在基于通过近似、校准或机器学习方法生成的暗物质晕目录集构建星系模拟目录时，此类示踪剂的本征性质分配是至关重要的一步，因为这些性质会影响模拟星系团的丰度和模拟星系的空间分布。我们探索在校准/学习方法的背景下，明确使用聚类信息来分配暗物质晕性质的可能性。目标是仅基于晕分布的相空间性质和暗物质密度场，检索作为重建性质函数的一次和二次大有效偏置的正确信号。该算法重建一组晕性质（如 virial 质量、最大圆周速度、浓度和自旋），并约束其重现一次和二次（或组装）偏置。该算法的关键要素是单独分配的大尺度有效偏置的实现、考虑晕排斥的多尺度方法以及晕性质的分层分配。该方法有助于分配旨在复制大尺度有效偏置（一次和二次）的晕性质。这比文献中先前的方法有所改进，尤其是在高质量群体中。我们设计了一种策略，用于重建通过校准/学习算法获得的暗物质晕的主要性质，其方式是预期的一点和两点统计量（在大尺度上）复制来自详细 N 体模拟的信号。我们鼓励将此策略（或我们算法的实现）应用于基于近似方法的暗物质晕模拟目录的生成。
英文摘要：
When constructing galaxy mock catalogs based on suits of dark matter halo catalogs generated with approximated, calibrated or machine-learning approaches, the assignment of intrinsic properties for such tracers is a step of paramount relevance, given that these can shape the abundance of mock galaxy cluster and the spatial distribution of mock galaxies. We explore the possibility to assign properties of dark matter halos within the context of calibrated/learning approaches, explicitly using clustering information. The goal is to retrieve the correct signal of primary and secondary large-effective bias as a function of properties reconstructed solely based on phase-space properties of the halo distribution and dark matter density field. The algorithm reconstructs a set halo properties (such as virial mass, maximum circular velocity, concentration and spin) constraint to reproduce both primary and secondary (or assembly) bias. The key ingredients of the algorithm are the implementation of individually-assigned large-scale effective bias, a multi-scale approach to account for halo exclusion and a hierarchical assignment of halo properties. The method facilitates the assignment of halo properties aiming at replicating the large-scale effective bias, both primary and secondary. This improves over over previous methods found in the literature, especially at the high mass population. We have designed an strategy to reconstruct the main properties of dark matter halos obtained by calibrated/learning algorithms, in a way that the expected one and two-point statistics (on large scales) replicates the signal from detailed N-body simulations. We encourage the application of this strategy (or the implementation of our algorithm) for the generation of mock catalogs of dark matter halos based on approximated methods.
We present a method for populating dark matter simulations with haloes of mass below the resolution limit. It is based on stochastically sampling a field derived from the density field of the halo catalogue, using constraints from the conditional halo mass function n(m|δ). We test the accuracy of the method and show its application in the context of building mock galaxy samples. We find that this technique allows precise reproduction of the two-point statistics of galaxies in mock samples constructed with this method. Our results demonstrate that the full information content of a simulation ca…
Secondary halo bias, commonly known as 'assembly bias,' is the dependence of halo clustering on a halo property other than mass. This prediction of the Lambda-Cold Dark Matter cosmology is essential to modelling the galaxy distribution to high precision and interpreting clustering measurements. As the name suggests, different manifestations of secondary halo bias have been thought to originate from halo assembly histories. We show conclusively that this is incorrect for cluster-size haloes. We present an up-to-date summary of secondary halo biases of high-mass haloes due to various halo proper…
We explore the phenomenon commonly known as halo assembly bias, whereby dark matter halos of the same mass are found to be more or less clustered when a second halo property is considered, for halos in the mass range $3.7 \times 10^{11} \; h^{-1} \mathrm{M_{\odot}} - 5.0 \times 10^{13} \; h^{-1} \mathrm{M_{\odot}}$. Using the Large Suite of Dark Matter Simulations (LasDamas) we consider nine commonly used halo properties and find that a clustering bias exists if halos are binned by mass or by any other halo property. This secondary bias implies that no single halo property encompasses all the …
Intensity mapping of 21-cm line by several radio telescope experiments will probe the large-scale structure of the Universe in the post-reionization epoch. It requires a theoretical framework of neutral hydrogen (HI) clustering, such as modelling of HI power spectrum for Baryon Acoustic Oscillations (BAO) analysis. We propose a new method for reconstructing the HI map from dark matter distribution using N-body simulations. Several studies attempt to compute the HI power spectrum with N-body simulations by pasting HI gas at the dark matter halo centre, assuming the relation between the halo and…
