo v e unrealistic variations between adjacent pixels. 5 We follow a similar procedure to the AD APTIVEBO X method employed by Merritt et al. ( 2020 ), by splitting each particle into 500 smaller particles which are then re-distributed in 3D according to a Gaussian distribution centred on the position of the original particle and with standard deviation set by the distance to the original particle’s 5th nearest neighbour. Finally, a 2D image is created by collapsing the particles along one of the axes and summing the flux across a 2D grid with elements of 0.2 ×0.2 arcsec 2 . For every cluster, we produce smoothed mock images in three projections ( xy , xz , and yz ). Each image is convolved with a PSF 6 and random Gaussian noise is added to simulate a predicted 4 As noted in Martin et al. ( 2022 ), different IMFs have close to equal effect on the brightness of the BCG and the ICL component so that the only qualitative impact on our results would be to increase or decrease the o v erall SB of the image. 5 The adaptive smoothing code used in this paper is available from github. com/ garrethmartin/ smooth3d 6 We use the g -band HSC (Miyazaki et al. 2012 ) 2D PSF measured by Montes et al. ( 2021 ) to 289 arcsec and extrapolated to 420 arcsec based on a powerlaw fit. The PSF FWHM is al w ays larger than the smoothing length in regions of interest (i.e. for the clusters). LSST 10-yr limiting SB of μr = 30.3 mag arcsec −2 (P. Yoachim, pri v ate communication). There is no variation in the noise level across the image and also choose to neglect other instrumental and astrophysical contaminants (e.g. foreground and background objects, Galactic cirrus, scattered light, ghosts, and diffraction spikes) which may be present in real imaging. Therefore, our results represent a best-case scenario for the various methods presented in this paper. Fig. 1 shows an example of an r -band smoothed mock image for one cluster from each simulation. In these images the lightest shade corresponds to a SB fainter than 30.3 mag arcsec −2 . 3 OBSERVATIONAL TECHNIQUES Deep images of clusters of galaxies show that the transition between the BCG and the ICL happens smoothly without a clear break point. Therefore, observ ers hav e had to devise techniques to study these components either together (BCG + ICL) or to separate them in order to study the ICL separately. In this section, we describe the eight observational algorithms to measure the BCG + ICL and/or ICL fraction of total cluster luminosity considered in this paper. These are presented grouped by the type of parent method: SB threshold in Section 3.1 , NP measures in Section 3.2 , CMs in Section 3.3 , MGF in Section 3.4 , and wavelet analysis in Section 3.5 . Each of these methods is carried out by different people, each of whom applies different pre-processing steps before they make the measurements. Therefore, in this work, we are testing complete image processing and analysis methods, not only different ICL methods, to determine how well the different groups’ measurements compare to one another. In order to calculate the BCG + ICL and ICL fractions as a function of the total cluster luminosity, the total luminosity of each cluster is measured by summing the luminosity in a circular aperture of radius R = 1 Mpc centred on the BCG. This outer radius was set to remo v e cluster radius as a potential source of uncertainty in the fraction measures. 3.1 Surface brightness threshold The easiest approach to separating the ICL from the galaxies in the cluster from an observational point of view is to use a SB threshold. This method defines all light below a certain SB threshold as the ICL. The method accounts for the contribution to the ICL from the outskirts of any of the cluster galaxies instead of only the BCG. Observations and simulations have shown that this method does a reasonable job in separating the BCG and the diffuse light (e.g. Feldmeier et al. 2004 ; Rudick et al. 2011 ; Cui et al. 2014 ) and that there are physical arguments for a SB threshold of μV = 26.5 mag arcsec −2 . Ho we ver, using this definition in observ ations is more complicated as the different SB depths of different images lead to different amounts of ICL being measured. It also misses the ICL projected o v er an y of the galaxies in the cluster. In this work, we have adopted a SB threshold of μr > 26 mag arcsec −2 . This method is denoted ‘SB Martinez-Lombilla’ and ‘Montes’ hereafter depending on the observer making the measurement (e.g. Montes et al. 2021 ; Mart ´ ınez-Lombilla et al. 2023a ). The ICL contribution is then the sum of the flux in all the pixels fainter than this threshold value and brighter than the SB limit of the mock images ( μr = 30.3 mag arcsec −2 ). Those pixels are within a circular aperture (Martinez-Lombilla) or elliptical (Montes) of R ∼1 Mpc centred on the BCG. The ellipticity of the aperture in the Montes method is based on the ellipticity of the BCG at large radius. The Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 Measuring intracluster light 777 MNRAS 528, 771–795 (2024) Figure 1. Log-scaled mock images of a random relaxed cluster from each simulation. Gaussian noise is added to each image to simulate a limiting SB μr = 30.3 mag arcsec −2 . Martinez-Lombilla method applied a 2x2 binning to the images (i.e. reduced the image size by 4, so the spatial resolution is 0.4 arcsec pixel −1 ) to ensure the analysis code ran in a reasonable time. 3.2 Non-parametric measures 3.2.1 1D non-parametric extraction In this method, denoted ‘Gonzalez’ hereafter, we follow the approach of DeMaio et al. ( 2018 ), which builds on Gonzalez, Zaritsky & Zabludoff ( 2007 ), in which the BCG + ICL SB is extracted in a series of logarithmically spaced circular annuli. As in DeMaio et al. ( 2018 ), the first step for this approach is to mask all detected galaxies in the image other than the BCG. 7 Cluster galaxies, which are detected with SEXTRACTOR , are masked with elliptical apertures extending out to three times the Kron radius. For each cluster, a few galaxies that lie close to the centroid of the BCG, and hence are not detected by SEXTRACTOR , are manually masked. Next, the median SB is calculated within logarithmically spaced annuli of width d log r = 0.15. The sky level is taken to be the median 7 In a few cases, two merging BCGs are each left unmasked. pixel value at r > 1.9 Mpc and this sk y lev el is subtracted from the profile level. While the simulations contain no sky contribution, this step was included to mimic true observations. The total flux within 1 Mpc is then calculated by integrating the SB in apertures extending out to this radius, using 1D interpolation to match the radial boundaries. To calculate the fractions, we sum the AUTO fluxes from SEXTRACTOR for all of the galaxies detected within the same 1 Mpc radius and take the ratio of these two fluxes. This approach makes no assumptions regarding the shape of the ICL profile, but because it relies on the median within annular apertures it may underestimate the total ICL if there are strong tidal features that are not well reflected in the median values. 3.2.2 2D non-parametric extraction In this method, denoted ‘Martinez-Lombilla’ hereafter, the BGC + ICL is directly measured from the mock images following the procedures described in Mart ´ ınez-Lombilla et al. ( 2023a ). This method consists of constructing a mask in which every source is mask ed, including f aint tidal tails of any kind, only allowing the BCG and ICL flux to remain. The mask is built from Python scripts using a threshold for detections of 1.1 σabo v e the image background level. Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 778 S. Brough et al. MNRAS 528, 771–795 (2024) Due to the wide variety of objects in the field, we use the ‘hot + cold’ masking method (e.g. Rix et al. 2004 ; Montes et al. 2021 ; Mart ´ ınezLombilla et al. 2023a , b ). As o v erlapping sources are frequently found in galaxy clusters (i.e. galaxy cluster members that o v erlap the ICL and the BCG), we unsharp-masked the original image prior to the application of the hot mask to increase the contrast. To unsharpmask, we convolved the image with a Gaussian filter (e.g. Montes et al. 2021 ; Mart ´ ınez-Lombilla et al. 2023a , b ) with σ= 5 pixels, and subtracted it from the original image. Finally, we radially increased all the masks as required by visual identification to a v oid including any source of faint light from the outskirts of the satellite galaxies in our BCG + ICL measurements. Then, we measure the BCG + ICL flux by summing the flux of the masked images within a circular aperture of R ∼1 Mpc around the BCG. We applied 2 ×2 binning to the images to speed up the analysis code. 3.3 Composite models The stellar envelope in the outer part of BCGs is observed to be an additional component to the single or double empirical model profiles (often S ´ ersic) that reproduce the inner regions of massive galaxies, as noted in several works (e.g. Gonzalez, Zaritsky & Zabludoff 2007 ; Seigar, Graham & Jerjen 2007 ; Donzelli, Muriel & Madrid 2011 ; Iodice et al. 2016 ; Spa v one et al. 2017 ; Ragusa et al. 2021 , 2022 ). The methods in this section include composites of multiple analytic models for light distribution of the BCG + ICL components. These methods account for the ICL projected o v er the BCG, but will fail to capture any component of ICL that is not symmetrically centred on the BCG. 3.3.1 1D de Vaucouleurs profile decomposition In this method, denoted ‘Ahad’ hereafter, we measure the fraction of light in the ICL component compared to the total cluster light within 1 Mpc radius using a single de Vaucouleurs profile fitting method as described in detail in Ahad, Bah ´ e & Hoekstra ( 2023 ). We first mask all the galaxies in the mock image except for the BCG by running SEXTRACTOR (Bertin & Arnouts 1996 ). The SEXTRACTOR segmentation maps are radially extended by 40 kpc before creating the masks to ensure that most parts of the diffuse light in the outskirts of satellite galaxies are excluded in our measurement. Then we measure the azimuthally averaged BCG + ICL SB profiles in logarithmic circular apertures centred on the BCG and fit the BCG light using a de Vaucouleurs profile. The BCG profile is then subtracted from the BCG + ICL profile to obtain the excess light at the outskirts, which we identify as the ICL and integrate out to the SB limit of the mock image (or 1 Mpc, whichever is smaller) to measure the total light in ICL. The total light in the BCG + ICL is measured by integrating the BCG + ICL SB profile out to the same SB limit as was used for the ICL, stated abo v e. The fraction of light in the BCG + ICL and ICL is obtained by dividing the total light in the corresponding components by the total cluster light within 1 Mpc radius, including the BCG, satellite galaxies, and the ICL component. 3.3.2 1D multicomponent decomposition In this method, denoted ‘Ragusa’ hereafter, we derive the total contribution of the faint outskirts of the BCG (stellar envelope plus ICL) as the integrated light from the transition radius ( R tr ) outwards by performing a 1D multicomponent decomposition of the BCG azimuthally averaged SB profiles, using 2 S ´ ersic profiles as described in detail in Ragusa et al. ( 2021 , 2022 , 2023 ). R tr is the distance from the galaxy centre where the contribution from the galaxy outskirts (i.e. stellar envelope plus diffuse light) starts to dominate the total light distribution. We model and subtract the BCGs in 2D (to their R tr ) from the mock images. We then carefully mask all the sources in the residual image (for the mock images these are just the cluster satellite galaxies) and then measure the ICL luminosity by fitting an e xponential la w to reproduce the diffuse ICL component and sum all the pixels beyond the transition radius. In order to derive the ICL fraction, we measure the total cluster luminosity by summing the contributions of all the satellite galaxies, the BCG up to its R tr and the ICL component. We also derived the BCG + ICL fraction, which is the luminosity of the ICL component plus that of the BCG up to its R tr . Although the mock images do not have a contribution from the observ ed sk y, the added noise must be taken into account given the low SB of the ICL. In studying observational data, it is crucial to a v oid edge effects in estimating residual background fluctuations. We estimate the average value of the background fluctuations by fitting the light in circular annuli of constant steps of 30 kpc between r = 1.7 and 1.9 Mpc, centred on the centre of the cluster, having carefully masked all the satellite galaxies. This average value, and its rms, are taken into account in all of the estimated values. 3.4 Multi-galaxy fitting The MGF methods model and remo v e all the galaxies in the image with either traditional analytical profiles (e.g. Giallongo et al. 2014 ; Morishita et al. 2017 ; Poliakov et al. 2021 ) or orthonormal mathematical bases (Jim ´ enez-Teja & Dupke 2016 ; Jim ´ enez-Teja et al. 2018 ). These methods separate galaxies and ICL for the whole image, thereby accounting for all of the ICL present, including that projected o v er g alaxies and around satellite g alaxies. 3.4.1 CICLE CHEFs Intracluster Light Estimator (CICLE; Jim ´ enez-Teja & Dupke 2016 ; Jim ´ enez-Teja et al. 2018 , 2019 , 2021 ; de Oliveira, Jim ´ enezTeja & Dupke 2022 ; Dupke et al. 2022 ; Jim ´ enez-Teja et al. 2023 ) is an algorithm that creates 2D models of the galaxies to disentangle them from the ICL. All galaxies are detected with SEXTRACTOR and fit using orthonormal mathematical bases composed by Chebyshev rational functions and Fourier series (CHEFs; Jim ´ enezTeja & Ben ´ ıtez 2012 ). The use of orthonormal bases guarantees that all morphologies – independently of the level of substructure, asymmetry, or irregularity –can be fit by the linear composition of the elements of the basis. The fact that Chebyshev polynomials do not tend to zero at the infinite end makes it possible to reco v er all the light from the extended wings of the galaxies. Additionally, Chebyshev polynomials are optimal to interpolate functions in their domain of definition, a property that is directly inherited by the CHEF bases. This means that CHEF models are built using a small number of components (typically, 10 CHEFs and 10 Fourier modes) and a higher number of elements is only needed if the galaxy is very large or shows a great level of detail. CHEF models are computed down to the noise level of the image or until the stellar haloes of the galaxies converge asymptotically, so it is straightforward to build models for all satellite galaxies in the cluster. Ho we ver, for the particular case of the BCG (and its extended halo, if it is present), CHEFs will model the galaxy and the ICL together, due to the spatial coincidence of Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 Measuring intracluster light 779 MNRAS 528, 771–795 (2024) the peak of the two surfaces in projection. Then, the limits of the BCG-dominated region are defined prior to the modelling, using a change in the curvature (the difference in the slope of the BCG + ICL composite surface) as the criterion to disentangle the BCG from the ICL. The fit is made in two-dimensions and does not make any prior assumption on the shape or possible symmetry of the ICL or the BCG. We obtain an ICL map by removing all CHEF models of the galaxies. If we just re-add the CHEF model of the BCG, we obtain the BCG + ICL map, with all satellite galaxies excised. Final ICL and BCG + ICL fractions are measured using these maps, estimating the flux within the fixed 1Mpc-radius aperture used in this work. This method is denoted ‘CICLE’ hereafter. The CICLE method applied a 2x2 binning to the images to speed up the processing. 