Central Logarithmic Slope Research Articles

NON-UNIVERSALITY OF DARK-MATTER HALOS: CUSPS, CORES, AND THE CENTRAL POTENTIAL

Dark-matter halos grown in cosmological simulations appear to have central NFW-like density cusps with mean values of $d\log\rho/d\log r \approx -1$, and some dispersion, which is generally parametrized by the varying index $\alpha$ in the Einasto density profile fitting function. Non-universality in profile shapes is also seen in observed galaxy clusters and possibly dwarf galaxies. Here we show that non-universality, at any given mass scale, is an intrinsic property of DARKexp, a theoretically derived model for collisionless self-gravitating systems. We demonstrate that DARKexp - which has only one shape parameter, $\phi_0$ - fits the dispersion in profile shapes of massive simulated halos as well as observed clusters very well. DARKexp also allows for cored dark-matter profiles, such as those found for dwarf spheroidal galaxies. We provide approximate analytical relations between DARKexp $\phi_0$, Einasto $\alpha$, or the central logarithmic slope in the Dehnen-Tremaine analytical $\gamma$-models. The range in halo parameters reflects a substantial variation in the binding energies per unit mass of dark-matter halos.

Early flattening of dark matter cusps in dwarf spheroidal galaxies

Simulations of the clustering of cold dark matter yield dark-matter halos that have central density cusps, but observations of totally dark-matter dominated dwarf spheroidal galaxies imply that they do not have cuspy central density profiles. We use analytic calculations and numerical modelling to argue that whenever stars form, central density cusps are likely to be erased. Gas that accumulates in the potential well of an initially cuspy dark-matter halo settles into a disc. Eventually the surface density of the gas exceeds the threshold for fragmentation into self-gravitating clouds. The clouds are massive enough to transfer energy to the dark-matter particles via dynamical friction on a short time-scale. The halo's central cusp is heated to form a core with central logarithmic density slope gamma=0 before stellar feedback makes its impact. Since star formation is an inefficient process, the clouds are disrupted by feedback when only a small fraction of their mass has been converted to stars, and the dark matter dominates the final mass distribution.

DWARF GALAXY DARK MATTER DENSITY PROFILES INFERRED FROM STELLAR AND GAS KINEMATICS

We present new constraints on the density profiles of dark matter (DM) halos in seven nearby dwarf galaxies from measurements of their integrated stellar light and gas kinematics. The gas kinematics of low mass galaxies frequently suggest that they contain constant density DM cores, while N-body simulations instead predict a cuspy profile. We present a data set of high resolution integral field spectroscopy on seven galaxies and measure the stellar and gas kinematics simultaneously. Using Jeans modeling on our full sample, we examine whether gas kinematics in general produce shallower density profiles than are derived from the stars. Although 2/7 galaxies show some localized differences in their rotation curves between the two tracers, estimates of the central logarithmic slope of the DM density profile, gamma, are generally robust. The mean and standard deviation of the logarithmic slope for the population are gamma=0.67+/-0.10 when measured in the stars and gamma=0.58+/-0.24 when measured in the gas. We also find that the halos are not under concentrated at the radii of half their maximum velocities. Finally, we search for correlations of the DM density profile with stellar velocity anisotropy and other baryonic properties. Two popular mechanisms to explain cored DM halos are an exotic DM component or feedback models that strongly couple the energy of supernovae into repeatedly driving out gas and dynamically heating the DM halos. We investigate correlations that may eventually be used to test models. We do not find a secondary parameter that strongly correlates with the central DM density slope, but we do find some weak correlations. Determining the importance of these correlations will require further model developments and larger observational samples. (Abridged)

An analytic distribution function for a mass-less cored stellar system in a cuspy dark-matter halo

We demonstrate the existence of distribution functions that can be used to represent spherical massless cored stellar systems embedded in cuspy dark matter halos with constant mildly tangential velocity anisotropy. In particular, we derive analytically the functional form of the distribution function for a Plummer stellar sphere in a Hernquist dark halo, for \beta_0 = -0.5 and for different degrees of embedding. This particular example satisfies the condition that the central logarithmic slope of the light profile \gamma_0 > 2 \beta_0. Our models have velocity dispersion profiles similar to those observed in nearby dwarf spheroidal galaxies. Hence they can be used to generate initial conditions for a variety of problems, including N-body simulations that may represent dwarf galaxies in the Local Group.

