Halo shapes constrained from a pure sample of central galaxies in KiDS-1000
Christos Georgiou, Henk Hoekstra, Konrad Kuijken, Maciej Bilicki, Andrej Dvornik, Thomas Erben, Benjamin Giblin, Catherine Heymans, Hendrik Hildebrandt, Jelte T. A. de Jong, Arun Kannawadi, Peter Schneider, Tim Schrabback, HuanYuan Shan, Angus H. Wright
AAstronomy & Astrophysics manuscript no. HaloEllipticity © ESO 2021February 9, 2021
Halo shapes constrained from a pure sample of central galaxies inKiDS-1000
Christos Georgiou (cid:63) , Henk Hoekstra , Konrad Kuijken , Maciej Bilicki , Andrej Dvornik , Thomas Erben , BenjaminGiblin , Catherine Heymans , , Hendrik Hildebrandt , Jelte T. A. de Jong , Arun Kannawadi , , Peter Schneider , TimSchrabback , HuanYuan Shan , , and Angus H. Wright Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA, Leiden, The Netherlands. Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32 /
46, 02-668, Warsaw, Poland. Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for CosmologicalLensing, 44780 Bochum, Germany Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121, Bonn, Germany. Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, the Netherlands Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA Shanghai Astronomical Observatory (SHAO), Nandan Road 80, Shanghai 200030, China University of Chinese Academy of Sciences, Beijing 100049, ChinaReceived < date > / Accepted < date > ABSTRACT
We present measurements of f h , the ratio of the aligned components of the projected halo and galaxy ellipticities, for a sample ofcentral galaxies using weak gravitational lensing data from the Kilo-Degree Survey (KiDS). Using a lens galaxy shape estimation thatis more sensitive to outer galaxy regions, we find f h = . ± .
20 for our full sample and f h = . ± .
19 for an intrinsically red(and therefore higher stellar-mass) sub-sample, rejecting the hypothesis of round halos and / or galaxies being un-aligned with theirparent halo at 2 . σ and 2 . σ , respectively. We quantify the 93.4% purity of our central galaxy sample using numerical simulations andoverlapping spectroscopy from the Galaxy and Mass Assembly survey. This purity ensures that the interpretation of our measurementsis not complicated by the presence of a significant fraction of satellite galaxies. Restricting our central galaxy ellipticity measurementto the inner isophotes, we find f h = . ± .
17 for our red sub-sample, suggesting that the outer galaxy regions are more alignedwith their dark matter halos compared to the inner regions. Our results are in agreement with previous studies and suggest that lowermass halos are rounder and / or less aligned with their host galaxy than samples of more massive galaxies, studied in galaxy groupsand clusters. Key words.
Gravitational lensing: weak - galaxies: general
1. Introduction
The current standard model of cosmology, dubbed Λ CDM, hasbeen very successful in describing a large number of indepen-dent cosmological probes, such as Cosmic Microwave Back-ground (CMB) observations (e.g. Planck Collaboration et al.2020), the galaxy clustering signal (e.g. Alam et al. 2017)and Baryon Acoustic Oscillations (e.g. Anderson et al. 2014;Bautista et al. 2018), among many others. According to thismodel, dark matter makes up for the majority of the matter den-sity content of the Universe and provides the seeds upon whichgalaxies and larger structures can form and evolve.From numerical simulations, it is understood that dark mat-ter forms halos that are roughly tri-axial, which appear ellipticalin projection (Dubinski & Carlberg 1991; Jing & Suto 2002).Estimation of the shape of these halos from observations can,therefore, be used as a test for the current cosmological model,as well as extensions to it, such as modifications to the gravitytheory or the dark matter component (e.g. Hellwing et al. 2013;L’Huillier et al. 2017; Peter et al. 2013; Elahi et al. 2014). (cid:63) [email protected]
Observationally, many attempts have been made towardsmeasuring halo ellipticities. Techniques include satellite dynam-ics (e.g. Brainerd 2005; Azzaro et al. 2007; Bailin et al. 2008;Nierenberg et al. 2011), tidal streams in the Milky Way (e.g.Helmi 2004; Law & Majewski 2010; Vera-Ciro & Helmi 2013),HI gas observations (e.g. Olling 1995; Banerjee & Jog 2008;O’Brien et al. 2010), planetary nebulae (e.g. Hui et al. 1995;Napolitano et al. 2011), X-ray observations (e.g. Donahue et al.2016) as well as strong lensing (e.g. Caminha et al. 2016), alsoaccompanied by stellar dynamics (e.g. van de Ven et al. 2010).These techniques rely on luminous tracers of the dark mattershape, which can lead to biases, complicate the interpretation ofthe measurements and cannot provide information on the largerscales of the dark matter halo, where visible light is absent.One observational technique that does not su ff er from thisdrawback is weak gravitational lensing, the coherent distortionof light rays from background sources from the intervening mat-ter distribution (for a review, see Bartelmann & Schneider 2001).Since gravitational lensing is sensitive to all matter (also non-baryonic), it serves as a great tool to study the dark matter ha-los. The distortion of the galaxy shapes due to weak lensingis very small, and in order to extract a measurable signal one Article number, page 1 of 12 a r X i v : . [ a s t r o - ph . GA ] F e b & A proofs: manuscript no. HaloEllipticity needs to statistically average over large ensembles of galaxies.If the stacking is done around other galaxies, a technique calledgalaxy-galaxy lensing, only the matter at the lens galaxy redshiftcontributes coherently to the lensing signal, and the structuresalong the line of sight simply add noise to the measurement.Tri-axial dark matter halos will cause an azimuthal variationin the weak lensing signal, enhancing it along the direction ofthe semi-major axis of the projected halo and reducing it alongthe semi-minor axis. For very massive structures, such as largegalaxy clusters, this variation is strong enough to be measuredfor individual (e.g. Corless et al. 2009; Umetsu et al. 2018) orstacked weak lensing maps of cluster samples (Evans & Bridle2009; Oguri et al. 2012). For galaxy-scale halos, this variationcan be measured by weighting the lensing measurements accord-ing to the halo’s semi-major axis.In most applications of weak lensing based measurements ofdark matter halo ellipticity, the lens galaxy semi-major axis isused as a proxy for the dark matter halo axis (Hoekstra et al.2004; Mandelbaum et al. 2006; Parker et al. 2007; van Uitertet al. 2012; Schrabback et al. 2015; van Uitert et al. 2017;Schrabback et al. 2020). The measured quantity is, then, theratio of the halo ellipticity to the galaxy ellipticity, weightedby the average mis-alignment angle between the two, i.e. f h = (cid:104) cos(2 ∆ φ h , g ) | (cid:15) h | / | (cid:15) g |(cid:105) . This makes the measurement of f h a usefulstep in determining the alignment between the dark matter haloand its host galaxy. The mis-alignment angle has been measuredin numerical simulations, with results from the most recent hy-drodynamical simulations suggesting a value of (cid:104) ∆ φ h , g (cid:105) ∼ ◦ (Tenneti et al. 2014; Velliscig et al. 2015; Chisari et al. 2017).The mis-alignment is decreasing with decreasing redshift and in-creasing halo mass, which suggests that massive central galaxiesare expected to carry most of the signal. Indeed van Uitert et al.(2017) detected a non-zero halo ellipticity with (cid:38) σ signifi-cance using only ∼ photometric galaxy sample, anduse these as lenses to measure the anisotropic weak lensing sig-nal around them. A galaxy sample with low satellite fraction willalso produce a more robust measurement, since satellite galaxylensing profiles across a wide range of scales complicate the in-terpretation of the measured signal of the full sample. We use thefourth data release of the Kilo-Degree-Survey (KiDS, Kuijkenet al. 2019) and construct an algorithm that preferentially se-lects central galaxies using apparent magnitudes and photomet-ric redshifts. These redshifts are obtained from a machine learn-ing technique, focussing on the bright-end sample of galaxies inKiDS, and achieve very high precision (Bilicki et al. 2018). Wevalidate our central galaxy selection by quantifying the sample’spurity using the group catalogue from the Galaxy And MassAssembly survey (GAMA, Driver et al. 2011; Robotham et al.2011), as well as mock galaxy catalogues from the Marenos-trum Institut de Ciéncies de l’Espai (MICE) Grand Challengerun (Crocce et al. 2015).In Sect. 2 we present the data used for constructing and val-idating our lens sample, consisting of highly pure central galax-ies, which we describe in detail in Sect. 3. The methodologyused to measure the lensing signal is described in Sect. 4. Theresults obtained are shown in Sect. 5 and we discuss the mea-surements and conclude with Sect. 6. To calculate angular diam-eter distances we use a flat Λ CDM cosmology with parametersobtained from the latest CMB constraints (Planck Collaborationet al. 2020), i.e. H = . / s / Mpc and Ω m , = .
