Einasto Profile Research Articles

Searching the Parameters of Dark Matter Halos on the Basis of Dwarf Galaxies’ Dynamics

Article devoted to searching the parameters of dark matter halos on the base of dwarf galaxies’ dynamics (Messier 32 and Leo I). For doing this, we propose the new approach founded on construction the coupled elliptical trajectory for a probe body in the gravitational fields of Newtonian potential and potential of dark matter’s halo. This allows more accuracy estimate its central density for the Navarro-Frenk-White profile and free parameter for the Einasto profile . Our result is in good correlation with results of other authors that are got by different numerical methods.

Gamma-rays from Heavy Minimal Dark Matter

Motivated by the Minimal Dark Matter scenario, we consider the annihilation into gamma rays of candidates in the fermionic 5-plet and scalar 7-plet representations of SU(2)L, taking into account both the Sommerfeld effect and the internal bremsstrahlung. Assuming the Einasto profile, we show that present measurements of the Galactic Center by the H.E.S.S. instrument exclude the 5-plet and 7-plet as the dominant form of dark matter for masses between 1 TeV and 20 TeV, in particular, the 5-plet mass leading to the observed dark matter density via thermal freeze-out. We also discuss prospects for the upcoming Cherenkov Telescope Array, which will be able to probe even heavier dark matter masses, including the scenario where the scalar 7-plet is thermally produced.

THE RADIAL PROFILE AND FLATTENING OF THE MILKY WAY’S STELLAR HALO TO 80 kpc FROM THE SEGUE K-GIANT SURVEY

We characterise the radial density, metallicity and flattening profile of the Milky Way's stellar halo, based on the large sample of 1757 spectroscopically confirmed giant stars from SDSS/SEGUE-2 after excising stars that were algorithmically attributed to apparent halo substructure (including the Sagittarius stream). Compared to BHB stars or RR Lyrae, giants are more readily understood tracers of the overall halo star population, with less bias in age or metallicity. The well-characterized selection function of the sample enables forward modelling of those data, based on ellipsoidal stellar density models, $\nu_* (R,z)$, with Einasto profiles and (broken) power laws for their radial dependence, combined with a model for the metallicity gradient and the flattening profile. Among models with constant flattening, these data are reasonably well fit by an Einasto profile of $n=3.1\pm 0.5$ with an effective radius $\rm r_{eff} = 15\pm2~$kpc and a flattening of $q=0.7\pm 0.02$; or comparably well by an equally flattened broken power-law, with radial slopes of $\alpha_{in}=2.1\pm 0.3$ and $\alpha_{out}=3.8\pm 0.1$, with a break-radius of $r_{break}=18\pm1$~kpc; this is largely consistent with earlier work. We find a modest, but significant metallicity gradient within the "outer" stellar halo, $\rm [Fe/H]$ decreasing outward. If we allow for a variable flattening $q = f(r_{GC} )$, we find the distribution of halo giants to be considerably more flattened at small radii, $q({\rm 10~kpc})\sim 0.57$, compared to $q(>30{\rm kpc})\sim 0.8$. Remarkably, the data are then very well fit by a single power-law of index $\rm \sim 4.2\pm0.1$ of the variable $r_q\equiv\sqrt{R^2+(z/q(r))^2}$. In this simple and better fitting model, there is a break in flattening at $\sim 20$~kpc, instead of a break in the radial density function.

Dark matter massive fermions and Einasto profiles in galactic haloes

On the basis of a fermionic dark matter model we fit rotation curves of The HI Nearby Galaxy Survey THINGS sample and compare our 3-parametric model to other models widely used in the literature: 2-parametric Navarro--Frenk--White, pseudoisothermal sphere, Burkhert models, and 3-parametric Einasto model, suggested as the new "standard dark matter profile" model in the paper by Chemin et. al., AJ 142 (2011) 109. The results from the fitting procedure provides evidence for an underlying fermionic nature of the dark matter candidate, with rest mass above the keV regime.

