We show an efficient way to compute wide-angle or all-sky statistics of galaxy intrinsic alignment in three-dimensional configuration space. For this purpose, we expand the two-point correlation function using a newly introduced spin-dependent tripolar spherical harmonic basis. Therefore, the angular dependences on the two line-of-sight (LOS) directions pointing to each pair of objects, which are degenerate with each other in the conventional analysis under the small-angle or plane-parallel (PP) approximation, are unambiguously decomposed. By means of this, we, for the first time, compute the wide-angle auto and cross correlations between intrinsic ellipticities, number densities and velocities of galaxies, and compare them with the PP-limit results. For the ellipticity-ellipticity and density-ellipticity correlations, we find more than $10\%$ deviation from the PP-limit results if the opening angle between two LOS directions exceeds $30^\circ - 50^\circ$. It is also shown that even if the PP-limit result is strictly zero, the non-vanishing correlation is obtained over the various scales, arising purely from the curved-sky effects. Our results indicate the importance of the data analysis not relying on the PP approximation in order to determine the cosmological parameters more precisely and/or find new physics via ongoing and forthcoming wide-angle galaxy surveys.
The ellipticity function of cosmic voids exhibits strong dependence on the amplitude of the linear matter power spectrum. Analyzing the most recent void catalogs constructed by Foster and Nelson from the fifth data release of the Sloan Digital Sky Survey, we measure observationally the ellipticity function of giant galaxy voids. Then, we incorporate the redshift distortion and galaxy bias effect into the analytic model of the void ellipticity function and fit it to the observational result by adjusting the value of the power-spectrum normalization with the help of the generalized chi^{2}-minim…
In this work we study the shape of the projected surface mass density distribution of galaxy clusters using weak-lensing stacking techniques. In particular, we constrain the average aligned component of the projected ellipticity, $ε$, for a sample of redMaPPer clusters ($0.1 \leq z < 0.4$). We consider six different proxies for the cluster orientation and measure $ε$ for three ranges of projected distances from the cluster centres. The mass distribution in the inner region (up to $700\,$kpc) is better traced by the cluster galaxies with a higher membership probability, while the outer region (…
We study the ellipticity of galaxy cluster halos as characterized by the distribution of cluster galaxies and as measured with weak lensing. We use monte-carlo simulations of elliptical cluster density profiles to estimate and correct for Poisson noise bias, edge bias and projection effects. We apply our methodology to 10,428 SDSS clusters identified by the redMaPPer algorithm with richness above 20. We find a mean ellipticity $= 0.271 \pm 0.002$ (stat) $\pm 0.031$ (sys) corresponding to an axis ratio $= 0.573 \pm 0.002$ (stat) $\pm 0.039$ (sys). We compare this ellipticity of the satellites t…
Estimating the ellipticity of dark matter haloes at the galaxy or galaxy-cluster scale can provide important constraints on the formation of galaxies or clusters, as well as on the nature of dark matter. We show in this paper that the spin-3 gravitational flexion can add useful information on the ellipticity of lensing haloes. We introduce a general formalism to decompose fields with arbitrary spin into radial and tangential components. The ratio of the tangential and radial flexion components directly estimates the lens ellipticity. We point out that any centroid offset will significantly bia…
Topic of this paper is the time-evolution of intrinsic correlations of galaxy ellipticities due to peculiar motion. In our model, the galaxy ellipticities are determined from the angular momentum of their host haloes, which can be computed from the fluctuations statistics of a Gaussian random field. Subsequent peculiar motion distorts the ellipticity field and causes changes in the ellipticity correlations. Using analogies between this problem of shifted ellipticity tensors and the displacements of polarisation tensors in gravitational lensing of the cosmic microwave background we compute E-mo…
Subject of this paper are intrinsic ellipticity correlations between galaxies, their statistical properties, their observability with future surveys and their interference with weak gravitational lensing measurements. Using an angular momentum-based, quadratic intrinsic alignment model we derive correlation functions of the ellipticity components and project them to yield the four non-zero angular ellipticity spectra $C^ε_E(\ell)$, $C^ε_B(\ell)$, $C^ε_C(\ell)$ and $C^ε_S(\ell)$ in their generalisation to tomographic surveys. For a Euclid-like survey, these spectra would have amplitudes smaller…
