NFW Mass Profile Research Articles

Upper limits on the dark matter content in globular clusters

We present a systematic analysis on the possible presence of dark mass components inside globular clusters (GCs). A spherical Jeans analysis is applied to the stellar kinematics of 10 nearby GCs. On top of the mass distribution provided by the luminous stellar component, we add either dark matter (DM), described by an NFW or Burkert mass profile, or an intermediate mass black-hole (IMBH), described by a point-like mass. Their existence would have important implications in the context of indirect DM searches. After profiling over the stellar parameters, we find no evidence neither for DM nor for IMBH. Upper limits on the two components are reported.

The mass profile of NGC 3377 from a Bayesian approach

ABSTRACT The mass profile for the moderately bright elliptical NGC 3377 is studied through a spherical Jeans analysis, combined with a Bayesian approach. The prior distributions are generated from dark matter simulations and observational constraints. The observational data set consist of Gemini/Gemini Multi-Object Spectrograph long-slit observations aligned with the major and minor axes of the galaxy, and are supplemented with data from the literature for the diffuse stellar component, globular clusters, and planetary nebulae. Although the galaxy is assumed to alternatively reside in central and satellite haloes, the comparison with literature results prefer the latter option. Several options of constant anisotropy are considered, as well as both NFW and Einasto mass profiles. The analysis points to an intermediate mass halo, presenting a virial mass around $(3.6\pm 0.6)\times 10^{11}\, {\rm M_{\odot }}$.

Phenomenological distribution of dark matter halos of galaxy comprising of stellar streams

Using the potential associated with NFW mass profile (Navarro et al. in Mon. Not. R. Astron. Soc. 402:21, 2010) enclosed at scale radius $r_{s}$ , we calculate the partition function of the clustering of dark halos comprising of stellar streams, which are the outcome of accretion of globular clusters or dwarf galaxies onto a massive host galaxy. The thermodynamics of the system of halos of stellar streams may provide crucial information on the properties of galaxy clustering. The distribution function is studied through statistical formalism. The study can give us an idea of the extended structure of galaxies and the contribution of halos to the thermodynamics and the mass content of the host galaxy. In an attempt to fit the theoretical orbital velocity to the galaxy rotation curve for the data available for galaxy $M33$ , we developed another potential that exactly leads to the best fit orbital velocity of the galaxy. Thus a phenomenological theory for the galaxy with a dark halo is established, with a new density profile.

Mass calibration of the CODEX cluster sample using SPIDERS spectroscopy – II. The X-ray luminosity–mass relation

ABSTRACT We perform the calibration of the X-ray luminosity–mass scaling relation on a sample of 344 CODEX clusters with z < 0.66 using the dynamics of their member galaxies. Spectroscopic follow-up measurements have been obtained from the SPIDERS survey, leading to a sample of 6658 red member galaxies. We use the Jeans equation to calculate halo masses, assuming an NFW mass profile and analysing a broad range of anisotropy profiles. With a scaling relation of the form $L_{\rm {X}} \propto \text{A}_{\rm {X}}M_{\text{200c}}^{\text{B}_{\rm {X}}} E(z)^2 (1+z)^{\gamma _{\rm {X}}}$, we find best-fitting parameters $\text{A}_{\rm {X}}=0.62^{+0.05}_{-0.06} (\pm 0.06)\times 10^{44}\, \mathrm{erg\, s^{-1}}$, $\text{B}_{\rm {X}}=2.35^{+0.21}_{-0.18}(\pm 0.09)$, $\gamma _{\rm {X}}=-2.77^{+1.06}_{-1.05}(\pm 0.79)$, where we include systematic uncertainties in parentheses and for a pivot mass and redshift of $3\times 10^{14}\, \mathrm{M}_\odot$ and 0.16, respectively. We compare our constraints with previous results, and we combine our sample with the SPT SZE-selected cluster subsample observed with XMM–Newton extending the validity of our results to a wider range of redshifts and cluster masses.