Using two sets of large $N$-body simulations, we study the origin of the correlations of halo assembly time ($z_{\rm f}$), concentration ($v_{\rm max}/v_{\rm 200}$) and spin ($λ$) with the large-scale evolved density field at given halo mass, i.e. the secondary bias. We find that the secondary bias is the secondary effect of the correlations of halo properties with the linear density estimated at the same comoving scale. Using the linear density on different scales, we find two types of correlations. The internal correlation, which reflects the correlation of halo properties with the mean line…
High-resolution cosmological N-body simulations are excellent tools for modelling the formation and clustering of dark matter haloes. These simulations suggest complex physical theories of halo formation governed by a set of effective physical parameters. Our goal is to extract these parameters and their uncertainties in a Bayesian context. We make a step towards automatising this process by directly comparing dark matter density projection maps extracted from cosmological simulations, with density projections generated from an analytical halo model. The model is based on a toy implementation …
We investigate the role of angular momentum in the clustering of dark matter haloes. We make use of data from two high-resolution N-body simulations spanning over four orders of magnitude in halo mass, from $10^{9.8}$ to $10^{14}\ h^{-1}\ \text{M}_\odot$. We explore the hypothesis that mass accretion in filamentary environments alters the angular momentum of a halo, thereby driving a correlation between the spin parameter $λ$ and the strength of clustering. However, we do not find evidence that the distribution of matter on large scales is related to the spin of haloes. We find that a halo's s…
Secondary halo properties beyond mass, such as the mass accretion rate (MAR), concentration, and the half mass scale, are essential in understanding the formation of large-scale structure and dark matter halos. In this paper, we study the impact of secondary halo properties on the galaxy-galaxy lensing observable, $ΔΣ$. We build an emulator trained on N-body simulations to model $ΔΣ$ and quantify the impact of different secondary parameters on the $ΔΣ$ profile. We focus on the impact of MAR on $ΔΣ$. We show that a 3$σ$ detection of variations in MAR at fixed halo mass could be achieved with th…
Secondary Dependence of Baryonic Effects on the Density Profile of Dark Matter Halos
Case Western Reserve University（凯斯西储大学）；Universidad de Sevilla（塞维利亚大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Bologna（意大利国家核物理研究所博洛尼分所）；Durham University（杜伦大学）；Harvard–Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）
Cosmological cluster-scale strong gravitational lensing probes the mass distribution of the dense cores of massive dark matter halos and the structures along the line of sight from background sources to the observer. It is frequently assumed that the primary lens mass dominates the lensing, with the contribution of secondary masses along the line of sight being neglected. Secondary mass structures may, however, affect both the detectability of strong lensing in a given survey and modify the properties of the lensing that is detected. In this paper, we utilize a large cosmological N-body simula…
Connecting clustering and the cosmic web:Observational constraints on secondary halo bias
CONICET. Instituto de Astronomía Teórica y Experimental (IATE)（阿根廷国家科学研究委员会理论天体物理学研究所）；Universidad Nacional de Córdoba (UNC). Observatorio Astronómico de Córdoba (OAC)（科尔多瓦国立大学科尔多瓦天文台）；Departamento de Física, Universidad Técnica Federico Santa María（圣马利亚技术大学物理系）
Magnetized plasmas within halos of galaxies leave their footprint on the polarized anisotropies of the cosmic microwave background. The two dominant effects for astrophysical halos are Faraday rotation generating rotation of the plane of linear polarization, and Faraday conversion inducing a leakage from linear polarization to circular polarization. We revisit these sources of secondary anisotropies by computing the angular power spectra of the Faraday rotation angle and of the Faraday conversion rate by the large scale structures. To this end, we use the halo model and we pay special attentio…
We use the improved IllustrisTNG300 magneto-hydrodynamical cosmological simulation to revisit the effect that secondary halo bias has on the clustering of the central galaxy population. With a side length of 205 $h^{-1}$Mpc and significant improvements on the sub-grid model with respect to the previous Illustris boxes, IllustrisTNG300 allows us to explore the dependencies of galaxy clustering over a large cosmological volume and wide halo-mass range. We show, at high statistical significance, that the halo assembly bias signal (i.e., the secondary dependence of halo bias on halo formation reds…
