Cosmic filaments in galaxy cluster outskirts: quantifying finding filaments in redshift space
Ulrike Kuchner, Alfonso Aragón-Salamanca, Agustín Rost, Frazer R. Pearce, Meghan E. Gray, Weiguang Cui, Alexander Knebe, Elena Rasia, Gustavo Yepes
MMNRAS , 1–12 (2021) Preprint 26 February 2021 Compiled using MNRAS L A TEX style file v3.0
Cosmic filaments in galaxy cluster outskirts: quantifying findingfilaments in redshift space
Ulrike Kuchner, ★ Alfonso Aragón-Salamanca, Agustín Rost, Frazer R. Pearce, Meghan E. Gray, Weiguang Cui, Alexander Knebe, , , Elena Rasia, , GustavoYepes , School of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, UK Instituto de Astronomía Teórica y Experimental (IATE), Laprida 854, Córdoba, Argentina Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ, United Kingdom Departamento de Física Teórica, Módulo 15, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain Centro de Investigación Avanzada en Física Fundamental (CIAFF), Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain International Centre for Radio Astronomy Research, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia Osservatorio Astronomico di Trieste, Istituto Nazionale di Astrofisica, Via Tiepolo, 11, I-34131 Trieste, Italy Institute for Fundamental, Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
Accepted 2021 February 22. Received 2021 February 05; in original form 2020 September 02
ABSTRACT
Inferring line-of-sight distances from redshifts in and around galaxy clusters is complicatedby peculiar velocities, a phenomenon known as the "Fingers of God" (FoG). This presents asignificant challenge for finding filaments in large observational data sets as these artificialelongations can be wrongly identified as cosmic web filaments by extraction algorithms. Up-coming targeted wide-field spectroscopic surveys of galaxy clusters and their infall regionssuch as the WEAVE Wide-Field Cluster Survey motivate our investigation of the impact ofFoG on finding filaments connected to clusters. Using zoom-in resimulations of 324 massivegalaxy clusters and their outskirts from The ThreeHundred project, we test methods typi-cally applied to large-scale spectroscopic data sets. This paper describes our investigation ofwhether a statistical compression of the FoG of cluster centres and galaxy groups can lead tocorrect filament extractions in the cluster outskirts. We find that within 5 𝑅 ( ∼ ℎ − Mpc)statistically correcting for FoG elongations of virialized regions does not achieve reliablefilament networks compared to reference filament networks based on true positions. This isdue to the complex flowing motions of galaxies towards filaments in addition to the clusterinfall, which overwhelm the signal of the filaments relative to the volume we probe. Whileinformation from spectroscopic redshifts is still important to isolate the cluster regions, andthereby reduce background and foreground interlopers, we expect future spectroscopic surveysof galaxy cluster outskirts to rely on 2D positions of galaxies to extract cosmic filaments.
Key words: large-scale structure of Universe – galaxies: clusters: general – galaxies: distances and redshifts– cosmology: observations – methods: data analysis – methods: observational
The present day Universe is pervaded by a network of filaments thatconnect groups and clusters brimming with galaxies. In standardcosmology, this highly anisotropic distribution of matter on largescales is the natural consequence of a hierarchical assembly underthe effect of gravity. The structure develops from the anisotropicgravitational collapse of initial density perturbations (Zel’dovich1970; Bond et al. 1996) building the backbone of the cosmic web. ★ E-mail: [email protected] (UK)
The contrast of the Universe increases with time as rich overden-sities grow in mass and density at the intersection of filamentswhile contracting in physical size. This is the environment in whichgalaxy clusters form, grow and continue to grow as ultimate man-ifestations of hierarchical structure formation through a series ofmergers and accretion from the cosmic web. Comparatively emptyvoids expand accordingly, growing to dominate the overall volumein the Universe. In the Zel’dovich approximation, anisotropic col-lapse has a well-defined sequence, whereby regions first compressto form walls, then filaments, before finally collapsing along eachdirection to form clusters (Lin et al. 1965; Arnold et al. 1982; Shan- © a r X i v : . [ a s t r o - ph . C O ] F e b U. Kuchner et al.
Figure 1.
The ideal case in which the filament extraction is based on knowledge of three dimensional positions (left panel) is not accessible through observations.Instead, significant redshift distortions that increase towards the centre of the cluster complicate the extraction of filaments around clusters. Left: true 3Dpositions of mock galaxies from The ThreeHundred project tailored to WEAVE observations with the reference filament network in black extracted usingthe DisPerSE software. Right: redshift distorted galaxy distribution with filaments using identical extraction steps for illustration. The black symbol indicatesthe position of an observer. The blue mesh shows a sphere of 5 𝑅 radius, equivalent to roughly 15 ℎ − Mpc, centred on the main halo of the cluster. Halospositioned inside this sphere are plotted with larger symbols. darin & Klypin 1984; Shandarin & Zeldovich 1989; Hidding et al.2013; Cautun et al. 2012). This general view of structure forma-tion is strengthened by comparing results from numerical simula-tions that have implemented Λ CDM cosmological models (Bond& Szalay 1983; Doroshkevich & Khlopov 1984) to observations.In a series of successes, ever improving cosmological simulations(e.g., Springel & Hernquist 2005; Klypin et al. 2011; Vogelsbergeret al. 2014) have been able to describe the formation and evolutionof large-scale structures that largely match the observed Universefrom galaxy surveys on comparable scales (e.g., de Lapparent et al.1986; Colless et al. 2001; Alpaslan et al. 2013).Today, the majority of mass relative to the volume occupied inthe Universe lies in the small regions of clusters and groups (Tempelet al. 2014; Cautun et al. 2012; Ganeshaiah Veena et al. 2019). Morespecifically, X-ray observations of the hot intracluster medium havelocated the bulk of gas to just beyond their virial radius and, impor-tantly, within the filaments that connect clusters to the cosmic web(see Walker et al. 2019, for a recent summary). Consequently, cos-mic filaments are fundamental in transporting both dark matter andbaryonic matter into clusters (Cautun et al. 2012; Kraljic et al. 2018).The outskirts of galaxy clusters are thus areas of increasing interestfor both cosmology and astrophysics. Cosmological simulations ofgalaxy cluster formation depict cluster outskirts as the playing fieldfor large-scale structure formation as it happens: the rich, thermal,kinematic and chemical content of merging sub-clusters, infallinggroups, clumps of gas and gas trapped in collapsed dark matter ha-los funnelled through cold filamentary