Density Profiles Of Dark Matter Halos Research Articles

Wormhole solutions under the effect of dark matter in f(R, L m ) gravity

In the background of f(R, L m ) gravity, this work investigates three distinct dark matter halo profiles to test the possibility of generalised wormhole geometry within the galactic halo regions. The current study aims to accomplish these goals by examining various dark matter profiles including universal rotation curves (URC), Navarro–Frenk–White (NFW) model-I, and NFW model-II inside two distinct f(R, L m ) gravity models. According to the f(R,Lm)=R2+Lmα model, the dark matter (DM) halo density profiles produce suitable shape functions that meet all the necessary requirements for exhibiting the wormhole geometries with appropriate choice of free parameters. In addition, to examine DM profiles under the f(R,Lm)=R2+(1+λR)Lm model, we consider a specific shape function. Further, we observed that the derived solution from both two models violates the null energy constraints, confirming that the DM supports wormholes to maintain in the galactic halo.

Impact of dark matter galactic halo models on wormhole geometry within f(Q,T) gravity

This study investigates the possible existence of wormhole solutions with dark matter galactic halo profiles in the background of f(Q,T) gravity. The primary focus of the current study is to find the significance of dark matter (DM) in the search for traversable wormhole solutions within galactic halos. Various dark matter profiles, such as Universal Rotation Curves (URC), Navarro-Frenk-White (NFW) model-I, and NFW model-II, are examined within two different f(Q,T) models. The DM halo density profiles generate appropriate shape functions under the linear model that satisfy all the essential conditions for presenting the wormhole geometries. Apart from that, we take into account an embedded wormhole-specific shape function to inspect DM profiles under the non-linear model. We noticed that the null energy conditions are violated by the obtained solution from each model, which confirms that the DM support wormholes to sustain in the galactic halo. The findings reveal that the solutions obtained for different density profiles of dark matter halos within generalized symmetric teleparallel gravity demonstrate viability.

Explaining Dark Matter Halo Density Profiles with Neural Networks.

We use explainable neural networks to connect the evolutionary history of dark matter halos with their density profiles. The network captures independent factors of variation in the density profiles within a low-dimensional representation, which we physically interpret using mutual information. Without any prior knowledge of the halos' evolution, the network recovers the known relation between the early time assembly and the inner profile and discovers that the profile beyond the virial radius is described by a single parameter capturing the most recent mass accretion rate. The results illustrate the potential for machine-assisted scientific discovery in complicated astrophysical datasets.

From particles to orbits: precise dark matter density profiles using dynamical information

ABSTRACT We introduce a new method to calculate dark matter halo density profiles from simulations. Each particle is ‘smeared’ over its orbit to obtain a dynamical profile that is averaged over a dynamical time, in contrast to the traditional approach of binning particles based on their instantaneous positions. The dynamical and binned profiles are in good agreement, with the dynamical approach showing a significant reduction in Poisson noise in the innermost regions. We find that the inner cusps of the new dynamical profiles continue inward all the way to the softening radius, reproducing the central density profile of higher resolution simulations within the 95 per cent confidence intervals, for haloes in virial equilibrium. Folding in dynamical information thus provides a new approach to improve the precision of dark matter density profiles at small radii, for minimal computational cost. Our technique makes two key assumptions that the halo is in equilibrium (phase mixed) and the potential is spherically symmetric. We discuss why the method is successful despite strong violations of spherical symmetry in the centres of haloes, and explore how substructures disturb equilibrium at large radii.