3.5 Wavelet decomposition The WD method separates ICL from all galaxies in the cluster using a multiscale approach. Like MGF this method also separates galaxies and ICL for the whole image, thereby accounting for all of the ICL present. 3.5.1 DAWIS Detection Algorithm with Wavelets for Intracluster light Studies ( DAWIS ; Ellien et al. 2021 ) is a recent addition to a series of multiscale, wavelet-based algorithms optimized for low SB astronomy (Adami et al. 2005 ; Da Rocha & Mendes de Oliveira 2005 ; Da Rocha, Ziegler & Mendes de Oliveira 2008 ; Ellien et al. 2019 ). Such algorithms use wavelet representation (Slezak, Durret & Gerbal 1994 ; Starck, Fadili & Murtagh 2007 ) and multiresolution vision models (Bijaoui & Ru ´ e 1995 ) to (i) disentangle the signal associated with small details from large-scale variations in analysed images (ii) model the noise and detect sources down to very faint SB (iii) model the 2D light distribution of these sources. The no v elty of DAWIS compared to previous wavelet-based algorithms is its iterative approach: it only models a few sources at once, starting with the brightest, and remo v es them from the image. It then repeats the process until it converges on a residual map containing only noise. The sources detected and modelled in each iteration usually do not correspond to entire astrophysical objects, but rather to substructures. The information content is dissected into small pieces, denoted atoms. Since no astronomical prior is given to the algorithm, the nature of one atom alone is purely artificial and relies on how DAWIS estimates and captures significant signal in the wavelet space at each iteration. Ho we ver, it is possible by selecting these atoms to synthesize images of actual astrophysical objects. The most trivial synthesis is the sum of all atoms of an image, which provides a completely de-noised version of the astrophysical field. To select atoms, three properties of interest are: the wavelet scale z at which it has been detected by DAWIS , the size S of the detected atom, and the spatial position of its intensity maximum in the image. Different classification schemes are tested utilizing these three parameters: (i) The hard wavelet threshold method is denoted ‘DAWIS-W’ hereafter. This separates based on the wavelet scale of atoms alone, without any other prior. The idea behind such a criterion is that a wavelet transform is a series of convolutions with a dilated kernel of size 2 z pixels. Therefore, each wavelet scale z corresponds (roughly) to a characteristic size 2 z . It is assumed here that the characteristic extent of the ICL in astronomical images is much larger than the characteristic size of galaxies. Therefore, the atoms associated with galaxies are expected to be detected mainly at small wavelet scales, while the atoms associated with the ICL are expected to be detected mainly at large wavelet scales. A hard separation can be performed by setting a specific wavelet scale as threshold (an approach taken by Ellien et al. 2021 ). In this work, the threshold is set to the wavelet scale z = 6. Within this scheme, the BCG is treated similarly to the rest of the satellite galaxies, and the atoms are classified either as ‘galaxy’ or as ‘ICL’. Including spatial information as an extra step allows atoms to be classified as either ‘galaxy’ or ‘BCG + ICL’. This is done by inserting a constraint for atoms classified as galaxies, which must be outside a radius r BCG from the centre of the image (corresponding to the centre of the BCG). (ii) This size separation method is denoted ‘DAWIS-SS’ hereafter and uses the size of restored atoms as a separation criterion rather than the wavelet scale. While both approaches appear similar, they provide different results. This is due to the fact that the actual size of detected atoms does not increase linearly with the wavelet scale. In this scheme, atoms are classified either as ‘galaxy’ or ‘ICL’, and the BCG is also treated similarly to satellite galaxies, or, by including spatial information, atoms are classified into ‘galaxy’ and ‘BCG + ICL’. The atom size threshold used in this work to separate ICL from galaxies is 150 kpc. (iii) The mixture of a wavelet-based analysis and the SB threshold method (Section 3.1 ) is denoted ‘DAWIS-SB’ hereafter. All the atoms of the image are summed to synthesize the entire de-noised galaxy cluster field, to which the SB threshold is then applied. The main difference with the regular SB threshold is that all sources have been detected through wavelet analysis leading to different limiting depths. No separation is made between the BCG and the rest of the satellites for this method. The three schemes tested for this analysis are of an o v ersimplistic nature as they are based on arbitrary single-value criteria. It is unlikely that they correctly capture all of the morphological differences of a whole cluster sample. Ho we ver, this analysis provides a first glance of the performance of DAWIS and shows how it compares to other measurements. While more complex selections are possible, they are beyond the scope of this study. Note that in order to reduce computation time, the cluster images analysed by DAWIS were rebinned by a factor of 4. 4 RESULTS Here we consider the BCG + ICL and ICL fractions measured directly from the simulations and using the observers’ methods from the mock images. 