streams are part of yet-to-beexplored accretion physics (Dekel et al. 2009; Danovich et al. 2012;Welker et al. 2019; Walker et al. 2019).Mapping cluster outskirts and identifying cosmic filamentsconnected to clusters, however, is not a trivial task, since the cosmicweb comprises a wide range of scales and densities that lead to a plethora of spatial patterns and morphologies. Filaments connectedto clusters are only one aspect of a complex multiscale picture thatencompasses thick filaments as well as thin tendrils on scales ofa few Mpc up to 100 Mpc and more, as well as sheetlike mem-branes easily mistaken as filaments in projection. The last decadehas seen a number of excellent methods to identify and classifyfeatures of the cosmic web (e.g., Aragón-Calvo et al. 2007; Sousbie2011; Cautun et al. 2012; Courtois et al. 2013; Tempel et al. 2014;Falck & Neyrinck 2015), each designed to tackle specific problemsto be applied to different kinds of data and thus disagreements areunderstandable and well documented (e.g., Libeskind et al. 2017;Rost et al. 2020b). Structure finding methods are successfully beingapplied to simulated and observed datasets alike, including photo-metric and spectroscopic surveys such as SDSS (Tempel et al. 2013;Kuutma et al. 2017; Chen et al. 2016; Malavasi et al. 2020), COS-MOS (Darvish et al. 2017; Laigle et al. 2017) and GAMA (Kraljicet al. 2018; Welker et al. 2019) amongst others (Malavasi et al.2016; Sarron et al. 2019; Santiago-Bautista et al. 2020). The maingoal of many of these studies is to investigate galaxy properties suchas mass, colour, morphology and gas content, and, increasingly so,alignments and spin orientation with respect to cosmic filaments.The interest is based on the well established finding that almostevery observable property of galaxies correlates with both galaxymass and galaxy environment, where environment can be definedin various ways, e.g., through local densities, as clusters vs. field, orcosmic web features. Determining and understanding the interplayof the physical processes behind this finding remains a fundamentalchallenge in understanding galaxy formation and evolution. The dif-ficulty lies in disentangling subtle competing processes that act ondifferent timescales (e.g., AGN feedback; Croton et al. 2006), withdifferent mass (e.g., starvation of gas supply; Larson et al. 1980),and environmental dependence (e.g., ram-pressure stripping; Gunn
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MNRAS000 , 1–12 (2021) inding filaments in redshift space & Gott 1972). In general, large-scale environmental effects are typ-ically found to be small compared to mass- and local density drivenprocesses and thus need to be controlled carefully for both stellarmass (e.g., Baldry et al. 2006), and environment (e.g., Peng et al.2010) if progress is to be made.In practice, defining and controlling for environment is notstraightforward due to different definitions, detection methods andtreatments, and could be the cause for some perceived disparityof reported results and interpretations (see Libeskind et al. 2017,for a detailed discussion). While modern hydrodynamical cosmo-logical simulations are imperative to provide a census, bridgingbetween simulations and observations requires the full understand-ing of the performance of observations in realistic setups. This paperrepresents a sequel to a paper devoted to the problem of mappingand characterizing filaments around galaxy clusters (Kuchner et al.2020, from here on Paper I). In Paper I, we used simulations todiscuss strategies and forecasts for observations. We presented testsof a filament extraction method on gas and mock galaxies, as well ascomparisons between detections in projected 2D and 3D positions.In the current paper, we take this one step further and consider find-ing filaments in observed redshift space. We focus on the specificchallenge of finding filaments around clusters based on an observedthree-dimensional distribution of mock galaxies. In observations of bound structures like galaxy groups and clusters,observed positions along the line of sight get distorted and elongateddue to peculiar velocities leading to inaccurate distance measure-ments. In addition, the amplitude of redshift space distortions differsdepending on the galaxy type and redshift (Coil 2013). Ultimately,this makes exploring the effects operating near and beyond the virialradii of galaxy clusters a challenging task.The phenomenon dubbed the “Fingers of God” (FoG, Tully &Fisher 1978) can be explained by considering that galaxies within avirialized structure at scales of ∼ ∼ ∼ ℎ − Mpc in each direction(Fig. 1). Distortions arise also on scales larger than ∼ .While redshift space distortions are useful tools to reveal theunderlying matter density and motions of galaxies, they complicatethe extraction of filaments and hamper a measurement of the two-point correlation function in real space (Coil 2013). In our attemptto prepare for upcoming spectroscopic surveys of galaxy clustersand their outskirts such as the WEAVE Wide-Field Cluster Survey(WWFCS, Kuchner et al. in prep), we therefore need to investigatehow peculiar velocities will impact the filament extraction.In the past, observers extracting the filaments of the cosmicweb on large scales have either corrected for this effect statisticallyby compressing or truncating the FoG, before extracting filamentsin 3D – as was successfully demonstrated on very large scales (e.g.,Tegmark et al. 2004; Jones et al. 2010; Kraljic et al. 2017, using theSDSS and GAMA surveys), and on super-cluster scales (Santiago-Bautista et al. 2020, using the SDSS survey) – or reassigned filamentsegments with an excess of alignment (Welker et al. 2019, also us-ing GAMA survey data). Alternatively, authors have resorted toextracting filaments based on a 2D projection of galaxies located inappropriate slices based on photometric redshifts, as was done bye.g., Laigle et al. (2017); Sarron et al. (2019). Observers are there-fore confronted with a choice: use the full 3D information includingredshifts (and potentially correct for the FoG effect), or use a 2D pro-jection. In Paper I, we have shown that the latter is a suitable optionto finding filaments in cluster outskirts, if spectroscopic redshiftsare provided to confine the cluster outskirt volume. By comparingfilament extractions based on simulations of cluster volumes, wedemonstrated that 2D filaments closely match their projected 3Dcounterparts. The goal of the current paper is to quantify the effectof redshift space distortions on filament finding and test whether aradial compression of cluster centres and groups in cluster outskirtspresents an improvement on the 2D filament extraction discussed inPaper I. As in Paper I, we use 324 simulations centered on massive galaxyclusters including their immediate surroundings out to a radius of15 ℎ − Mpc from The ThreeHundred project (Cui et al. 2018).Briefly, the cluster simulations are zoom-in resimulations of the 324most massive clusters at 𝑧 = Ω M = . , Ω B = . , Ω Λ = . , ℎ = . , 𝜎 = . 𝑛 𝑠 = .