Dark matter halo mass functions and density profiles from mass and energy cascade

Halo abundance and structure play a central role for modeling structure formation and evolution. Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of −4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo structure formation leads to halo or particle random walk with a position-dependent waiting time tau _g. First, the inverse mass cascade from small to large scales leads to the halo random walk in mass space with tau _gpropto m_h^{-lambda }, where m_h is the halo mass and lambda is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different lambda for haloes below and above a critical mass scale m_h^*, i.e. a double-lambda halo mass function. Second, a double-gamma density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time tau _g propto Phi (r)^{-1} propto r^{-gamma }, where Phi is the gravitational potential and r is the particle distance to halo center. Theory predicts gamma =2/3 that leads to a cuspy density profile with an inner slope of −4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are just special cases of proposed models. The small scale permanence can be identified due to the scale-independent rate of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the -4/3 scaling law (rho _h propto r^{-4/3}) on small scales. Theory predicts the halo number density scales with halo mass as propto m_h^{-1.9}, while the halo mass density scales as propto m_h^{4/9}. Results were compared against the Illustris simulations. This new perspective provides a theory for nearly universal halo mass functions and density profiles.

Looking for Traces of Nonminimally Coupled Dark Matter in the X-COP Galaxy Clusters Sample

We look for possible evidence of a nonminimal coupling (NMC) between dark matter (DM) and gravity using data from the X-COP compilation of galaxy clusters. We consider a theoretically motivated NMC that may dynamically arise from the collective behavior of the coarse-grained DM field (e.g., via Bose–Einstein condensation) with averaging/coherence length L NMC. In the Newtonian limit, the NMC modifies the Poisson equation by a term proportional to the Laplacian of the DM density itself. We show that this term, when acting as a perturbation over the standard Navarro–Frenk–White (NFW) profile of cold DM particles, can yield DM halo density profiles capable of correctly fitting galaxy clusters’ pressure profiles with an accuracy comparable to and, in some cases, even better than the standard cold DM NFW profile. We also show that the observed relation between the NMC length scale and the virial mass found in Gandolfi et al. for late-type galaxies is consistent with the relation we find in the current work, suggesting that the previously determined power-law scaling law holds up to galaxy cluster mass scales.

Weak-lensing peak statistics – steepness versus height

ABSTRACTIn weak-lensing cosmological studies, peak statistics is sensitive to non-linear structures and thus complementary to cosmic shear two-point correlations. In this paper, we explore a new approach, namely, the peak steepness statistics, with the overall goal to understand the cosmological information embedded there in comparison with the commonly used peak height statistics. We perform the analyses with ray-tracing simulations considering different sets of cosmological parameters Ωm and σ8. A theoretical model to calculate the abundance of high peaks based on steepness is also presented, which can well describe the main trend of the peak distribution from simulations. We employ Δχ2 and Fisher analyses to study the cosmological dependence of the two peak statistics using our limited sets of simulations as well as our theoretical model. Within our considerations without including potential systematic effects, the results show that the steepness statistics tends to have higher sensitivities to the cosmological parameters than the peak height statistics and this advantage is diluted with the increase of the shape noise. Using the theoretical model, we investigate the physical reasons accounting for the different cosmological information embedded in the two statistics. Our analyses indicate that the projection effect from large-scale structures plays an important role to enhance the gain from the steepness statistics. The redshift and cosmology dependence of dark matter halo density profiles also contributes to the differences between the two statistics.

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.

Constraints on dark matter self-interaction from the internal density profiles of X-COP galaxy clusters

The fundamental properties of the postulated dark matter (DM) affect the internal structure of gravitationally bound structures. In the cold dark matter paradigm, DM particles interact only via gravity. Their distribution is well represented by an Einasto profile with shape parameter α ≈ 0.18 in the smallest dwarf galaxies or the most massive galaxy clusters alike. Conversely, if DM particles self-interact via additional forces, we expect the mass density profiles of DM halos to flatten in their central regions, thereby increasing the Einasto shape parameter. We measured the structural properties of 12 massive galaxy clusters from observations of their hot gaseous atmosphere, using the X-ray observatory XMM-Newton, and of the Sunyaev-Zel’dovich effect using the Planck all-sky survey. After removing morphologically disturbed systems, we measured Einasto shape parameters with mean ⟨α⟩=0.19 ± 0.03 and intrinsic scatter σα = 0.06, which is in close agreement with the prediction of the cold dark matter paradigm. We used cosmological hydrodynamical simulations of cluster formation with self-interacting DM (BAHAMAS-SIDM) to determine how the Einasto shape parameter depends on the self-interaction cross section. We used the fitted relation to turn our measurements of α into constraints on the self-interaction cross section, which imply σ/m < 0.19 cm2 g−1 (95% confidence level) at collision velocity vDM − DM ∼ 1000 km s−1. This is lower than the interaction cross section required for DM self-interactions to solve the core-cusp problem in dwarf spheroidal galaxies, unless the cross section is a strong function of velocity.