Radio observations discovered large scale non thermal sources in the central Mpc regions of dynamically disturbed galaxy clusters (radio halos). The morphological and spectral properties of these sources suggest that the emitting electrons are accelerated by spatially distributed and gentle mechanisms, providing some indirect evidence for turbulent acceleration in the inter-galactic-medium (IGM). Only deep upper limits to the energy associated with relativistic protons in the IGM have been recently obtained through gamma and radio observations. Yet these protons should be (theoretically) the m…
The precision anticipated from next-generation cosmic microwave background (CMB) surveys will create opportunities for characteristically new insights into cosmology. Secondary anisotropies of the CMB will have an increased importance in forthcoming surveys, due both to the cosmological information they encode and the role they play in obscuring our view of the primary fluctuations. Quadratic estimators have become the standard tools for reconstructing the fields that distort the primary CMB and produce secondary anisotropies. While successful for lensing reconstruction with current data, quad…
We employ the hydrodynamical simulation IllustrisTNG to inform the galaxy-halo connection of the Luminous Red Galaxy (LRG) and Emission Line Galaxy (ELG) samples of the Dark Energy Spectroscopic Instrument (DESI) survey at redshift z ~ 0.8. Specifically, we model the galaxy colors of IllustrisTNG and apply sliding DESI color-magnitude cuts, matching the DESI target densities. We study the halo occupation distribution model (HOD) of the selected samples by matching them to their corresponding dark matter halos in the IllustrisTNG dark matter run. We find the HOD of both the LRG and ELG samples …
Atomic hydrogen (H I) gas, mostly residing in dark matter halos after cosmic reionization, is the fuel for star formation. Its relation with properties of host halo is the key to understand the cosmic H I distribution. In this work, we propose a flexible, empirical model of H I-halo relation. In this model, while the H I mass depends primarily on the mass of host halo, there is also secondary dependence on other halo properties. We apply our model to the observation data of the Arecibo Fast Legacy ALFA Survey (ALFALFA), and find it can successfully fit to the cosmic H I abundance ($Ω_{\rm HI}$…
Scaling relations among dark matter (DM) and stellar quantities are a valuable tool to constrain formation scenarios and the evolution of galactic structures. However, most of the DM properties are actually not directly measured, but derived through model dependent mass mapping procedures. It is therefore crucial to adopt theoretically and observationally well founded models. We use here an updated version of the secondary infall model (SIM) to predict the halo density profile, taking into account the effects of angular momentum, dissipative friction and baryons collapse. The resulting family …
We use N-body simulations to investigate the radial dependence of the density and velocity dispersion in cold dark matter (CDM) halos. In particular, we explore how closely Q rho/sigma^3, a surrogate measure of the phase-space density, follows a power-law in radius. Our study extends earlier work by considering, in addition to spherically-averaged profiles, local Q-estimates for individual particles, Q_i; profiles based on the ellipsoidal radius dictated by the triaxial structure of the halo, Q_i(r'); and by carefully removing substructures in order to focus on the profile of the smooth halo, …
Directionally sensitive dark matter (DM) direct detection experiments present the only way to observe the full three-dimensional velocity distribution of the Milky Way halo local to Earth. In this work we compare methods for extracting information about the local DM velocity distribution from a set of recoil directions and energies in a range of hypothetical directional and non-directional experiments. We compare a model independent empirical parameterisation of the velocity distribution based on an angular discretisation with a model dependent approach which assumes knowledge of the functiona…
Halo bias is the main link between the matter distribution and dark matter halos. In its simplest form, halo bias is determined by halo mass, but there are known additional dependencies on other halo properties which are of consequence for accurate modeling of galaxy clustering. Here we present the most precise measurement of these secondary-bias dependencies on halo age, concentration, and spin, for a wide range of halo masses spanning from 10$^{10.7}$ to 10$^{14.7}$ $h^{-1}$ M$_{\odot}$. At the high-mass end, we find no strong evidence of assembly bias for masses above M$_{vir}$ $\sim10^{14}…
