The Correlation Function of Clusters of Galaxies and the Amplitude of Mass Fluctuations in the Universe

We show that if a sample of galaxy clusters is complete above some mass threshold, then hierarchical clustering theories for structure formation predict its autocorrelation function to be determined purely by the cluster abundance and by the spectrum of linear density fluctuations. Thus if the shape of the initial fluctuation spectrum is known, its amplitude $\sigma_8$ can be estimated directly from the correlation length of a cluster sample in a way which is independent of the value of $\Omega_0$. If the cluster mass corresponding to the sample threshold is also known, it provides an independent estimate of the quantity $\sigma_8\Omega_0^{0.6}$. Thus cluster data should allow both $\sigma_8$ and $\Omega_0$ to be determined observationally. We explore these questions using N-body simulations together with a simple but accurate analytical model based on extensions of Press-Schechter theory. Applying our results to currently available data we find that if the linear fluctuation spectrum has a shape similar to that suggested by the APM galaxy survey, then a correlation length $r_0$ in excess of 20\mpch for Abell clusters would require $\sigma_8>1$, while r_0<15\mpch would require $\sigma_8<0.5$. With conventional estimates of the relevant mass threshold these imply \Omega_0\la 0.3 and \Omega_0\ga 1 respectively.Comment: Latex, 25 pages (including 8 PS figures). The PS-file of the paper is also available via anonymous ftp at: ftp://ibm-3.mpa-garching.mpg.de/pub/jing/xicc.ps . Submitted to MNRAS. In the replaced version, a typo in Eq.(1a) is fixe

Satellites and haloes of dwarf galaxies

We study the abundance of satellite galaxies as a function of primary stellar mass using the Sloan Digital Sky Survey/Data Release 7 (SDSS/DR7) spectroscopic catalogue. In contrast with previous studies, which focused mainly on bright primaries, our central galaxies span a wide range of stellar mass, 107.5 ⩽ Mpri*/M⊙ ⩽ 1011, from dwarfs to central cluster galaxies. Our analysis confirms that the average number of satellites around bright primaries, when expressed in terms of satellite-to-primary stellar mass ratio (msat*/M*pri), is a strong function of Mpri*. On the other hand, satellite abundance is largely independent of primary mass for dwarf primaries (Mpri* < 1010 M⊙). These results are consistent with galaxy formation models in the Λ cold dark matter (ΛCDM) scenario. We find excellent agreement between SDSS data and semianalytic mock galaxy catalogues constructed from the Millennium-II Simulation. Satellite galaxies trace dark matter substructure in ΛCDM, so satellite abundance reflects the dependence on halo mass, M200, of both substructure and galaxy stellar mass (M*). Since dark matter substructure is almost scale free, the dependence of satellite abundance on primary mass results solely from the well-defined characteristic mass in the galaxy mass-halo mass relation. On dwarf galaxy scales, where models predict a power-law scaling, M*∝M2.5200, similarity is preserved and satellite abundance is independent of primary mass. For primaries brighter than the characteristic mass of the M*–M200 relation, satellite abundance increases strongly with primary mass. Our results provide strong support for the steep, approximately power-law dependence of dwarf galaxy mass on halo mass envisioned in ΛCDM galaxy formation models

Early structure in Lambda CDM

We use a novel technique to simulate the growth of one of the most massive progenitors of a supercluster region from redshift z 80, when its mass was about 10 M, until the present day. Our nested sequence of N-body resimulations allows us to study in detail the structure both of the dark matter object itself and of its environment. Our effective resolution is optimal at redshifts of 49, 29, 12, 5 and 0 when the dominant object has mass 1.2 × 105, 5 × 107, 2 × 1010, 3 × 1012 and 8 × 1014 h1 M, respectively, and contains 106 simulation particles within its virial radius. Extended Press–Schechter (EPS) theory correctly predicts both this rapid growth and the substantial overabundance of massive haloes we find at early times in regions surrounding the dominant object. Although the large-scale structure in these regions differs dramatically from a scaled version of its present-day counterpart, the internal structure of the dominant object is remarkably similar. Molecular hydrogen cooling could start as early as z 49 in this object, while cooling by atomic hydrogen becomes effective at z 39. If the first stars formed in haloes with virial temperature 2000 K, their comoving abundance at z= 49 should be similar to that of dwarf galaxies today, while their comoving correlation length should be 2.5 h1 Mpc

Voids in the Simulated Local Universe

We use simulations of the formation and evolution of the galaxy population in the Local Universe to address the issue of whether the standard theoretical model succeeds in producing empty regions as large and as dark as the observed nearby ones. We follow the formation of galaxies in an LCDM universe and work with mock catalogues which can resolve the morphology of LMC sized galaxies, and the luminosity of objects 6 times fainter. We look for a void signature in sets of virialized haloes selected by mass, as well as in mock galaxy samples selected according to observationally relevant quantities, like luminosity, colour, or morphology. We find several void regions with diameter 10 Mpc/h in the simulation where gravity seems to have swept away even the smallest haloes we were able to track. We probe the environment density of the various populations and compute luminosity functions for galaxies residing in underdense, mean density and overdense regions. We also use nearest neighbour statistics to check possible void populations, taking $L_{*}$ spirals as reference neighbours. Down to our resolution limits, we find that all types of galaxies avoid the same regions, and that no class appears to populate the voids defined by the bright galaxies.Comment: 14 pages, 6 figures. Submitted to MNRAS. A high-resolution version of Figure 1 and galaxy populations analysed here are available at http://www.mpa-garching.mpg.de/NumCos/CR/Voids