Mass calibration of the CODEX cluster sample using SPIDERS spectroscopy – I. The richness–mass relation

Abstract We use galaxy dynamical information to calibrate the richness–mass scaling relation of a sample of 428 galaxy clusters that are members of the CODEX sample with redshifts up to z ∼ 0.7. These clusters were X-ray selected using the ROSAT All-Sky Survey (RASS) and then cross-matched to associated systems in the redMaPPer (the red sequence Matched-filter Probabilistic Percolation) catalogue from the Sloan Digital Sky Survey. The spectroscopic sample we analyse was obtained in the SPIDERS program and contains ∼7800 red member galaxies. Adopting NFW mass and galaxy density profiles and a broad range of orbital anisotropy profiles, we use the Jeans equation to calculate halo masses. Modelling the scaling relation as $\lambda \propto \text{A}_{\lambda } {M_{\text{200c}}}^{\text{B}_{\lambda }} ({1+z})^{\gamma _{\lambda }}$, we find the parameter constraints $\text{A}_{\lambda }=38.6^{+3.1}_{-4.1}\pm 3.9$, $\text{B}_{\lambda }=0.99^{+0.06}_{-0.07}\pm 0.04$, and $\gamma _{\lambda }=-1.13^{+0.32}_{-0.34}\pm 0.49$, where we present systematic uncertainties as a second component. We find good agreement with previously published mass trends with the exception of those from stacked weak lensing analyses. We note that although the lensing analyses failed to account for the Eddington bias, this is not enough to explain the differences. We suggest that differences in the levels of contamination between pure redMaPPer and RASS + redMaPPer samples could well contribute to these differences. The redshift trend we measure is more negative than but statistically consistent with previous results. We suggest that our measured redshift trend reflects a change in the cluster galaxy red sequence (RS) fraction with redshift, noting that the trend we measure is consistent with but somewhat stronger than an independently measured redshift trend in the RS fraction. We also examine the impact of a plausible model of correlated scatter in X-ray luminosity and optical richness, showing it has negligible impact on our results.

Galaxy kinematics and mass calibration in massive SZE-selected galaxy clusters toz = 1.3

The galaxy phase-space distribution in galaxy clusters provides insights into the formation and evolution of cluster galaxies, and it can also be used to measure cluster mass profiles. We present a dynamical study based on $\sim$3000 passive, non-emission line cluster galaxies drawn from 110 galaxy clusters. The galaxy clusters were selected using the Sunyaev-Zel'dovich effect (SZE) in the 2500~deg$^2$ SPT-SZ survey and cover the redshift range $0.2 < z < 1.3$. We model the clusters using the Jeans equation, while adopting NFW mass profiles and a broad range of velocity dispersion anisotropy profiles. The data prefer velocity dispersion anisotropy profiles that are approximately isotropic near the center and increasingly radial toward the cluster virial radius, and this is true for all redshifts and masses we study. The pseudo-phase-space density profile of the passive galaxies is consistent with expectations for dark matter particles and subhalos from cosmological $N$-body simulations. The dynamical mass constraints are in good agreement with external mass estimates of the SPT cluster sample from either weak lensing, velocity dispersions, or X-ray $Y_X$ measurements. However, the dynamical masses are lower (at the 2.2$\sigma$ level) when compared to the mass calibration favored when fitting the SPT cluster data to a $\Lambda$CDM model with external cosmological priors, including CMB anisotropy data from Planck. The discrepancy grows with redshift, where in the highest redshift bin the ratio of dynamical to SPT+Planck masses is $\eta=0.63^{+0.13}_{-0.08}\pm0.06$ (statistical and systematic), corresponding to a $2.6\sigma$ discrepancy.

Testing Modified Dark Matter with galaxy clusters: Does dark matter know about the cosmological constant?