4.1 Simulated BCG mass, BCG + ICL and ICL fractions The upper panel of Fig. 2 shows the simulated BCG + ICL mass compared to the cluster mass for each of the 61 simulated clusters across the 4 simulations. The middle panel of Fig. 2 shows the BCG + ICL fractions, i.e. M (BCG + ICL) /M ∗, Tot , measured directly from the simulations in an aperture of radius 0–1 Mpc. The simulated BCG + ICL mass increases with increasing cluster mass in the top panel, as e xpected giv en the underlying BCG-halo mass relationship (e.g. Brough et al. 2008 ; Lidman et al. 2012 ), but the simulated BCG + ICL fraction does not increase with cluster mass suggesting that the satellite galaxy contribution also increases o v er this cluster mass range. The simulated BCG + ICL fractions are given in Table 1 Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 786 S. Brough et al. MNRAS 528, 771–795 (2024) Figure 7. Simulated BCG + ICL (upper panel) and ICL fraction (lower panel) of mass as a function of the fraction of luminosity compared to the simulated BCG + ICL or ICL fraction of mass. The different simulations are indicated in the legend. compared to the ICL. To explore this question, the simulation cubes were re-made applying a mass-to-light ratio to the stellar particles to create luminosity-based simulation cubes using the simple stellar population models used to create the mock images. The simulators re-measured their BCG + ICL and ICL fractions on the luminosity cubes. Fig. 7 suggests that there are small, simulation-dependent offsets in the mass-light ratios. Table 1 gives the simulated ratios. (M BCG + ICL /M ∗, Tot )/(L BCG + ICL /L Tot ) ranges from ∼0.96 ±0.04 for Magneticum to 1.10 ±0.29 for Horizon-AGN. The simulated (M ICL /M ∗, Tot )/(L ICL /L Tot ) is generally larger than for the BCG + ICL fraction and ranges from ∼0.98 ±0.62 for Hydrangea to 1.39 ±0.34 for Horizon-AGN. The scatter around these ratios makes the values consistent with 1 and so this is not the cause of the systematic offsets observed between the observers and the simulators, rather it is an additional source of scatter in any comparison of simulated compared to observed BCG + ICL or ICL fractions. Comparing between observations and simulations is often a significant element of ICL analyses (e.g. Montes et al. 2021 ) and the different simulations apply different star formation models which produce different metallicities and ages for their stellar particles. This analysis gives an idea of the scatter that these differences potentially introduce to that comparison. 5.2 Projection effects The differences we observe between the observations and simulations could be a result of the different projections that observers are measuring their fractions o v er. Fig. 8 shows examples of the BCG + ICL (upper panel) and ICL (lower panel) fractions measured for four clusters, two with small (left-hand panels) and two with large (right-hand panels) standard deviations around the mean observed fractions over all the measurements. We calculate the ‘Projection Scatter’ of the fractions o v er the projections ( xy , xz , and zy ) measured for each cluster by each observer and scale this by the mean fraction calculated for that cluster by that observer, i.e. Projection Scatter = (Max frac, cluster −Min frac, cluster )/(2 ×Mean frac, cluster ). We calculate half of the maximum-minimum range rather than the standard deviation Figure 8. Observed BCG + ICL (upper panel) and ICL (lower panel) fractions for each projection ( xy , xz , and zy given by the legend) measured by each observer for clusters selected by the standard deviations around the mean observed fractions over all the measurements. The left-hand panels show clusters with small standard deviations (cluster 10 has mean BCG + ICL fraction 0.55 ±0.03, Mean Projection Scatter = 0.07; cluster 7 000 000 087 has mean ICL fraction 0.14 ±0.02, Mean Projection Scatter = 0.22). The right-hand panels show clusters with large standard deviations (cluster 157 has mean BCG + ICL fraction 0.56 ±0.08, Mean Projection Scatter = 0.21; cluster 2033 has mean ICL fraction 0.15 ±0.06, Mean Projection Scatter = 0.70). The cluster name and simulation are given in the top-left of each panel. The dashed lines give the simulated fractions (0–1 Mpc Aperture for the upper panels and 100 kpc–1 Mpc Aperture for the lower panels) and the solid lines illustrate the mean observed fraction over all methods). Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 Measuring intracluster light 787 MNRAS 528, 771–795 (2024) Figure 9. Mean projection scatter of BCG + ICL fraction (upper panel) and ICL fraction (lower panel) across the three different ( xy , xz , and zy ) simulation projections for each of the observed measurements. The error bars indicate the standard deviation. as not all clusters have measurements for all three projections for each observer. We then calculate the mean and standard deviation around that ‘Projection Scatter’ o v er all of the clusters measured by that observer. Fig. 9 shows the Mean Projection Scatter for the BCG + ICL (upper panel) and ICL fractions (lower panel) for each observational method. There is significant scatter in the observed fractions between the different projections. The mean values for the BCG + ICL fractions are given in Table 2 and range from 0.03 ±0.02 for Ragusa to 0.14 ±0.11 for DAWIS-W, with an o v erall mean of 0.08 ±0.08, i.e. an uncertainty from projection effects of 8 per cent. The lower panel of Fig. 9 shows that the scatter as a result of projection effects is more significant for the observed ICL fractions. This is a result of the ICL fractions in the denominator of the Projection Scatter being smaller. The mean values for the ICL fractions are given in Table 3 , with the differences ranging from 0.06 ±0.04 for SB Martinez-Lombilla to 0.22 ±0.15 for DAWISSS, and 0.13 ±0.11 o v erall, an uncertainty from projection effects on ICL fractions of 13 per cent. The differences in mean projection scatter between observers could be a result of their analysing different numbers of clusters (e.g. Fig. B1 ). We tested this by measuring the Projection Scatter for a smaller sample of clusters that have BCG + ICL fractions measured by at least 6 out of 7 observers (26 clusters) and ICL fractions measured by at least 7 out of 8 observers (28 clusters). We find that the Mean Projection Scatter changed by at most 0.01, well within the standard deviations of the measurements. This suggests that the number of clusters analysed does not play a significant role in the differences in mean projection scatter between observers. The observation-based analysis presented here often depends on the detection (and deblending) of the galaxies in the images. When observers were making their measurements, some found that some projections revealed galaxies (especially close to the BCG) that were unnoticed by SEXTRACTOR (or similar detection and/or deblending codes) in other projections. These undetected galaxies will play an important role in the final scatter displayed in Fig. 9 , as well as in the number of clusters with observed-simulated N > 0. Many of the techniques described here use SEXTRACTOR or similar to detect sources, so the ICL measurement problem is not only the separation of galaxy light from the ICL but sometimes also galaxy detection itself. Another projection effect with a strong impact on some measurements (most notably DAWIS) is the apparent morphology of the cluster. As clusters appear to have different shapes under different projections, the simple criteria separations applied by the different DAWIS techniques here are not able to cohesively capture the range of cluster shapes, which results in large measurement scatters. This analysis of the effects of projection shows that the randomness of projection effects produces larger uncertainties when trying to isolate the ICL than when isolating the BCG + ICL. The differences as a result of projection effects are consistent with the offsets between the observed and simulated measures for BCG + ICL fractions seen in Figs 3 but are not large enough to explain the offsets between the observed and simulated measures for the ICL fractions seen in Fig. 4 . Projection effects clearly provide a potential source of scatter in the observed measurements, but do not explain the systematic offsets. Rudick et al. ( 2011 ) also examined the effect of 9 different viewing angles on their ICL fractions. They found that their ICL fractions varied by ±0.02 on ICL fractions that ranged from 0.1 to 0.26. By our metric that is equi v alent to projection effects of 8–20 per cent, consistent with our findings of ∼13 per cent. It is interesting that we find a similar offset of Observed-Simulated BCG + ICL and ICL fractions for each of the observational methods compared to the simulations. This suggests that the inherent difference of measuring ICL in different projections is significantly larger than the measurement scatter. In essence, we find that it is important to consider projection in any comparison between observations and simulations as it has a significant impact. 