Density Profiles Of Dark Halos Research Articles

Strong orientation dependence of surface mass density profiles of dark haloes at large scales

We study the dependence of surface mass density profiles, which can be directly measured by weak gravitational lensing, on the orientation of haloes with respect to the line-of-sight direction, using a suite of $N$-body simulations. We find that, when major axes of haloes are aligned with the line-of-sight direction, surface mass density profiles have higher amplitudes than those averaged over all halo orientations, over all scales from $0.1$ to $100\,\mathrm{Mpc}/h$ we studied. While the orientation dependence at small scales is ascribed to the halo triaxiality, our results indicate even stronger orientation dependence in the so-called two-halo regime, up to $100\,\mathrm{Mpc}/h$. The orientation dependence for the two-halo term is well approximated by a multiplicative shift of the amplitude and therefore a shift in the halo bias parameter value. The halo bias from the two-halo term can be overestimated or underestimated by up to $\sim 30 \%$ depending on the viewing angle, which translates into the bias in estimated halo masses by up to a factor of two from halo bias measurements. The orientation dependence at large scales originates from the anisotropic halo-matter correlation function, which has an elliptical shape with the axis ratio of $\sim 0.55$ up to $100\, \mathrm{Mpc}/h$. We discuss potential impacts of halo orientation bias on other observables such as optically selected cluster samples and a clustering analysis of large-scale structure tracers such as quasars.

MATCHING THE DARK MATTER PROFILES OF dSph GALAXIES WITH THOSE OF SIMULATED SATELLITES: A TWO-PARAMETER COMPARISON

We compare the dark matter halos' structural parameters derived for four Milky Way dwarf spheroidal galaxies to those of subhalos found in cosmological $N$-body simulations. We confirm that estimates of the mass at a single fixed radius are fully consistent with the observations. However, when a second structural parameter such as the logarithmic slope of the dark halo density profile measured close to the half-light radius is included in the comparison, we find little to no overlap between the satellites and the subhalos. Typically the right mass subhalos have steeper profiles at these radii than measurements of the dSph suggest. Using energy arguments we explore if it is possible to solve this discrepancy by invoking baryonic effects. Assuming that feedback from supernovae can lead to a reshaping of the halos, we compute the required efficiency and find entirely plausible values for a significant fraction of the subhalos and even as low as 0.1%. This implies that care must be taken not to exaggerate the effect of supernovae feedback as this could make the halos too shallow. These results could be used to calibrate and possibly constrain feedback recipes in hydrodynamical simulations.

A universality of dark-halo surface density for the Milky Way and Andromeda dwarf satellites as a probe of the coldness of dark matter

AbstractWe propose a new astrophysical test on the nature of dark matter based on the properties of dark halos associated with dwarf spheroidal galaxies. The method adopts a mean surface density of a dark halo defined within a radius of maximum circular velocity, which is derivable for a wide variety of galaxies with any dark-matter density profiles. We find that even though dark halo density profiles are derived based on the different assumptions for each galaxy sample, this surface density is generally constant across a wide mass range of galaxy. We find that at higher halo-mass scales, this constancy for real galaxies can be naturally reproduced by both cold and warm dark matter (CDM and WDM) models. However, at low-mass scales, for which we have estimated from the Milky Way and Andromeda dwarf satellites, the mean surface density derived from WDM models largely deviates from the observed constancy, whereas CDM models are in reasonable agreement with observations.

A statistical-mechanical explanation of dark matter halo properties

Cosmological N-body simulations have revealed many empirical relationships of dark matter halos, yet the physical origin of these halo properties still remains unclear. On the other hand, the attempts to establish the statistical mechanics for self-gravitating systems have encountered many formal difficulties, and little progress has been made for about fifty years. The aim of this work is to strengthen the validity of the statistical-mechanical approach we have proposed previously to explain the dark matter halo properties. By introducing an effective pressure instead of the radial pressure to construct the specific entropy, we use the entropy principle and proceed in a similar way as previously to obtain an entropy stationary equation. An equation of state for equilibrated dark halos is derived from this entropy stationary equation, by which the dark halo density profiles with finite mass can be obtained. We also derive the anisotropy parameter and pseudo-phase-space density profile. All these predictions agree well with numerical simulations in the outer regions of dark halos. Our work provides further support to the idea that statistical mechanics for self-gravitating systems is a viable tool for investigation.