We discuss the possibility that the cold dark matter mass profiles contain information on the cosmological constant [Formula: see text], and that such information constrains the nature of cold dark matter (CDM). We call this approach Modified Dark Matter (MDM). In particular, we examine the ability of MDM to explain the observed mass profiles of 13 galaxy clusters. Using general arguments from gravitational thermodynamics, we provide a theoretical justification for our MDM mass profile. In order to properly fit the shape of the mass profiles in galaxy clusters, we find it necessary to generalize the MDM mass profile from the one we used previously to fit galactic rotation curves. We successfully compare it to the NFW mass profiles both on cluster and galactic scales, though differences in form appear with the change in scales. Our results suggest that indeed the CDM mass profiles contain information about the cosmological constant in a nontrivial way.

Combining strong lensing and dynamics in galaxy clusters: integrating MAMPOSSt within LENSTOOL

We present a new framework were we simultaneously fit strong lensing (SL) and dynamical data. The SL analysis is based on LENSTOOL, and the dynamical analysis uses MAMPOSSt code, which we have integrated into LENSTOOL. After describing the implementation of this new tool, we apply it on the galaxy group SL2S\,J02140-0535 ($z_{\rm spec}=0.44$), which we have already studied in the past. We use new VLT/FORS2 spectroscopy of multiple images and group members, as well as shallow X-ray data from \xmm. We confirm that the observed lensing features in SL2S\,J02140-0535 belong to different background sources. One of this sources is located at $z_{\rm spec}$ = 1.017 $\pm$ 0.001, whereas the other source is located at $z_{\rm spec}$ = 1.628 $\pm$ 0.001. With the analysis of our new and our previously reported spectroscopic data, we find 24 secure members for SL2S\,J02140-0535. Both data sets are well reproduced by a single NFW mass profile: the dark matter halo coincides with the peak of the light distribution, with scale radius, concentration, and mass equal to $r_s$ =$82^{+44}_{-17}$ kpc , $c_{200}$ = $10.0^{+1.7}_{-2.5}$, and $M_{200}$ = $1.0^{+0.5}_{-0.2}$ $\times$ 10$^{14}$M$_{\odot}$ respectively. These parameters are better constrained when we fit simultaneously SL and dynamical information. The mass contours of our best model agrees with the direction defined by the luminosity contours and the X-ray emission of SL2S\,J02140-0535. The simultaneous fit lowers the error in the mass estimate by 0.34 dex, when compared to the SL model, and in 0.15 dex when compared to the dynamical method.The combination of SL and dynamics tools yields a more accurate probe of the mass profile of SL2S\,J02140-0535 up to $r_{200}$. However, there is tension between the best elliptical SL model and the best spherical dynamical model.

Radial alignment of elliptical galaxies by the tidal force of a cluster of galaxies

Unlike the random radial orientation distribution of field elliptical galaxies, galaxies in a cluster are expected to point preferentially towards the center of the cluster, as a result of the cluster's tidal force on its member galaxies. In this work an analytic model is formulated to simulate this effect. The deformation time scale of a galaxy in a cluster is usually much shorter than the time scale of change of the tidal force; the dynamical process of the tidal interaction within the galaxy can thus be ignored. An equilibrium shape of a galaxy is then assumed to be the surface of equipotential, which is the sum of the self-gravitational potential of the galaxy and the tidal potential of the cluster at this location. We use a Monte-Carlo method to calculate the radial orientation distribution of these galaxies, by assuming the NFW mass profile of the cluster and the initial ellipticity of field galaxies. The radial angles show a single peak distribution centered at zero. The Monte-Carlo simulations also show that a shift of the reference center from the real cluster center weakens the anisotropy of the radial angle distribution. Therefore, the expected radial alignment cannot be revealed if the distribution of spatial position angle is used instead of that of radial angle. The observed radial orientations of elliptical galaxies in cluster Abell~2744 are consistent with the simulated distribution.