Evidence for the inside-out growth of the stellar mass distribution in galaxy clusters sincez~1

We study the radial number density and stellar mass density distributions of satellite galaxies in a sample of 60 massive clusters at 0.04<z<0.26 selected from the Multi-Epoch Nearby Cluster Survey (MENeaCS) and the Canadian Cluster Comparison Project (CCCP). In addition to ~10,000 spectroscopically confirmed member galaxies, we use deep ugri-band imaging to estimate photometric redshifts and stellar masses, and then statistically subtract fore-, and background sources using data from the COSMOS survey. We measure the galaxy number density and stellar mass density distributions in logarithmically spaced bins over 2 orders of magnitude in radial distance from the BCGs. For projected distances in the range 0.1<R/R200<2.0, we find that the stellar mass distribution is well-described by an NFW profile with a concentration of c=2.03+/-0.20. However, at smaller radii we measure a significant excess in the stellar mass in satellite galaxies of about $10^{11}$ Msun per cluster, compared to these NFW profiles. We do obtain good fits to generalized NFW profiles with free inner slopes, and to Einasto profiles. To examine how clusters assemble their stellar mass component over cosmic time, we compare this local sample to the GCLASS cluster sample at z~1, which represents the approximate progenitor sample of the low-z clusters. This allows for a direct comparison, which suggests that the central parts (R<0.4 Mpc) of the stellar mass distributions of satellites in local galaxy clusters are already in place at z~1, and contain sufficient excess material for further BCG growth. Evolving towards z=0, clusters appear to assemble their stellar mass primarily onto the outskirts, making them grow in an inside-out fashion.

The doubloon models of dark haloes and galaxies

A family of spherical halo models with flat circular velocity curves is presented. This includes models in which the rotation curve has a finite central value but declines outwards (like the Jaffe model). It includes models in which the rotation curve is rising in the inner parts, but flattens asymptotically (like the Binney model). The family encompasses models with both finite and singular (cuspy) density profiles. The self-consistent distribution function depending on binding energy $E$ and angular momentum $L$ is derived and the kinematical properties of the models discussed. These really describe the properties of the total matter (both luminous and dark). For comparison with observations, it is better to consider tracer populations of stars. These can be used to represent elliptical galaxies or the spheroidal components of spiral galaxies. Accordingly, we study the properties of tracers with power-law or Einasto profiles moving in the doubloon potential. Under the assumption of spherical alignment, we provide a simple way to solve the Jeans equations for the velocity dispersions. This choice of alignment is supported by observations on the stellar halo of the Milky Way. Power-law tracers have prolate spheroidal velocity ellipsoids everywhere. However, this is not the case for Einasto tracers, for which the velocity ellipsoids change from prolate to oblate spheroidal near the pole. Asymptotic forms of the velocity distributions close to the escape speed are also derived, with an eye to application to the high velocity stars in the Milky Way. Power-law tracers have power-law or Maxwellian velocity distributions tails, whereas Einasto tracers have super-exponential cut-offs.

A realistic assessment of the CTA sensitivity to dark matter annihilation

We estimate the sensitivity of the upcoming CTA gamma-ray observatory to DM annihilation at the Galactic centre, improving on previous analyses in a number of significant ways. First, we perform a detailed analyses of all backgrounds, including diffuse astrophysical emission for the first time in a study of this type. Second, we present a statistical framework for including systematic errors and estimate the consequent degradation in sensitivity. These errors may come from e.g. event reconstruction, Monte Carlo determination of the effective area or uncertainty in atmospheric conditions. Third, we show that performing the analysis on a set of suitably optimised regions of interest makes it possible to partially compensate for the degradation in sensitivity caused by systematics and diffuse emission. To probe dark matter with the canonical thermal annihilation cross-section, CTA systematics like non-uniform variations in acceptance over a single field of view must be kept below the 0.3% level, unless the dark matter density rises more steeply in the centre of the Galaxy than predicted by a typical Navarro-Frenk-White or Einasto profile. For a contracted r−1.3 profile, and systematics at the 1% level, CTA can probe annihilation to bb̄ at the canonical thermal level for dark matter masses between 100 GeV and 10 TeV.