96 (Ade et al. 2016)) . To achieve this, all particles withina sphere with radius of 15 ℎ − Mpc from the cluster centre at 𝑧 = We followed the method described in Paper I, where we use halos withmasses 𝑀 halo > × ℎ − M (cid:12) as tracers of filaments, extracted withDisPerSE using a persistence threshold 𝜎 = . https://the300-project.orgMNRAS , 1–12 (2021) U. Kuchner et al. the TREEPM+SPH code Gadget-X (Beck et al. 2015; Rasia et al.2015) with full physics galaxy formation modules. A more detaileddescription of the simulations is available in Cui et al. (2018).In Paper I, we introduced a sample of mock galaxies that wasinspired by upcoming surveys of galaxy clusters and their outskirts.Most notably, mock galaxies are tailored to mimic observationsfrom the Wide-Field Cluster Survey (WWFCS), but are equallyapplicable to the 4MOST cluster survey (Finoguenov et al. 2019)and other planned surveys. These surveys are designed for detailedstudies of the galaxy distribution in cluster infall regions, unveil pre-processing mechanisms considered to be responsible for observedenvironmental trends and research their constraints to cosmology.With this in mind, we construct a mock galaxy sample using ha-los identified by the AHF halo finder (Knollmann & Knebe 2009;Knebe et al. 2011), which considers gas, stars and dark matterself-consistently. Halo properties like luminosity, stellar mass andpeculiar velocity are based on the bound particles that account for ahalo. We select halos in z=0 clusters that mimic the number countsand observable properties used to select galaxies for the WWFCSSurvey: we aim for 4000 – 6000 galaxies per cluster structure within5 𝑅 with stellar masses roughly 𝑀 ∗ > ℎ − M (cid:12) . We refer tothese halos as mock galaxies.This data set is suitable to answer the question we pose insection 2. The AHF catalogue provides simulated peculiar velocities[Vx,Vy,Vz] at the positions [x,y,z] of each halo. To simulate redshiftdistortions, we translate the peculiar velocities along the line of sight– arbitrarily chosen to be in the direction of the y-axis – into distancesand perturb each mock galaxy with this number (proportionate toits velocity relative to the centre). As a result we obtain galaxiespositioned at [x,y p ,z], where y p stands for perturbed in y direction.We thus mimic Finger-of-God-like perturbations for all simulationvolumes (Fig. 1 shows one example) with the aim to investigate thequality of filament finding in 3D space, approximating observations. In this work we use the topological filament extraction code Dis-PerSE (Sousbie 2011). The code identifies topologically significantfeatures in tesselated density fields that are calculated from an inputof discrete positions of – in the present case – mock galaxies, eitherin 3D or 2D. The final network is constructed as a number of smallsegments that trace the ridges of the density field, referred to as skeleton , as well as topologically robust critical points, i.e., saddlepoints and nodes. The input of a signal-to-noise criterium allows theuser to recover a robust network with control over the scales at whichfilaments are found. This persistence measure (often expressed interms of standard deviations 𝜎 of a minimal signal-to-noise ratio)refers to the ratio of the value of two critical points in a topologicallysignificant pair. Depending on the application, DisPerSE thereforeoffers oversight over whether faint tendrils should be included (witha tradeoff of increased noise) or if the analysis should focus on largescale, collapsed cosmic filaments. The scientific questions we ask inthis body of work relate to galaxies in large filaments. In Paper I wecompared mock galaxy networks to networks based on the under-lying gas distribution and found a persistence threshold of 𝜎 = . 𝜎 in the present work, weiterate through a series of DisPerSE runs with a range of steadilyincreasing persistence thresholds from 𝜎 = 𝜎 = .
5. When weassess the goodness of the network under review, we define the mostsuccessful setup as the network where (1) the number of filamentsin the comparing network (i.e., the predicted network) converges
Figure 2.
Top: Delaunay tessellation based on mock galaxies perturbedby the redshift space distortion used by DisPerSE to identify filaments,in a slice of thickness 75 kpc around the centre of one example cluster.Fingers of God structures along the LoS are clearly visible and picked upby the filament finding algorithm. This is shown in the yellow network inthe middle panel. Blue dots mark nodes, green stars saddle points and blacktriangles bifurcations. As a comparison, the red dashed network is the resultof running DisPerSE on the true 3D positions. The background shows the2D histograms of the mock galaxies in redshift space. Bottom: Probabilitydistribution of the distances between skeletons of filament networks fromperturbed and true mock galaxies for the entire sample of 324 clusters. Pinkcurves show the distance measured from perturbed skeleton to the referenceskeleton, blue curves show the distance from the reference skeleton to theperturbed skeleton. We test a range of 𝜎 -thresholds (see text) and showa result where both the numbers of filaments in each skeletons and theirmedian distance converge. Dotted lines use segments outside 𝑅 , dashedlines include them. Vertical lines show medians of the distances betweenfilament extractions, values are printed in the legend.MNRAS000
Top: Delaunay tessellation based on mock galaxies perturbedby the redshift space distortion used by DisPerSE to identify filaments,in a slice of thickness 75 kpc around the centre of one example cluster.Fingers of God structures along the LoS are clearly visible and picked upby the filament finding algorithm. This is shown in the yellow network inthe middle panel. Blue dots mark nodes, green stars saddle points and blacktriangles bifurcations. As a comparison, the red dashed network is the resultof running DisPerSE on the true 3D positions. The background shows the2D histograms of the mock galaxies in redshift space. Bottom: Probabilitydistribution of the distances between skeletons of filament networks fromperturbed and true mock galaxies for the entire sample of 324 clusters. Pinkcurves show the distance measured from perturbed skeleton to the referenceskeleton, blue curves show the distance from the reference skeleton to theperturbed skeleton. We test a range of 𝜎 -thresholds (see text) and showa result where both the numbers of filaments in each skeletons and theirmedian distance converge. Dotted lines use segments outside 𝑅 , dashedlines include them. Vertical lines show medians of the distances betweenfilament extractions, values are printed in the legend.MNRAS000 , 1–12 (2021) inding filaments in redshift space to the number of filaments of the reference network (i.e., the true network), (2) the median distance between skeletons 𝐷 skel is small and (3) the distributions of both projections (i.e., 𝐷 predicted , true and 𝐷 true , predicted ) converge (Malavasi et al. 2016). However, in thepresent case where we use a fixed reference network, this last pointis less important. Therefore, our measure of goodness relies ona combination of the number of filaments and the Dskel distribu-tions, both in terms of reducing Dskel in general and minimising thedistance between the means of the distributions. For further expla-nations of the extraction code, we refer the reader to Sousbie (2011),while a more detailed description of how we applied DisPerSE toextract filaments and compute 𝐷 skel can be found in Paper I. The top panel of Fig. 2 shows the DisPerSE-view of an examplecluster with mass of 1 . × ℎ − M (cid:12) in redshift space. The black-and-white image visualises the Delaunay tesselation in a slice of75 kpc about the center of the cluster used by the algorithm to findfilaments. Like in Fig. 1, we see that the FoG structure dominatesthe centre. However, this system also shows the presence of a groupin the same slice and thus a second FoG is picked up.In the middle panel of the figure, we show the 2D histogramof the entire mock galaxy population in redshift space in the back-ground and two networks in superposition: the yellow skeleton isthe best filament network found for mock galaxies in redshift space.The red-dashed skeleton is our reference framework, based on thetrue positions of the same galaxies. We assess the extraction inthe bottom panel, cycling through a range of persistence thresh-olds and considering both projections, as described in the previ-ous section. The user’s choice of a persistence threshold greatlyinfluences the nature of the network. Removing low persistencepairs (simplification) is the algorithm’s main way to filter noiseor remove “non-meaningful” structures. Following Sousbie (2011),Laigle et al. (2017) and others, and described in detail in Paper I,we compute 𝐷 skel , the distances between the two skeletons we wishto compare, in all 324 cluster volumes and plot their differentialdistributions (PDF). The solid line is the PDF of distances of thesum of all skeletons (i.e., using all segments from 324 clusters),the dotted line is the result for segments outside 𝑅 . The verticallines indicate the corresponding medians, which range from 1.8 –2.8 ℎ − Mpc. Because the volume inside 𝑅 is small, mediansthat include segments inside 𝑅 < 𝑅 are always lower. This isbecause inside 𝑅 , segments lie close to each other. Comparingthese numbers with other realizations of filament extractions offersa quantitative assessment of how close the method is to the idealcase of having knowledge of true positions.In the following sections, we will test whether we are able to re-cover the reference network after correcting for the FoG effect. As ameasure of success, we will compare results of the corrected frame-works to the network we recovered from the 2D projections of galax-ies (i.e., 𝐷 skel = . . ℎ − Mpc, see Paper I) and marked asyellow bands in the plots. For reference, the distance of two random 𝐷 skel is defined as the probability distribution function (PDF) of thedistances between each segment of the predicted framework and its closestsegment in the true framework (Sousbie et al. 2009) Tuning the goodness measure and finding the best parameters presents anobvious route into machine learning. While we do not explore this possibilityhere, The ThreeHundred sample offers a suitable playground for machinelearning algorithms.