5.3 Where does the BCG end, and where does the ICL start? One of the main questions when trying to define the ICL is where it starts to dominate. Without kinematic information available it is difficult to separate the BCG and the ICL to study the ICL and its e volution separately. Ho we v er, man y analyses hav e observ ed a change in the slope of the SB profile of the BCG + ICL, suggesting that the ICL starts to dominate at that point. The observed ICL fractions are more consistent with the simulated 100 kpc–1 Mpc aperture fractions than with the smaller inner apertures. Does this mean that the BCG-ICL transition is at 100 kpc for these clusters? Fig. 10 explores the radius at which the observers find the mock images to transition from BCG-dominated to ICLdominated. The radius is the mean across the measured simulated projections. We note that some of the measured radii extend to much larger radii than the transition radii that observers have measured from observations to date (e.g. ∼70–100 kpc, Montes et al. 2021 ). We do not observe a relationship of radius with cluster mass o v er this mass range. Table 4 gives the mean radii for each observer across the clusters they were able to measure. These mean radii vary from 89 ±31 kpc for DAWIS-SS to 161 ±37 kpc for DAWIS-W. The o v erall mean radius of 128 ±51 kpc is consistent with the 100 kpc inner radius applied by the simulators. Chen et al. ( 2022 ) investigated the BCG-ICL transition in a stacked image of 3000 clusters (0.2 < z < 0.3) in the SDSS gri bands, and Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 788 S. Brough et al. MNRAS 528, 771–795 (2024) Figure 10. The radius (kpc) at which observers find the light to transition from BCG-dominated to ICL-dominated –the radius is the mean across the different ( xy , xz , and zy ) projections in the simulations. The upper panel shows the radius as a function of cluster mass and the lower panel shows a histogram of each observer’s method. Table 4. Mean radius (kpc) at which observers find the mock images to transition from BCG-dominated to ICL-dominated. N is the number of clusters they were able to measure. Mean radii for each observer. Observer N Mean radius (kpc) SB Threshold SB Martinez-Lombilla 19 114 ±33 Montes 23 110 ±35 CM Ahad 50 137 ±70 Ragusa 34 136 ±44 MGF CICLE 18 151 ±15 WD DAWIS-SS 61 89 ±31 DAWIS-W 61 161 ±37 Mean 128 ±51 measured their BCG + ICL stellar surface mass profile down to 32 mag arcsec −2 in the r -band. They decomposed the profile into three components, an inner de Vaucouleurs’ profile, an outer ICL that follows the dark matter distribution measured from weak lensing, and a transitional component between 70 and 200 kpc that represents the excess component in the diffuse light that cannot be described by the sum of a de Vaucouleurs’ profile and an ICL mass profile that follows the dark matter. They found that the ratio of the transitional component to the total diffuse mass peaks around 100 kpc. This could explain why we find a mean transition radius of ∼128 kpc. Contini, Chen & Gu ( 2022 ) analysed their semi-analytic model to investigate the transition region between the BCG and the ICL. They defined this transition radius as the distance where the ICL accounts for 90 per cent of the total BCG + ICL mass. They found that the transition radius is independent of both BCG + ICL and halo mass and an average transition radius of 60 kpc, and as large as 100 kpc. Proctor et al. ( 2024 ) used Gaussian Mixture Models to separate the ICL component in EAGLE simulations. The y e xamined the transition radius where the ICL starts to dominate the stellar light, finding it to be ∼100 kpc for clusters of mass M 200 c ∼10 14 M , with a strong dependence on cluster mass. While a 100 kpc aperture radius is not physically moti v ated, it appears that it is a reasonable approximation if we are comparing simulations with observations, as the ICL fractions in observations resemble those of the 100 kpc aperture in simulations for clusters with M 200 c ∼10 14–14.5 M at z ∼0. 5.4 Converting between image-based and kinematic ICL fractions We explore how the image-based and kinematic ICL fractions are related in simulations and observations in Fig. 11 . Here, we use the notation f ICL, aperture, simulated and f ICL, image, observed to indicate the image-based ICL fractions (simulated 100 kpc–1 Mpc aperture and observed measures), and f ICL, kinematic, simulated to indicate the kinematic ICL fractions (simulated measures). The kinematic ICL component is measured by decomposing the velocity component of the simulated galaxy clusters in 3D space using a double-Maxwellian distribution (Remus et al. 2017 ), very different from the imagebased methods. The top row (panels a and b) of Fig. 11 shows the simulated measurements and the bottom row (panels c and d) the observed measurements, while the left-hand panels (a and c) show the relationships as a function of the kinematic ICL fraction and the righthand panels (b and d) show the relationship as a function of the imagebased ICL fractions. We find that the kinematic and image-based ICL fractions appear to be correlated in both the simulated and the observed measures. We calculate the Pearson correlation coefficients and find that the simulations relationships shown in Fig. 11 (panels a and b) have p-values of 0.038 and 1.2 ×10 −16 , respectively, and the observed relationships (panels c and d) p-values of 1.9 ×10 −12 and 6.4 ×10 −70 , respecti vely, sho wing that these are all significant correlations, with the exception of panel a which is only significant at a ∼2 σlevel. We note that the Magneticum simulations can be seen to lie off the distribution in panel a. We re-calculate the correlation coefficients excluding these data. Without the Magneticum data the simulations relationships (panels a and b) have p-values of 0.001 and 5.7 ×10 −6 , respectively, and the observed relationships (panels c and d) have p-values of 2.5 ×10 −16 and 8.9 ×10 −37 , respectively, i.e. all of these relationships correlate significant at a > 3 σlevel. Given that these relationships are significant, we are able to estimate the simulated kinematic ICL fraction from an observed, Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 Measuring intracluster light 789 MNRAS 528, 771–795 (2024) (a) (b) (c) (d) Figure 11. Relationship between ICL fractions measured by image-based and kinematic methods. Here, we use the notation f ICL, aperture, simulated and f ICL, image, observed to indicate the image-based ICL fractions (simulated 100 kpc–1 Mpc aperture and observed measures) and f ICL, kinematic, simulated to indicate the kinematic ICL fractions (simulated measures). The top row (panels a and b) shows the simulated measurements and the bottom row (panels c and d) the observed measurements while the left-hand panels (a and c) show the relationships as a function of the simulated kinematic ICL fraction and the right-hand panels (b and d) show the relationships as a function of the image-based ICL fraction (simulated in b and observed in d). Estimating image-based or kinematic ICL fractions on the basis of the other is possible using the straight-line fits to the observed measures shown by the solid lines in the lower panels and given in equations ( 1 ; left-hand panel) and ( 2 ; right-hand panel). image-based, ICL fraction and vice versa. To achieve this we fit a straight line to all of the observed data, finding the relationships given in equations ( 1 ) and ( 2 ), shown by the solid lines in panels c and d of Fig. 11 , respectively. The relationships described by equations ( 1 ) and ( 2 ) do not change beyond the uncertainties given when we re-fit them excluding the Magneticum data. f ICL , image , obs f ICL , kin , sim = ( −0 . 