Investigating intrinsic alignments (IAs) of galaxy shapes is important not only to constrain cosmological parameters unbiasedly from gravitational lensing but also to extract cosmological information complimentary to galaxy clustering analysis. We derive simple and useful formulas for the various IA statistics, including the intrinsic ellipticity--ellipticity correlation, the gravitational shear--intrinsic ellipticity correlation, and the velocity-intrinsic ellipticity correlation functions. The angular dependence of each statistic is explicitly given, namely the angle between the line-of-sigh…
The galaxy intrinsic alignment is a severe challenge to precision cosmic shear measurement. We propose to self-calibrate the induced gravitational shear-galaxy intrinsic ellipticity correlation (the GI correlation, \citealt{Hirata04b}) in weak lensing surveys with photometric redshift measurement. (1) We propose a method to extract the intrinsic ellipticity-galaxy density cross correlation (I-g) from the galaxy ellipticity-density measurement in the same redshift bin. (2) We also find a generic scaling relation to convert the extracted I-g correlation to the demanded GI correlation. We perform…
We investigate the effects of halo ellipticity and alignment with larger-scale structure on the galaxy correlation function. We base our analysis on the galaxy formation models of Guo et al. (2011), run on the Millennium Simulations. We quantify the importance of these properties of the galaxy distribution by randomizing the angular positions of satellite galaxies within haloes, either coherently or individually, while keeping the distance to their respective central galaxies fixed. We find that the effect of disrupting the alignment with larger-scale structure is a ~2 per cent decrease in the…
Aims. The predictions of the ellipticity of the dark matter halos from models of structure formation are notoriously difficult to test with observations. A direct measurement would give important constraints on the formation of galaxies, and its effect on the dark matter distribution in their halos. Here we show that galaxy-galaxy flexion provides a direct and potentially powerful method for determining the ellipticity of (an ensemble of) elliptical lenses. Methods. We decompose the spin-1 flexion into a radial and a tangential component. Using the ratio of tangential-to- radial flexion, which…
We develop a method for performing a weak lensing analysis using only measurements of galaxy position angles. By analysing the statistical properties of the galaxy orientations given a known intrinsic ellipticity distribution, we show that it is possible to obtain estimates of the shear by minimizing a $χ^2$ statistic. The method is demonstrated using simulations where the components of the intrinsic ellipticity are taken to be Gaussian distributed. Uncertainties in the position angle measurements introduce a bias into the shear estimates which can be reduced to negligible levels by introducin…
The statistical properties of the ellipticities of galaxy images depend on how galaxies form and evolve, and therefore constrain models of galaxy morphology, which are key to the removal of the intrinsic alignment contamination of cosmological weak lensing surveys, as well as to the calibration of weak lensing shape measurements. We construct such models based on the halo properties of the Millennium Simulation and confront them with a sample of 90,000 galaxies from the COSMOS Survey, covering three decades in luminosity and redshifts out to z=2. The ellipticity measurements are corrected for …
We extend the 3-point intrinsic alignment self-calibration technique to the gravitational shear-intrinsic ellipticity-intrinsic ellipticity (GII) bispectrum. The proposed technique will allow the measurement and removal of the GII intrinsic alignment contamination from the cross-correlation weak lensing signal. While significantly decreased from using cross-correlations instead of auto-correlation in a single photo-z bin, the GII contamination persists in adjacent photo-z bins and must be accounted for and removed from the lensing signal. We relate the GII and galaxy density-intrinsic elliptic…
Dipolar power asymmetry in wide-angle correlations of galaxy density, velocity and ellipticity
Institute of Astronomy and Astrophysics Academia Sinica（中央研究院天文及天文物理研究所）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo（东京大学宇宙线研究所理研数理宇宙学前沿研究中心卡弗里宇宙物理数学研究所）；Theory Center, Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK)（高能加速器研究机构粒子核物理研究所理论中心）；Department of Economics, Management and Information Science, Onomichi City University（尾道市立大学经济经营管理信息科学系）