Figure 3.
In order to correct for the Fingers of God effect, we compressdistorted mock galaxies of virialized structures. Top: First, we identify andnormalize all perturbed galaxies inside 2 𝑅 of the main cluster halo (bluepoints), proxy for the cluster itself. The result is a compressed FoG (redpoints). We show cluster 1 of 324 as an example. The blue sphere indicates15 ℎ − Mpc, roughly equivalent to 5 𝑅 . Bottom: Assessment of DisPerSEfilament extraction on corrected FoG data over the whole ensemble of 324clusters. Probability distribution of distances between two skeletons in eachcluster: one is extracted from true [x,y,z] positions of mass-weighted mockgalaxies, the other from a perturbed [x,y p ,z] distribution as in observed red-shift space, but with the central 2 𝑅 compressed [x, y c ,z] as explained insec. 4.1. Solid line: distance between all segments of the skeletons, dottedline: only segments outside 𝑅 are compared. Median distances are in-dicated in the legend. Distances are calculated from both projections (i.e., 𝐷 skel [ predicted , true ] in pink and 𝐷 skel [ true , predicted ] in blue). skeletons in our sample (i.e., comparing randomly selected pairsof cluster networks) leads to 𝐷 skel = . . ℎ − Mpc for allsegments and segments outside of 𝑅 respectively. The recent publications by Kraljic et al. (2017) and Santiago-Bautista et al. (2020) are based on observations in large volumesof up to several hundred Mpc . Both studies extracted filamentsafter radially compressing dense regions – groups in the case ofKraljic et al. (2017) and clusters in the case of Santiago-Bautistaet al. (2020). However, solutions for traditional large-scale structuresurveys that extend over several hundred Mpc may not be appli-cable in the case of finding filaments in the immediate vicinity ofclusters where the field of view only extends a few virial radii ofthe cluster. In large surveys, ∼
5% of all filaments suffer from FoGeffects of groups Welker et al. (2019), whereas filaments in cluster
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U. Kuchner et al. outskirts are much more commonly affected (see Fig. 1). In addi-tion, as Welker et al. (2019) pointed out, a correction based on thecompression of groups can only be applied for rich groups ( (cid:38) ∼
90 and 3900 ℎ − Mpc − .The authors also used a list of filament candidates – identified aschains of at least three clusters – as a prior to select the superclusterswith the most promising filaments. They identified galaxy systems(large groups and clusters) in each of the 46 supercluster complexesbefore applying a virial approximation to correct the positions of thegalaxies through scaling the comoving distances along a cylinder ofradius 𝑅 aperture = 𝑅 vir to the calculated virial radius. The statisticalcompression of the FoG used in both examples (i.e., Kraljic et al.2017; Santiago-Bautista et al. 2020) therefore assumes virializationfor group and cluster-sized nodes, thus imposing that the distribu-tions in positions inside the groups are isotropic. This is not the casefor cluster outskirts.Following the successful method of correcting FoG distortionspresented in Kraljic et al. (2017) and Santiago-Bautista et al. (2020),we identify suitable areas in the simulated volumes that are moststrongly affected by redshift distortions. In observations, one wouldhave to find centres of clusters and groups – Robotham et al. (2011)gives an example of how this can be determined observationally– and estimate a suitable radius experimentally. While it is impor-tant to note that uncertainties are large, especially for lower masssystems (Old et al. 2014), this can be done e.g., through a virialapproximation as is explained in Santiago-Bautista et al. (2020) andbased on an algorithm presented in Biviano et al. (2006). All galax-ies projected inside the cylinder of this aperture radius and withvelocities deviating significantly from the mean cluster velocity (todetermine the length of the cylinder along the line of sight) can thusbe defined as FoG galaxies. The aim of the experiment we presentin this paper is to test the "best case scenario" using simulations,where we benefit from the a priori knowledge of true positions,cluster properties such as 𝑅 and a limited volume. We are there-fore able to determine members of virialized structures based onthe true positions [x,y,z] of mock galaxies, i.e., an idealized case.We consider a filament extraction successful if they improve the 2Dclassification. The densest regions in our cluster volumes, and therefore areasmost affected by FoG distortions, are the cluster centres. Using truepositions [x,y,z], we define cluster centres as galaxies within 2 𝑅 of the main halo of the AHF catalogue, where 𝑅 is the radius ofa sphere where the mean density is 200 times the critical density ofthe Universe. In The ThreeHundred simulations, we use the mainhalo as a proxy for the cluster itself and its position as the centreof mass. In the simulated observations, all galaxies are redshiftdistorted [x,y p ,z] as explained in Sec. 3.1.To test the impact of correcting for the FoG of the clustercentre, we compress the (perturbed) selected cluster centre galaxiesradially. This is done by scaling the y p positions of each FoG galaxy (a) Identification of groups outside 2R (b) Compression of group FoG Figure 4.