The Milky Way rotation curve in Horava-Lifshitz theory

The Horava - Lifshitz (HL) theory has recently attracted a lot of interest as a viable solution to some quantum gravity related problems and the presence of an effective cosmological constant able to drive the cosmic speed up. We show here that, in the weak field limit, the HL proposal leads to a modification of the gravitational potential because of two additive terms (scaling respectively as $r^2$ and $r^{-4}$) to the Newtonian $1/r$ potential. We then derive a general expression to compute the rotation curve of an extended system under the assumption that the mass density only depends on the cylindrical coordinates $(R, z)$ showing that the HL modification induces a dependence of the circular velocity on the mass function which is a new feature of the theory. As a first exploratory analysis, we then try fitting the Milky Way rotation curve using its visible components only in order to see whether the HL modified potential can be an alternative to the dark matter framework. This turns out not to be the case so that we argue that dark matter is still needed, but the amount of dark matter and the dark halo density profile have to be revised according to the new HL potential.

HOBBY-EBERLY TELESCOPE OBSERVATIONS OF THE DARK HALO IN NGC 821

We present line-of-sight stellar velocity distributions of elliptical galaxy NGC 821 obtained to approximately 100 arcsec (over 2 effective radii) with long-slit spectroscopy from the Hobby-Eberly Telescope. Our measured stellar line-of-sight velocity distributions are larger than the planetary nebulae measurements at similar radii. We fit axisymmetric orbit-superposition models with a range of dark halo density profiles, including two-dimensional kinematics at smaller radii from SAURON data. Within our assumptions, the best-fitted model gives a total enclosed mass of 2.0x10^11 M_sun within 100 arcsec, with an accuracy of 2%; this mass is equally divided between halo and stars. At 1R_e the best-fitted dark matter halo accounts for 13% of the total mass in the galaxy. This dark halo is inconsistent with previous claims of little to no dark matter halo in this galaxy from planetary nebula measurements. We find that a power-law dark halo with a slope 0.1 is the best-fitted model; both the no dark halo and NFW models are worse fits at a greater than 99% confidence level. NGC 821 does not appear to have the expected dark halo density profile. The internal moments of the stellar velocity distribution show that the model with no dark halo is radially anisotropic at small radii and tangentially isotropic at large radii, while the best-fitted halo models are slightly radially anisotropic at all radii. We test the potential effects of model smoothing and find that there are no effects on our results within the errors. Finally, we run models using the planetary nebula kinematics and assuming our best-fitted halos and find that the planetary nebulae require radial orbits throughout the galaxy.

MASS DISTRIBUTION IN HICKSON COMPACT GROUPS OF GALAXIES

This study presents the mass distribution for a sample of 18 late-type galaxies in nine Hickson Compact Groups. We used rotation curves from high resolution 2D velocity fields of Fabry-Perot observations and J-band photometry from the 2MASS survey, in order to determine the dark halo and the visible matter distributions. The study compares two halo density profile, an isothermal core-like distribution and a cuspy one. We also compare their visible and dark matter distributions with those of galaxies belonging to cluster and field galaxies coming from two samples: 40 cluster galaxies of Barnes et al (2004) and 35 field galaxies of Spano et al. (2008). The central halo surface density is found to be constant with respect to the total absolute magnitude similar to what is found for the isolated galaxies. This suggests that the halo density is independent to galaxy type and environment. We have found that core-like density profiles fit better the rotation curves than cuspy-like ones. No major differences have been found between field, cluster and compact group galaxies with respect to their dark halo density profiles.