We present weak lensing constraints on the ellipticity of galaxy-scale matter haloes and the galaxy-halo misalignment. Using data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), we measure the weighted-average ratio of the aligned projected ellipticity components of galaxy matter haloes and their embedded galaxies, $f_\mathrm{h}$, split by galaxy type. We then compare our observations to measurements taken from the Millennium Simulation, assuming different models of galaxy-halo misalignment. Using the Millennium Simulation we verify that the statistical estimator used remove…
Cosmological simulations predict that galaxies are embedded into triaxial dark matter haloes, which appear approximately elliptical in projection. Weak gravitational lensing allows us to constrain these halo shapes and thereby test the nature of dark matter. Weak lensing has already provided robust detections of the signature of halo flattening at the mass scales of groups and clusters, whereas results for galaxies have been somewhat inconclusive. Here we combine data from five surveys (NGVSLenS, KiDS/KV450, CFHTLenS, CS82, and RCSLenS) in order to tighten observational constraints on galaxy-s…
Weak gravitational lensing has become a powerful probe of large-scale structure and cosmological parameters. Precision weak lensing measurements require an understanding of the intrinsic alignment of galaxy ellipticities, which can in turn inform models of galaxy formation. It is hypothesized that elliptical galaxies align with the background tidal field and that this alignment mechanism dominates the correlation between ellipticities on cosmological scales (in the absence of lensing). We use recent large-scale structure measurements from the Sloan Digital Sky Survey to test this picture with …
We study intrinsic alignments (IA) of galaxy image shapes within the Illustris cosmic structure formation simulations. We investigate how IA correlations depend on observable galaxy properties such as stellar mass, apparent magnitude, redshift, and photometric type, and on the employed shape measurement method. The correlations considered include the matter density-intrinsic ellipticity (mI), galaxy density-intrinsic ellipticity (dI), gravitational shear-intrinsic ellipticity (GI), and intrinsic ellipticity-intrinsic ellipticity (II) correlations. We find stronger correlations for more massive…
Subject of this paper are the statistical properties of ellipticity alignments between galaxies evoked by their coupled angular momenta. Starting from physical angular momentum models, we bridge the gap towards ellipticity correlations, ellipticity spectra and derived quantities such as aperture moments, comparing the intrinsic signals with those generated by gravitational lensing, with the projected galaxy sample of EUCLID in mind. We investigate the dependence of intrinsic ellipticity correlations on cosmological parameters and show that intrinsic ellipticity correlations give rise to non-Ga…
The galaxy intrinsic alignment causes the galaxy ellipticity-ellipticity power spectrum between two photometric redshifts to decrease faster with respect to the redshift separation $Δz^P$, for fixed mean redshift. This offers a valuable diagnosis on the intrinsic alignment. We show that the distinctive dependences of the GG, II and GI correlations on $Δz^P$ over the range $|Δz^P|\la 0.2$ can be understood robustly without strong assumptions on the intrinsic alignment. This allows us to measure the intrinsic alignment within each conventional photo-z bin of typical size $\ga 0.2$, through lensi…
We constrain the average halo ellipticity of ~2 600 galaxy groups from the Galaxy And Mass Assembly (GAMA) survey, using the weak gravitational lensing signal measured from the overlapping Kilo Degree Survey (KiDS). To do so, we quantify the azimuthal dependence of the stacked lensing signal around seven different proxies for the orientation of the dark matter distribution, as it is a priori unknown which one traces the orientation best. On small scales, the major axis of the brightest group/cluster member (BCG) provides the best proxy, leading to a clear detection of an anisotropic signal. In…
Cosmic shear is a powerful method to constrain cosmology, provided that any systematic effects are under control. The intrinsic alignment of galaxies is expected to severely bias parameter estimates if not taken into account. We explore the potential of a joint analysis of tomographic galaxy ellipticity, galaxy number density, and ellipticity-number density cross-correlations to simultaneously constrain cosmology and self-calibrate unknown intrinsic alignment and galaxy bias contributions. We treat intrinsic alignments and galaxy biasing as free functions of scale and redshift and marginalise …