In a second step, we identify groups based on halos outside 2 𝑅 of the cluster with high velocity dispersions and find members within 𝑅 of that host halo (panel a). Then, we compress the FoG distortions fromthese groups (blue filled circles in panel b) in addition to cluster centres asshown in Fig. 3. The blue spheres indicate 1, 2 and 5 𝑅 of cluster 1 of324 as an example. Large red spheres indicate the position of groups, theirsizes are scaled to the number of members which can also be read out in theinsert of the top panel. radially to inside 2 𝑅 . For each galaxy cluster, we thus normalizeall FoG galaxies to within 2 𝑅 of the cluster. In appendix A, weassess this process and show that the compressed galaxies resemblethe distribution of true central galaxy positions adequately well inthe context of this exercise. All galaxies contributing to the FoGwithin a radius 2 𝑅 are thus re-distributed to [x, y c ,z], where y c stands for compressed, in a sphere of radius 2 𝑅 about the centre.All other galaxies in the simulation box remain perturbed, as theywould appear in observations. Fig. 3 gives an example of the isolatedFoG from all mock galaxies (i.e, galaxies obtained according to thesurvey’s selection function) within 2 𝑅 (blue dots). The buildupof red points in the centre are the same mock galaxies, but nowcompressed to within a sphere with radius 2 𝑅 . Note that 2 𝑅 does not always correct every "FoG galaxy". We also tested whetherother choices could improve the result and considered compressinggalaxies within 1 𝑅 , as was suggested by Santiago-Bautista et al.(2020). We found that this was not large enough. Extending the MNRAS000
In a second step, we identify groups based on halos outside 2 𝑅 of the cluster with high velocity dispersions and find members within 𝑅 of that host halo (panel a). Then, we compress the FoG distortions fromthese groups (blue filled circles in panel b) in addition to cluster centres asshown in Fig. 3. The blue spheres indicate 1, 2 and 5 𝑅 of cluster 1 of324 as an example. Large red spheres indicate the position of groups, theirsizes are scaled to the number of members which can also be read out in theinsert of the top panel. radially to inside 2 𝑅 . For each galaxy cluster, we thus normalizeall FoG galaxies to within 2 𝑅 of the cluster. In appendix A, weassess this process and show that the compressed galaxies resemblethe distribution of true central galaxy positions adequately well inthe context of this exercise. All galaxies contributing to the FoGwithin a radius 2 𝑅 are thus re-distributed to [x, y c ,z], where y c stands for compressed, in a sphere of radius 2 𝑅 about the centre.All other galaxies in the simulation box remain perturbed, as theywould appear in observations. Fig. 3 gives an example of the isolatedFoG from all mock galaxies (i.e, galaxies obtained according to thesurvey’s selection function) within 2 𝑅 (blue dots). The buildupof red points in the centre are the same mock galaxies, but nowcompressed to within a sphere with radius 2 𝑅 . Note that 2 𝑅 does not always correct every "FoG galaxy". We also tested whetherother choices could improve the result and considered compressinggalaxies within 1 𝑅 , as was suggested by Santiago-Bautista et al.(2020). We found that this was not large enough. Extending the MNRAS000 , 1–12 (2021) inding filaments in redshift space radius even further, however, would go too far considering the wholefield of view only extends out to 5 𝑅 . Twice 𝑅 was thus chosenas a suitable compromise.To assess whether the compression of FoG galaxies improvesthe filament extraction, we compare locations of extracted Dis-PerSE skeletons as before (see Sec. 3.3). This is shown in thebottom panel of Fig. 3, that quantifies the discrepancy/similaritiesbetween the reference mock galaxy-skeleton based on true positions[x,y,z] and skeletons retrieved after the FoG compression over thewhole ensemble of clusters . This means that we extract filamentsfrom mock galaxies that have been perturbed according to redshiftdistortions [x,y p ,z], but "FoG galaxies" are compressed to [x, y c ,z]and compare the result to the reference network. Here, we showthe result of our procedure to finding the best fit for the persistencethreshold, in this case 𝜎 = .
6. The medians in Fig. 3 reveal thatsegments of the two networks are roughly 2 ℎ − Mpc apart, whichmeans that this is not an adequate solution to the problem and doesnot lead to any significant improvement over the original FoG sce-nario shown in Fig. 2. For comparison, in Paper I, we found goodagreements between networks of different tracers when 𝐷 skel isbetween 0.5 and 0.7 ℎ − Mpc.
Similar to Fingers of God around cluster centres, we also find anartificial stretching of groups along the line of sight resulting in thecreation of spurious filaments in the same direction. As a next stepto improving filament finding in redshift space, we therefore applythe same compression procedure not only for cluster centres, butalso for galaxy groups. Fig. 4 shows the step of identifying groups(middle panel, 4a) and what the FoG look like on group scales(lower panel, 4b).We first identify group centres by looking for halos outside2 𝑅 of the cluster with high (1D) velocity dispersions ( 𝜎 >300 km/s). Each halo within 1 𝑅 of this host halo is tagged as agroup member. Note that this definition is different to identifyinggroups based on their halo/sub-halo status known in the simula-tions (e.g., Arthur et al. 2016, using the same data set) and yieldsa smaller number of groups. Classifying groups based on sub-halostatus relies on knowledge of whether halos lie within a commonisodensity contour, with a subsequent removal of objects outside thehost’s R . With an eye to observations, groups may be more easilydefined based on their velocity dispersion as demonstrated here, orother more commonly used methods, such as the Friends-of-Friendsmethod. The exact choice of group identification method should bebased on the individual science case and available data, and doesnot alter our conclusions.In The ThreeHundred volumes, we find groups of variousrichness (indicated by the size of the red spheres in Fig. 4). Inten regions of 324, a second cluster with M > h − h − M (cid:12) ,where M refers to the mass enclosed within a sphere of radiusR , is found in addition to the main cluster. In this exercise, wetreat the second cluster in the same way as all groups. Therefore,some groups may host several hundred group members, others onlya few. We compress each group’s FoG (Fig. 4b) as described in theprevious section and run DisPerSE on the mock galaxies samplethat is constituted of galaxies that are (1) compressed if they arewithin the central 2 𝑅 , (2) compressed if they are within groupregions, i.e., within 1 𝑅 of high velocity dispersion halos and (3)perturbed elsewhere (top panel of Fig. 5). The resulting PDF can beseen in the bottom panel of Fig. 5.Even in the case where in addition to the FoG from cluster Figure 5.
