Concentration-mass Relation Research Articles

Improved halo model calibrations for mixed dark matter models of ultralight axions

Abstract We study the implications of relaxing the requirement for ultralight axions to account for all dark matter in the Universe by examining mixed dark matter (MDM) cosmologies with axion fractions f ≤ 0.3 within the fuzzy dark matter (FDM) window 10−25 eV ≲ m ≲ 10−23 eV. Our simulations, using a new MDM gravity solver implemented in AxiREPO, capture wave dynamics across various scales with high accuracy down to redshifts z ≈ 1. We identify halos with Rockstar using the CDM component and find good agreement of inferred halo mass functions (HMFs) and concentration–mass relations with theoretical models across redshifts z = 1 − 10. This justifies our halo finder approach a posteriori as well as the assumptions underlying the MDM halo model AxionHMcode. Using the inferred axion halo mass–cold halo mass relation Ma(Mc) and calibrating a generalised smoothing parameter α to our MDM simulations, we present a new version of AxionHMcode. The code exhibits excellent agreement with simulations on scales k < 20 h cMpc−1 at redshifts z = 1 − 3.5 for f ≤ 0.1 around the fiducial axion mass m = 10−24.5 eV = 3.16 × 10−25 eV, with maximum deviations remaining below 10 %. For axion fractions f ≤ 0.3, the model maintains accuracy with deviations under 20 % at redshifts z ≈ 1 and scales k < 10 h cMpc−1, though deviations can reach up to 30 % for higher redshifts when f = 0.3. Reducing the run-time for a single evaluation of AxionHMcode to below 1 minute, these results highlight the potential of AxionHMcode to provide a robust framework for parameter sampling across MDM cosmologies in Bayesian constraint and forecast analyses.

Cosmological simulations of scale-dependent primordial non-Gaussianity

We present the results of a set of cosmological N-body simulations with standard ΛCDM cosmology but characterized by a scale-dependent primordial non-Gaussianity of the local type featuring a power-law dependence of the f NL loc(k) at large scales followed by a saturation to a constant value at smaller scales where non-linear growth leads to the formation of collapsed cosmic structures. Such models are built to ensure consistency with current Cosmic Microwave Background bounds on primordial non-Gaussianity yet allowing for large effects of the non-Gaussian statistics on the properties of non-linear structure formation. We show the impact of such scale-dependent non-Gaussian scenarios on a wide range of properties of the resulting cosmic structures, such as the non-linear matter power spectrum, the halo and sub-halo mass functions, the concentration-mass relation, the halo and void density profiles, and we highlight for the first time that some of these models might mimic the effects of Warm Dark Matter for several of such observables.

Baryonic Imprints on DM Halos: the concentration-mass relation and its dependence on halo and galaxy properties

The halo concentration-mass relation has ubiquitous use in modeling the matter field for cosmological and astrophysical analyses, and including the imprints from galaxy formation physics is tantamount to its robust usage. Many analyses, however, probe the matter around halos selected by a given halo/galaxy property – rather than by halo mass – and the imprints under each selection choice can be different. We employ the CAMELS simulation suite to quantify the astrophysics and cosmology dependence of the concentration-mass relation, , when selected on five properties: (i) velocity dispersion, (ii) formation time, (iii) halo spin, (iv) stellar mass, and (v) gas mass. We construct simulation-informed nonlinear models for all properties as a function of halo mass, redshift, and six cosmological/astrophysical parameters, with a mass range . There are many mass-dependent imprints in all halo properties, with clear connections across different properties and non-linear couplings between the parameters. Finally, we extract the relation for subsamples of halos that have scattered above/below the mean property- relation for a chosen property. Selections on gas mass or stellar mass have a significant impact on the astrophysics/cosmology dependence of , while those on any of the other three properties have a significant (mild) impact on the cosmology (astrophysics) dependence. We show that ignoring such selection effects can lead to errors of ≈25% in baryon imprint modelling of . Our nonlinear model for all properties is made publicly available.