Discovering the building blocks of dark matter halo density profiles with neural networks

The density profiles of dark matter halos are typically modeled using empirical formulas fitted to the density profiles of relaxed halo populations. We present a neural network model that is trained to learn the mapping from the raw density field containing each halo to the dark matter density profile. We show that the model recovers the widely used Navarro-Frenk-White profile out to the virial radius and can additionally describe the variability in the outer profile of the halos. The neural network architecture consists of a supervised encoder-decoder framework, which first compresses the density inputs into a low-dimensional latent representation, and then outputs $\ensuremath{\rho}(r)$ for any desired value of radius $r$. The latent representation contains all the information used by the model to predict the density profiles. This allows us to interpret the latent representation by quantifying the mutual information between the representation and the halos' ground-truth density profiles. A two-dimensional representation is sufficient to accurately model the density profiles up to the virial radius; however, a three-dimensional representation is required to describe the outer profiles beyond the virial radius. The additional dimension in the representation contains information about the infalling material in the outer profiles of dark matter halos, thus discovering the splashback boundary of halos without prior knowledge of the halos' dynamical history.

Core-collapse, evaporation, and tidal effects: the life story of a self-interacting dark matter subhalo

ABSTRACT Self-interacting dark matter (SIDM) cosmologies admit an enormous diversity of dark matter (DM) halo density profiles, from low-density cores to high-density core-collapsed cusps. The possibility of the growth of high central density in low-mass haloes, accelerated if haloes are subhaloes of larger systems, has intriguing consequences for small-halo searches with substructure lensing. However, following the evolution of ${\lesssim}10^8 \, \mathrm{M}_\odot$ subhaloes in lens-mass systems (${\sim}10^{13}\, \mathrm{M}_\odot$) is computationally expensive with traditional N-body simulations. In this work, we develop a new hybrid semi-analytical + N-body method to study the evolution of SIDM subhaloes with high fidelity, from core formation to core-collapse, in staged simulations. Our method works best for small subhaloes (≲1/1000 host mass), for which the error caused by dynamical friction is minimal. We are able to capture the evaporation of subhalo particles by interactions with host halo particles, an effect that has not yet been fully explored in the context of subhalo core-collapse. We find three main processes drive subhalo evolution: subhalo internal heat outflow, host-subhalo evaporation, and tidal effects. The subhalo central density grows only when the heat outflow outweighs the energy gain from evaporation and tidal heating. Thus, evaporation delays or even disrupts subhalo core-collapse. We map out the parameter space for subhaloes to core-collapse, finding that it is nearly impossible to drive core-collapse in subhaloes in SIDM models with constant cross-sections. Any discovery of ultracompact dark substructures with future substructure lensing observations favours additional degrees of freedom, such as velocity-dependence, in the cross-section.

Towards a universal model for the density profiles of dark matter haloes

ABSTRACT It is well established from cosmological simulations that dark matter (DM) haloes are not precisely self-similar and an additional parameter, beyond their concentration, is required to accurately describe their spherically averaged mass density profiles. We present, for the first time, a model to consistently predict both halo concentration, c, and this additional ‘shape’ parameter, α, for a halo of given mass and redshift for a specified cosmology. Following recent studies, we recast the dependence on mass, redshift, and cosmology to a dependence on ‘peak height’. We show that, when adopting the standard definition of peak height, which employs the so-called spherical top hat (STH) window function, the concentration–peak height relation has a strong residual dependence on cosmology (i.e. it is not uniquely determined by peak height), whereas the α–peak height relation is approximately universal when employing the STH window function. Given the freedom in the choice of window function, we explore a simple modification of the STH function, constraining its form so that it produces universal relations for concentration and α as a function of peak height using a large suite of cosmological simulations. It is found that universal relations for the two density profile parameters can indeed be derived and that these parameters are set by the linear power spectrum, P(k), filtered on different scales. We show that the results of this work generalize to any (reasonable) combination of P(k) and background expansion history, H($z$), resulting in accurate predictions of the density profiles of DM haloes for a wide range of cosmologies.