23 ±0 . 03) f ICL , kin , sim + (0 . 36 ±0 . 02) (1) f ICL , image , obs f ICL , kin , sim = (1 . 38 ±0 . 06) f ICL , image , obs + (0 . 033 ±0 . 009) (2) Re-arranging equation ( 1 ) allows estimation of an observed, imagebased, ICL fraction from the simulated kinematic ICL fraction and equation ( 2 ) enables the reverse, estimating the simulated kinematic ICL fraction from an observed, image-based, ICL fraction. Further understanding how image-based and kinematic measurements of BCG + ICL and ICL fractions relate to one another is a very interesting problem that we will explore in greater detail in a later paper. 5.5 Cluster relaxedness and BCG + ICL fraction As mentioned in Section 2.2 , the galaxy cluster sample from the large Magneticum simulation volume had to be selected in an automated fashion as there are too many galaxy clusters in the studied mass range to select them by hand. As the aim of this study is to test the separation of the ICL and BCG components, more relaxed clusters are generally preferable as they a v oid scatter from the presence of significant substructure. Therefore, we applied a selection criterion that is an excellent tracer for the degree of relaxation of a galaxy cluster, namely the mass fraction of the 8th most massive substructure, f 8 , with smaller values of f 8 denoting more relaxed clusters, because in a relaxed cluster the substructures are less prominent (see Kimmig et al. 2023 , for more details). Fig. 12 shows the simulated measurement of the BCG + ICL fraction relative to the total stellar mass of the galaxy cluster for the full sample of more than 1000 galaxy clusters from the Magneticum Box2b, as a function of their total halo mass M 200c , stacked and colour-coded according to the average f 8 within a bin. The BCG + ICL fractions of the full Magneticum sample are consistent with our Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 790 S. Brough et al. MNRAS 528, 771–795 (2024) Figure 12. The fraction of mass in BCG + ICL as compared to the total stellar mass within the virial radius, r vir , for all clusters of Box2b of the Magneticum Pathfinder simulation, coloured by the mass fraction of the eighth subhalo, f 8 . Clusters with smaller f 8 are more relax ed. Ov erlayed are the Magneticum clusters selected for this work (magenta diamonds), comprised primarily of v ery relax ed clusters. finding that there is no trend of the BCG + ICL fraction with cluster mass. Ho we ver, there is a clear trend for the BCG + ICL fraction to be higher for more relaxed galaxy clusters (up to 80 per cent, bluer symbols), and smaller for clusters that are currently assembling (down to 20 per cent, redder symbols). This might be expected, as more relaxed galaxy clusters have had more time to disrupt the accreted galaxies and add their stellar content to the BCG and/or the ICL. Note, ho we ver, that there is scatter in this relation so clusters that are currently assembling with large BCG + ICL fractions and vice versa also exist. The galaxy clusters selected for this study are shown as magenta diamonds in Fig. 12 . Most of the selected clusters are at the uppermost range of BCG + ICL fraction compared to the full galaxy cluster sample, as expected due to their selection as relaxed systems. This explains the origin of the large BCG + ICL fractions found for the Magneticum clusters in comparison to the other simulations included in this study, as seen in Fig. 2 . The middle panel of Fig. 2 also shows that the lowest BCG + ICL fraction found for the Magneticum sample marks the most relaxed cluster from Box4, which is still somewhat unrelaxed as the volume of the simulation is too small to harbour large relaxed clusters at z = 0. This system can be seen to be consistent with the BCG + ICL fractions for the other simulations which have similar box sizes (Table A1 ). As the BCG + ICL fraction for this cluster agrees well with similar clusters (in mass and relaxation) from the less resolved Magneticum simulation volume (Box2b), this provides confidence that any differences are not a result of the different simulation resolutions. To test whether the increased scatter added to the analysis by including the relaxed Magneticum clusters affects our ability to distinguish between different measurement methods, we repeated our analysis without those 14 systems. We found that the mean Observed-Simulated BCG + ICL fractions for each method reduced by at most 0.01, with no change in the standard deviation around those. The mean o v erall observ ed-simulated BCG + ICL fractions was −0.05 ±0.06 (a change from −0.06 ±0.06). The mean observed-simulated (100 kpc–1 Mpc aperture) ICL fractions for each method changed a little more with reductions of 0.01–0.02 in the fractions and 0.01–0.04 in the standard deviations. This resulted in a mean o v erall observ ed-simulated ICL fraction of −0.06 ±0.04 (a change from −0.09 ±0.07). While this did reduce the scatter for each method, all the measurement methods changed similarly, meaning that even when excluding the Magneticum clusters we find no evidence of an offset in measured BCG + ICL or ICL fraction as a result of the observational method employed. Given the impact of cluster relaxation on BCG + ICL and ICL fractions seen in Figs 2 and 12 , we will explore this question in more detail in a later paper. 