2. Data
Measuring the anisotropic lensing signal requires a wide surveyof deep imaging data, so that accurate unbiased galaxy shapescan be measured and the lensing signal can be statistically ex-tracted. For this reason, we use data from KiDS. Moreover, mas-sive central galaxies are expected to yield the highest signal-to-noise ratio (SNR) for anisotropic lensing; we thus need a way ofselecting a pure sample of central galaxies as well as a means tovalidate our selection. To this end, we make use of the GAMAsurvey, as well as mock catalogues from the MICE Grand Chal-lenge galaxy catalogue.
KiDS (de Jong et al. 2015, 2017; Kuijken et al. 2019) is a deepimaging ESO public survey carried out using the VLT SurveyTelescope and the OmegaCam camera. The survey has covered1,350 deg of the sky in three patches in the northern and south-ern equatorial hemispheres, in four broad band filters ( u , g , r and i ). The mean limiting magnitudes are 24.23, 25.12, 25.02and 23.68, for the four filters respectively (5 σ in a 2 (cid:48)(cid:48) aperture).The survey was specifically designed for weak lensing scienceand the image quality is high, with small nearly round point-spread function (PSF), especially in the r -band observations,which were taken during dark time with the best seeing con-ditions. We use the fourth data release of the survey, with 10061 × image tiles (KiDS-1000).KiDS is complemented by the VISTA Kilo-Degree InfraredGalaxy Survey (VIKING, Edge et al. 2013), which has imagedthe same footprint as KiDS in the near-infrared (NIR) Z , Y , J , H and K s bands. This addition allows for the determination of moreaccurate photometric redshifts from 9 broad band filters. Forour source galaxy sample, redshifts are retrieved with the tem-plate fitting Bayesian Photometric Redshift (BPZ) code (Benítez2000; Coe et al. 2006), applied to the 9 band photometry. To es-timate source redshift distributions, we use the direct calibrationscheme to weight the overlapping spectroscopic sample accord-ing to our photometric one. The process is described in detail inHildebrandt et al. (2020).For our lens sample, we require more precise redshift esti-mates that will help in a more accurate lensing measurement, aswell as in building a more robust central galaxy sample. Hence,we choose to use a bright ( m r (cid:46)
20) sample with photomet-ric redshifts estimated with the artificial neural network machinelearning code ANNz2 (Sadeh et al. 2016), as presented in Bil-icki et al. (2018), but now extended to the full KiDS-1000 sam-ple (Bilicki et al. 2021). This sample was trained on the highlycomplete GAMA spectroscopic redshift catalogue (98 .
5% com-pleteness at flux limit m r < . (cid:104) δ z (cid:105) = (cid:104) z phot − z spec (cid:105) (cid:39) − and scatter σ δ z (cid:39) . + z ).Thanks to the addition of VIKING data over the full KiDS-1000 area (Kuijken et al. 2019), the default photo- z solution isnow based on 9-band photometry. In this work, however, we useredshifts obtained from the optical u g ri band photometry aloneas, since the lens sample is bright and relatively low-redshift,NIR photometry does not significantly improve the photometricredshift estimation (see Bilicki et al. 2018 for more details). In http: // kids.strw.leidenuniv.nlArticle number, page 2 of 12hristos Georgiou et al.: Halo shapes constrained from a pure sample of central galaxies in KiDS-1000 addition, using the NIR photometry would introduce additionalmasking to our data, due to some gaps in VIKING coverage,which would reduce our lens galaxy sample. As we will showin Sect. 3, improving the redshift accuracy further (e.g. withNIR data) does not significantly increase the purity of our cen-tral sample, whereas increasing the survey area equips us witha larger sample for a more precise measurement. We restrict thelens redshifts to 0 . < z l < .