Top: example cluster 0001 – the most massive of The ThreeHun-dred simulations – showing compressed groups and compressed central2 𝑅 (red points) while the rest of the galaxies are perturbed in the y di-rection according to redshift distortions (blue points). The outer blue meshshows a sphere of 15 ℎ − Mpc radius, roughly comparable to 5 𝑅 , centredon the main halo of the cluster. Middle: comparison of extracted filamentsin this example cluster. One is extracted from true [x,y,z] positions of mockgalaxies as before (our reference filament network in red-dashed lines), andthe other is based on the perturbed [x,y p ,z] galaxy distribution as in observedredshift space but with the central 2 𝑅 as well as all groups compressed[x, y 𝑐 ,z] (in yellow). Nodes were compressed before extraction. The back-ground shows the 2D histogram of the galaxy distribution. Nodes, saddlepoints etc. are marked as described in Fig. 2.Bottom: the PDF of the distances between segments of the skeletons overthe whole ensemble of clusters shows only minor improvements.MNRAS , 1–12 (2021) U. Kuchner et al.
Figure 6.
In observed redshift space, the positions of filament galaxies areapparently perturbed, similar to clusters or groups. The 2D density plotshows the distance from all mock galaxies outside 2 𝑅 and outside groupsto their nearest filament segment in Mpc on the x-axis and perturbationalong the line of sight on the y-axis. This visualization paints a clear pictureof the magnitude of the perturbations of infalling cluster galaxies in redshiftspace.The red dashed line indicates a characteristic thickness of a filament(1 ℎ − Mpc) as determined in Paper I. The majority of mock galaxies aredistorted by a few Mpc, but galaxies can be perturbed by up to 10 ℎ − Mpc. centres, those from groups – prominent nodes in the network –are compressed, the extraction does not improve significantly andtherefore does not outperform the extraction based on projected 2Dpositions.This is evident from the large distances between the skele-tons (We report a median distance of 1.3 ℎ − Mpc and 2.5 ℎ − Mpcfor all segments and 1.5 ℎ − Mpc and 2.1 ℎ − Mpc for segments out-side 1 𝑅 , Fig. 5). The two values refer to the two projections ofcalculating 𝐷 skel . As before, the same care was taken with updatingthe DisPerSE setup iteratively.Both the large distance between networks in the quantitativeassessment shown in Fig. 5 as well as the qualitative inspectionof overlaying networks confirms that compressing virialized struc-tures in the small volumes of cluster outskirts is not sufficient torobustly find the same filaments in 3D observed space as in 3D truepositional space. In summary, minimising the node contributionsby compressing dense regions in cluster volumes has not improvedthe filament extraction significantly. The average distance betweenskeletons in observed redshift space and skeletons extracted afterthe compression process is 𝐷 skel ∼ . ℎ − Mpc. In appendix B,we discuss two alternative approaches: connecting groups and re-jecting galaxies in high-density regions. Neither test was able toconsiderably improve the filament finding, let alone perform betterthan filament finding in 2D.
In the previous sections we have seen that at the relatively smallscales of cluster outskirts, finding filaments in redshift space maynot be achievable using velocity information as a third dimension.The volumes are dominated by the main cluster, but even if wesuccessfully correct for the kinematic artifacts from cluster centresand groups through a compression of FoGs, the smearing of thefilaments themselves makes the filament finding with DisPerSEunreliable. The top panel in Fig. 5 gives a sense of this washing outof filaments, i.e., the perturbations of the filaments themselves. Inredshift space, the apparent distribution of galaxies around filamentsis much more diffuse than in true positions and appear elongated– much like Fingers of God. Above the galaxy mass limit thatwe are using in this study (M halo > × h − M (cid:12) or ∼ M ∗ > × h − M (cid:12) ), these "filament FoG" dominate the cluster outskirtvolume and are the reason why we struggle to find filaments inredshift space. In Fig. 6 we demonstrate the extent of these "filament FoGs" andthus quantitatively reveal the practical reasons for the difficulty offinding filaments in redshift space in the vicinity of clusters. Theplot shows the distortion from true positions by peculiar velocitiesin Mpc/h as a function of distance to the filament network (D skel ),also in Mpc/h. The plot is based on all mock galaxies outside 2 𝑅 and outside groups for all clusters combined. The kernel densityestimation shows this distribution as a smooth indication of densityin addition to 2D density contours. Note that there are noticeablecluster-to-cluster variations depending on the degree of substructurein each cluster volume. The red dashed line indicates a character-istic thickness of filaments, as determined by gas density profiles(see Paper I), implying that mock galaxies with a maximal orthog-onal distance of 1 ℎ − Mpc to the skeleton are "inside" filaments.This is of course a simplified view, since filaments are diffuse con-structions of cooled filament gas concentrated around the filamentspine without a clear edge. However, it helps to associate galaxiesto filaments and illustrates the apparent spread of filament galax-ies. The 2D density contours reveal that the apparent positions ofmost mock galaxies inside filaments are typically perturbed by a fewMpc, with some up to 10 ℎ − Mpc ([y - y p ]). Given we only probe avolume of radius 15 ℎ − Mpc around the cluster, this explains whyour attempts to extract filaments in 3D using [x,y p ,z] have failedand assessments show large discrepancies of around 2 ℎ − Mpc incomparison to filaments based on [x,y,z] positions (Fig. 3 and 5).As a consequence, DisPerSE is struggling to find filaments.Large scale deviations from real positions correlate with orien-tation to the line-of-sight (Fig. 1). We therefore investigated whethera specific orientation of filaments with respect to the line-of-sightmight be responsible for the large perturbations. We extracted twosets of filaments, those parallel and those perpendicular to the line-of-sight within 20 degrees and allowing for curvature of filaments.We did this in the reference and the perturbed networks and com-pared each set. While, on average, there are comparatively moreparallel filaments in the perturbed networks due to the stretchedFoGs, sets of perturbed filaments in either orientation are uncorre-lated to the corresponding reference filaments. This means that nospecific orientation can be made responsible.