Cosmological gravity on all scales. Part III. Non-linear matter power spectrum in phenomenological modified gravity

Model-independent tests of gravity with cosmology are important when testing extensions to the standard cosmological model. To maximise the impact of these tests one requires predictions for the matter power spectrum on non-linear scales. In this work we validate the ReACT approach to the non-linear matter power spectrum against a suite of phenomenological modified gravity N-body simulations with a time-varying gravitational constant, covering a wider range of parameter space than previously examined. This vanilla application of ReACT has limited range and precision due to the different concentration-mass relation c(M) that occurs when gravity is modified. We extend this approach with a fitting function for a modified concentration-mass relation, allowing for accurate (1%) computation of the matter power spectrum up k = 2 h Mpc-1 across a substantial range of parameter space. This fitting function allows precision model-independent tests of modified gravity to be carried out using the data from upcoming large scale structure surveys.

Entropy optimization in bio-convective chemically reactive flow of micropolar nanomaterial with activation energy and gyrotactic microorganisms

Entropy optimization in bio-convective chemically reactive flow of micropolar nanomaterial with activation energy and gyrotactic microorganisms

Confirmation of an Anomalously Low Dark Matter Content for the Galaxy NGC 1052-DF4 from Deep, High-resolution Continuum Spectroscopy

NGC 1052-DF4 was found to be the second “galaxy lacking dark matter” in the NGC 1052 group, based on its velocity dispersion of km s−1 as measured from the radial velocities of seven of its globular clusters. Here we verify this result by measuring the stellar velocity dispersion of the galaxy. We observed the diffuse stellar light in NGC 1052-DF4 with the Keck Cosmic Web Imager in its highest-resolution mode, with km s−1. With a total science + sky exposure time of 34 hr, the resulting spectrum is exceptional in both its spectral resolution and its signal-to-noise ratio of 23 Å−1. We find a stellar velocity dispersion of km s−1, consistent with the previous measurement from the globular clusters. Combining both measurements gives a fiducial dispersion of km s−1. The implied dynamical mass within the half-light radius is . The expected velocity dispersion of NGC 1052-DF4 from the stellar mass alone is 7 ± 1 km s−1, and for a Navarro–Frenk–White (NFW) halo that follows the stellar mass–halo mass relation and the halo mass–concentration relation, the expectation is ∼30 km s−1. The low velocity dispersion rules out a normal NFW dark matter halo, and we confirm that NGC 1052-DF4 is one of at least two galaxies in the NGC 1052 group that have an anomalously low dark matter content. While any viable model for their formation should explain the properties of both galaxies, we note that NGC 1052-DF4 now poses the largest challenge, as it has the most stringent constraints on its dynamical mass.

An emulator-based halo model in modified gravity – I. The halo concentration–mass relation and density profile

ABSTRACT In this series of papers, we present an emulator-based halo model for the non-linear clustering of galaxies in modified gravity cosmologies. In the first paper, we present emulators for the following halo properties: the halo mass function, concentration–mass relation and halo-matter cross-correlation function. The emulators are trained on data extracted from the forge and bridge suites of N-body simulations, respectively, for two modified gravity (MG) theories: f(R) gravity, and the DGP model, varying three standard cosmological parameters Ωm0, H0, σ8, and one MG parameter, either $\bar{f}_{R0}$ or rc. Our halo property emulators achieve an accuracy of ${\lesssim}1\ \hbox{per cent}$ on independent test data sets. We demonstrate that the emulators can be combined with a galaxy–halo connection prescription to accurately predict the galaxy–galaxy and galaxy–matter correlation functions using the halo model framework.

The MUSE-Faint survey

Aims. We use the stellar line-of-sight velocities of Antlia B (Ant B), a faint dwarf galaxy in the NGC 3109 association, to derive constraints on the fundamental properties of scalar field dark matter (SFDM), which was originally proposed to solve the small-scale problems faced by cold dark matter models. Methods. We used the first spectroscopic observations of Ant B, a distant (d ∼ 1.35 Mpc) faint dwarf (MV = −9.7, M⋆ ∼ 8 × 105 M⊙), from MUSE-Faint, a survey of ultra-faint dwarfs conducted using the Multi Unit Spectroscopic Explorer. By measuring the line-of-sight velocities of stars in the 1′×1′ field of view, we identified 127 stars as members of Ant B, which enabled us to model its dark matter density profile with the Jeans modelling code GRAVSPHERE. We implemented a model for SFDM into GRAVSPHERE and used this to place constraints on the self-coupling strength of this model. Results. We find a virial mass of M200 ≈ 1.66−0.92+2.51 × 109 M⊙ and a concentration parameter of c200 ≈ 17.38−4.20+6.06 for Ant B. These results are consistent with the mass-concentration relations in the literature. We constrain the characteristic length scale of the repulsive self-interaction RTF of the SFDM model to RTF ≲ 180 pc (68% confidence level), which translates to a self-coupling strength of g/m2c4 ≲ 5.2 × 10−20 eV−1 cm3. The constraint on the characteristic length scale of the repulsive self-interaction is inconsistent with the value required to match observations of the cores of dwarf galaxies in the Local Group, suggesting that the cored density profiles of those galaxies are not caused by SFDM.