Orbit-based dynamical models of the Sculptor dSph galaxy

We have developed spherically symmetric dynamical models of dwarf spheroidal (dSph) galaxies using Schwarzschild's orbit superposition method. This type of modelling yields constraints both on the total mass distribution (e.g. enclosed mass and scale radius) and on the orbital structure of the system (e.g. velocity anisotropy). This method is thus less prone to biases introduced by assumptions in comparison to the more commonly used Jeans modelling, and it allows us to put reliable constraints on their dark matter content. Here we present our results for the Sculptor dSph galaxy, after testing our methods on mock data sets. We fit both the second and fourth velocity moment profiles to break the mass–anisotropy degeneracy. For an Navarro, Frenk & White (NFW) dark matter halo profile, we find that the mass of Sculptor within 1 kpc is M1 kpc = (1.03 ± 0.07) × 108 M⊙, and that its velocity anisotropy profile is tangentially biased and nearly constant for radii beyond ∼100 pc. The preferred concentration (c ∼ 15) is low for its dark matter mass but consistent within the scatter found in N-body cosmological simulations. When we let the value of the central logarithmic slope α vary, we find that the best-fitting model has α = 0, although an NFW cusp or shallower is consistent at the 1σ confidence level. On the other hand, very cuspy density profiles with logarithmic central slopes α < −1.5 are strongly disfavoured for Sculptor.

Measuring the total and baryonic mass profiles of the very massive CASSOWARY 31 strong lens. A fossil system at z ≃ 0.7?★

We investigate the total and baryonic mass distributions in deflector number 31 of the Cambridge And Sloan Survey Of Wide ARcs in the skY (CASSOWARY). We confirm spectroscopically a four-image lensing system at redshift 1.4870 with VLT/X-shooter observations. The lensed images are distributed around a bright early-type galaxy at redshift 0.683, surrounded by several smaller galaxies at similar photometric redshifts. We use available optical and X-ray data to constrain the deflector total, stellar, and hot gas mass through, respectively, strong lensing, stellar population analysis, and plasma modelling. We derive a total mass projected within the Einstein radius R_Ein = 70 kpc of (40 +/- 1) x 10^12 M_Sun, and a central logarithmic slope of -1.7 +/- 0.2 for the total mass density. Despite a very high stellar mass and velocity dispersion of the central galaxy of (3 +/- 1) x 10^12 M_Sun and (450 +/- 80) km/s, respectively, the cumulative stellar-to-total mass profile of the deflector implies a remarkably low stellar mass fraction of 20% (3%-6%) in projection within the central galaxy effective radius R_e = 25 kpc (R = 100 kpc). We also find that the CSWA 31 deflector has properties suggesting it to be among the most distant and massive fossil systems studied so far. The unusually strong central dark matter dominance and the possible fossil nature of this system renders it an interesting target for detailed tests of cosmological models and structure formation scenarios.

TESTING PHOTOMETRIC DIAGNOSTICS FOR THE DYNAMICAL STATE AND POSSIBLE INTERMEDIATE-MASS BLACK HOLE PRESENCE IN GLOBULAR CLUSTERS

Surface photometry is a necessary tool to establish the dynamical state of stars clusters. We produce realistic HST-like images from N-body models of star clusters with and without central intermediate-mass black holes (IMBHs) in order to measure their surface brightness profiles. The models contain ~600,000 individual stars, black holes of various masses between 0% to 2% of the total mass, and are evolved for a Hubble time. We measure surface brightness and star count profiles for every constructed image in order to test the effect of intermediate mass black holes on the central logarithmic slope, the core radius, and the half-light radius. We use these quantities to test diagnostic tools for the presence of central black holes using photometry. We find that the the only models that show central shallow cusps with logarithmic slopes between -0.1 and -0.4 are those containing central black holes. Thus, the central logarithmic slope seems to be a good way to choose clusters suspect of containing intermediate-mass black holes. Clusters with steep central cusps can definitely be ruled out to host an IMBH. The measured r_c/r_h ratio has similar values for clusters that have not undergone core-collapse, and those containing a central black hole. We notice that observed Galactic globular clusters have a larger span of values for central slope and r_c/r_h than our modeled clusters, and suggest possible reasons that could account for this and contribute to improve future models.

NEW LIMITS ON AN INTERMEDIATE-MASS BLACK HOLE IN OMEGA CENTAURI. II. DYNAMICAL MODELS

We present a detailed dynamical analysis of the projected density and kinematical data available for the globular cluster Omega Cen. We solve the spherical anisotropic Jeans equation to predict the projected profiles of the RMS velocity in each of the three orthogonal coordinate directions (line of sight, proper motion radial, and proper motion tangential). We fit the models to new HST star count and proper motion data near the cluster center presented in Paper I, combined with existing ground-based measurements. We also derive and model the Gauss-Hermite moments of the observed proper motion distributions. The projected density profile is consistent with being flat near the center, with an upper limit gamma=0.07 on the central logarithmic slope. The RMS proper motion profile is also consistent with being flat near the center, and there are no unusually fast-moving stars. The models provide a good fit and yield a 1-sigma upper limit MBH < 1.2E4 solar masses on the mass of a possible intermediate-mass black hole (IMBH). The inferred upper limit corresponds to MBH/Mtot < 0.43%. We combine this with results for other clusters and discuss the implications for globular cluster IMBH demographics. Tighter limits will be needed to rule out or establish whether globular clusters follow the same black hole demographics correlations as galaxies. The arguments put forward by Noyola et al. (2008) to suspect an IMBH in Omega Cen are not confirmed by our study; the IMBH mass they suggested is firmly ruled out.