MNRAS000
MNRAS000 , 1–12 (2021) inding filaments in redshift space In order to understand the underlying reasons for this complica-tion, it can be helpful to look at how matter flows between differentmorphological components of the cosmic web. The vast observa-tional Cosmic Flows program (e.g., Courtois et al. 2011, 2013;Tully et al. 2014) of peculiar velocities in our local Universe (up to30,000 km/s) has shown how mass flows along and towards struc-tures of the cosmic web. Their detailed maps of observed (andreconstructed three-dimensional) motions of galaxies offer a valu-able input to the translation from redshift space to physical space.It reveals that the local dynamics in both low- and high-densityregions greatly impact the inferred density distribution that con-stitutes the input to a filament extraction from observations. Thevelocity information from Cosmic Flows offers clear signatures offlows that converge on major filaments and then progress towardpeaks of the galaxy distribution . While clusters are undoubtedlythe greatest basins of attraction for galaxies, matter thus also movestowards filaments.To further our understanding of the problem explored in thispaper, and thus explain the perturbations shown in Fig. 6, we nowfocus on the small scale flow patterns initiated by the collapse offilaments . We therefore investigate how galaxies are flowing per-pendicular to the reference filaments in 3D and separated from theirmovement towards the clusters. This movement is independent ofthe orientation of filaments. To achieve this, we first need to takeout the bulk infall towards the centre of the cluster (i.e., the averagemotion of galaxies towards the cluster, assumed to be radial). Thiswas done by averaging the velocity component toward the cluster inradial bins and correcting the velocity of each mock galaxy accord-ingly. Fig. 7 shows the resulting isolated radial velocity componenttowards filaments (i.e., orthogonal to each segment of the skeleton)of all mock galaxies in 324 simulations towards the filaments (ex-tracted from true galaxy positions [x,y,z]) as a function of distanceto the skeleton in Mpc/h. Negative velocities imply a movementtowards the skeleton and the typical "thickness" of a filament isindicated by the yellow dashed vertical line (see discussion above).Very close to the centre of the filament, large random motions av-eraging at 0 km/s (comparable to a filament velocity dispersionof ∼
300 km/s) make it impossible to isolate any collapse velocity.However, away from the spine of the filament, we detect a signalof negative velocities, i.e., velocities that indicate that galaxies arestatistically falling toward the filaments, which is in addition to themovement towards the cluster centre. Red lines mark the median(solid line) and lower and upper quartiles (dotted lines) of this col-lapse velocity, which we may envision as a "flow towards filaments".Following this median line from higher distances to lower distances(i.e., towards filaments), we see that galaxies "stream" towards fila-ments with an average collapse velocity of 200 km/s.Fig. 7 shows results of galaxy flows in highly complex environ-ments. Firstly, we focus on z=0, where filaments could be relativelymore disturbed than at earlier times. Cosmological hydrodynamicalsimulations show that at higher redshifts, satellite galaxies and gasfall nearly radially along well-defined cold filamentary streams tothe centre of massive halos on extremely short time-scales (Duboiset al. 2012). Secondly, we focus on clusters and cluster outskirts, See also Ma & Scott (2014) for a general overview of the cosmic velocityfield and Trowland et al. (2012) for a discussion on the manifestation of thesystemic bulk flows of filaments from numerical simulations. In this work, we describe streaming motions as motions in the rest-frameof the cluster, defined by the mean of all mock galaxies within 𝑅 . Figure 7.
Collapse velocity of mock galaxies towards filaments. This plotshows a typical "infall velocity" of ∼
200 km/s of all mock galaxies outside2 𝑅 and inside 10 ℎ − Mpc of the cluster, plotted as a function of distanceto the filament spine (for filaments determined on [x,y,z] positions). The yel-low dashed line indicates a characteristic thickness of filaments (1 ℎ − Mpc)as determined in Paper I and red lines mark the median, lower and upperquartiles of the radial velocity component. where filaments are exposed to highly mixed and turbulent envi-ronments, where the gas undergoes significant shocks (Power et al.2019) and filaments become relevant locations of collapse. Veloc-ity flows in these exceptional regions in the Universe deserve athorough discussion. In Rost et al. (2020a) we do exactly that andinvestigate velocity flows of gas and dark matter around clusters inmuch greater detail, using the same simulations.
Observations are dotted with obstacles to overcome. These includemagnitude limits, volume limits, biases of multiple sorts, incom-pleteness, sparse sampling and the redshift space distortions we fo-cused on in this paper. Studies that benefit from the large areas theycover – often with a tradeoff of higher redshifts – like SDSS (Yanet al. 2013; Martínez et al. 2015; Poudel et al. 2017), GAMA (Al-paslan et al. 2016; Kraljic et al. 2018) and VIPERS (Malavasi et al.2017) reconstruct the web in 3D by connecting high density nodes,usually galaxy groups, over large distances. On supercluster scales,mapping filaments can be achieved through identifying bridges be-tween cluster pairs (Cybulski et al. 2014) and elongated chain-likestructures between dense galaxy systems (Santiago-Bautista et al.2020).Our study is narrowing down on environments where a fil-ament reconstruction in 3D has not been successfully describedbefore. This is likely due to the combination of the relatively smallvolume/region on the sky and the complex accumulation of largelyunvirialized systems of galaxies that dynamically interact and flowbetween the features of the cosmic web. Accounting for the pertur-bations caused by the peculiar velocities and transforming them toreal space has proven to be a challenge in this narrow regime: ve-
MNRAS , 1–12 (2021) U. Kuchner et al. locities can only be measured in the radial direction, distances havelarge uncertainties, and deviations from cosmic expansion are veryuncertain for individual objects (Courtois et al. 2013). The methodof defining the web kinematically by directly mapping galaxy pe-culiar velocity flows is so far restricted to the very nearby Universe(Tully et al. 2014; Dupuy et al. 2019).How, then, can we trace filaments around clusters in observa-tions if the valuable information of thousands of spectra of galaxiesis not offering easy-to-obtain positions (distances) in the line ofsight direction? Surveys that will attempt to map filaments in clus-ter outskirts may have to fall back to 2D reconstructions. In Paper I,we discussed a comparison between filaments obtained based on3D positions and 2D projections (2D positions on the sky) of mockgalaxies. We saw that, to a large extent, the two methods trace thesame cosmic structures with median D skel =0.51 ℎ − Mpc for allsegments and D skel =0.61 ℎ − Mpc for segments outside of 𝑅 .This is far superior to the values that we obtained through the stepswe undertook in the present paper. Using 2D projections thereforeproved to be a good alternative in the presented case.In addition, Paper I provided numbers to evaluate the impactof projections on recovery rates for galaxies associated to filamentsfound in 2D compared to 3D (Sec. 3.5.2). We defined galaxiesin filaments as galaxies with orthogonal distances smaller than0.7 ℎ − Mpc or 1 ℎ − Mpc. While apparently there are more galaxiesclose to filaments due to the projection onto a plane, the contamina-tion rate was relatively moderate: we found that 67% (75%) of allmock galaxies in filaments of thickness 0.7 ℎ − Mpc (1 ℎ − Mpc) arestill correctly identified in 2D. To put this into perspective, this truepositive rate was still 5 times higher than if we randomly selectedgalaxies, where only 14% are located in filaments.In order to reach this quality and unambiguously study the pro-jected filaments in cluster outskirts, narrow volumes around clustersneed to be identified. All our tests were performed in a controlledvolume of a sphere with 15 ℎ − Mpc radius around the cluster. Evenhigh precision photometric redshifts will struggle to reach this levelof accuracy. Only spectroscopic redshifts with higher accuracy andprecision along the line of sight allow us to isolate the environmentto the area of interest. This will be possible for targeted clusteroutskirt campaigns with instruments such as WEAVE and 4MOST.Using WWFCS as an example, we expect radial velocities fromWEAVE with uncertainties smaller than 25 km/s, and because pe-culiar motions induce distance errors of the order of many Mpc,spectroscopic redshifts will ensure that we only probe galaxiesin the volume of 5 𝑅 radius around the cluster (comparable to15 ℎ − Mpc). The large number of optical fibers and an optimisedtargeting strategy will lead to a high density of galaxies with spec-troscopic redshifts corresponding to this volume. For WWFCS, wecalculated that we will reach between 4000 and 6000 spectroscopi-cally confirmed cluster structure members for each of the 16 clusterswith at most ∼
3% incompleteness. Similar numbers can be expectedfor other cluster outskirt surveys. This is the basis for successfullycharacterizing filaments connected to galaxy clusters in observa-tions. Spectroscopic information will therefore still be vital for theselection of galaxies, however they will not be used directly for theinput to finding filaments in the small region of cluster outskirts.For that, we will resort to a 2D extraction.