Prospects for dark matter searches in the pMSSM

We investigate the prospects for detection of neutralino dark matter in the 19-parameter phenomenological MSSM (pMSSM). We explore very wide ranges of the pMSSM parameters but pay particular attention to the higgsino-like neutralino at the ~ 1 TeV scale, which has been shown to be a well motivated solution in many constrained supersymmetric models, as well as to a wino-dominated solution with the mass in the range of 2-3 TeV. After summarising the present bounds on the parameter space from direct and indirect detection experiments, we focus on prospects for detection of the Cherenkov Telescope Array (CTA). To this end, we derive a realistic assessment of the sensitivity of CTA to photon fluxes from dark matter annihilation by means of a binned likelihood analysis for the Einasto and Navarro-Frenk-White halo profiles. We use the most up to date instrument response functions and background simulation model provided by the CTA Collaboration. We find that, with 500 hours of observation, under the Einasto profile CTA is bound to exclude at the 95% C.L. almost all of the ~ 1 TeV higgsino region of the pMSSM, effectively closing the window for heavy supersymmetric dark matter in many realistic models. CTA will be able to probe the vast majority of cases corresponding to a spin-independent scattering cross section below the reach of 1-tonne underground detector searches for dark matter, in fact even well below the irreducible neutrino background for direct detection. On the other hand, many points lying beyond the sensitivity of CTA will be within the reach of 1-tonne detectors, and some within collider reach. Altogether, CTA will provide a highly sensitive way of searching for dark matter that will be partially overlapping and partially complementary with 1-tonne detector and collider searches, thus being instrumental to effectively explore the nearly full parameter space of the pMSSM.

Statistical mechanics of self-gravitating systems: Mixing as a criterion for indistinguishability

We propose an association between the phase-space mixing level of a self-gravitating system and the indistinguishability of its constituents (stars or dark matter particles). This represents a refinement in the study of systems exhibiting incomplete violent relaxation. Within a combinatorial analysis similar to that of Lynden-Bell, we make use of this association to obtain a distribution function that deviates from the Maxwell-Boltzmann distribution, increasing its slope for high energies. Considering the smallness of the occupation numbers for large distances from the center of the system, we apply a correction to Stirling's approximation which increases the distribution slope also for low energies. The distribution function thus obtained presents some resemblance to the "S" shape of distributions associated with cuspy density profiles (as compared to the distribution function obtained from the Einasto profile), although it is not quite able to produce sharp cusps. We also argue how the association between mixing level and indistinguishability can provide a physical meaning to the assumption of particle-permutation symmetry in the N-particle distribution function, when it is used to derive the one-particle Vlasov equation, which raises doubts about the validity of this equation during violent relaxation.

Bayes-x: a Bayesian inference tool for the analysis of X-ray observations of galaxy clusters

We present the first public release of our Bayesian inference tool, Bayes-X, for the analysis of X-ray observations of galaxy clusters. We illustrate the use of Bayes-X by analysing a set of four simulated clusters at z=0.2-0.9 as they would be observed by a Chandra-like X-ray observatory. In both the simulations and the analysis pipeline we assume that the dark matter density follows a spherically-symmetric Navarro, Frenk and White (NFW) profile and that the gas pressure is described by a generalised NFW (GNFW) profile. We then perform four sets of analyses. By numerically exploring the joint probability distribution of the cluster parameters given simulated Chandra-like data, we show that the model and analysis technique can robustly return the simulated cluster input quantities, constrain the cluster physical parameters and reveal the degeneracies among the model parameters and cluster physical parameters. We then analyse Chandra data on the nearby cluster, A262, and derive the cluster physical profiles. To illustrate the performance of the Bayesian model selection, we also carried out analyses assuming an Einasto profile for the matter density and calculated the Bayes factor. The results of the model selection analyses for the simulated data favour the NFW model as expected. However, we find that the Einasto profile is preferred in the analysis of A262. The Bayes-X software, which is implemented in Fortran 90, is available at http://www.mrao.cam.ac.uk/facilities/software/bayesx/.