Strong lensing in Abell 1703: constraints on the slope of the inner dark matter distribution

In this article, we apply strong lensing techniques in Abell 1703, a massive X-ray luminous galaxy cluster at z=0.28. Our analysis is based on imaging data both from space and ground in 8 bands, complemented with a spectroscopic survey. Abell 1703 looks rather circular from the general shape of its multiply imaged systems and present a dominant giant elliptical cD galaxy in its centre. This cluster exhibits a remarkable bright 'central ring' formed by 4 bright images at z_{spec}=0.888 located very close to the cD galaxy, providing observational constraints that are potentially very interesting to probe the central mass distribution. The stellar contribution from the cD galaxy (~1.25 10^{12} M_{sun} within 7) is accounted for in our parametric mass modelling, and the underlying smooth dark matter component distribution is described using a generalized NFW profile parametrized with a central logarithmic slope \alpha. We find that within the range where observational constraints are present (from ~5 to ~50), the slope of the dark matter distribution in Abell1703 is equal to 1.09^{+0.05}_{-0.11} (3\sigma confidence level). The concentration parameter is equal to c_{200} ~ 3.5, and the scale radius is constrained to be larger than the region where observational constraints are available. Within this radius, the 2D mass is equal to M(50)=2.4 10^{14} M_{\sun}. We cannot draw any conclusions on cosmological models at this point since we lack results from realistic numerical simulations containing baryons to make a proper comparison. We advocate the need for a sample of observed and simulated unimodal relaxed galaxy clusters in order to make reliable comparisons, and potentially provide a test of cosmological models.

Detection of non-ordered central gas motions in a sample of four low surface brightness galaxies

Aims. We present integral-field spectroscopy of the ionized gas in the central regions of four galaxies with a low surface brightness disk taken with the Visible Multi Object Spectrograph at the Very Large Telescope and aimed at testing the accuracy in the determination of the central logarithmic slope α of the mass density radial profile ρ(r) ∝ r α in this class of objects. Methods. For all the sample galaxies we subtracted the best-fit model of gas in circular motions from the observed velocity field and derived the residuals. Only ESO-LV5340200 is characterized by a regular velocity field. We extracted the velocity curves of this galaxy along several position angles, in order to estimate the uncertainty in deriving the central gradient of the total mass density from long-slit spectroscopy. Results. We report the detection of strong non-ordered motions of the ionized gas in three out of four sample galaxies. The deviations have velocity amplitudes and spatial scales that keep it from being possible to disentangle the cuspy and core density radial profiles.

Dark matter halo profiles in scale-free cosmologies

We explore the dependence of the central logarithmic slope of dark matter halo density profiles α on the spectral index n of the linear matter power spectrum P(k) using cosmological N-body simulations of scale-free models [i.e. P(k) ∝kn]. These simulations are based on a set of clear, reproducible and physically motivated criteria that fix the appropriate starting and stopping times for runs, and allow one to compare haloes across models with different spectral indices and mass resolutions. For each of our simulations we identify samples of well-resolved haloes in dynamical equilibrium and we analyse their mass profiles. By parametrizing the mass profile using a ‘generalized’ Navarro, Frenk & White profile in which the central logarithmic slope α is allowed to vary while preserving the r−3 asymptotic form at large radii, we obtain preferred central slopes for haloes in each of our models. There is a strong correlation between α and n, such that α becomes shallower as n becomes steeper. However, if we normalize our mass profiles by r−2, the radius at which the logarithmic slope of the density profile is −2, we find that these differences are no longer present. This is apparent if we plot the maximum slope as a function of r/r−2– we find that the profiles are similar for haloes forming in different n models. This reflects the importance of concentration, and reveals that the concentrations of haloes forming in steep-n cosmologies tend to be smaller than those of haloes forming in shallow-n cosmologies. We conclude that there is no evidence for convergence to a unique central asymptotic slope, at least on the scales that we can resolve.

The Nature of Dark Matter and the Density Profile and Central Behavior of Relaxed Halos

We show that the two basic assumptions of the model recently proposed by Manrique and coworkers for the universal density profile of cold dark matter (CDM) halos, namely, that these objects grow inside out during periods of smooth accretion and that their mass profile and its radial derivatives are all continuous functions, are both well understood in terms of the very nature of CDM. Those two assumptions allow one to derive the typical density profile of halos of a given mass from the accretion rate characteristic of the particular cosmology. This profile was shown by Manrique and coworkers to recover the results of numerical simulations. In the present paper, we investigate its behavior beyond the ranges covered by present-day N-body simulations. We find that the central asymptotic logarithmic slope depends crucially on the shape of the power spectrum of density perturbations: it is equal to a constant negative value for power-law spectra and has central cores for the standard CDM power spectrum. The predicted density profile in the CDM case is well fitted by the 3D Sersic profile over at least 10 decades in halo mass. The values of the Sersic parameters depend on the mass of the structure considered. A practical procedure is provided that allows one to infer the typical values of the best NFW or Sersic fitting law parameters for halos of any mass and redshift in any given standard CDM cosmology.