5, as outside of this range thephoto- z s are less well constrained (Bilicki et al. 2018); this cutanyway removes a small fraction of the lens sample ( < -reduced r -band images with the lens fit shapemeasurement method (Miller et al. 2007, 2013, Giblin et al.,in prep.). This method is a likelihood-based algorithm thatfits surface brightness profiles to observed galaxy images, andtakes into account the convolution with the PSF. Using a self-calibrating scheme, it has been shown to measure shear of galax-ies to percent level accuracy, in simulated KiDS r -band images(Fenech Conti et al. 2017; Kannawadi et al. 2019).Shears are obtained using lens fit for galaxies with an r -bandmagnitude larger than 20, which does not allow us to use thesefor shapes of our lens sample. In addition, lens fit is optimised forsmall SNR galaxies and a set-up for measuring bright galaxiesis not readily available. To acquire shape information for ourlens sample we apply the DEIMOS shape measurement method(Melchior et al. 2011) on the A stro W ise reduced r -band KiDSimages.DEIMOS is based on measuring weighted surface bright-ness moments from galaxy images and using these to infer thegalaxy’s ellipticity. Unlike other moment-based techniques, it al-lows for a mathematically accurate correction of the PSF convo-lution with the galaxy’s light profile avoiding any assumptionson the profile or behaviour of the PSF. The accuracy of this cor-rection is only limited by the accuracy of the PSF modelling.Moreover, a correction for the necessary radial weighting, em-ployed during moment measurement, is used; higher-order mo-ments are calculated in order to approximate the unweightedgalaxy moments from measured weighted moments.To model the PSF we use shapelets (Refregier 2003); orthog-onal Hermite polynomials multiplied with Gaussian functionsthat can be linearly combined to describe image shapes. The pro-cess is described in Kuijken et al. (2015), where the model hasbeen shown to perform very well in KiDS imaging data, display-ing very small residual correlation between the modelled ellip-ticities and the ones measured by using the stars in the image. Tomeasure galaxy moments, we use an elliptical Gaussian weightfunction, following a per-galaxy matching procedure. The sizeof the weight function is tied to the scale of this Gaussian, andwe use two di ff erent scales in this work, equal to the isophote ofthe galaxies r iso and 1 . r iso (defined at 3 σ above the background,see Georgiou et al. 2019b for more details). We use these twovalues to probe potential di ff erences in the measured ellipticityratio with the galaxy scale probed; a larger weight function willreveal more of the shape of the outer galaxy regions. Neighbour-ing sources in the image are masked using segmentation mapsfrom SE xtractor (Bertin & Arnouts 1996). A detailed descrip-tion of the shape measurement process can be found in Georgiouet al. (2019b).For the GAMA galaxy sample, which is very similar in prop-erties to the lens sample used here, Georgiou et al. (2019b)showed that the multiplicative bias on the ellipticity (not shear) is https: // / theli / http: // / lower than 1%, and does not depend strongly on the galaxy prop-erties. This is attributed to the great flexibility of the DEIMOSmethod, as well as the fact that these galaxies have a very highSNR in the KiDS imaging data (with a mean SNR ∼
300 in r -band images) and are generally very well resolved compared tothe PSF size.In our analysis, we do not probe the lensing signal on verylarge scales and, therefore, we do not subtract the signal aroundrandom points, which in any case has been shown to be con-sistent with zero in other KiDS weak lensing measurements(Dvornik et al. 2017). Additive bias in the shape measurementsis not expected to bias the spherically averaged gravitationalshear measurements. The anisotropic lensing measurements arenot expected to be a ff ected either, since sources and lenses weremeasured using di ff erent shape measurement methods, and anyadditive biases (which are anyway measured to be negligiblysmall) are not expected to be correlated. Multiplicative biasesare also not expected to play a significant role, since they af-fect the isotropic and anisotropic lensing signal in the sameway, which would leave the measurement of halo ellipticity un-a ff ected. Furthermore, multiplicative bias for the lens shapeshave been shown to be on the sub-percent level (Georgiou et al.2019b), and do not a ff ect the calculation of the position angle ofthe lens. GAMA (Driver et al. 2009, 2011; Liske et al. 2015) is a spec-troscopic survey carried out with the Anglo-Australian Tele-scope, using the AAOmega multi-object spectrograph. It pro-vides spectroscopic information for ∼ ,
000 galaxies over fivesky patches of ∼
60 deg area each for a total coverage of ∼ . The three equatorial patches (G09, G12, G15) have a com-pleteness of 98.5% and are flux limited to r petrosian < . i < . z trainingwe used only the deeper and more complete equatorial data. Wehave verified that adding G23 does not improve the photo- z esti-mates (see Bilicki et al. 2021, for more details).The unique aspect of the GAMA sample is the high com-pleteness, together with the fact that no pre-selection is made onthe target galaxies besides imposing a flux limit and removingstars and point-like quasars (Baldry et al. 2010). This nullifiesany selection e ff ects and provides the means to produce a highlypure and accurate group catalogue (Robotham et al. 2011). Thiscatalogue is produced using a friends-of-friends based algorithmto define galaxy groups and assign galaxies to them. We use thisgroup catalogue to validate our central galaxy sample selectionfrom our lens galaxy sample, and quantify its purity, assumingthe satellites identified in the catalogue to be the true satellitesof the sample. We use the 10th version of this group catalogue,which does not contain the G23 region. After masking the lenssample according to the KiDS mask, we are left with ∼ , http: // / Article number, page 3 of 12 & A proofs: manuscript no. HaloEllipticity . . . . . z . . . . . . . S a t e lli t e f r a c t i o n Fig. 1.
The satellite fraction ( N sat / N all ) in the GAMA galaxy sample, inbins of redshift. The GAMA group catalogue used in this work is suscepti-ble to imperfections, especially for the more massive groups.Robotham et al. (2011) showed that the number of high richnessgroups was lower than what was expected from mock group cat-alogues specifically designed for validation of the group findingalgorithm. In addition, Jakobs et al. (2018) found, using hydro-dynamical simulations, that the group algorithm tends to frag-ment larger groups into smaller ones. Because of this, we chooseto also validate our central sample selection using mock galaxycatalogues from a cosmological simulation, the MICE GrandChallenge run (Crocce et al. 2015).MICE is an N-body simulation containing ∼ × dark-matter particles in a (3 h − Gpc) comoving volume, fromwhich a mock galaxy catalogue has been built, using Halo Oc-cupation Distribution and Abundance Matching techniques (Car-retero et al. 2015). Halos are resolved down to few 10 M (cid:12) / h .The catalogue contains information for a large number of galaxyproperties, such as apparent magnitude, stellar mass, as well asa distinction of the galaxies into centrals and satellites, whichwe use in this work. Other applications of the catalogue includegalaxy clustering, weak lensing and higher-order statistics (Fos-alba et al. 2015a,b; Ho ff mann et al. 2015). We downloaded thepublicly available version 2 of the catalogue from cosmohub (Carretero et al. 2017). From the 5000 deg that the whole mockcatalogue covers, we cut out 200 deg and select galaxies withapparent SDSS-like r -band magnitude of < .
3. Central galaxy sample
In order to optimally extract the anisotropic weak lensing signalof elliptical dark matter halos, it is important to exclude galaxiesin our sample that reside in sub-halos, i.e. satellite galaxies (seee.g. van Uitert et al. 2017). Because of the hierarchical structureformation, central galaxies are commonly found in overdenseregions of the Universe where other neighbouring galaxies arealso likely to be found. Based on this, we developed an algorithmto search for galaxies in our sample that have a high chance ofbeing a central halo galaxy. https: // cosmohub.pic.es . . . . . Cylinder radius [Mpc /h ] . . . . P u r i t y GAMAGAMA low- z MICEMICE M ∗ MICE R Fig. 2.
Purity of our central galaxy sample, as a function of fixedcylinder radius used to identify centrals in overdense regions. Linesconnect the individual points. In solid blue we show results from theGAMA + KiDS-1000 overlap, over the photometric redshift space of0 . < z < .