CLASH: WEAK-LENSING SHEAR-AND-MAGNIFICATION ANALYSIS OF 20 GALAXY CLUSTERS

We present a joint shear-and-magnification weak-lensing analysis of a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters at 0.19<z<0.69 selected from the Cluster Lensing And Supernova survey with Hubble (CLASH). Our analysis uses wide-field multi-color imaging, taken primarily with Suprime-Cam on the Subaru Telescope. From a stacked shear-only analysis of the X-ray-selected subsample, we detect the ensemble-averaged lensing signal with a total signal-to-noise ratio of ~25 in the radial range of 200 to 3500kpc/h. The stacked tangential-shear signal is well described by a family of standard density profiles predicted for dark-matter-dominated halos in gravitational equilibrium, namely the Navarro-Frenk-White (NFW), truncated variants of NFW, and Einasto models. For the NFW model, we measure a mean concentration of $c_{200c}=4.01^{+0.35}_{-0.32}$ at $M_{200c}=1.34^{+0.10}_{-0.09} 10^{15}M_{\odot}$. We show this is in excellent agreement with Lambda cold-dark-matter (LCDM) predictions when the CLASH X-ray selection function and projection effects are taken into account. The best-fit Einasto shape parameter is $\alpha_E=0.191^{+0.071}_{-0.068}$, which is consistent with the NFW-equivalent Einasto parameter of $\sim 0.18$. We reconstruct projected mass density profiles of all CLASH clusters from a joint likelihood analysis of shear-and-magnification data, and measure cluster masses at several characteristic radii. We also derive an ensemble-averaged total projected mass profile of the X-ray-selected subsample by stacking their individual mass profiles. The stacked total mass profile, constrained by the shear+magnification data, is shown to be consistent with our shear-based halo-model predictions including the effects of surrounding large-scale structure as a two-halo term, establishing further consistency in the context of the LCDM model.

The effects of galaxy shape and rotation on the X-ray haloes of early-type galaxies – II. Numerical simulations

By means of high-resolution 2D hydrodynamical simulations, we study the evolution of the hot interstellar medium (ISM) for a large set of early-type galaxy models, characterized by various degrees of flattening and internal rotation. The galaxies are described by state-of-the-art axisymmetric two-component models, tailored to reproduce real systems; the dark matter haloes follow the Navarro–Frenk–White or the Einasto profile. The gas is produced by the evolving stars, and heated by Type Ia supernovae. We find that, in general, the rotation field of the ISM in rotating galaxies is very similar to that of the stars, with a consequent negligible heating contribution from thermalization of the ordered motions. The relative importance of flattening and rotation in determining the final X-ray luminosity LX and temperature TX of the hot haloes is a function of the galactic mass. Flattening and rotation in low-mass galaxies favour the establishment of global winds, with the consequent reduction of LX. In medium- to high-mass galaxies, flattening and rotation are not sufficient to induce global winds; however, in the rotating models, the nature of the gas flows is deeply affected by conservation of angular momentum, resulting in a reduction of both LX and TX.

Relaxation of dark matter halos: how to match observational data?

We show that moderate energy relaxation in the formation of dark matter halos invariably leads to profiles that match those observed in the central regions of galaxies. The density profile of the central region is universal and insensitive to either the seed perturbation shape or the details of the relaxation process. The profile has a central core; the multiplication of the central density by the core radius is almost independent of the halo mass, in accordance with observations. In the core area the density distribution behaves as an Einasto profile with low index ($n\sim 0.5$); it has an extensive region with $\rho\propto r^{-2}$ at larger distances. This is exactly the shape that observations suggest for the central region of galaxies. On the other hand, this shape does not fit the galaxy cluster profiles. A possible explanation of this fact is that the relaxation is violent in the case of galaxy clusters; however, it is not violent enough when galaxies or smaller dark matter structures are considered. We discuss the reasons for this.