ACKNOWLEDGEMENTS
We thank the referee for providing useful feedback to this study.This work has been made possible by The ThreeHundred col- laboration , which benefits from financial support of the EuropeanUnion’s Horizon 2020 Research and Innovation programme underthe Marie Skłodowskaw-Curie grant agreement number 734374, i.e.the LACEGAL project. The ThreeHundred simulations used inthis paper have been performed in the MareNostrum Supercom-puter at the Barcelona Supercomputing Center, thanks to CPUtime granted by the Red Española de Supercomputación. UK ac-knowledges support from the Science and Technology FacilitiesCouncil through grant number RA27PN. AK is supported by MI-CIU/FEDER under research grant PGC2018-094975-C21. He fur-ther acknowledges support from the Spanish Red Consolider Multi-Dark FPA2017-90566-REDC and thanks Ride for nowhere. GY ac-knowleges financial suport from MICIU/FEDER through researchgrant number PGC2018-094975-C21. ER acknowledges fundingthrough the agreement ASI-INAF n.2017-14-H.0The authors contributed to this paper in the following ways: UK,AAS, MEG, AR and FRP formed the core team. UK ran Dis-PerSE, analysed the data, produced the plots and wrote the paperwith ongoing input from the core team and valuable commentsfor improvement from collaborating co-authors. GY supplied thesimulation data; AK the halo catalogues. DATA AVAILABILITY
Data available on request to The ThreeHundred collaboration.
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APPENDIX A: ASSESSMENT OF THE FOGCOMPRESSION ALGORITHM
In this appendix, we investigate whether the compression algorithmadequately reproduces the real positions of galaxies in dense envi-ronments. Fig. A1 demonstrates that radially scaling the distancesalong the FoG to the virial radius represents the true positions inthe cluster centre very well. We follow the approach by Santiago-Bautista et al. (2020), but with the advantage that we know centrepositions and size of 𝑅 . This simple process is very similar towhat was also used in Kraljic et al. (2017). In Fig. A1, we show acomparison of true 3D galaxy positions (blue triangles) and posi-tions of FoG galaxies after the compression algorithm (red points).In the first two rows, we print different rotations of four randomly se-lected cluster centres ( 𝑅 < 𝑅 ) to showcase a variety of masses.Each plot depicts a different cluster and the blue sphere encompasses2 𝑅 of that cluster. Overall, the distribution of red points is com-parable to the distribution of blue triangles. The KDE plots in thelower row show the distribution of true y-positions and y-positionsafter compression in 1D and 2D over all 324 cluster centres com-bined. We chose y to be the direction of LoS. The compression leadsto a slightly wider result, revealing that the algorithm is not able tofully reproduce the compactness of cluster centres. However, thisis not our goal. We remind the reader that our aim is not to findfilaments in this region. We aim to find reliable filaments in theoutskirts, i.e., outside of this region. The goal is to create a node inthe centre that can be identified by DisPerSE as a maximum. Note MNRAS , 1–12 (2021) U. Kuchner et al.
Figure A1.
Assessment of the FoG algorithm: we compare true 3D po-sitions of galaxies within 2 𝑅 (blue triangles) with the same galaxiesperturbed in redshift space (FoG) and then compressed (red dots). The firstfour figures show example clusters showcasing the range of masses andmorphologies covered by The ThreeHundred in different angles. Thebottom row shows two plots in which we contrast the distributions of trueand compressed y-positions,our selected "line of sight" direction. Whilethe distribution of compressed galaxies is slightly wider than the compactcentres in true positions, the compression algorithm resembles the overalldistribution sufficiently well for our purpose. that close to the centre, filaments will overlap and we discussed thisvolume effect in Paper I. Therefore, we cannot comment on filamentpositions very close to the central node without correcting for thevolume first. APPENDIX B: ADDITIONAL TESTSB1 Connecting groups
Large groups with many members are prominent nodes in the fila-ment network around clusters. In our attempt to find possible waysto identifying filaments using 3D data in observations, we testedwhether a filament network could be achieved by simply connect-ing the compressed groups and cluster centre (as explained in Sec.4), thus completely omitting any galaxies not located in virializedstructures for the DisPerSE extraction. While this may work on verylarge scales, we found that it does not work on the limited volumeswe are investigating. This was true also when we expanded the groupsearch far beyond the 5 𝑅 volume we study here. This approach Figure B1.
Removing galaxies in high density regions (within 2 𝑅 of thecluster centre and groups) leaves an underdense/empty region. The figureshows the Delaunay tesselation which is the base for finding filaments wihtDisPerSE. simply excludes too many mock galaxies to resemble meaningfulfilament networks. B2 Finding filaments without nodes
In an additional approach we tested filament extractions after re-jecting galaxies in high-density regions, i.e., galaxies located withingroups and the cluster centre are removed prior to DisPerSE runs.The aim of this exercise is to omit all FoG "structures" of virializedregions, leaving the perturbed galaxies in the infall regions. As aresult, DisPerSE interpreted the denser "shells" around these emptyregions as dense ridges akin to filaments. The skeletons tend to fol-low ring-like features around empty central regions. Fig. B1 helpsto understand the issue. We calculate 𝐷 skel = . − . ℎ − Mpc incomparison to the reference skeleton. Therefore, at the small scalesand detailed level that we seek to find filaments, this approach is noadequate solution. Filling this hole with a centralized concentrationof mass to this (to find a maximum/node) is essentially the same asthe approach of compressing FoGs into a ball in the centre.
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