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Register a new userDynamical flows through Dark Matter Haloes II: one and two points statistics at the virial radius
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Dominique Aubert
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In a serie of three papers, the dynamical interplay between environments and dark matter haloes is investigated, while focussing on the dynamical flows through their virial sphere. Our method relies on both cosmological simulations, to constrain the environments, and an extension to the classical matrix method to derive the response of the halo (see Pichon & Aubert (2006), paper I). The current paper focuses on the statistical characterisation of the environments surrounding haloes, using a set of large scale simulations. Our description relies on a `fluid halocentric representation where the interactions between the halo and its environment are investigated in terms of a time dependent external tidal field and a source term characterizing the infall. The method is applied to 15000 haloes, with masses between 5 x 10^12 Ms and 10^14 Ms evolving between z = 1 and z = 0. The net accretion at the virial radius is found to decrease with time, resulting from both an absolute decrease of infall and from a growing contribution of outflows. Infall is found to be mainly radial and occurring at velocities ~ 0.75 V200. Outflows are also detected through the virial sphere and occur at lower velocities ~ 0.6 V200 on more circular orbits. The external tidal field is found to be strongly quadrupolar and mostly stationnary, possibly reflecting the distribution of matter in the halos near environment. The coherence time of the small scale fluctuations of the potential hints a possible anisotropic distribution of accreted satellites. The flux density of mass on the virial sphere appears to be more clustered than the potential while the shape of its angular power spectrum seems stationnary.
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We combine ASCA and ROSAT X-ray data to constrain the radial dark matter distribution in the primary cluster of A2256, free from the isothermality assumption. Both instruments indicate that the temperature declines with radius. The region including the central galaxy has a multicomponent spectrum, which results in a wide range of allowed central temperatures. We find that the secondary subcluster has a temperature and luminosity typical of a rich cluster; however, the ASCA temperature map shows no signs of an advanced merger. It is therefore assumed that the primary cluster is in hydrostatic equilibrium. The data then require dark matter density profiles steeper than rho ~ r^-2.5 in its outer part. Acceptable models have a total mass within r=1.5 Mpc (the virial radius) of 6.0+-1.5 10^14 Msun at the 90% confidence, about 1.6 times smaller than the mass derived assuming isothermality. Near the center, dark matter profiles with and without central cusps are consistent with the data. Total mass inside the X-ray core (r=0.26 Mpc) is 1.28+-0.08 10^14 Msun, which exceeds the isothermal value by a factor of 1.4. Although the confidence intervals above may be underestimates since they do not include possible asymmetry and departures from hydrostatic equilibrium, the behavior of the mass distribution, if applicable to other clusters, can bring into better agreement X-ray and lensing mass estimates, but aggravate the ``baryon catastrophe. The observed considerable increase in the gas content with radius, not anticipated by simulations, may imply that a significant fraction of thermal gas energy comes from sources other than gravity and merger shocks.
Elliptical galaxies are modelled with a a 4-component model: Sersic stars, LCDM dark matter (DM), hot gas and central black hole. DM is negligible in the inner regions, which are dominated by stars and the central black hole. This prevents any kinematical estimate (using a Jeans analysis) of the inner slope of the DM density profile. The gas fraction rises, but the baryon fraction decreases with radius, at least out to 10 effective radii (R_e). Even with line-of-sight velocity dispersion (VD) measurements at 4 to 6 R_e with 20 km/s accuracy and perfectly known velocity anisotropy, the total mass within the virial radius (r_v) is uncertain by a factor over 3. The DM distributions found in LCDM simulations are consistent with the stellar VD profiles, but appear inconsistent with the low VDs measured by Romanowsky et al. (2003) of planetary nebulae between 2 and 5 R_e, which imply such low M/Ls that the baryon fraction within r_v must be greater than the universal value. Replacing the NFW DM model by the new model of Navarro et al. (2004) decreases slightly the VD at a given radius. So, given the observed VD measured at 5 R_e, the inferred M/L within r_v is 40% larger than predicted with the NFW model. Folding in the slight (strong) radial anisotropy found in LCDM (merger) simulations, which is well modelled (much better than with the Osipkov-Merritt formula) with beta(r) = 1/2 r/(r+a), the inferred M/L within r_v is another 1.6 (2.4) times higher than for the isotropic NFW model. Thus, the DM model and radial anisotropy can partly explain the low PN VDs, but not in full. In an appendix, single integral expressions are derived for the VDs in terms of the tracer density and total mass profiles, for 3 anisotropic models: radial, Osipkov-Merritt, and the model above, for general radial profiles of luminosity density and mass.