5.6 On the scalability of the obser v ational methods How easy is it to apply each of these observational methods to large amounts of data, like that shortly to be available for the LSST (e.g. Montes 2019 ; Brough et al. 2020 ) and Euclid surv e ys (e.g. Euclid Collaboration et al. 2022a , b )? The SB threshold is the easiest and simplest method to apply and in this particular case, where there are no foreground stars or background galaxies, does not require masking. It does not assume a particular morphology for the ICL but the threshold itself can vary as a result of different photometric bands and redshifts, leading to different ICL fractions, making this a challenging method to compare between studies. The CM methods require masking of the data. This process often still requires manual intervention which leads to the lower number of clusters analysed using those methods presented here. Ho we ver, our analysis shows that these methods are among the most consistent with the simulations (considering the 100 kpc–1 Mpc aperture ICL fraction measure) and show a similar level of uncertainty from projection effects (6 (NP) and 4 per cent (CM) for BCG + ICL Fraction and 6 (SB) and 9 per cent (CM) for ICL fraction). The Ahad CM measure presented here has been designed to analyse large numbers of systems and does mask automatically (Ahad, Bah ´ e & Hoekstra 2023 ). We find it to give good fidelity compared to the simulation measures and a similar level of uncertainty with respect to projection effects. It does have a slightly larger standard deviation around the Mean Projection Scatter for ICL fraction, but that may be expected as we move to more automated measures. The CICLE MGF and DAWIS WD algorithms are easier to run on larger samples than any but the Ahad algorithm. We find the CICLE MGF algorithm provides fractions that are closest to the simulations (Tables 2 and 3 ), for both the BCG + ICL and the ICL fractions. Additionally, the impact of projection effects on CICLE is comparable to that of the NP and CM techniques. The DAWIS WD fractions have a similar low offset but more scatter compared to the simulation measures and we find a much higher level of uncertainty from projection effects with the current iteration of the algorithm used in this analysis. It is only very recently that we have had the prospect of enough ICL observations that ICL-measurement algorithms have needed to be scalable to large samples. This e x ercise shows that effort is still needed to make existing algorithms scalable and to tune new methods to have the fidelity of earlier methods. We will make a subset of these data publicly available to provide a standard dataset to check the fidelity of new BCG + ICL or ICL measurement algorithms as they are developed. 6 CONCLUSIONS We have applied eight currently used observational measures (SB threshold, NP measures, CMs, MGF, and WD) to mock images of 61 galaxy clusters from four of the most widely used cosmological Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 Measuring intracluster light 791 MNRAS 528, 771–795 (2024) hydrodynamical simulations (Horizon-AGN, Dubois et al. 2014 ; Hydrangea, Bah ´ e et al. 2017 ; Magneticum, Dolag et al. 2017 ; and Illustris-TNG, Nelson et al. 2019 ). We then compared the results obtained with the observational methods with the amount of ICL predicted in the simulations using five simulated measures (four aperture-based 0–1 Mpc, 30 kpc–1 Mpc, 50 kpc–1 Mpc, 100 kpc–1 Mpc, and one kinematic-based). From this analysis, we conclude the following. (i) On average, the different simulations give more or less consistent BCG + ICL (o v erall mean 0.58 ±0.14) and ICL (o v erall mean 0.38 ±0.16) fractions, with the exception of Magneticum whose higher fractions are shown to be a result of selecting very relaxed clusters from this simulation. (ii) The dif ferent observ ational techniques gi ve surprisingly consistent BCG + ICL (o v erall mean 0.51 ±0.12) and ICL (o v erall mean 0.13 ±0.05) fractions. The dif ferent observ ational techniques all tend to be biased to underestimate the BCG + ICL (mean difference −0.05 ±0.09) and ICL (mean difference −0.09 ±0.08, 100 kpc–1 Mpc aperture) fractions when compared with measurements from the simulations. We find that the simulated 100 kpc–1 Mpc aperture fraction is the most consistent with the observed ICL fractions, among all radii considered in this work. (iii) The values of the ICL fractions measured by kinematic separation are significantly larger than the observed fractions with an o v erall mean (observ ed-simulated) =−0.51 ±0.14. Such significant differences suggest that observers and simulators are measuring two very different quantities. We find that these measurements are related and offer fitted relations (equations 1 and 2 ) to enable observers to estimate kinematic ICL fractions from image-based measurements and vice versa. (iv) Exploring the reasons for the offsets in the observedsimulation fractions, we do not find a single source for the offset, but we do find several potential sources of increased measurement uncertainty: (1) The choice of cube size containing the cluster has a minor impact on measurement uncertainty. (2) The different simulations use different star formation models that give their stellar particles different ages and metallicities; this adds an additional source of scatter in any comparison of simulated compared to observed BCG + ICL or ICL fractions. (3) Projection effects are substantial in these measurements and cause uncertainties of 3–14 per cent (o v erall mean 0.08 ±0.08) for BCG + ICL fractions and 6–22 per cent for ICL fractions (o v erall mean 0.13 ±0.11). (v) We find a mean observed BCG-ICL transition radius of 128 ±51 kpc. Simulated ICL fractions measured by excising an inner radius of 100 kpc appear to be a reasonable approximation for the image-based ICL fraction in clusters with 10 14 −14 . 5 M at z ∼0 when compared with measurements from observations. Therefore, to separate the ICL and obtain a robust quantity for analysis, 100 kpc is the minimum inner radius that one would wish to use for such a separation. (vi) Comparing the different methods and algorithms, we note that measuring the combined BGC + ICL fraction has the least bias and scatter and is least affected by projection effects of all of the measures. The SB threshold, NP measure and CM methods are among the methods most consistent with the simulations and show the lowest impact from projection effects. Howev er, the y hav e some known issues, and only one of the algorithms tested here is set up for analysing larger samples ( N > 50) by masking automatically (Ahad, Bah ´ e & Hoekstra 2023 ). The CICLE MGF (Jim ´ enez-Teja & Dupke 2016 ) and DAWIS WD (Ellien et al. 2019 ) algorithms are better set up for analysing larger samples. CICLE is most consistent with the simulations and has projection effects that are comparable to the NP measure and CM methods. Ho we ver, the measured fractions from DAWIS have more scatter compared to the simulation measures and a higher level of uncertainty from projection effects in the algorithm’s current form. (vii) We recommend that new algorithms be explored based on these methods to respond to the influx of data from the next generation of imaging surv e ys like LSST and Euclid. To assist with this, we make a subset of these data publicly available to provide a standard data set to test new BCG + ICL or ICL measurement algorithms as they are developed. (viii) Due to the uncertainties we find induced by projection effects and the different ways of measuring BCG + ICL and ICL fractions, we suggest that authors do not constrain models with analyses of single clusters at low redshift. We also recommend that relationships examined using homogeneous samples and methods will be significantly more robust than more heterogeneous comparisons. The caveat to all of these conclusions is the effects of cluster mergers on these measurements. We also note that no observational bias has been taken into account in our analysis. We will explore these and related questions in future papers. ACKNOWLEDGEMENTS We thank the anonymous referee for their very constructive comments that have improved the final paper. SB acknowledges funding support from the Australian Research Council through a Disco v ery Project DP190101943. YB acknowledges funding from the Dutch Research Organisation (NWO) through Veni grant number 639.041.751 and financial support from the