Intrinsically aligned galaxy shapes are one of the most important systematics in cosmic shear measurements. So far theoretical studies of intrinsic alignments almost exclusively focus on their statistics at the two-point level. Results from numerical simulations, however, suggest that third-order measures might be even stronger affected. We therefore investigate the (angular) bispectrum of intrinsic alignments. In our fully analytical study we describe intrinsic galaxy ellipticities by a physical alignment model, which makes use of tidal torque theory. We derive expressions for the various com…
If properly calibrated, the shapes of galaxy clusters can be used to investigate many physical processes: from feedback and quenching of star formation, to the nature of dark matter. Theorists frequently measure shapes using moments of inertia of simulated particles'. We instead create mock (optical, X-ray, strong- and weak-lensing) observations of the twenty-two most massive ($\sim10^{14.7}\,M_\odot$) relaxed clusters in the BAHAMAS simulations. We find that observable measures of shape are rounder. Even when moments of inertia are projected into 2D and evaluated at matched radius, they overe…
Precision weak gravitational lensing experiments require measurements of galaxy shapes accurate to <1 part in 1000. We investigate measurement biases, noted by Voigt and Bridle (2009) and Melchior et al. (2009), that are common to shape measurement methodologies that rely upon fitting elliptical-isophote galaxy models to observed data. The first bias arises when the true galaxy shapes do not match the models being fit. We show that this "underfitting bias" is due, at root, to these methods' attempts to use information at high spatial frequencies that has been destroyed by the convolution with …
Gauss-Hermite and Gauss-Laguerre ("shapelet") decompositions of images have become important tools in galaxy modeling, particularly for the purpose of extracting ellipticity and morphological information from astronomical data. However, the standard shapelet basis functions cannot compactly represent galaxies with high ellipticity or large Sersic index, and the resulting underfitting bias has been shown to present a serious challenge for weak-lensing methods based on shapelets. We present here a new convolution relation and a compound "multi-scale" shapelet basis to address these problems, and…
Subject of this paper is the weak lensing effect on galaxies that show intrinsically correlated ellipticities. In our model, we investigate the distortion of the ellipticity field if the galaxies experience an apparent shift in their position by weak lensing deflection and compare this effect to the shearing effect induced by tidal fields. Starting with a derivation of intrinsic ellipticity spectra by employing a tidal torquing model generating galactic angular momenta, we model the galaxy ellipticity by assuming that the galactic disk forms perpendicularly to the host halo angular momentum di…
In this paper we present a power spectrum formalism that combines the full three-dimensional information from the galaxy ellipticity field, with information from the cosmic microwave background (CMB). We include in this approach galaxy cosmic shear and galaxy intrinsic alignments, CMB deflection, CMB temperature and CMB polarisation data; including the inter-datum power spectra between all quantities. We apply this to forecasting cosmological parameter errors for CMB and imaging surveys for Euclid-like, Planck, ACTPoL, and CoRE-like experiments. We show that the additional covariance between t…
There is a growing interest in utilizing intrinsic alignment (IA) of galaxy shapes as a geometric and dynamical probe of cosmology. In this paper we present the first measurements of IA in a modified gravity model using the gravitational shear-intrinsic ellipticity correlation (GI) and intrinsic ellipticity-ellipticity correlation (II) functions of dark-matter halos from $f(R)$ gravity simulations. By comparing them with the same statistics measured in $Λ$CDM simulations, we find that the IA statistics in different gravity models show distinguishable features, with a trend similar to the case …
We report the first constraints on the growth rate of the universe, $f(z)σ_8(z)$, with intrinsic alignments (IAs) of galaxies. We measure the galaxy density-intrinsic ellipticity cross-correlation and intrinsic ellipticity autocorrelation functions over $0.16 < z < 0.7$ from luminous red galaxies (LRGs) and LOWZ and CMASS galaxy samples in the Sloan Digital Sky Survey (SDSS) and SDSS-III BOSS survey. We detect clear anisotropic signals of IA due to redshift-space distortions. By combining measured IA statistics with the conventional galaxy clustering statistics, we obtain tighter constraints o…