In this second paper on the entire virial region of the relaxed fossil cluster RXJ1159+5531, we present a hydrostatic analysis of the hot intracluster medium (ICM). For a model consisting of ICM, stellar mass from the central galaxy (BCG), and an NFW dark matter (DM) halo, we obtain good descriptions of the projected radial profiles of ICM emissivity and temperature. The BCG stellar mass is clearly detected with M_star/L_K = 0.61 +/- 0.11 solar, consistent with stellar population synthesis models for a Milky-Way IMF. We obtain a halo concentration, c_200 =8.4 +/- 1.0, and virial mass, M_200 = 7.9 +/- 0.6 x 10^13 M_sun. For its mass, the inferred concentration is larger than most relaxed halos produced in cosmological simulations with Planck parameters, consistent with RXJ1159+5531 forming earlier than the general halo population. The baryon fraction at r_200, f_b,200 = 0.134 +/- 0.007, is slightly below the Planck value (0.155) for the universe. When we account for the stellar baryons associated with non-central galaxies and the uncertain intracluster light, f_b,200 increases by ~0.015, consistent with the cosmic value. Performing our analysis in the context of MOND still requires a large DM fraction (85.0% +/- 2.5% at r=100 kpc) similar to that obtained using the standard Newtonian approach. The detection of a plausible stellar BCG mass component distinct from the NFW DM halo in the total gravitational potential suggests that ~10^14 M_sun represents the mass scale above which dissipation is unimportant in the formation of the central regions of galaxy clusters. (Abridged)
This paper is an extension of the paper by Del Popolo, Chan, and Mota (2020) to take account the effect of dynamical friction. We show how dynamical friction changes the threshold of collapse, $delta_c$, and the turn-around radius, $R_t$. We find numerically the relationship between the turnaround radius, $R_{rm t}$, and mass, $M_{rm t}$, in $Lambda$CDM, in dark energy scenarios, and in a $f(R)$ modified gravity model. Dynamical friction gives rise to a $R_{rm t}-M_{rm t}$ relation differing from that of the standard spherical collapse. In particular, dynamical friction amplifies the effect of shear, and vorticity already studied in Del Popolo, Chan, and Mota (2020). A comparison of the $R_{rm t}-M_{rm t}$ relationship for the $Lambda$CDM, and those for the dark energy, and modified gravity models shows, that the $R_{rm t}-M_{rm t}$ relationship of the $Lambda$CDM is similar to that of the dark energy models, and small differences are seen when comparing with the $f(R)$ models. The effect of shear, rotation, and dynamical friction is particularly evident at galactic scales, giving rise to a difference between the $R_{rm t}-M_{rm t}$ relation of the standard spherical collapse of the order of $simeq 60%$. Finally, we show how the new values of the $R_{rm t}-M_{rm t}$ influence the constraints to the $w$ parameter of the equation of state.
Simple but flexible dynamical models are useful for many purposes, including serving as the starting point for more complex models or numerical simulations of galaxies, clusters, or dark matter haloes. We present SpheCow, a new light-weight and flexible code that allows one to easily explore the structure and dynamics of any spherical model. Assuming an isotropic or Osipkov-Merritt anisotropic orbital structure, the code can automatically calculate the dynamical properties of any model with either an analytical density profile or an analytical surface density profile as starting point. We have extensively validated SpheCow using a combination of comparisons to analytical and high-precision numerical calculations, as well as the calculation of inverse formulae. SpheCow contains readily usable implementations for many standard models, including the Plummer, Hernquist, NFW, Einasto, Sersic, and Nuker models. The code is publicly available as a set of C++ routines and as a Python module, and it is designed to be easily extendable, in the sense that new models can be added in a straightforward way. We demonstrate this by adding two new families of models in which either the density slope or the surface density slope is described by an algebraic sigmoid function. We advocate the use of the SpheCow code to investigate the full dynamical structure for models for which the distribution function cannot be expressed analytically and to explore a much wider range of models than is possible using analytical models alone.
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