In previous works we proposed the Reverse Zeldovich Approximation (RZA) method, which can be used to estimate the cosmological initial conditions underlying the galaxy distribution in the Local Universe using peculiar velocity data. In this paper, we apply the technique to run constrained cosmological simulations from the RZA-reconstructed initial conditions, designed to reproduce the large-scale structure of the Local Universe. We test the method with mock peculiar velocity catalogues extracted from a reference simulation. We first reconstruct the initial conditions of this reference simulati…
In this paper, in the framework of the secondary infall model, the correlation between the central surface density and the halo core radius of galaxy, and cluster of galaxies, dark matter haloes was analyzed, this having recently been studied on a wide range of scales. We used Del Popolo (2009) secondary infall model taking into account ordered and random angular momentum, dynamical friction, and dark matter (DM) adiabatic contraction to calculate the density profile of haloes, and then these profiles are used to determine the surface density of DM haloes. The main result is that $r_\ast$ (the…
We use results from a constrained, cosmological MHD simulation of the Local Universe to predict radio halos and their evolution for a volume limited set of galaxy clusters and compare to current observations. The simulated magnetic field inside the clusters is a result of turbulent amplification within them, with the magnetic seed originating from star-burst driven, galactic outflows. We evaluate three models, where we choose different normalizations for the Cosmic Ray proton population within clusters. Similar to our previous analysis of the Coma cluster (Donnert et al. 2010), the radial prof…
The gravitational coupling between large-scale perturbations and small-scale perturbations leads to anisotropic distortions of the small-scale matter distribution. The measured local small-scale power spectrum can thus be used to infer the large-scale matter distribution. In this paper, we present a new tidal reconstruction algorithm for reconstructing large-scale modes using the full three-dimensional tidal shear information. We apply it to simulated dark matter halo fields and the reconstructed large-scale density field correlates well with the original matter density field on large scales, …
Halo assembly bias is the secondary dependence of the clustering of dark-matter haloes on their assembly histories at fixed halo mass. This established dependence is expected to manifest itself on the clustering of the galaxy population, a potential effect commonly known as galaxy assembly bias. Using the IllustrisTNG300 magnetohydrodynamical simulation, we analyse the dependence of the properties and clustering of galaxies on the shape of the specific mass accretion history of their hosting haloes (sMAH). We first show that several halo and galaxy properties strongly correlate with the slope …
We explore the potential of the kinetic Sunyaev-Zel'dovich (kSZ) effect as the cornerstone of a future observational probe for halo spin bias, the secondary dependence of halo clustering on halo spin at fixed halo mass. Using the IllustrisTNG magneto-hydrodynamical cosmological simulation, we measure both the kSZ and the thermal SZ (tSZ) effects produced by the baryonic content of more than 50,000 haloes within the halo mass range $11 < \log_{10} ({\rm M_{vir}}/ h^{-1} {\rm M_{\odot}}) \lesssim 14.5$. First, we confirm that the magnitude of both effects depends strongly on the total gas and vi…
We explore two widely used empirical models for the galaxy-halo connection, subhalo abundance matching (SHAM) and the halo occupation distribution (HOD) and compare their predictions with the hydrodynamical simulation IllustrisTNG (TNG) for a range of statistics that quantify the galaxy distribution at $n_{\rm gal}\approx1.3\times10^{-3}\,[{\rm Mpc}/h]^{-3}$. We observe that in their most straightforward implementations, both models fail to reproduce the two-point clustering measured in TNG. We find that SHAM models constructed using the relaxation velocity, $V_{\rm relax}$, and the peak veloc…
We present an MHD simulation of the emergence of a radio minihalo in a galaxy cluster core in a "secondary" model, where the source of the synchrotron-emitting electrons is hadronic interactions between cosmic-ray protons with the thermal intracluster gas, an alternative to the "reacceleration model" where the cosmic ray electrons are reaccelerated by turbulence induced by core sloshing, which we discussed in an earlier work. We follow the evolution of cosmic-ray electron spectra and their radio emission using passive tracer particles, taking into account the time-dependent injection of electr…