Low-metallicity stellar halo populations as tracers of dark matter haloes

Abstract We analyse the density profiles of the stellar halo populations in eight Milky Way mass galaxies, simulated within the Λcold dark matter scenario. We find that accreted stars can be well fitted by an Einasto profile, as well as any subsample defined according to metallicity. We detect a clear correlation between the Einasto fitting parameters of the low-metallicity stellar populations and those of the dark matter (DM) haloes. The correlations for stars with [Fe/H] &amp;lt; −3 allow us to predict the shape of the dark matter profiles within residuals of ∼10 per cent, in case the contribution from in situ stars remains small. Using Einasto parameters estimated for the stellar halo of the Milky Way and assuming the later formed with significant contributions from accreted low-mass satellite, our simulations predict α ∼ 0.15 and r2 ∼ 15 kpc for its dark matter profile. These values, combined with observed estimations of the local DM density, yield an enclosed DM mass at ∼8 kpc in the range 3.9–6.7 × 1010 M⊙, in agreement with recent observational results. These findings suggest that low-metallicity stellar haloes could store relevant information on the DM haloes. Forthcoming observations would help us to further constrain our models and predictions.

Dark matter in disc galaxies – II. Density profiles as constraints on feedback scenarios

The disparity between the density profiles of galactic dark matter haloes predicted by dark matter only cosmological simulations and those inferred from rotation curve decomposition, the so-called cusp–core problem, suggests that baryonic physics has an impact on dark matter density in the central regions of galaxies. Using a Markov Chain Monte Carlo analysis of galactic rotation curves we constrain density profiles and an estimated minimum radius for baryon influence, r1, which we couple with a feedback model to give an estimate of the fraction of matter within that radius that must be expelled to produce the observed halo profile. We examine the rotation curves of eight galaxies taken from the THINGS (The HI Nearby Galaxy Survey) data set and determine constraints on the radial density profiles of their dark matter haloes. For some of the galaxies, both cored haloes and cosmological ρ ∝ r−1 cusps are excluded which requires finely tuned baryonic feedback. For galaxies which exhibit extended cores in their haloes (e.g. NGC 925), the use of a split power-law halo profile yields models without the unphysical, sharp features seen in models based on the Einasto profile. We have found there is no universal halo profile which can describe all the galaxies studied here.

A very simple cusped halo model

We introduce a very simple model of a dark halo. It is a close relative of Hernquist's model, being generated by the same transformation but this time applied to the logarithmic potential rather than the point mass. The density is proportional to (distance)$^{-1}$ at small radii, whilst the rotation curve is flat at large radii. Isotropic and radially anisotropic distributions functions are readily found, and the intrinsic and line of sight kinematical quantities are available as simple formulae. We also provide an analytical approximation to the Hamiltonian as a function of the actions. As an application, we study the kinematic properties of stellar haloes and tracers in elliptical galaxies. We show that the radial velocity dispersion of a power-law population in a galaxy with a flat rotation curve always tends to the constant value. This holds true irrespective of the anisotropy or the lengthscales of the dark or luminous matter. An analogous result holds for the line of sight or projected velocity dispersion of a power-law surface brightness profile. The radial velocity dispersion of Population II stars in the Milky Way is a strongly declining function of Galactocentric radius. So, if the rotation curve is flat, we conclude that the stellar halo density cannot follow a power-law at large radii, but must decrease more sharply (like an Einasto profile) or be abruptly truncated at large radii. Both the starcount and kinematic data of the Milky Way stellar halo are well-represented by an Einasto profile with index $m\approx 2$ and effective radius $\approx 20$ kpc.