5. We also show the results for redshifts between 0 . < z < . . < z < .
5. The red dash-dotted line are results obtained when welook for the most massive (in terms of stellar mass) galaxy in the cylin-der centre, instead of the brightest one. Finally, the purple dense dash-dotted line represents results obtained when, instead of a fixed cylinderradius we use multiples k of the galaxy’s R to define the radius size,with k = { , , , } . In this case, we plot the median value of the cylin-der radius on the x -axis, corresponding to the four di ff erent values ofpurity obtained. The algorithm is as follows: For every galaxy in our sample,we search for neighbouring galaxies inside a cylinder in sky andredshift space. The cylinder radius has a fixed physical lengthwhile the depth of the cylinder is determined by the accuracyof our redshift estimation. If neighbouring galaxies are indeedfound, we ask the question whether the galaxy we selected, thatlies in the middle of the cylinder, is the brightest galaxy (in the r -band) inside that cylinder. If this is true, we identify this galaxyas a central. We tested two di ff erent cylinder depths, ± d z and ± z (where d z is the redshift uncertainty, equal to ∼ . + z )for our lens galaxy sample) and chose the latter which was foundto perform better. We test the performance of this algorithm on the GAMA galaxysurvey sample as well as the mock galaxy catalogues from theMICE simulation. The spectroscopic information together withthe high completeness of the GAMA sample allows the construc-tion of a highly accurate group galaxy catalogue, which we usehere to identify central and satellite galaxies. We select centralgalaxies by removing any galaxy that is a satellite (we keep bothbrightest group galaxies as well as field galaxies, the latter areexpected to live in their own isolated dark matter halo or havesatellites around them too faint to detect).However, imperfections are present in this group catalogue(see Sect. 2.3). Therefore, we also use the MICE mock galaxycatalogues to validate our algorithm, where we know a priori thecentral and satellite galaxies. We mimic the photometric redshiftuncertainty in the mock catalogue redshifts by adding a randomnumber to them, drawn from a Gaussian distribution with scaleequal to the redshift uncertainty, i.e. ∼ . + z ). Article number, page 4 of 12hristos Georgiou et al.: Halo shapes constrained from a pure sample of central galaxies in KiDS-1000
We show the performance of our algorithm in Fig. 2, wherewe plot the purity (number of true centrals we identify over thetotal number of centrals we identify) of our central galaxy sam-ple, as a function of the fixed cylinder radius used. When usingthe GAMA survey as a reference, we see that we can achieve pu-rity of up to ∼
94 % for the largest cylinder radius. We can alsosee that the purity of the sample increases when a larger cylin-der is used, which is expected as it is less likely to mis-identifya very bright nearby satellite as a central when using a largercylinder, that is more likely to also contain the central galaxy.We also check the purity of our sample in low-redshift galax-ies (0 . < z < .
3) of the GAMA sample, where the satellitefraction remains high, around ∼
27 % (Fig. 1), since the algo-rithm could under-perform in this satellite-rich redshift space.We find, however, that the purity of the central sample is higherin this regime, building confidence in the validity of our centralsample selection.Results from applying the algorithm to the MICE2 mockgalaxy catalogue are also shown in Fig. 2. We see that the valuesfor purity that we achieve are very similar to the values we getusing GAMA, except for when using the largest cylinder radius.This means that, for the largest radius, the actual purity of ourcentral sample is higher than the one we measure using GAMA.In addition, we try to optimise our central selection by us-ing the stellar masses in the mock galaxy catalogues. First, wemodify the algorithm so as to select the most massive galaxy inthe cylinder’s centre, instead of the brightest one. For this, weuse the stellar mass present in the MICE catalogues, and plot thepurity in Fig. 2. The performance is worse compared to usingapparent brightness, suggesting that the central galaxy is moreoften the brightest one in the halo, but not the most massive, interms of stellar mass.Lastly, instead of using a fixed cylinder radius to search foroverdense regions, we use a per-galaxy cylinder radius, tied tothe R of the galaxy. To compute this, we use the stellar-to-halo mass relation computed for GAMA central galaxies (vanUitert et al. 2016), M c ∗ ( M h ) = M ∗ , ( M h / M h , ) β [1 + ( M h / M h , )] β − β , (1)where M c ∗ is the stellar mass of the central galaxy and M h thehalo mass. We use the best-fit values from van Uitert et al. (2016)for the rest of the parameters in this model and solve numericallyfor M h . We then compute the R from M h ≡ π (200 ¯ ρ m ) R / ρ m = . × h M (cid:12) / Mpc is the comoving matter den-sity. As can be seen from Fig. 2, the purity of the sample gener-ally increases when using a more per-galaxy optimised cylinder.It is clear that increasing the cylinder radius increases thepurity of our central galaxy sample, but this comes at a cost.Specifically, the completeness of the sample drops as the radiusincreases, and we end up with fewer galaxies for our analysis.This is expected, as larger cylinders will encompass more andmore central galaxies, making the sample less complete. Eventhe gain using the galaxy R as a cylinder radius causes thecompleteness to drop by ∼ ff erence in magnitude from thebrightest one. If two galaxies are in the same overdensity butare too close in magnitude, it is possible that the centre of thehalo does not correspond to the brightest galaxy. Therefore, wereject centrals that have a galaxy inside the same cylinder up to .
00 0 .
05 0 .
10 0 .
15 0 .
20 0 .
25 0 . Magnitude difference limit . . . . . P u r i t y Cylinder depth = 0 . z ) , radius = 0 . Mpc /h . . . . . . C o m p l e t e n e ss Fig. 3.
Purity (solid, left y -axis) and completeness (dashed, right y -axis) of our central galaxy sample after rejecting centrals with a galaxybrighter than a magnitude di ff erence from the central’s brightness,shown on the x -axis. The cylinder used was fixed at 0.6 Mpc / h . Linesconnect the individual points. a magnitude di ff erence limit. We plot the purity of the centralsample following this procedure, as a function of the magnitudedi ff erence limit for a fixed cylinder of 0.6 Mpc / h radius in Fig.3. We see that the purity increases as the magnitude di ff erencelimit increases, but the completeness drops.Based on this, we choose to use a magnitude di ff erence limitof 0.1 in our final sample. To increase the sample size whilenot compromising much on its purity, we opt for using a fixedcylinder radius of 0.6 Mpc / h . With this setup, we achieve a pu-rity of 93.4%, as quantified from the overlap with the GAMAgroup catalogue. The total number of central galaxies for thewhole KiDS-1000 area, after masking, is 138,607. Shape mea-surements are successfully obtained for 115,930 galaxies usinga weight function with scale equal to r iso and 117,601 galaxiesusing 1 . r iso . z accuracy Interestingly, the purity of the sample seems to plateau forlarge cylinders. To understand this better, we repeated the anal-ysis using the mock galaxy catalogues and sampling photo-metric redshifts with three di ff erent values of accuracy, d z = { . , . , . } (1 + z ). The first choice represents our lensgalaxy sample, the second corresponds to the photometric red-shifts achievable for Luminous Red Galaxies (LRGs, Rozo et al.2016; Vakili et al. 2019), and the last one is the expected redshiftaccuracy from a narrow-band based survey, such as the Physicsof the Accelerated Universe (PAUS Eriksen et al. 2019).The results are shown in Fig. 4, where we plot the purityand completeness for the di ff erent redshift accuracies. We alsochange the size of the cylinder in redshift space according to theredshift accuracy. Interestingly, the purity of the sample remainsroughly the same in all three cases. As the redshift accuracy andcylinder depth reduces, we see that the completeness of the sam-ple increases as well. From this we conclude that improvementsto the purity cannot be made by reducing the redshift uncertainty.The lack of improvement in purity can be understood if inlower mass groups the central halo galaxy does not always cor-respond to the brightest galaxy (see e.g. Lange et al. 2018). In-creasing the redshift accuracy allows for better determination ofcentrals in less massive halos, which, however, are expected to Article number, page 5 of 12 & A proofs: manuscript no. HaloEllipticity . . . . . Cylinder radius [Mpc /h ] . . . . P u r i t y Cylinder depth = 2∆ z (1 + z ) ∆ z = 0 . z = 0 . z = 0 . . . . . . C o m p l e t e n e ss Fig. 4.