Galaxy scaling laws, such as the Tully-Fisher, mass-size and Fall relations, can provide extremely useful clues on our understanding of galaxy formation in a cosmological context. Some of these relations are extremely tight and well described by one single parameter (mass), despite the theoretical existence of secondary parameters such as spin and concentration, which are believed to impact these relations. In fact, the residuals of these scaling laws appear to be almost uncorrelated with each other, posing significant constraints on models where secondary parameters play an important role. He…
We present a new method for determining Weakly Interacting Massive Particle (WIMP) properties in future tonne scale direct detection experiments which accounts for uncertainties in the Milky Way (MW) smooth dark matter distribution. Using synthetic data on the kinematics of MW halo stars matching present samples from the Sloan Digital Sky Survey, complemented by local escape velocity constraints, we demonstrate that the local dark matter density can be constrained to approximately 20% accuracy. For low mass WIMPs, we find that a factor of two error in the assumed local dark matter density lead…
To extract information from the clustering of galaxies on non-linear scales, we need to model the connection between galaxies and halos accurately and in a flexible manner. Standard halo occupation distribution (HOD) models make the assumption that the galaxy occupation in a halo is a function of only its mass, however, in reality, the occupation can depend on various other parameters including halo concentration, assembly history, environment, spin, etc. Using the IllustrisTNG hydrodynamic simulation as our target, we show that machine learning tools can be used to capture this high-dimension…
Future ground-based CMB experiments will generate competitive large-scale structure datasets by precisely characterizing CMB secondary anisotropies over a large fraction of the sky. We describe a method for constraining the growth rate of structure to sub-1% precision out to $z\approx 1$, using a combination of galaxy cluster peculiar velocities measured using the kinetic Sunyaev-Zel'dovich (kSZ) effect, and the velocity field reconstructed from galaxy redshift surveys. We consider only thermal SZ-selected cluster samples, which will consist of $\mathcal{O}(10^4-10^5)$ sources for Stage 3 and …
One of the most promising mechanisms for producing radio halos (RHs) in galaxy clusters is the reacceleration of cosmic-ray electrons by turbulences. However, the origin of the seed electrons for the reacceleration is still poorly constrained. In the secondary scenario, most of the seed electrons are injected via collision of proton cosmic-rays, while non-thermal electrons are directly injected in the primary scenario. In this paper, we examine the two scenarios for the seed electrons with the observed statistical properties of RHs, combining two methods: following the temporal evolutions of t…
We present a new algorithm which groups the subhaloes found in cosmological N- body simulations by structure finders such as SUBFIND into dark matter haloes whose formation histories are strictly hierarchical. One advantage of these `Dhaloes' over the commonly used friends-of-friends (FoF) haloes is that they retain their individual identity in cases when FoF haloes are artificially merged by tenuous bridges of particles or by an overlap of their outer diffuse haloes. Dhaloes are thus well-suited for modelling galaxy formation and their merger trees form the basis of the Durham semi-analytic g…
High precision cosmological distance measurements towards individual objects such as time delay gravitational lenses or type Ia supernovae are affected by weak lensing perturbations by galaxies and groups along the line of sight. In time delay gravitational lenses, "external convergence," kappa, can dominate the uncertainty in the inferred distances and hence cosmological parameters. In this paper we attempt to reconstruct kappa, due to line of sight structure, using a simple halo model. We use mock catalogues from the Millennium Simulation, and calibrate and compare our reconstructed P(kappa)…
On the dependence of galaxy assembly bias on the selection criteria, number density, and redshift of galaxy samples
Universidad Complutense de Madrid（马德里康普顿斯大学）；Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology（巴塞罗那高等物理研究所（IFAE），巴塞罗那科学技术学院）
The two-point clustering of dark matter halos is influenced by halo properties besides mass, a phenomenon referred to as halo assembly bias. Using the depth of the gravitational potential well, $V_{\rm max}$, as our secondary halo property, in this paper we present the first study of the scale-dependence assembly bias. In the large-scale linear regime, $r\geq10h^{-1}{\rm Mpc},$ our findings are in keeping with previous results. In particular, at the low-mass end ($M_{\rm vir}<M_{\rm coll}\approx10^{12.5}{\rm M}_{\odot}$), halos with high-$V_{\rm max}$ show stronger large-scale clustering relat…