Constraining interacting dark energy models with the halo concentration–mass relation

ABSTRACT The interacting dark energy (IDE) model is a promising alternative cosmological model that has the potential to solve the fine-tuning and coincidence problems by considering the interaction between dark matter and dark energy. Previous studies have shown that the energy exchange between the dark sector components in this model can significantly affect the dark matter halo properties. In this study, by utilizing a large set of cosmological N-body simulations, we analyse the redshift evolution of the halo concentration–mass (c–M) relation in the IDE model, and show that the c–M relation is a sensitive proxy of the interaction strength parameter ξ2, especially at lower redshifts. Furthermore, we construct parametrized formulae to quantify the dependence of the c–M relation on ξ2 at redshifts ranging from z = 0 to z = 0.6. Our parametrized formulae provide a useful theoretical tool in constraining ξ2 with the observational c–M relation. As a first attempt, we use the data from X-ray, gravitational lensing, and galaxy rotational curve observations and obtain a tight constraint on ξ2, i.e. ξ2 = 0.071 ± 0.034. Our work demonstrates that the halo c–M relation, which reflects the halo assembly history, is a powerful probe to constrain the IDE model.

Baryonic imprints on DM haloes: the concentration–mass relation in the C amels simulations

ABSTRACT The physics of baryons in haloes, and their subsequent influence on the total matter phase space, has a rich phenomenology and must be well understood in order to pursue a vast set of questions in both cosmology and astrophysics. We use the Cosmology and Astrophysics with MachinE Learning Simulation (Camels) suite to quantify the impact of four different galaxy formation parameters/processes (as well as two cosmological parameters) on the concentration–mass relation, cvir−Mvir. We construct a simulation-informed non-linear model for concentration as a function of halo mass, redshift, and six cosmological/astrophysical parameters. This is done for two galaxy formation models, IllustrisTNG and Simba, using 1000 simulations of each. We extract the imprints of galaxy formation across a wide range in mass $M_{\rm vir}\in [10^{11}, 10^{14.5}] \, {\rm M}_\odot \, h^{-1}$ and in redshift z ∈ [0, 6] finding many strong mass- and redshift-dependent features. Comparisons between the IllustrisTNG and Simba results show the astrophysical model choices cause significant differences in the mass and redshift dependence of these baryon imprints. Finally, we use existing observational measurements of cvir−Mvir to provide rough limits on the four astrophysical parameters. Our non-linear model is made publicly available and can be used to include Camels-based baryon imprints in any halo model-based analysis.

A non-parametric approach to the relation between the halo mass function and internal dark matter structure of haloes

Context. Galaxy cluster masses are usually defined as the mass within a spherical region enclosing a given matter overdensity (in units of the critical density). Converting masses from one overdensity definition to another can have several useful applications. Aims. In this article we present a generic non-parametric formalism that allows one to accurately map the halo mass function between two different mass overdensity definitions using the distribution of halo sparsities defined as the ratio of the two masses. We show that changing mass definitions reduces to modelling the distribution of halo sparsities. Methods. Using standard transformation rules of random variates, we derive relations between the halo mass function at different overdensities and the distribution of halo sparsities. Results. We show that these relations reproduce the N-body halo mass functions from the Uchuu simulation within the statistical errors at a few percent level. Furthermore, these relations allow the halo mass functions at different overdensities to be related to parametric descriptions of the halo density profile. In particular, we discuss the case of the concentration-mass relation of the Navarro-Frenk-White profile. Finally, we show that the use of such relations allows us to predict the distribution of sparsities of a sample of haloes of a given mass, thus opening the way to inferring cosmological constraints from individual galaxy cluster sparsity measurements.