Purity (solid lines) of our central galaxy sample selection asa function of the fixed cylinder radius. Lines connect the individualpoints. Results shown for three di ff erent simulated photometric red-shift accuracies. The depth of the cylinder is equal to ± y -axis, overplotted with dashed lines. carry a weaker signal of halo ellipticity. Therefore, it is better toincrease the area of the survey, if possible, instead of the redshiftaccuracy. This justifies our choice to use the much larger areaKiDS-1000 data, compared to the spectroscopic redshifts of theGAMA survey, for our analysis. We present here the characteristics of the final sample of cen-tral galaxies we compiled. The sample’s properties are obtainedfor the overlap of our KiDS-1000 sample with the GAMA sur-vey, where an extensive photometry and stellar mass catalogue isused (
StellarMassesLambdarv20,
Taylor et al. 2011; Wrightet al. 2016). This catalogue provides estimates of the stellarmass, absolute magnitudes and restframe colours of galaxies us-ing fits to galaxy SEDs from photometry in the optical + NIRbroad bands.In addition, we split the central sample into intrinsically redand blue galaxies. To do so, we isolate the red sequence galaxiesby inspecting the distribution of apparent g − i colour versus m r in 10 linear redshift bins in the redshift range of the lens sam-ple. With this division, we obtain 62426 red and 53504 blue lensgalaxy sub-samples. Their average ellipticity modulo is the sameas for the full sample, but their distributions show that slightlymore blue galaxies have ellipticities with absolute values below0 . . ∼ M (cid:12) and 10 . M (cid:12) , respectively.In addition to this, we show the distribution of restframe g − i colours, corrected for dust extinction, in the bottom panel of Fig.5, again for the full KiDS-1000 and central (all, blue and red)galaxy sample. We see that the central galaxy sample consistsof generally more red galaxies than the full sample. We also seethat the colour distributions of our selection of red and blue cen- log M ∗ [ log M (cid:12) ] . . . . . . . p ( l og M ∗ ) FullAll centralsRed centralsBlue centrals − . . . . . . . . g − i p ( g − i ) Fig. 5.
Top: normalised distribution of stellar mass of the full sample(in filled grey) and our central galaxy sample (in black, red and blue forall, red and blue centrals, respectively) in the GAMA overlap.
Bottom: normalised distribution of restframe, dust corrected g − i colour for thesame galaxy samples. trals generally follows the expected restframe g − i distribution,building confidence in our colour selection. We note, that a smallnumber of relatively blue galaxies enter our red galaxy sample,which is an e ff ect of our imperfect colour split based on pho-tometric redshift data and a visual inspection. However, giventhe number of these galaxies, we do not expect a cleaner sampleselection to alter our results.
4. Methodology
Gravitational lensing has the e ff ect of coherently distorting lightrays of background galaxies (sources) from the intervening mat-ter along the line of sight. Since galaxies are biased tracers ofthe matter density in the Universe, one expects to find a corre-lation between the position of foreground galaxies (lenses) andsource galaxy shapes. In its weak regime, the e ff ect is very small,and the observed ellipticities of source galaxies are only a ff ectedon the order of 1%. Large statistical ensembles of lens-sourcegalaxy pairs are therefore required to extract the weak lensingsignal.In this work, both for lens and source galaxies, we use thethird flattening, (cid:15) = (cid:15) + i (cid:15) , as an ellipticity measure, which isrelated to the semi-minor to semi-major axis ratio, q , by | (cid:15) | = (1 − q ) / (1 + q ). We can then express the tangential and cross Article number, page 6 of 12hristos Georgiou et al.: Halo shapes constrained from a pure sample of central galaxies in KiDS-1000 ellipticity of source galaxies with respect to the lens position as (cid:15) + = − (cid:15) cos(2 θ ) − (cid:15) sin(2 θ ) , (2) (cid:15) × = (cid:15) sin(2 θ ) − (cid:15) cos(2 θ ) , (3)where θ is the position angle of the line connecting the lens-source galaxy pair. When averaged over pairs, (cid:15) + provides anunbiased but noisy estimate of the gravitational shear γ , i.e. (cid:104) (cid:15) + (cid:105) ≈ γ + , which can then be related to the excess surface massdensity through ∆Σ ( R ) = ¯ Σ ( < R ) − Σ ( R ) = γ + ( R ) Σ crit , (4)with Σ crit the critical surface density, defined by Σ crit = c π G D s D l D ls . (5)In the above equation, c and G are the speed of light and gravita-tional constant, respectively, D s is the angular diameter distanceto the source galaxy, D l to the lens galaxy and D ls between thelens and source galaxy. Note that (4) holds true only when con-sidering an azumuthally averaged ensemble of lenses.The isotropic (azimuthally averaged) part of the lensing sig-nal can be calculated from the data using the estimator (cid:99) ∆Σ = (cid:32) (cid:80) ls w ls (cid:15) + Σ crit (cid:80) ls w ls (cid:33) , (6)where the sum runs over all lens-source galaxy pairs, that fall ina given projected radius bin. We weight each pair with ellipticityweights, w s , computed by lens fit, which accounts for uncertaintyin the shear estimate, and define w ls = w s Σ − . (7)Since galaxy redshifts are computed through photometry, it isimportant to account for the full posterior redshift distribution ofsource galaxies, p ( z s ) (see Sect. 2.1), when computing Σ crit . Thisis done with equation Σ − = π Gc (cid:90) ∞ z l D l ( z l ) D ls ( z l , z s ) D s ( z s ) p ( z s )d z s . (8) We model the anisotropic part of the lensing signal following theformalism presented in Schrabback et al. (2015) which is basedon work by Natarajan & Refregier (2000) and Mandelbaum et al.