New multiply-lensed galaxies identified in ACS/NIC3 observations of Cl0024+1654 using an improved mass model

We present an improved strong-lensing analysis of Cl0024+1654 ($z$=0.39) using deep HST/ACS/NIC3 images, based on 33 multiply-lensed images of 11 background galaxies. These are found with a model that assumes mass approximately traces light, with a low order expansion to allow for flexibility on large scales. The model is constrained initially by the well known 5-image system ($z$=1.675) and refined as new multiply-lensed systems are identified using the model. Photometric redshifts of these new systems are then used to constrain better the mass profile by adopting the standard cosmological relation between redshift and lensing distance. Our model requires only 6 free parameters to describe well all positional and redshift data. The resulting inner mass profile has a slope of $d\log M/d\log r\simeq -0.55$, consistent with new weak-lensing measurements where the data overlap, at $r\simeq200$ kpc/$h_{70}$. The combined profile is well fitted by a high concentration NFW mass profile, $C_{\rm vir}\sim 8.6\pm1.6$, similar to other well studied clusters, but larger than predicted with standard $\Lambda$CDM. A well defined radial critical curve is generated by the model and is clearly observed at $r \simeq 12\arcsec$, outlined by elongated images pointing towards the centre of mass. The relative fluxes of the multiply-lensed images are found to agree well with the modelled magnifications, providing an independent consistency check.

Comparisons between Isothermal and NFW Mass Profiles for Strong‐Lensing Galaxy Clusters

While both isothermal and NFW-based mass models for galaxy clusters are widely adopted in strong-lensing studies, they cannot easily be distinguished based solely on observed positions of arcs and arclets. We compare the magnifications predicted for giant arcs obtained from isothermal and NFW profiles, taking axially symmetric and asymmetric mass distributions into account. We find that arc magnifications can differ strongly between the two types of density profile even if the image morphology is well reproduced. Magnifications by lenses with NFW density profiles are usually larger than those for lenses with singular or nearly singular isothermal density profiles, unless the latter have large cores. Asymmetries play an important role. We illustrate our results with the two well-studied clusters, MS 2137 and A370. We confirm earlier results showing that both isothermal and NFW mass models can very well reproduce the observed arcs, radial arcs, and other arclets. While the mass model for MS 2137 is not very well constrained, the two types of mass models produce strongly differing critical curves and caustics for A370. We find that the NFW mass profile is preferred for A370. We identify new arclet candidates in the field of A370. Redshift estimates allowed by the lens model are consistent with results in the literature, where available. Three newly found counterimages are suggested to arise from an active, dust-enshrouded star-forming galaxy at z approximate to 1.1.

A CFH12k lensing survey of X-ray luminous galaxy clusters

We describe the weak lensing methodology we have applied to multi-colour CFH12k imaging of a homogeneously- selected sample of luminous X-ray clusters at z ∼ 0.2. The aim of our survey is to understand the variation in cluster structure and dark matter profile within rich clusters. The method we describe converts a fully reduced CFH12k image into constraints on the cluster mass distribution in two steps: (1) determination of the true shape of faint (lensed) galaxies, including object detection, point spread function (PSF) determination, galaxy shape measurement with errors; (2) conversion of the faint galaxy catalogue into reliable mass constraints using a range of 1D and 2D lensing techniques. Mass estimates are derived indepen- dently from each of the three images taken in separate filters to quantify the systematic uncertainties. Finally, we compare the cluster mass model to the light distribution of cluster members as derived from our imaging data. To illustrate the method, we apply it to the well-studied cluster Abell 1689 (z = 0.184). In this cluster, we detect the gravitational shear signal out to ∼ 3M pc at >3-σ significance. The two-dimensional mass reconstruction has a ∼10-σ significance peak centered on the brightest clus- ter galaxy. The weak lensing profile is well fitted by a NFW mass profile with M200 = 14.1 +6.3 −4.7 × 10 14 M