Accurate analytic mass–scale relations for dark matter haloes of all masses and redshifts

ABSTRACTCUSP is a powerful formalism that recovers, from first principles and with no free parameter, all the macroscopic properties of dark matter haloes found in cosmological N-body simulations and unveils the origin of their characteristic features. Since it is not restricted by the limitations of simulations, it covers the whole mass and redshift ranges. In the present Paper we use CUSP to calculate the mass–scale relations holding for halo density profiles fitted to the usual NFW and Einasto functions in the most relevant cosmologies and for the most usual mass definitions. We clarify the origin of these relations and provide accurate analytic expressions holding for all masses and redshifts. The performance of those expressions is compared to that of previous models and to the mass–concentration relation spanning more than 20 orders of magnitude in mass at z = 0 obtained in recent simulations of a 100 GeV WIMP universe.

The Concentration–Mass relation of massive, dynamically relaxed galaxy clusters: agreement between observations and ΛCDM simulations

ABSTRACT The relationship linking a galaxy cluster’s total mass with the concentration of its mass profile and its redshift is a fundamental prediction of the Cold Dark Matter (CDM) paradigm of cosmic structure formation. However, confronting those predictions with observations is complicated by the fact that simulated clusters are not representative of observed samples where detailed mass profile constraints are possible. In this work, we calculate the symmetry-peakiness-alignment (SPA) morphology metrics for maps of X-ray emissivity from the three hundred project hydrodynamical simulations of galaxy clusters at four redshifts, and thereby select a sample of morphologically relaxed, simulated clusters, using observational criteria. These clusters have on average earlier formation times than the full sample, confirming that they are both morphologically and dynamically more relaxed than typical. We constrain the concentration–mass–redshift relation of both the relaxed and complete sample of simulated clusters, assuming power-law dependences on mass (κm) and 1 + z (κζ), finding κm = −0.12 ± 0.07 and κζ = −0.27 ± 0.19 for the relaxed subsample. From an equivalently selected sample of massive, relaxed clusters observed with Chandra, we find κm = −0.12 ± 0.08 and κζ = −0.48 ± 0.19, in good agreement with the simulation predictions. The simulated and observed samples also agree well on the average concentration at a pivot mass and redshift providing further validation of the ΛCDM paradigm in the properties of the largest gravitationally collapsed structures observed. This also represents the first clear detection of decreasing concentration with redshift, a longstanding prediction of simulations in data.

The three hundredproject: a machine learning method to infer clusters of galaxy mass radial profiles from mock Sunyaev–Zel’dovich maps

ABSTRACTWe develop a machine learning algorithm to infer the three-dimensional cumulative radial profiles of total and gas masses in galaxy clusters from thermal Sunyaev–Zel’dovich effect maps. We generate around 73 000 mock images along various lines of sight using 2522 simulated clusters from the three hundred project at redshift z < 0.12 and train a model that combines an auto-encoder and a random forest. Without making any prior assumptions about the hydrostatic equilibrium of the clusters, the model is capable of reconstructing the total mass profile as well as the gas mass profile, which is responsible for the Sunyaev–Zel’dovich effect. We show that the recovered profiles are unbiased with a scatter of about 10 per cent, slightly increasing towards the core and the outskirts of the cluster. We selected clusters in the mass range of $10^{13.5} \le M_{200} /({{\, h^{-1}\,{\rm {{\rm M}_{\odot }}}}}) \le 10^{15.5}$, spanning different dynamical states, from relaxed to disturbed haloes. We verify that both the accuracy and precision of this method show a slight dependence on the dynamical state, but not on the cluster mass. To further verify the consistency of our model, we fit the inferred total mass profiles with a Navarro–Frenk–White model and contrast the concentration values with those of the true profiles. We note that the inferred profiles are unbiased for higher concentration values, reproducing a trustworthy mass–concentration relation. The comparison with a widely used mass estimation technique, such as hydrostatic equilibrium, demonstrates that our method recovers the total mass that is not biased by non-thermal motions of the gas.