(2006). The excess surface mass density of a lens is modelled as ∆Σ model ( r , ∆ θ ) = ∆Σ iso ( r )[1 + f rel ( r ) | (cid:15) h , a | cos(2 ∆ θ )] . (9)In the above, ∆Σ iso is the excess surface mass density for a spher-ical halo (estimated from data using Eq. (6)) and ∆ θ is the po-sition angle coordinate in the lens plane, measured from thehalo’s semi-major axis. The ellipticity of the halo is probed bythe galaxy’s ellipticity, therefore, we are sensitive only to thealigned component of the halo ellipticity with the galaxy, | (cid:15) h , a | The anisotropy of the elliptical halo’s lensing is described by f rel ( r ), which depends on the assumed halo density profile andis generally a function of the projected separation r . For ellipti-cal halos not described by a single power-law, f rel ( r ) needs tobe computed numerically (see e.g. Mandelbaum et al. 2006),and we interpolate this quantity (using a cubic interpolation)from tabulated values. In order to avoid systematic biases in our anisotropic lensing signal measurement, it is also necessary todefine the excess surface mass with lens and source ellipticitiesrotated by π/
4, where we have ∆Σ , model ( r , ∆ θ ) = ∆Σ iso ( r )[4 f rel , ( r ) | (cid:15) h , a | cos(2 ∆ θ + π/ , (10)where f rel , ( r ) is obtained in the same manner as f rel ( r ).The quantity of interest is the ratio of the halo ellipticitymodulo to the galaxy ellipticity modulo, ˜ f h = | (cid:15) h | / | (cid:15) g | . How-ever, we can only measure this quantity weighted by the averagemis-alignment angle between the halo and host galaxy’s semi-major axis, ∆ φ h , g . Consequently, the measured quantity f h = ˜ f h (cid:104) cos(2 ∆ φ h , g ) (cid:105) (where we also assume that the mis-alignmentangle does not depend on | (cid:15) h | ). In order to extract f h from data,we use the following estimators, (cid:100) f ∆Σ = (cid:80) ls w ls (cid:15) + Σ crit | (cid:15) l | cos(2 φ ls ) (cid:80) ls w ls | (cid:15) l | cos (2 φ ls ) , (11)and (cid:91) f ∆Σ = − (cid:80) ls w ls (cid:15) × Σ crit | (cid:15) l | sin(2 φ ls ) (cid:80) ls w ls | (cid:15) l | sin (2 φ ls ) , (12)where φ ls is the angle between the lens semi-major axis andthe position vector connecting the lens-source galaxy pair.These two estimators can be predicted from f h f rel ∆Σ iso and f h f rel , ∆Σ iso , respectively. However, the estimators are easilycontaminated by systematic errors in the lensing signal measure-ments, such as imperfections due to incorrect PSF modelling orcosmic shear from structures between the lens and the observer(Mandelbaum et al. 2006; Schrabback et al. 2015). An estima-tor insensitive to these systematic e ff ects can be constructed bysubtracting the two, (cid:91) ( f − f ) ∆Σ = (cid:100) f ∆Σ − (cid:91) f ∆Σ . (13)For measuring the ellipticity ratio, we use this estimator, and theanalysis we follow is described below. f h To measure f h from data, we consider the two estimators x i = (cid:99) ∆Σ i and y i = (cid:91) ( f − f ) ∆Σ i / ( f rel ( r i ) − f ref , ( r i )), where the index i runs over the radial bins over which we calculate the lensing sig-nal and r i is the central value of that bin. These are two randomGaussian variables, which prohibits us from simply computingtheir fraction m = y i / x i , which would lead to a biased estimateof f h . To overcome this, we consider, for a given m , the quan-tity y i − mx i . This is a random Gaussian variable drawn from N (0 , w − i ), with w − i = σ y + m σ x and σ x , σ y are the error on themeasured estimators x i and y i , respectively (Mandelbaum et al.2006).The following sum ratio (cid:80) i w i ( y i − mx i ) (cid:80) i w i ∼ N (cid:32) , (cid:80) i w i (cid:33) (14)is also a random Gaussian variable. Based on this, we determineconfidence intervals of ± σ in measuring m , by considering theinequality − Z (cid:112)(cid:80) i w i < (cid:80) i w i ( y i − mx i ) (cid:80) i w i < + Z (cid:112)(cid:80) i w i . (15)We use m drawn from a grid and calculate f h by requiring f h = m ( Z = ± σ intervals by setting Z = Article number, page 7 of 12 & A proofs: manuscript no. HaloEllipticity ±
1. In addition, we compute the reduced χ from n radial binsusing χ = (cid:80) i w i ( y i − m ( Z = x i ) n − . (16)This method does not take into account the o ff -diagonal elementsof the covariance matrix of our measurements. These, however,where estimated to be very small (see Sect. 5), with the standarddeviation of the correlation matrix o ff -diagonal elements being4 × − .
5. Halo Ellipticity
We measure the weak lensing signal around our central galaxysample using 25 radial bins, logarithmically spaced between 20kpc / h and 1.2 Mpc / h . We restrict the sample to lens galaxieswith well defined ellipticities, 0 . < (cid:15) l < .