This is the second part of a thorough investigation of the redshift-space effects that affect void properties and the impact they have on cosmological tests. Here, we focus on the void-galaxy cross-correlation function, specifically, on the projected versions that we developed in a previous work. The pillar of the analysis is the one-to-one relationship between real and redshift-space voids above the shot-noise level identified with a spherical void finder. Under this mapping, void properties are affected by three effects: (i) a systematic expansion as a consequence of the distortions induced …
We investigate cosmological parameter inference from realistic simulated weak lensing image data using only galaxy position angles, as opposed to full-ellipticity information. We demonstrate that input shear fields can be accurately reconstructed using only the statistics of source galaxy position angles and that, from these shear fields, we can successfully recover power spectra and infer the input cosmology. This paper builds on previous work on angle-only weak lensing estimation by extending the method to deal with variable and anisotropic PSF convolution and variable shear fields. Previous…
There is a growing interest of using the intrinsic alignment (IA) of galaxy images as a tool to extract cosmological information complimentary to galaxy clustering analysis. Recently, Okumura & Taruya derived useful formulas for the intrinsic ellipticity--ellipticity correlation, the gravitational shear--intrinsic ellipticity correlation, and the velocity--intrinsic ellipticity correlation functions based on the linear alignment (LA) model. In this paper, using large-volume $N$-body simulations, we measure these alignment statistics in real and redshift space and compare them to the LA and non…
We study the effects on the number counts of sub-millimetre galaxies due to gravitational lensing. We explore the effects on the magnification cross section due to halo density profiles, ellipticity and cosmological parameter (the power-spectrum normalisation $σ_8$). We show that the ellipticity does not strongly affect the magnification cross section in gravitational lensing while the halo radial profiles do. Since the baryonic cooling effect is stronger in galaxies than clusters, galactic haloes are more concentrated. In light of this, a new scenario of two halo population model is explored …
In this work we investigate the environmental dependence of the intrinsic ellipticity correlations in cosmic shear surveys. We use the quadratic and linear alignment model to describe the contributions by spiral and elliptical galaxies, respectively. The density field is in both cases described by a Gaussian random field and ellipticity correlation functions that are conditional on the environment of the galaxies are constructed by sampling random values for the tidal tensor and inertial tensor. The covariance of the Gaussian random process from which the tensor entries are drawn is decomposed…
UNIONS-3500 Weak Lensing: I. A Galaxy Shape Catalogue in the Northern Sky
Université Paris-Saclay（巴黎萨克雷大学）；Université Paris Cité（巴黎西岱大学）；CEA（法国原子能和替代能源委员会）；CNRS（法国国家科学研究中心）；Department of Astronomy, Steward Observatory, University of Arizona（亚利桑那大学斯图尔德天文台天文学系）；Dipartimento di Fisica - Sezione di Astronomia, Università di Trieste（的里雅斯特大学物理系天文学分部）；INAF-Osservatorio Astronomico di Trieste（意大利国家天体物理研究所的里雅斯特天文台）；IFPU, Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；Department of Physics, McWilliams Center for Cosmology and Astrophysics, Carnegie Mellon University（卡内基梅隆大学麦威廉斯宇宙学与天体物理学中心物理系）；Aix-Marseille Université（艾克斯-马赛大学）；Ruhr University Bochum（波鸿鲁尔大学）
The shape of dark matter haloes plays a critical role in constraining cosmology with upcoming large-scale structure surveys. In this paper, we study the correlations between the triaxial shapes and formation histories in dark matter haloes in the MultiDark Planck 2 N-body cosmological simulation. We find that halo ellipticity is strongly correlated with halo properties that serve as proxies of halo formation history, such as halo concentration and the peak-centroid offset. In particular, the correlation between halo ellipticity and halo concentration is nearly independent of the halo density p…
We present new measurements of dark matter distributions in 25 X-ray luminous clusters by making a full use of the two-dimensional (2D) weak lensing signals obtained from high-quality Subaru/Suprime-Cam imaging data. Our approach to directly compare the measured lensing shear pattern with elliptical model predictions allows us to extract new information on the mass distributions of individual clusters, such as the halo ellipticity and mass centroid. We find that these parameters on the cluster shape are little degenerate with cluster mass and concentration parameters. By combining the 2D fitti…