Quantified diffuse light in compact groups of galaxies

ABSTRACT The vast majority of stars in galaxy groups are contained within their constituent galaxies. Some small fraction of stars is expected, however, to follow the global dark matter (DM) potential of the group. In compact groups, interactions between the galaxies should be frequent. This leads to a more intensive material stripping from the group members, which finally forms an intra-group light component (IGL). Therefore, the distribution of the IGL should be related to the distribution of the total mass in the compact group and its dynamical status. In this study, we consider the distribution and fraction of the IGL in a sample of 36 Hickson compact groups (HCGs). We use deep observations of these compact groups (down to surface brightness ∼28 mag arcsec−2 in the r band) obtained with the WISE 28-in. telescope. For five HCGs with a bright symmetric IGL component, we carry out multicomponent photometric decomposition to simultaneously fit the galaxy profiles and the IGL. For the remaining groups, we only fit the profiles of their constituent galaxies. We find that the mean surface brightness of the IGL correlates with the mean morphology of the group: it becomes brighter in the groups with a larger fraction of early-type galaxies. On the other hand, the IGL brightness depends on the total luminosity of the group. The IGL profile tends to have a Sérsic index n ∼ 0.5−1, which is generally consistent with the mass density profile of DM haloes in compact groups obtained from cosmological simulations.

Joint gas and stellar dynamical models of WLM: an isolated dwarf galaxy within a cored, prolate DM halo

ABSTRACT We present multitracer dynamical models of the low-mass (M* ∼ 107), isolated dwarf irregular galaxy WLM in order to simultaneously constrain the inner slope of the dark matter (DM) halo density profile (γ) and flattening (qDM), and the stellar orbital anisotropy (βz, βr). For the first time, we show how jointly constraining the mass distribution from the H i gas rotation curve and solving the Jeans equations with discrete stellar kinematics lead to a factor of ∼2 reduction in the uncertainties on γ. The mass-anisotropy degeneracy is also partially broken, leading to reductions on uncertainty by ${\sim} 30{{\ \rm per\ cent}}$ on Mvir (and ${\sim} 70{{\ \rm per\ cent}}$ at the half-light radius) and ${\sim} 25{{\ \rm per\ cent}}$ on anisotropy. Our inferred value of γ = 0.3 ± 0.1 is robust to the halo geometry, and in excellent agreement with predictions of stellar feedback-driven DM core creation. The derived prolate geometry of the DM halo with qDM = 2 ± 1 is consistent with Lambda cold dark matter simulations of dwarf galaxy haloes. While self-interacting DM (SIDM) models with σ/mX ∼ 0.6 can reproduce this cored DM profile, the interaction events may sphericalize the halo. The simultaneously cored and prolate DM halo may therefore present a challenge for SIDM. Finally, we find that the radial profile of stellar anisotropy in WLM (βr) follows a nearly identical trend of increasing tangential anisotropy to the classical dwarf spheroidals, Fornax and Sculptor. Given WLM’s orbital history, this result may call into question whether such anisotropy is a consequence of tidal stripping in only one pericentric passage or if it instead is a feature of the largely self-similar formation and evolutionary pathways for some dwarf galaxies.