The density profiles of dark matter haloes contain rich information about their growth history and physical properties. One particularly interesting region is the splashback radius, $R_{\rm sp}$, which marks the transition between particles orbiting in the halo and particles undergoing first infall. While the dependence of $R_{\rm sp}$ on the recent accretion rate is well established and theoretically expected, it is not clear exactly what parts of the accretion history $R_{\rm sp}$ responds to, and what other halo properties might additionally influence its position. We comprehensively invest…
In the present paper, we improve the "Extended Secondary Infall Model" (ESIM) of Williams et al. (2004) to obtain further insights on the cusp/core problem. The model takes into account the effect of ordered and random angular momentum, dynamical friction and baryon adiabatic contraction in order to obtain a secondary infall model more close to the collapse reality. The model is applied to structures on galactic scales (normal and dwarf spiral galaxies) and on cluster of galaxies scales. The results obtained suggest that angular momentum and dynamical friction are able, on galactic scales, to …
We derive the weight function w(M) to apply to dark-matter halos that minimizes the stochasticity between the weighted halo distribution and its underlying mass density field. The optimal w(M) depends on the range of masses being used in the estimator. In N-body simulations, the Poisson estimator is up to 15 times noisier than the optimal. Implementation of the optimal weight yields significantly lower stochasticity than weighting halos by their mass, bias or equal. Optimal weighting could make cosmological tests based on the matter power spectrum or cross-correlations much more powerful and/o…
Understanding the galaxy-halo connection is fundamental for contemporary models of galaxy clustering. The extent to which the haloes' assembly history and environment impact galaxy clustering (a.k.a. galaxy assembly bias; GAB), remains a complex and challenging problem. Using a semi-analytic galaxy formation model, we study the individual contributions of different secondary halo properties to the GAB signal. These are obtained by comparing the clustering of stellar-mass selected samples to that of shuffled samples where the galaxies are randomly reassigned to haloes of fixed mass and a specif…
Observational Evidence of Velocity Anisotropy Assembly Bias in Galaxy Clusters
CONICET. Instituto de Astronomía Teórica y Experimental (IATE)（阿根廷国家科学研究委员会理论与实验天体物理研究所）；Universidad Nacional de Córdoba (UNC). Observatorio Astronómico de Córdoba (OAC)（科尔多瓦国立大学科尔多瓦天文台）；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）；Centre for Particle Cosmology, University of Pennsylvania（宾夕法尼亚大学粒子宇宙学中心）；Departamento de Física, Universidad Técnica Federico Santa María（智利费德里科·Santa María理工大学物理系）
We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias $b_1$ and $b_2$ on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy $α$ to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work which exploits the near-Lognormal shape of the distribution of $α$ and results in very high precision calibrations. We present convenient fitting functions for the dependence of $b_1$ and…
Reconstructing the local density field with combined convolutional and point cloud architecture
Ecole Polytechnique Rte de Saclay, 91120 Palaiseau, France（巴黎-萨克雷高等理工学院）；Center for Data-Driven Discovery Kavli IPMU, UTIAS, The University of Tokyo（数据驱动发现中心）；The University of Tokyo（东京大学）
The reconstruction of the initial conditions of the Universe is an important topic in cosmology, particularly in the context of sharpening the measurement of the baryon acoustic oscillation (BAO) peak. Nonlinear reconstruction algorithms developed in recent years, when applied to late-time matter fields, can recover to a substantial degree the initial density distribution, however, when applied to sparse tracers of the matter field, the performance is poorer. In this paper we apply the Shi et al. non-linear reconstruction method to biased tracers in order to establish what factors affect the r…
A steepening feature in the outer density profiles of dark matter halos indicating the splashback radius has drawn much attention recently. Possible observational detections have even been made for galaxy clusters. Theoretically, Adhikari et al. have estimated the location of the splashback radius by computing the secondary infall trajectory of a dark matter shell through a growing dark matter halo with an NFW profile. However, since they imposed a shape of the halo profile rather than computing it consistently from the trajectories of the dark matter shells, they could not provide the full sh…