95. The median red-shift of the lenses is 0.26 and their average ellipticity is 0.188 forshapes obtained using weight function of r iso and 0.183 when us-ing 1 . r iso . We fit the isotropic weak lensing signal with an NFWprofile (Navarro et al. 1996; Wright & Brainerd 2000), while fix-ing the concentration-mass relation to Du ff y et al. (2008), c = . (cid:32) M × M (cid:12) / h (cid:33) − . (1 + z ) − . , (17)to finally obtaining an estimate for the scale radius r s . This isthen used to calculate f rel ( r ) and f rel , ( r ). We note that our mea-surements of f h are not very sensitive to the concentration-massrelation. Changing the constant in Eq. (17) by 20% shifts ourmeasured value by at most ∼ . σ , therefore we do not con-sider a more complicated relation. In NFW profile fits, we usethe mean redshift of the full lens sample. We also restrict the fitto the range from 40 kpc / h up to 200 kpc / h . The first limit min-imises signal from baryons in the centre of the halo, as well ascontamination of the source galaxy’s shear by the extended lightof each lens (Schrabback et al. 2015; Sifón et al. 2018). The up-per limit ensures that we do not include contributions from the2-halo term when fitting the lensing signal. This is a conserva-tive limit since we do not expect a strong 2-halo term in our lens-ing signal given that our galaxy sample has very small satellitegalaxy contamination.To calculate the covariance of our measurements we use abootstrap technique. We sample 10 random bootstrap samplesfrom the lens catalogue (with replacement) and use this data vec-tor to calculate the covariance matrix, obtaining error bars forour measurements from its diagonal elements. This techniqueignores errors due to sample variance from large-scale structure.However, these are expected to be negligible given the scaleswe probe. We test this by computing the covariance and errorsfrom a per-area bootstrap technique, dividing the survey into 1deg patches and computing the lensing signal in each patch. Wethen select 10 random bootstrap patches, weighting them by thenumber of lenses (since patches with significantly fewer than av-erage lenses will have a more uncertain signal measurement) andarrive at fully consistent error bars. We also find the o ff -diagonalelements of the covariance matrix to be negligible on all scales,justifying the analysis outlined in Sect. 4.2.We present our measurements in Fig. 6 for the case whenthe shape of the lens galaxy is measured using a weight func-tion with scale equal to r iso . Results around the full, red andblue lens galaxy sample are shown in the left, right and middlecolumn, respectively. The first row shows the isotropic lensing signal measurement, spherically averaged, as well as the best-fit NFW profile, with the ranges used in the fit indicated withdashed vertical lines. We also overplot the isotropic lensing sig-nal obtained from the full KiDS-1000 bright-end catalogue inthe same redshift range in the top left panel, for comparison. Wesee that our central galaxy sample is generally more massive andis not a ff ected by a strong 2-halo term, contrary to the full sam-ple. The resulting average halo mass for the three sub-samplescan be seen in Table 1. We have also checked that ∆Σ , which iscalculated by substituting the tangential with the cross ellipticitycomponent in Eq. (6), is consistent with zero across all measuredscales. This is expected, since a spherically averaged cross com-ponent is not generated by gravitational lensing, and serves as auseful sanity check for a potential systematic o ff set.In the next three rows of Fig. 6, we present the measurementof the anisotropic lensing signal for the three sub-samples. Weuse these measurements to calculate the ellipticity ratio, f h , fol-lowing Sect. 4.2, as well as the 1- σ confidence intervals. For the f h measurement, we use scales from 40 kpc / h up to the estimated r for the corresponding galaxy sample, which can be seen asdashed lines in the figure. For visualisation, we overplot the best-fit NFW profile of the corresponding galaxy sample, multipliedby f rel , f rel , or their di ff erence, accordingly, as well as the best-fit value of f h .The resulting values of f h , as well as the reduced χ of thefit are presented in Table 1. We see that the ellipticity ratio isfitted reasonably well, as expressed by the χ values. For thefull sample we measure an ellipticity ratio of 0.27 with a 1.5- σ statistical significance. For the red galaxies, the measured ratio ishigher, 0.34, and the significance also increases to 2- σ . Finally,we do not measure a significant ellipticity ratio for blue galaxies. Following the results presented in the previous section, we re-measure the ellipticity ratio, f h , using lens galaxy shapes with aweight function of scale equal to 1 . r iso . By using a larger weightfunction, the measured shapes will be more sensitive to the mor-phology of outer galaxy regions. The mean ellipticity of the lenssample is measured to be very similar when using the two weightfunctions (with a di ff erence of 0.005) and their distributions wereinspected to be nearly the same. Therefore, any di ff erence mea-sured in f h will be directly related to di ff erences in the meanmis-alignment angle, (cid:104) cos(2 ∆ φ h , g ) (cid:105) .The isotropic lensing signal obtained with the larger weightfunction is statistically the same, given that the lensing sampleis not systematically di ff erent. We show the anisotropic lensingmeasurements in the last row of Figure 6 with green diamonds,and the model obtained using the best-fit f h for a large weightfunction with a dashed red line (see also Table 1). The measuredsignal for ( f − f ) ∆Σ is higher, although only at a level of ∼ σ .When analysing the full sample, we measure an f h = . ± .
20, which is ∼ . f h = . ± .
19 and f h = . ± . . σ , while bluegalaxies are still found to have a value f h fully consistent withzero.From this analysis it is suggested that outer galaxy regionsare more aligned with the shape of the dark matter halo. This is inagreement with other observations, where central galaxies wherefound to be more aligned with their satellite galaxy distributions Article number, page 8 of 12hristos Georgiou et al.: Halo shapes constrained from a pure sample of central galaxies in KiDS-1000
Table 1.
Results from fits to the weak lensing signal, for the full sample, as well as the red and blue central galaxy sub-samples. The mean stellarmass is shown for galaxies in the KiDS-1000 and GAMA overlap, quoted from the
StellarMassesLambdarv20 catalogue. We also show thebest-fit and error of M from the NFW profile fits to the isotropic weak lensing signal as well as the resulting ellipticity ratio f h fit, with itsreduced χ , according to Sect. 4.2, obtained using the two di ff erent weight function sizes to measure lens galaxy shapes (see Sect. 2.1). Sample M ∗ [10 M (cid:12) ] M [10 M (cid:12) ] f h ( r wf / r iso = χ ( r wf / r iso = f h ( r wf / r iso = . χ ( r wf / r iso = . . ± .
16 0 . + . − . .
14 0 . ± .
20 1 . . ± .
30 0 . ± .
17 0 .
80 0 . ± .
19 0 . . ± .
14 0 . ± .
53 0 .
83 0 . ± .
55 1 . ff ectingthe outer, less bound galaxy regions more strongly, or the factthat infalling material to the central galaxy generally follows theellipticity of the dark matter halo. Our analysis closely follows work done in previous studies.Mandelbaum et al. (2006) used a very similar estimator on amuch larger lens sample, split in colour and luminosity. For theirL6 luminosity bin, which is closer to the mean luminosity of oursample, they found f h = . ± .
12 for red and f h = . + . − . for blue galaxies, but note that a sign inconsistency in theirmodel computation might have a ff ected these results (Schrab-back et al. 2015). van Uitert et al. (2012) also studied a largelens sample consisting of less massive galaxies than ours, andfound f h = . ± . , . ± .
15 and − . + . − . for all, redand blue lens samples, respectively. Following the same method-ology, Schrabback et al. (2015) studied a sample of lenses splitin colour and stellar mass, and found f h = − . ± .
25 for all redlenses and f h = . + . − . for all blue ones. They also providedpredictions of f h from the Millennium Simulation (Springel et al.2005), which agrees with the values we obtain here. The studiesabove used almost identical methodology as in this work andlens samples much larger than ours, but which were likely con-taminated by satellite galaxies. Our study indicates the impor-tance of selecting central galaxies for an anisotropic lensing sig-nal measurement.The pioneering work of Hoekstra et al. (2004) and Parkeret al. (2007), conducted similar measurements of f h for singleband photometric data and found f h = . + . − . and f h = . ± .
10, respectively. However, these results were not corrected forthe spurious signal introduced by other e ff ects that align lensand source ellipticities. This may have biased the resulting fhmeasurements to high values (Schrabback et al. 2015).Focussing on the brightest group galaxies (BGG) of theGAMA group catalogue specifically (using groups with morethan 5 members), van Uitert et al. (2017) detected an halo ellip-ticity of (cid:15) h = . ± .