The Dekel-Zhao profile: a mass-dependent dark-matter density profile with flexible inner slope and analytic potential, velocity dispersion, and lensing properties

ABSTRACTWe explore a function with two shape parameters for the dark-matter halo density profile subject to baryonic effects, which is a special case of the general Zhao family of models applied to simulated dark-matter haloes by Dekel et al. This profile has variable inner slope and concentration parameter, and analytic expressions for the gravitational potential, velocity dispersion, and lensing properties. Using the Numerical Investigation of a Hundred Astrophysical Objects cosmological simulations, we find that it provides better fits than the Einasto profile and the generalized NFW profile with variable inner slope, in particular towards the halo centres. We show that the profile parameters are correlated with the stellar-to-halo mass ratio Mstar/Mvir. This defines a mass-dependent density profile describing the average dark-matter profiles in all galaxies, which can be directly applied to observed rotation curves of galaxies, gravitational lenses, and semi-analytic models of galaxy formation or satellite–galaxy evolution. The effect of baryons manifests itself by a significant flattening of the inner density slope and a 20 per cent decrease of the concentration parameter for Mstar/Mvir = 10−3.5–10−2, corresponding to $M_{\rm star} \!\sim \! 10^{7-10}\, \mathrm{ M}_\odot$. The accuracy by which this profile fits simulated galaxies is similar to certain multiparameter mass-dependent profiles, but its fewer parameters and analytic nature make it most desirable for many purposes.

A new class of galaxy models with a central BH – I. The spherical case

ABSTRACTThe dynamical properties of spherically symmetric galaxy models, where a Jaffe stellar density profile is embedded in a total mass density decreasing as r−3 at large radii, are presented. The orbital structure of the stellar component is described by the Osipkov–Merritt anisotropy; the dark matter halo is isotropic, and a black hole is added at the centre of the galaxy. First, the conditions for a nowhere negative and monotonically decreasing dark matter halo density profile are derived; this profile can be made asymptotically coincident with an NFW profile at the centre and large radii. Then, the minimum value of the anisotropy radius for phase-space consistency is derived as a function of the galaxy parameters. The Jeans equations for the stellar component are solved analytically; the projected velocity dispersion at the centre and large radii is also obtained, for generic values of the anisotropy radius. Finally, analytical expressions for the terms entering the Virial Theorem are derived, and the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability is determined as a function of the galaxy parameters. The presented models, built following an approach already adopted in our previous works, can be a useful starting point for a more advanced modelling of the dynamics of elliptical galaxies, and can be easily implemented in numerical simulations requiring a realistic dynamical model of a galaxy.

New mass bound on fermionic dark matter from a combined analysis of classical dSphs

ABSTRACTDwarf spheroidal galaxies (dSphs) are the most compact dark-matter-dominated objects observed so far. The Pauli exclusion principle limits the number of fermionic dark matter particles that can compose a dSph halo. This results in a well-known lower bound on their particle mass. So far, such bounds were obtained from the analysis of individual dSphs. In this paper, we model dark matter halo density profiles via the semi-analytical approach and analyse the data from eight ‘classical’ dSphs assuming the same mass of dark matter fermion in each object. First, we find out that modelling of Carina dSph results in a much worse fitting quality compared to the other seven objects. From the combined analysis of the kinematic data of the remaining seven ‘classical’ dSphs, we obtain a new 2σ lower bound of m ≳ 190 eV on the dark matter fermion mass. In addition, by combining a sub-sample of four dSphs – Draco, Fornax, Leo I, and Sculptor – we conclude that 220 eV fermionic dark matter appears to be preferred over the standard cold dark matter at about the 2σ level. However, this result becomes insignificant if all seven objects are included in the analysis. Future improvement of the obtained bound requires more detailed data, both from ‘classical’ and ultra-faint dSphs.