Universal structure of dark matter haloes over a mass range of 20 orders of magnitude

Cosmological models in which dark matter consists of cold elementary particles predict that the dark halo population should extend to masses many orders of magnitude below those at which galaxies can form1,2,3. Here we report a cosmological simulation of the formation of present-day haloes over the full range of observed halo masses (20 orders of magnitude) when dark matter is assumed to be in the form of weakly interacting massive particles of mass approximately 100 gigaelectronvolts. The simulation has a full dynamic range of 30 orders of magnitude in mass and resolves the internal structure of hundreds of Earth-mass haloes in as much detail as it does for hundreds of rich galaxy clusters. We find that halo density profiles are universal over the entire mass range and are well described by simple two-parameter fitting formulae4,5. Halo mass and concentration are tightly related in a way that depends on cosmology and on the nature of the dark matter. For a fixed mass, the concentration is independent of the local environment for haloes less massive than those of typical galaxies. Haloes over the mass range of 10−3 to 1011 solar masses contribute about equally (per logarithmic interval) to the luminosity produced by dark matter annihilation, which we find to be smaller than all previous estimates by factors ranging up to one thousand3

Missing dark matter in dwarf galaxies?

We use cosmological hydrodynamical simulations of the APOSTLE project along with high-quality rotation curve observations to examine the fraction of baryons in ΛCDM haloes that collect into galaxies. This ‘galaxy formation efficiency’ correlates strongly and with little scatter with halo mass, dropping steadily towards dwarf galaxies. The baryonic mass of a galaxy may thus be used to place a lower limit on total halo mass and, consequently, on its asymptotic maximum circular velocity. A number of observed dwarfs seem to violate this constraint, having baryonic masses up to 10 times higher than expected from their rotation speeds, or, alternatively, rotating at only half the speed expected for their mass. Taking the data at face value, either these systems have formed galaxies with extraordinary efficiency – highly unlikely given their shallow potential wells – or their dark matter content is much lower than expected from ΛCDM haloes. This ‘missing dark matter’ is reminiscent of the inner mass deficit of galaxies with slowly rising rotation curves, but cannot be explained away by star formation-induced ‘cores’ in the dark mass profile, since the anomalous deficit applies to regions larger than the luminous galaxies themselves. We argue that explaining the structure of these galaxies would require either substantial modification of the standard ΛCDM paradigm or else significant revision to the uncertainties in their inferred mass profiles, which should be much larger than reported. Systematic errors in inclination may provide a simple resolution to what would otherwise be a rather intractable problem for the current paradigm

Outskirts of Nearby Disk Galaxies: Star Formation and Stellar Populations

The properties and star formation processes in the far-outer disks of nearby spiral and dwarf irregular galaxies are reviewed. The origin and structure of the generally exponential profiles in stellar disks is considered to result from cosmological infall combined with a non-linear star formation law and a history of stellar migration and scattering from spirals, bars, and random collisions with interstellar clouds. In both spirals and dwarfs, the far-outer disks tend to be older, redder and thicker than the inner disks, with the overall radial profiles suggesting inside-out star formation plus stellar scattering in spirals, and outside-in star formation with a possible contribution from scattering in dwarfs. Dwarf irregulars and the far-outer parts of spirals both tend to be gas dominated, and the gas radial profile is often non-exponential although still decreasing with radius. The ratio of H-alpha to far-UV flux tends to decrease with lower surface brightness in these regions, suggesting either a change in the initial stellar mass function or the sampling of that function, or a possible loss of H-alpha photons.Comment: 20 pages, 8 figures, Invited review, Book chapter in "Outskirts of Galaxies", Eds. J. H. Knapen, J. C. Lee and A. Gil de Paz, Astrophysics and Space Science Library, Springer, in pres

Renormalization-group running of the cosmological constant and its implication for the Higgs boson mass in the Standard Model

The renormalization-group equation for the zero-point energies associated with vacuum fluctuations of massive fields from the Standard Model is examined. Our main observation is that at any scale the running is necessarily dominated by the heaviest degrees of freedom, in clear contradistinction with the Appelquist & Carazzone decoupling theorem. Such an enhanced running would represent a disaster for cosmology, unless a fine-tuned relation among the masses of heavy particles is imposed. In this way, we obtain $m_H \simeq 550 GeV$ for the Higgs mass, a value safely within the unitarity bound, but far above the more stringent triviality bound for the case when the validity of the Standard Model is pushed up to the grand unification (or Planck) scale.Comment: 11 pages, LaTex2

Alignment of galaxy spins in the vicinity of voids

We provide limits on the alignment of galaxy orientations with the direction to the void center for galaxies lying near the edges of voids. We locate spherical voids in volume limited samples of galaxies from the Sloan Digital Sky Survey using the HB inspired void finder and investigate the orientation of (color selected) spiral galaxies that are nearly edge-on or face-on. In contrast with previous literature, we find no statistical evidence for departure from random orientations. Expressed in terms of the parameter c, introduced by Lee & Pen to describe the strength of such an alignment, we find that c<0.11(0.13) at 95% (99.7%) confidence limit within a context of a toy model that assumes a perfectly spherical voids with sharp boundaries.Comment: 8 pages, 4 figures; v2 discussion expanded, references fixed, matches version accepted by JCA