Lensing properties of the Einasto profile in terms of the Meijer G function

In N-body simulations of cold dark matter, it has been found that three-parameter models, particularly the Einasto profile, yield better fits to a wide range of dark matter haloes than two parameter models like the Navarro-Frenk-White profile. Recently, the analytical properties of the Einasto profile has been studied, allowing closed expressions for its surface mass density and lensing properties in terms of the Fox H and Meijer G functions, using a Mellin transform formalism. These expressions are valid for all values of the Einasto index in terms of the Fox H function, and valid for integer and half-integer values of Einasto index in terms of the Meijer G function. In this paper, we derive expressions for lensing properties of the Einasto profile for all rational values of the Einasto index in terms of the Meijer G function. Equivalency between these expressions and other recent results is also discussed.

THE BARYONIC SELF SIMILARITY OF DARK MATTER

The cosmological simulations indicates that the dark matter haloes have specific self similar properties. However the halo similarity is affected by the baryonic feedback, the momentum injected by the supernovae re-shape the dark matter core and transform it to a flat density core, with a scale length imposed by the baryonic feedback. Additionally the baryon feedback impose also an equilibrium condition, which when coupled with the imposed baryonic scale length induce a new type of similarity. The new self similar solution implies that the acceleration generated by dark matter is scale free, which in turns implies that the baryonic acceleration at a reference radius is also scale free. Constant dark matter and baryonic accelerations at a reference radius have effectively been observed for a large class of different galaxies, which is in support of this approach. The new self similar properties implies that the total acceleration at larger distances is scale free, the transition between the dark matter and baryons dominated regime occurs at a constant acceleration, and the maximum of the velocity curve which defines the amplitude of the velocity curve at larger distances is proportional to $M^{\frac{1}{4}}$. These results demonstrates that in this self similar model, cold dark matter is consistent with the basics of MOND phenomenology for the galaxies. In agreement with the observation the coincidence between the self similar model and MOND is expected to break at the scale of clusters of galaxies. Some numerical experiments shows that the behavior of the density near the origin is closely approximated by a Einasto profile.

Cold dark matter haloes in the Planck era: evolution of structural parameters for Einasto and NFW profiles

We present the evolution of the structure of relaxed cold dark matter haloes in the cosmology from the Planck satellite. Our simulations cover 5 decades in halo mass, from dwarf galaxies to galaxy clusters. Due to the increased matter density and power spectrum normalization the concentration mass relation in the Planck cosmology has a 20 percent higher normalization at redshift z=0 compared to WMAP cosmology. We confirm that CDM haloes are better described by the Einasto profile; for example, at scales near galaxy half-light radii CDM haloes have significantly steeper density profiles than implied by NFW fits. There is a scatter of 0.2 dex in the Einasto shape parameter at fixed halo mass, adding further to the diversity of CDM halo profiles. The evolution of the concentration mass relation in our simulations is not reproduced by any of the analytic models in the literature. We thus provide a simple fitting formula that accurately describes the evolution between redshifts z=5 to z=0 for both NFW and Einasto fits. Finally, the observed concentrations and halo masses of spiral galaxies, groups and clusters of galaxies at low redshifts are in good agreement with our simulations, suggesting only mild halo response to galaxy formation on these scales.

GALAXY HALO FORMATION IN THE ABSENCE OF VIOLENT RELAXATION AND A UNIVERSAL DENSITY PROFILE OF THE HALO CENTER

While N-body simulations testify to a cuspy profile of the central region of dark matter halos, observations favor a shallow, cored density profile of the central region of at least some spiral galaxies and dwarf spheroidals. We show that a central profile, very close to the observed one, inevitably forms in the center of dark matter halos if we make a supposition about a moderate energy relaxation of the system during the halo formation. If we assume the energy exchange between dark matter particles during the halo collapse is not too intensive, the profile is universal: it depends almost not at all on the properties of the initial perturbation and is very akin, but not identical, to the Einasto profile with a small Einasto index n ∼ 0.5. We estimate the size of the "central core" of the distribution, i.e., the extent of the very central region with a respectively gentle profile, and show that the cusp formation is unlikely, even if the dark matter is cold. The obtained profile is in good agreement with observational data for at least some types of galaxies but clearly disagrees with N-body simulations.