On the early evolution of Local Group dwarf galaxy types: star formation and supernova feedback

According to star formation histories (SFHs), Local Group dwarf galaxies can be broadly classified in two types: those forming most of their stars before $z=2$ (${\it fast}$) and those with more extended SFHs (${\it slow}$). The most precise SFHs are usually derived from deep but not very spatially extended photometric data; this might alter the ratio of old to young stars when age gradients are present. Here we correct for this effect and derive the mass formed in stars by $z=2$ for a sample of 16 Local Group dwarf galaxies. We explore early differences between ${\it fast}$ and ${\it slow}$ dwarfs, and evaluate the impact of internal feedback by supernovae (SN) on the baryonic and dark matter (DM) component of the dwarfs. ${\it Fast}$ dwarfs assembled more stellar mass at early times and have larger amounts of DM within the half-light radius than ${\it slow}$ dwarfs. By imposing that ${\it slow}$ dwarfs cannot have lost their gas by $z=2$, we constrain the maximum coupling efficiency of SN feedback to the gas and to the DM to be $\sim$10%. We find that internal feedback alone appears insufficient to quench the SFH of ${\it fast}$ dwarfs by gas deprivation, in particular for the fainter systems. Nonetheless, SN feedback can core the DM halo density profiles relatively easily, producing cores of the sizes of the half-light radius in ${\it fast}$ dwarfs by $z=2$ with very low efficiencies. Amongst the "classical" Milky Way satellites, we predict that the smallest cores should be found in Draco and Ursa Minor, while Sculptor and Fornax should host the largest ones.

Two-component Jaffe models with a central black hole – I. The spherical case

Dynamical properties of spherically symmetric galaxy models where both the stellar and total mass density distributions are described by the Jaffe (1983) profile (with different scale-lenghts and masses), are presented. The orbital structure of the stellar component is described by Osipkov--Merritt anisotropy, and a black hole (BH) is added at the center of the galaxy; the dark matter halo is isotropic. First, the conditions required to have a nowhere negative and monothonically decreasing dark matter halo density profile, are derived. We then show that the phase-space distribution function can be recovered by using the Lambert-Euler $W$ function, while in absence of the central BH only elementary functions appears in the integrand of the inversion formula. The minimum value of the anisotropy radius for consistency is derived in terms of the galaxy parameters. The Jeans equations for the stellar component are solved analytically, and the projected velocity dispersion at the center and at large radii are also obtained analytically for generic values of the anisotropy radius. Finally, the relevant global quantities entering the Virial Theorem are computed analytically, and the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability is determined as a function of the galaxy parameters. The presented models, even though highly idealized, represent a substantial generalization of the models presentd in Ciotti et al. (2009), and can be useful as starting point for more advanced modeling the dynamics and the mass distribution of elliptical galaxies.

Baryon effects on the dark matter haloes constrained from strong gravitational lensing

Simulations are expected to be the powerful tool to investigate the baryon effects on dark matter (DM) halos. Recent high resolution, cosmological hydrodynamic simulations (\citealt{Cintio14}, DC14) predict that the inner density profiles of DM halos depend systematically on the ratio of stellar to DM mass ($M_{\ast}/M_{\rm halo}$) which is thought to be able to provide good fits to the observed rotation curves of galaxies. The DC14 profile is fitted from the simulations which are confined to $M_{\rm halo}\le 10^{12}M_{\sun}$, in order to investigate the physical processes that may affect all halos, we extrapolate it to much larger halo mass, including that of galaxy clusters. The inner slope of DC14 profile is flat for low halo mass, it approaches 1 when the halo mass increases towards $10^{12}M_{\sun}$ and decreases rapidly after that mass. We use DC14 profile for lenses and find that it predicts too few lenses compared with the most recent strong lensing observations SQLS (\citealt{Inada12}). We also calculate the strong lensing probabilities for a simulated density profile which continues the halo mass from the mass end of DC14 ($\sim 10^{12}M_{\sun}$) to the mass that covers the galaxy clusters (\citealt{Schaller15}, Schaller15), and find that this Schaller15 model predict too many lenses compared with other models and SQLS observations. Interestingly, Schaller15 profile has no core, however, like DC14, the rotation curves of the simulated halos are in excellent agreement with observational data. Furthermore, we show that the standard two-population model SIS+NFW cannot match the most recent SQLS observations for large image separations.