The eROSITA Final Equatorial-Depth Survey (eFEDS)

Context.We present the results of a systematic X-ray analysis of optically rich galaxy clusters detected by the Subaru Hyper Suprime-Cam (HSC) survey in the eROSITA Final Equatorial-Depth Survey (eFEDS) field.Aims.Through a joint analysis of the SRG (Spectrum Roentgen Gamma)/eROSITA and Subaru/HSC surveys, we aim to investigate the dynamical status of the optically selected clusters and to derive the cluster scaling relations.Methods.The sample consists of 43 optically selected galaxy clusters with a richness >40 in the redshift range of 0.16–0.89. We systematically analyzed the X-ray images and emission spectra using the eROSITA data. We identified the brightest cluster galaxy (BCG) using the optical and far-infrared databases. We evaluated the cluster’s dynamical status by measuring three quantities: offset between the X-ray peak and BCG position, the gas concentration parameter, and the number of galaxy-density peaks. We investigated the luminosity–temperature and mass–luminosity relations based on eROSITA X-ray spectra and HSC weak-lensing data analyses.Results.Based on these three measurements, we estimated the fraction of relaxed clusters to be 2(< 39)%, which is smaller than that of the X-ray-selected cluster samples. After correcting for a selection bias due to the richness cut, we obtained a shallowL−Tslope of 2.1 ± 0.5, which is consistent with the predictions of the self-similar model and the baseline model incorporating a mass–concentration relation. TheL−Mslope of 1.5 ± 0.3 is in agreement with the above-cited theoretical models as well as the data on the shear-selected clusters in the eFEDs field.Conclusions.Our analysis of high-richness optical clusters yields a small fraction of relaxed clusters and a shallow slope for the luminosity–temperature relation. This suggests that the average X-ray properties of the optical clusters are likely to be different from those observed in the X-ray samples. Thus, the joint eROSITA and HSC observations are a powerful tool in extending the analysis to a larger sample and understanding the selection effect with a view to establish cluster scaling relations.

Discriminating power of milli-lensing observations for dark matter models

Context. The nature of dark matter (DM) is still under intense debate. Subgalactic scales are particularly critical, as different, currently viable DM models make diverse predictions on the expected abundance and density profile of DM haloes on these scales. Aims. We investigate the ability of subgalactic DM haloes to act as strong lenses on background compact sources, producing gravitational lensing events on milli-arcsecond scales (milli-lenses), for different DM models. For each DM scenario, we explore whether a sample of ∼5000 distant sources is sufficient to detect at least one milli-lens. Methods. We developed a semi-analytical model to estimate the milli-lensing optical depth as a function of the source’s redshift for various DM models. We employed the Press-Schechter formalism, as well as results from recent N-body simulations to compute the halo mass function, taking into account the appropriate spherically averaged density profile of haloes for each DM model. We treated the lensing system as a point-mass lens and invoked the effective surface mass density threshold to calculate the fraction of a halo that acts as a gravitational lens. We studied three classes of dark matter models: cold DM, warm DM, and self-interacting DM. Results. We find that haloes consisting of warm DM turn out to be optically thin for strong gravitational milli-lensing (zero expected lensing events). Cold DM haloes may produce lensing events depending on the steepness of the concentration-mass relation. Self-interacting DM haloes can efficiently act as gravitational milli-lenses only if haloes experience gravothermal collapse, resulting in highly dense central cores.

The ultramarine simulation: properties of dark matter haloes before redshift 5.5

ABSTRACT We introduce the Ultramarine simulation, an extremely large N-body simulation of the structure formation and evolution to redshift 5.5 at which cosmic reionization was just completed. The simulation evolves 2.1 trillion particles within a 512 h−1 Mpc cube and has an unprecedented mass and force resolution for large volume simulations of this kind, 5.6 × 106 h−1 M⊙ and 1.2 h−1 kpc, respectively. We present some basic statistical results of the simulation, including the halo mass function, halo bias parameter as well as halo mass-concentration relation at high redshifts, and compare them with some existing representative models. We find excellent agreement with some models on the high redshift halo mass functions, but neither the halo bias factor nor halo mass-concentration relation. All halo bias models for comparison over-predicate high redshift halo bias by large factors, an accurate fit to our simulation is given. High redshift dark matter haloes still can be reasonably described with NFW model, the halo mass-concentration relations are monotonic, with more massive haloes having lower concentration, in disfavour of the upturn feature reported by some studies. The mass concentration relation has little evolution between $z$ = 5.5 to $z$ = 10, in contrast to strong evolution predicted by most existing models. In addition, concentration parameters of high redshift dark matter haloes are much lower than most model predictions.