CONSTRAINING DARK ENERGY FROM THE SPLITTING ANGLE STATISTIC OF STRONG GRAVITATIONAL LENSES

Utilizing the CLASS statistical sample, we investigate the constraint of the splitting angle statistic of strong gravitational lenses (SGL) on the equation-of-state parameter w = p/rho of the dark energy in the flat cold dark matter (CDM) cosmology. Through the comoving number density of dark halos described by the Press-Schechter theory, dark energy affects the efficiency with which dark-matter concentrations produce strong lensing signals. The constraints on both constant w and time-varying w(z) = w(0) + w(a)z/(1 + z) from the SGL splitting angle statistic are consistently obtained by adopting a two-model combined mechanism of a dark halo density profile matched at the mass scale M(c). Our main observations are that (1) the resulting model parameter M(c) is found to be M(c) similar to 1.4 for both constant w and time-varying w(z), which is larger than M(c) similar to 1 obtained in literatures; (2) the fitting results for the constant w are found to be w = -0.89(-0.26)(+0.49) and w = -0.94(-0.16)(+0.57) for the source redshift distributions of the Gaussian models g(z(s)) and g(c)(z(s)), respectively, which are consistent with the Lambda CDM at 95% C.L.; (3) the time-varying w(z) is found to be sigma(8) = 0.74: (M(c); w(0), w(a)) = (1.36; -0.92, -1.31) and (M(c); w(0), w(a)) = (1.38;-0.89, -1.21) for g(z(s)) and g(c)(z(s)), respectively; the influence of sigma(8) is investigated and found to be sizable for sigma(8) = 0.74-0.90. After marginalizing the likelihood functions over the cosmological parameters (Omega(M), h, sigma(8)) and the model parameter Mc, we find that the data of SGL splitting angle statistic lead to the best-fit results (w(0), w(a)) =(-0.88(-1.03)(+0.65),-1.55(-1.88)(+1.77)) and (w(0), w(a)) = (-0.91(-1.46)(+0.60),- 1.60(-2.57)+(1.60)) for g(z(s)) and g(c)(z(s)), respectively.

Understanding the halo-mass and galaxy-mass cross-correlation functions

We use the Millennium Simulation (MS) to measure the cross-correlation between halo centres and mass (or equivalently the average density profiles of dark haloes) in a Lambda cold dark matter (ACDM) cosmology. We present results for radii in the range 10 h -1 kpc < r < 30 h -1 Mpc and for halo masses in the range 4 x 10 10 < M 200 < 4 x 10 14 h -1 M ⊙ . Both at z = 0 and at z = 0.76 these cross-correlations are surprisingly well fitted if the inner region is approximated by a density profile of NFW or Einasto form, the outer region by a biased version of the linear mass autocorrelation function, and the maximum of the two is adopted where they are comparable. We use a simulation of galaxy formation within the MS to explore how these results are reflected in cross-correlations between galaxies and mass. These are directly observable through galaxy-galaxy lensing. Here also we find that simple models can represent the simulation results remarkably well, typically to ≤10 per cent. Such models can be used to extend our results to other redshifts, to cosmologies with other parameters, and to other assumptions about how galaxies populate dark haloes. Our galaxy formation simulation already reproduces current galaxy-galaxy lensing data quite well. The characteristic features predicted in the galaxy-galaxy lensing signal should provide a strong test of the ACDM cosmology as well as a route to understanding how galaxies form within it.