Swiss National Science Foundation (SNSF) under project 200021 213076. YJ-T acknowledges financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 898633, the MSCA IF Extensions Program of the Spanish National Research Council (CSIC), the State Agency for Research of the Spanish MCIU through the Center of Excellence Severo Ochoa award to the Instituto de Astrof ´ ısica de Andaluc ´ ıa (SEV2017-0709), and grant CEX2021-001131-S funded by MCIN/AEI/ 10.13039/501100011033. MM acknowledges the Project PCI2021122072-2B, financed by MICIN/AEI/10.13039/501100011033, and the European Union ‘NextGenerationEU’/RTRP and IAC project P/302302. This work used the DiRAC@Durham facility managed by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility ( www.dirac.ac.uk). The equipment was funded by BEIS capital funding via STFC capital grants ST/K00042X/1, ST/P002293/1, and ST/R002371/1, Durham University and STFC operations grant ST/S003908/1. DiRAC is part of the National eInfrastructure. LK acknowledges support by the COMPLEX project from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program grant agreement ERC-2019-AdG 882679. DATA AVAILABILITY The Horizon-AGN data used in this work can be obtained upon request from ht tps://www.horizon-simulation.org/dat a.ht ml . The Hydrangea simulation data are publicly available at https: //ft p.st rw.leidenuniv.nl/bahe/Hydrangea /. Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 792 S. 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Brough et al. MNRAS 528, 771–795 (2024) Table A1. Cosmological MHD simulations of massive clusters of galaxies adopted in this work. Here, we include only cosmological models, i.e. simulations that start from cosmologically moti v ated initial conditions on large spatial scales, which are run to z ∼0. These simulations differ in which they adopt not only different codes (smooth-particle hydrodynamics, adaptive-mesh refinement, meshless or moving mesh) but also different underlying galaxy formation models. All simulations include feedback from super-massive black holes, but with varying choices and implementations. IllustrisTNG includes MHD. Magneticum includes thermal conduction. Simulation project Hydrangea Horizon-AGN Magneticum IllustrisTNG Run(s) Hydrangea Zooms AGN Box4, Box2b TNG100 Code GADGET-3 RAMSES GADGET-3 AREPO Lo west av ailable redshift z = 0 z = 0 z = 0.2 z = 0 Box size (com Mpc) 3200 a 142 68, 909 111 Star-particle mass resolution (10 6 M ) 1.8 2.0 2.6, 50 1.4 # clusters with M 200c ≥10 14 M 24 14 3, 4268 14 # clusters analyzed in this paper b 27 14 1, 13 11  CDM cosmology Planck2014 WMAP7 WMAP7 Planck2015 Planck Collaboration ( 2014 ) Komatsu et al. ( 2011 ) Komatsu et al. ( 2011 ) Planck Collaboration ( 2016 ) Star formation density threshold density-threshold density-threshold density-threshold Stellar feedback: method direct ISM heating direct (momentum and energy) direct energy, temporary temporary hydro decoupling decoupled momentum Stellar feedback: timing stochastic,  T = 10 7.5 K continuous (winds + SNII + SNIa) † (continuous thermal, probabilistic continuous probabilistic, ∝ SFR winds) ∝ SNII, continuous thermal ∝ SNIa Stellar feedback: feedback thermal kinetic + thermal kinetic + thermal kinetic + thermal (warm) Stellar feedback: orientation random isotropic isotropic isotropic SMBH: seed mass (10 6 M ) 0.1 0.12, 0.45 1.2 SMBH: accretion Eddington/Bondi–Hoyle–Lyttleton Eddington/Bondi–Hoyle–Lyttleton Bondi–Hoyle SMBH feedback: mode(s) thermal thermal (high), kinetic (low) dual: radio/quasar mode ∗dual:high-state/low-state SMBH feedback: timing stochastic,  T = 10 9 K continuous contineous continuous/pulsated SMBH feedback: energy thermal thermal/kinetic thermal thermal/kinetic SMBH feedback: orientation random isotropic (high)/bipolar (low) isotropic isotropic Simulation/Method References Schaye et al. ( 2015 ) Dubois et al. ( 2014 ) Hirschmann et al. ( 2014 ) ♣ Bah ´ e et al. ( 2017 ) Teklu et al. ( 2015 ) a Here, the box size denotes the size of the parent box: Hydrangea comprises a number of so-called zoom-in simulations, with haloes identified and resimulated out of a large parent box. b For this paper, we focus on clusters in a narrow mass range, namely: log 10 ( M 200c / M ) = [14 . 0 , 14 . 5]. Additionally, in the case of the Magneticum run Box2b, we apply additional selection criteria based on relaxedness (see text for details). † SNII: (Girardi et al. 2000 ), winds: (Leitherer, Robert & Drissen 1992 ), SNIa: (Matteucci & Greggio 1986 ) ∗Fabjan et al. ( 2010 ) ♣ Marinacci et al. ( 2018 ); Naiman et al. ( 2018 ); Nelson et al. ( 2018 ); Springel et al. ( 2018 ); Pillepich et al. ( 2018b ); Nelson et al. ( 2019 ) APPENDIX B: FRACTIONS PER CLUSTER Fig. B1 shows the average of all the observed BCG + ICL (left) and ICL (right) fractions per cluster, as a function of cluster mass. The measurements are colour-coded by the number of individual observer measurements per cluster. This shows that the average fractions do not depend on the number of measurements included in the average. Downloaded from https://academic.oup.com/mnras/article/528/1/771/7471605 by Consejo Superior de Investigaciones Cientificas (Books) user on 19 November 2024 Measuring intracluster light 795 MNRAS 528, 771–795 (2024) Figure B1. The mean BCG + ICL (left-hand panel) and ICL (right-hand panel) fractions averaged over all measures as a function of cluster mass. The colours indicate the number of measurements made for each cluster. The error bars indicate the minimum and maximum fraction measured for each cluster. 1 School of Physics, University of New South Wales, NSW 2052, Australia 2 Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the Netherlands 3 Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique F ´ ed ´ erale de Lausanne (EPFL), Observatoire de Sauverny, CH-1290 Versoix, Switzerland 4 Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, UK 5 Anton Pannekoek Institute for Astronomy & GRAPPA, University of Amsterdam, Science Park 904, NL-1098 XH, Amsterdam, the Netherlands 6 Department of Astronomy, University of Florida, Gainesville, FL 32611, USA 7 Instituto de Astrof ´ ısica de Andaluc ´ ıa–CSIC, Glorieta de la Astronom ´ ıa s/n, E-18008 Granada, Spain 8 Observat ´ orio Nacional - MCTI (ON), Rua Gal. Jos ´ e Cristino 77, S ˜ ao Crist ´ ov ˜ ao, 20921-400, Rio de Janeiro, Brazil 9 Universit ¨ ats-Sternwarte M ¨ unc hen, Sc heinerstr 1, D-81679 M ¨ unc hen, Germany 10 Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Korea 11 Steward Observatory, University of Arizona, 933 N. Cherry A ve, T ucson, AZ 85719, USA 12 Instituto de Astrof ´ ısica de Canarias, c/ V ´ ıa L ´ actea s/n, E-38205 - La Laguna, Tenerife, Spain 13 Departamento de Astrof ´ ısica, Universidad de La Laguna, E-38205 - La La guna, Tenerife , Spain 14 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA 15 Max-Planck-Institut f ¨ ur Astronomie, K ¨ onigstuhl 17, D-69117 Heidelberg, Germany 16 INAF-Astronomical Observatory of Capodimonte, Salita Moiariello 16, I-80131 Naples, Italy 17 University of Naples ‘Federico II’, Via Cinthia 21, Naples I-80126, Italy 18 Astrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK 19 Department of Astronomy, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA This paper has been typeset from a T E X/L A T E X file prepared by the author. ©The Author(s) 2023. 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