Quantum fluctuations masquerade as haloes: bounds on ultra-light dark matter from quadruply imaged quasars

ABSTRACT Ultra-light dark matter (ULDM) refers to a class of theories, including ultra-light axions, in which particles with mass $m_{\psi } \lt 10^{-20}\, \rm {eV}$ comprise a significant fraction of the dark matter. A galactic scale de Broglie wavelength distinguishes these theories from cold dark matter (CDM), suppressing the overall abundance of structure on sub-galactic scales, and producing wave-like interference phenomena in the density profiles of haloes. With the aim of constraining the particle mass, we analyse the flux ratios in a sample of 11 quadruple-image strong gravitational lenses. We account for the suppression of the halo mass function and concentration–mass relation predicted by ULDM theories, and the wave-like fluctuations in the host halo density profile, calibrating the model for the wave interference against numerical simulations of galactic-scale haloes. We show that the granular structure of halo density profiles, in particular, the amplitude of the fluctuations, significantly impacts image flux ratios, and therefore inferences on the particle mass derived from these data. We infer relative likelihoods of CDM to ULDM of 8:1, 7:1, 6:1, and 4:1 for particle masses $\log _{10}(m_\psi /\rm {eV})\in [-22.5,-22.25], [-22.25,-22.0],[-22.0,-21.75], [-21.75,-21.5]$, respectively. Repeating the analysis and omitting fluctuations associated with the wave interference effects, we obtain relative likelihoods of CDM to ULDM with a particle mass in the same ranges of 98:1, 48:1, 26:1, and 18:1, highlighting the significant perturbation to image flux ratios associated with the fluctuations. Nevertheless, our results disfavour the lightest particle masses with $m_{\psi } \lt 10^{-21.5}\, \rm {eV}$, adding to mounting pressure on ultra-light axions as a viable dark matter candidate.

On the road to per cent accuracy VI: the non-linear power spectrum for interacting dark energy with baryonic feedback and massive neutrinos

ABSTRACT Understanding non-linear structure formation is crucial for fully exploring the data generated by stage IV surveys, requiring accurate modelling of the power spectrum. This is challenging for deviations from Λ cold dark matter, but we must ensure that alternatives are well tested, to avoid false detections. We present an extension of the halo model reaction framework for interacting dark energy. We modify the halo model including the additional force present in the Dark Scattering model and implement it into ReACT. The reaction is combined with a pseudo-spectrum from EuclidEmulator2 and compared to N-body simulations. Using standard mass function and concentration-mass relation, we find predictions to be 1 per cent accurate at z = 0 up to k = 0.8 h Mpc−1 for the largest interaction strength tested (ξ = 50 b GeV−1), improving to 2 h Mpc−1 at z = 1. For smaller interaction strength (10 b GeV−1), we find 1 per cent agreement at z = 1 up to scales above 3.5 h Mpc−1, being close to 1 h Mpc−1 at z = 0. Finally, we improve our predictions with the inclusion of baryonic feedback and massive neutrinos and study degeneracies between the effects of these contributions and those of the interaction. Limiting the scales to where our modelling is 1 per cent accurate, we find a degeneracy between the interaction and feedback, but not with massive neutrinos. We expect the degeneracy with feedback to be resolvable by including smaller scales. This work represents the first analytical tool for calculating the non-linear spectrum for interacting dark energy models.

The Effect of Adiabatic Compression on Dark Matter Halos and the Radial Acceleration Relation

Abstract We use a semiempirical model to investigate the radial acceleration relation (RAR) in a cold dark matter (CDM) framework. Specifically, we build 80 model galaxies covering the same parameter space as the observed galaxies in the SPARC database, assigning them to dark matter (DM) halos using abundance-matching and halo mass–concentration relations. We consider several abundance-matching relations, finding some to be a better match to the kinematic data than others. We compute the unavoidable gravitational interactions between baryons and their DM halos, leading to an overall compression of the original Navarro–Frenk–White (NFW) halos. Before halo compression, high-mass galaxies lie approximately on the observed RAR, whereas low-mass galaxies display up-bending “hooks” at small radii due to DM cusps, making them deviate systematically from the observed relation. After halo compression, the initial NFW halos become more concentrated at small radii, making larger contributions to rotation curves. This increases the total accelerations, moving all model galaxies away from the observed relation. These systematic deviations suggest that the CDM model with abundance matching alone cannot explain the observed RAR. Further effects (e.g., feedback) would need to counteract the compression with precisely the right amount of halo expansion, even in high-mass galaxies with deep potential wells where such effects are generally predicted to be negligible.