Weak gravitational lensing analyses are fundamentally limited by the intrinsic, non-Gaussian distribution of galaxy shapes. We explore alternative statistics for samples of ellipticity measurements that are unbiased, efficient, and robust. We take the non-linear mapping of gravitational shear and the effect of noise into account. We then discuss how the distribution of individual galaxy shapes in the observed field of view can be modeled by fitting Fourier modes to the shear pattern directly. We simulated samples of galaxy ellipticities, using both theoretical distributions and real data for e…
While awaiting direct velocity measurement of gas motions in the hot intracluster medium, we rely on indirect probes, including gas perturbations in galaxy clusters. Using a sample of $\sim 80$ clusters in different dynamic states from Omega500 cosmological simulations, we examine scaling relations between the fluctuation amplitudes of gas density, $δρ/ρ$, pressure, $δP/P$, X-ray surface brightness, Sunyaev-Zeldovich (SZ) y-parameter, and the characteristic Mach number of gas motions, $M_{\rm 1d}$. In relaxed clusters, accounting for halo ellipticities reduces $δρ/ρ$ or $δP/P$ by a factor of u…
Constraining Galaxy Cluster Triaxiality via Weak Lensing --- I. Preparation for the Rubin Data Beyond Leading Order
NSF-DOE Vera C. Rubin Observatory / SLAC National Accelerator Laboratory（NSF-DOE薇拉·C·鲁宾天文台/SLAC国家加速器实验室）；Kavli Institute for Particle Astrophysics and Cosmology, Stanford University（斯坦福大学卡弗里粒子天体物理学与宇宙学研究所）；Department of Physics and Astronomy, Stony Brook University（纽约州立大学石溪分校物理与天文学系）；Carnegie Mellon University（卡内基梅隆大学）；Faculty of Physics, Ludwig-Maximilians-Universit at（路德维希-马克西米利安大学物理学院）；University of Michigan（密歇根大学）；NSF’s National Optical-Infrared Astronomy Research Laboratory（美国国家光学红外天文研究实验室）；Istituto Nazionale di Astrofisica（意大利国家天体物理研究所）；Univ. Grenoble Alpes, CNRS, LPSC-IN2P3（格勒诺布尔阿尔卑斯大学/CNRS/LPSC-IN2P3）；Department of Physics, Brown University（布朗大学物理系）
We use a statistical sample of galaxy clusters from a large cosmological $N$-body$+$hydrodynamics simulation to examine the relation between morphology, or shape, of the X-ray emitting intracluster medium (ICM) and the mass accretion history of the galaxy clusters. We find that the mass accretion rate (MAR) of a cluster is correlated with the ellipticity of the ICM. The correlation is largely driven by material accreted in the last $\sim 4.5$~Gyr, indicating a characteristic time-scale for relaxation of cluster gas. Furthermore, we find that the ellipticity of the outer regions ($R\sim R_{\rm …
Joint Geometric and Dynamical Constraints on Cosmology from Anisotropies in Galaxy Intrinsic-Alignment Correlations
Academia Sinica Institute of Astronomy and Astrophysics (ASIAA)（中央研究院天文及天文物理研究所）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（卡弗里宇宙物理学起源研究所（世界顶级学术研究中心）、东京大学宇宙射线研究所）
Properties of galaxies like their absolute magnitude and their stellar mass content are correlated. These correlations are tighter for close pairs of galaxies, which is called galactic conformity. In hierarchical structure formation scenarios, galaxies form within dark matter halos. To explain the amplitude and the spatial range of galactic conformity two--halo terms or assembly bias become important. With the scale dependent correlation coefficients the amplitude and the spatial range of conformity are determined from galaxy and halo samples. The scale dependent correlation coefficients are i…
In this work, we combine ellipticity and major axis position angle measurements from the Sloan Digital Sky Server Data Release 16 (SDSS DR16) with the group finder algorithm of Rodriguez \& Merchán to determine the alignment of the central galaxies with the surrounding structures and satellite galaxies lying in their group. We use two independent methods: A modified version of the two-point cross-correlation function and the angle between the central galaxy orientation and the satellite galaxies relative position. The first method allows us to study the inner and outer regions of the cluster, …
Weak lensing three-point statistics are powerful probes of the structure of dark matter halos. We propose to use the correlation of the positions of galaxies with the shapes of background galaxy pairs, known as the halo-shear-shear correlation (HSSC), to measure the mean halo ellipticity and the abundance of subhalos in a statistical manner. We run high-resolution cosmological $N$-body simulations and use the outputs to measure the HSSC for galaxy halos and cluster halos. Non-spherical halos cause a characteristic azimuthal variation of the HSSC, and massive subhalos in the outer region near t…