Constraining the Magnetic Effects on HiRotation Curves and the Need for Dark Halos

The density profiles of dark halos are usually inferred from the rotation curves of disk galaxies based on the assumption that the gas is a good tracer of the gravitational potential of the galaxies. Some authors have suggested that magnetic pinching forces could alter significantly the rotation curves of spiral galaxies. In contrast to other studies that have concentrated on the vertical structure of the disk, here we focus on the problem of magnetic confinement in the radial direction to determine the magnetic effects on the H I rotation curves. It is shown that azimuthal magnetic fields hardly speed up H I disks of galaxies as a whole. In fact, based on virial constraints we show that the contribution of galactic magnetic fields to the rotation curves cannot be larger than ~10 km s-1 at the outermost point of H I detection, if the galaxies did not contain dark matter at all, and is up to 20 km s-1 in the conventional dark halo scenario. The procedure to estimate the maximum effect of magnetic fields is general and applicable to any particular galaxy disk. The inclusion of the surface terms, namely, the intergalactic (thermal, magnetic, or ram) pressure, does not change our conclusions. Other problems related to the magnetic alternative to dark halos are highlighted. The relevance of magnetic fields in the cuspy problem of dark halos is also discussed.

Gravitational Lens Statistics as a Probe of Halo Profiles

Recent development of the structure formation theory based on the cold dark matter scenario implies that a number of larger separation lensed quasars, for which a confirmed detection has not yet been achieved, will be observed in the ongoing large-scale surveys such as the 2dF survey and SDSS. We show that statistics of such large separation lenses can be a powerful probe of the density profile of dark halos. After we summarize the current status of the lens surveys in the 2dF and SDSS, we focus our discussion on what information can be extracted from these lens surveys. in addition, we also propose statistics of differential time delays between multiple images as an alternative probe of the density profile of dark halos.

Modeling Intracluster Gas in Triaxial Dark Halos: An Analytic Approach

We present the first physical model for the nonspherical intracluster gas distribution in hydrostatic equilibrium under the gravity of triaxial dark matter halos. Adopting the concentric triaxial density profiles of dark halos with constant axis ratios proposed by Jing and Suto in 2002, we derive an analytical expression for the triaxial halo potential on the basis of perturbation theory and find the hydrostatic solutions for the gas density and temperature profiles in both isothermal and polytropic equations of state. The resulting isopotential surfaces are well approximated by triaxial ellipsoids with the eccentricities dependent on the radial distance. We also find a formula for the eccentricity ratio between the intracluster gas and the underlying dark halo. Our results allow one to determine the shapes of the underlying dark halos from the observed intracluster gas through X-ray and/or Sunyaev-Zeldovich effect clusters.

The differential energy distribution of the universal density profile of dark halo

We study the differential energy distribution of dark matter halos, carrying out cosmological N-body simulation. From our simulation, we give an analytical formula of the differential energy distribution of dark matter in the halos. Density distribution from the analytical formula is consistent with the Navarro, Frenk, and White (NFW) profile. We find that a parameter in our analytical formula of differential energy distribution is related with the slope of inner cusp of dark halo. We discuss physical reason of form of the analytical formula.

Constraints on the Baryonic Compression and Implications for the Fraction of Dark Halo Lenses

We predict the fraction of dark halo lenses, that is, the fraction of lens systems produced by the gravitational potential of dark halos, on the basis of a simple parametric model of baryonic compression. The fraction of dark halo lenses primarily contains information on the effect of baryonic compression and the density profile of dark halos and is expected to be insensitive to cosmological parameters and source population. The model that we adopt comprises the galaxy formation probability pg(M), which describes the global efficiency of baryonic compression, and the ratio of circular velocities of galaxies to virial velocities of dark halos, ?v = vc/vvir, which describes how the inner structure of dark halos is modified because of baryonic compression. The model parameters are constrained from the velocity function of galaxies and the distribution of image separations in gravitational lensing, although the degeneracy between model parameters still remains. We show that the fraction of dark halo lenses depends strongly on ?v and the density profile of dark halos, such as inner slope ?. This means that the observation of the fraction of dark halos can break the degeneracy between model parameters if the density profile of dark halo lenses is fully settled. On the other hand, by restricting ?v to a physically plausible range, we can predict the lower limit of the fraction of dark halo lenses on the basis of our model. Our result indicates that steeper inner cusps of dark halos (? 1.5) or too centrally concentrated dark halos are inconsistent with the lack of dark halo lenses in observations.