12, using the BGG semi-major axis asa proxy for the halo’s orientation and focussing on scales below250 kpc. Similar ellipticity has also been detected for dark matterhalos of galaxy clusters (Evans & Bridle 2009; Clampitt & Jain2016; Shin et al. 2018; Umetsu et al. 2018). For comparison, wefind (cid:15) h = . . − . for the full sample and (cid:15) h = . ± . . × M (cid:12) , and cluster central galaxies being typicallymore massive than that. In order to check whether more massivegalaxies in our sample have an higher ellipticity ratio, we selectgalaxies based on stellar mass, obtained by running Le Phare (Il-bert et al. 2006) on the KiDS-1000 9-band photometry (Wrightet al. in prep.). Using all galaxies with M ∗ > . × M (cid:12) wefind f h = . ± .
19, which is slightly higher than the value forthe whole sample.The ellipticity we obtain is significantly lower than what ismeasured in galaxy groups. This suggests that either halos ofgalaxy groups and clusters are more elliptical than those of rela-tively isolated galaxies or that the mean misalignment betweenhalos and galaxies is smaller for group and cluster central galax-ies. In cosmological simulations, higher mass halos where foundto be more elliptical and less misaligned with their host galaxythan lower mass ones, which agrees with the trend observedhere (e.g. Tenneti et al. 2014; Velliscig et al. 2015; Chisari et al.2017). However, we do not measure a significant increase in f h when we restrict our sample to high stellar mass galaxies, whichleaves the interpretation unclear.Another possible reason for the discrepancy may be di ff er-ences in the shape measurement of the lenses. Shapes of lensgalaxies were derived using a generally large weight function invan Uitert et al. (2017) (private communication). We measurea larger f h when using a larger weight function for measuringshapes of lens galaxies in our sample, which might explain atleast part of the low halo ellipticity value we find in comparisonto galaxy groups.
6. Conclusions
In this work we measure the anisotropic lensing signal andhalo-to-galaxy ellipticity ratio of galaxies for a bright sample( m r (cid:46)
20) with accurate redshifts acquired through a machinelearning technique, trained on a similar spectroscopic sample(GAMA, m r , petro < . r -band) in a cylindrical area. We assess the purity of ourcentral galaxy sample using the overlap with GAMA and findthe purity to be = . Our sample consists of both BGG and field galaxies, the latter ex-pected to be either isolated galaxies or BGGs of groups whose satellitesare too faint to be detected within the imposed magnitude limit.Article number, page 9 of 12 & A proofs: manuscript no. HaloEllipticity c ∆ Σ [ h M (cid:12) / p c ] All centrals
CentralsFull Red centrals Blue centrals − − R d f ∆ Σ [ M (cid:12) / p c ] − − − − − . − . − . . . . . R d f ∆ Σ [ M (cid:12) / p c ] − . − . − . . . . . − . − . − . . . . . − Radial distance [Mpc /h ] − − R d ( f − f ) ∆ Σ [ M (cid:12) / p c ] small wf large wf − Radial distance [Mpc /h ] − − small wf large wf − Radial distance [Mpc /h ] − − Fig. 6.
Measurements of the weak lensing signal around our central galaxy sample. The first column shows results obtained for all centrals, whilethe second and third columns show results for the red and blue sub-samples, respectively (with open circles placed for negative measurements).The first row shows the isotropic lensing signal, the second and third row show the anisotropic lensing signal obtained with the estimators of Eqs.(11)-(12), while the last row shows the di ff erence, Eq. (13). The best-fit NFW profile is overplotted on the first row, with dashed vertical linesdepicting the ranges that were used during the fit. We also show the isotropic lensing signal of the full KiDS-1000 sample in grey points, as acomparison to the signal obtain using only the central galaxies. For the next rows we show the best-fit NFW profile multiplied by the best-fit f h and f rel , f rel , and their di ff erence, respectively, as well as the ranges used during the fit with dashed lines. In the last row, with green diamondsand red dashed line we show the data and model with the best-fit f h obtained using a larger weight function of r wf = . r iso for measuring the lensgalaxy shapes. split the lens sample in intrinsically red and blue galaxies. Us-ing the measured lensing signal, we extract the ellipticity ra-tio f h (weighted by the misalignment angle between the galaxyand the halo semi-major axis) using an estimator una ff ected bysystematic errors, such as incorrect PSF modelling and cos-mic shear. We measure f h = . + . − . for the full sample and f h = . ± .
17 for an intrinsically red sub-sample, respec-tively, while for blue galaxies the ratio is fully consistent withzero. Our measurements are in agreement with predictions based on cosmological simulations and we demonstrate the importanceof using a highly pure sample of central galaxies for the halo el-lipticity measurement.Our results are generally in agreement with studies of simi-lar galaxy samples. However, we find a significantly lower haloellipticity when we compare to central galaxies of galaxy groupsand clusters. Cosmological simulations predict that lower masshalos are rounder and / or more misaligned with their host halothan more massive ones, which may explain part of this dif- Article number, page 10 of 12hristos Georgiou et al.: Halo shapes constrained from a pure sample of central galaxies in KiDS-1000 ference. Using shape estimates that are more sensitive to outergalaxy regions, we find a higher value for f h , specifically 0 . ± . . ± .
19 for the full and red sample, respectively, rejectingthe hypothesis of round halos and / or randomly aligned galaxieswith respect to their parent halo at 2 . . σ . This suggeststhere is a galaxy-scale dependence of the mis-alignment angle ∆ φ h , g , with outer regions of the host galaxy being more alignedwith its dark matter halo.Our results can also be connected with the di ff erence foundbetween the predicted galaxy intrinsic alignment signal of darkmatter halos and the observationally measured alignment ofgalaxies, which are found to have a much lower signal (e.g. Fal-tenbacher et al. 2009; Okumura et al. 2009). In addition, galaxyintrinsic alignments have been observed to depend on the galaxyproperties, with more luminous (and therefore massive) galax-ies indicating a stronger alignment amplitude than less luminousones (Singh et al. 2015; Johnston et al. 2019). This trend of thealignment signal is in the same direction with the decreasingmisalignment of halos and galaxies with increasing halo massseen here and in cosmological simulations. References
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Acknowledgements.
The author list is divided into three tiers; the first three au-thors co-wrote this paper, MB provided infrastructure data as well as made asignificant informative contribution to the paper, and the rest of the authorscontributed infrastructure and are listed alphabetically. We acknowledge fund-ing from the European Research Council through grant numbers 770935 (AD,HHi, AW) and 647112 (CH, BG). HHo and AK acknowledges support fromVici grant 639.043.512, financed by the Netherlands Organisation for ScientificResearch (NWO). JTAdJ is supported by the NWO through grant 621.016.402.KK acknowledges support by the Alexander von Humboldt Foundation, theRoyal Society and Imperial College. MB is supported by the Polish Ministryof Science and Higher Education through grant DIR / WK / /