Observational Constraints on the Self‐interacting Dark Matter Scenario and the Growth of Supermassive Black Holes

We consider the consequences of SIDM for a velocity dependent cross section per unit mass. Accretion of SIDM onto seed black holes can produce supermassive black holes that are too large for certain combinations of parameters,which is used to obtain a new constraint on the dark matter interaction. Constraints due to other considerations are presented and previous ones are generalized. The black hole constraint is extremely sensitive to the slope \alpha, of the inner density profile of dark halos. For the most probable value of \alpha=1.3, there exists a narrow range in parameter space, such that all constraints are satisfied. However, the adiabatic compression of the dark halo by baryons as they cool and contract in normal galaxies yields a steeper cusp, \alpha=1.7. This gives a tighter constraint, which would exclude SIDM as a possible solution to the purported problems with CDM in the absence of other dynamical processes. Nevertheless, SIDM with parameters consistent with this stronger constraint, can explain the ubiquity of supermassive black holes in the centers of galaxies. A ``best fit'' model is presented which reproduces the supermassive black hole masses and their observed correlations with the velocity dispersion of the host bulges. Specifically, the fourth power dependence of black hole mass on velocity dispersion is a direct consequence of the power spectrum having an index of n=-2. Although the dark matter collision rates for this model are too small to directly remedy problems with CDM, mergers between dark halos harboring supermassive black holes at high redshift could ameliorate the cuspy halo problem. This scenario also explains the lack of comparable supermassive black holes in bulgeless galaxies like M33.

The dynamical evolution of substructure

The evolution of substructure embedded in non-dissipative dark haloes is studied through N-body simulations of isolated systems, both in and out of initial equilibrium, complementing cosmological simulations of the growth of structure. We determine by both analytic calculations and direct analysis of the N-body simulations the relative importance of various dynamical processes acting on the clumps, such as the removal of material by global tides, clump–clump heating, clump–clump merging and dynamical friction. The ratio of the internal clump velocity dispersion to that of the dark halo is an important parameter; as this ratio approaches a value of unity, heating by close encounters between clumps becomes less important, while the other dynamical processes continue to increase in importance. Our comparison between merging and disruption processes implies that spiral galaxies cannot be formed in a protosystem that contains a few large clumps, but can be formed through the accretion of many small clumps; elliptical galaxies form in a more clumpy environment than do spiral galaxies. Our results support the idea that the central cusp in the density profiles of dark haloes is the consequence of self-limiting merging of small, dense haloes. This implies that the collapse of a system of clumps/substructure is not sufficient to form a cD galaxy, with an extended envelope; plausibly, subsequent accretion of large galaxies is required. The post-collapse system is in general triaxial, with rounder systems resulting from fewer, but more massive, clumps. Persistent streams of material from disrupted clumps can be found in the outer regions of the final system, and at an overdensity of around 0.75, can cover 10 to 30 per cent of the sky.

Gravitational Lens Statistics and the Density Profile of Dark Halos

We investigate the influence of the inner profile of lens objects on gravitational lens statistics taking into account of the effect of magnification bias and both the evolution and the scatter of halo profiles. We take the dark halos as the lens objects and consider the following three models for the density profile of dark halos; SIS (singular isothermal sphere), the NFW (Navarro Frenk White) profile, and the generalized NFW profile which has a different slope at smaller radii. The mass function of dark halos is assumed to be given by the Press-Schechter function. We find that magnification bias for the NFW profile is order of magnitude larger than that for SIS. We estimate the sensitivity of the lensing probability of distant sources to the inner profile of lenses and to the cosmological parameters. It turns out that the lensing probability is strongly dependent on the inner density profile as well as on the cosmological constant. We compare the predictions with the largest observational sample, the Cosmic Lens All-Sky Survey. The absence or presence of large splitting events in larger surveys currently underway such as the 2dF and SDSS could set constraints on the inner density profile of dark halos.

Probing the Core Structure of Dark Halos with Tangential and Radial Arc Statistics

We study the arc statistics of gravitational lensing generated by dark matter halos in order to probe their density profile. We characterize the halo profile by two parameters, the inner slope of the central cusp α and the median amplitude of the concentration parameter, cnorm, for a halo of mass 1014 h-1 M☉ at z = 0 and compute the numbers of tangential and radial arcs produced by gravitational lensing of galaxy clusters. We find that the number of arcs divided by the number of halos is a good statistic that is sensitive to both cnorm and α with very weak dependence on the cosmological parameters. If arc samples with well-defined selection criteria for the clusters become available, one can strongly constrain both cnorm and α. While our tentative comparison with the existing observational data indicates that the inner density profile of dark halos is indeed as steep as predicted by recent simulations (α ~ 1.5), homogeneous samples of tangential and radial arcs are required for more quantitative discussions.

The Differential Energy Distribution of the Universal Density Profile of Dark Halos

We study the differential energy distribution of dark matter halos by carrying out a cosmological N-body simulation. We give an analytical formula for the differential energy distribution of dark matter in the halos obtained by the numerical simulation. From the analytical formula we reconstruct the density profile described by the Navarro, Frenk, & White (NFW) profile. The NFW profile is consistent with the analytical formula of our fractional mass distribution. We find a parameter in our analytical formula for the differential energy distribution that is related to the slope of the inner cusp of the dark halo. We obtain the distribution function for the NFW profile, which has a sharp cutoff at the high binding energy. We discuss physical reasons for the form of the analytical formula.

Semianalytical Models for Lensing by Dark Halos. I. Splitting Angles

We use the semianalytical approach to analyze gravitational lensing of remote quasars by foreground dark halos in various cold dark matter (CDM) cosmologies in order to determine the sensitivity of the predictions for probabilities of image separations to the input assumptions regarding the properties of halos and cosmological models. The power spectrum of primordial fluctuations is normalized by the cluster abundance constraints. The mass function of dark halos is assumed to be given by the Press-Schechter function. The mass density profile of dark halos is alternatively taken to be the singular isothermal sphere (SIS), the Navarro-Frenk-White (NFW) profile, or the generalized NFW profile. The cosmologies being considered include the Einstein-de Sitter model (SCDM), the open model (OCDM), and the flat Λ-model (LCDM). As expected, we find that the lensing probability is extremely sensitive to the mass density profile of lenses (dark halos) and somewhat less so to the mean mass density in the universe and the amplitude of primordial fluctuations. NFW halos are very much less effective in producing multiple images than SIS halos. For NFW lenses, the SCDM model produces fewer lensing events than the OCDM/LCDM models by 2 orders of magnitude. For SIS lenses, the SCDM model produces more lensing events with small splitting angles and fewer lensing events with large splitting angles than the OCDM/LCDM models, which is due to the fact that for large-mass halos, the Press-Schechter function is very sensitive to the amplitude of primordial fluctuations. In all cases the difference between the OCDM model and the LCDM model is not dramatic. None of these models are consistent with current observations: the SIS models predict too many large splitting lenses, while the NFW models predict too few small splitting lenses. Essentially, the observed high ratio of small splitting to large splitting lenses is not predicted correctly. This indicates that there must be at least two populations of halos in the universe: small-mass halos with a steep inner density slope and large-mass halos with a shallow inner density slope. A combination of SIS and NFW halos can reasonably reproduce the current observations if we choose the mass for the transition from SIS to NFW to be ~1013 M☉, as might plausibly occur because of baryonic cooling and contraction in lower mass systems. Additionally, there is a tendency for CDM models to have too much power on small scales, i.e., too much mass concentration. From our sensitivity studies it appears that the cures proposed for other apparent difficulties of CDM would help here as well, an example being the warm dark matter variant, which is shown to produce fewer large splitting lenses than the corresponding CDM model by 1 order of magnitude.