The effects of primordial non-Gaussianity on the cosmological reionization

We investigate the effects of non-Gaussianity in the primordial density field on the reionization history. We rely on a semi-analytic method to describe the processes acting on the intergalactic medium (IGM), relating the distribution of the ionizing sources to that of dark matter haloes. Extending previous work in the literature, we consider models in which the primordial non-Gaussianity is measured by the dimensionless non-linearity parameter f _NL, using the constraints recently obtained from cosmic microwave background data. We predict the ionized fraction and the optical depth at different cosmological epochs assuming two different kinds of non-Gaussianity characterized by a scale-independent and a scale-dependent f _NL and comparing the results to those for the standard Gaussian scenario. We find that a positive f _NL enhances the formation of high-mass haloes at early epochs when reionization begins, and, as a consequence, the IGM ionized fraction can grow by a factor of up to 5 with respect to the corresponding Gaussian model. The increase of the filling factor has a small impact on the reionization optical depth and is of the order of ∼10 per cent if a scale-dependent non-Gaussianity is assumed. Our predictions for non-Gaussian models are in agreement with the latest Wilkinson Microwave Anisotropy Probe results within the error bars, but a higher precision is required to constrain the scale dependence of non-Gaussianity.     

Constraints on primordial non-Gaussianity from a needlet analysis of the WMAP-5 data

We look for a non-Gaussian signal in the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-year temperature anisotropy maps by performing a needlet-based data analysis. We use the foreground-reduced maps obtained by the WMAP team through the optimal combination of the W, V and Q channels, and perform realistic non-Gaussian simulations in order to constrain the non-linear coupling parameter f _NL. We apply a third-order estimator of the needlet coefficients skewness and compute the  χ²  statistics of its distribution. We obtain  −80 < f _NL < 120  at 95 per cent confidence level, which is consistent with a Gaussian distribution and comparable to previous constraints on the non-linear coupling. We then develop an estimator of f _NL based on the same simulations and we find consistent constraints on primordial non-Gaussianity. We finally compute the three-point correlation function in needlet space: the constraints on f _NL improve to  −50 < f _NL < 110  at 95 per cent confidence level.     

The effect of primordial non-Gaussianity on the topology of large-scale structure

We study the effect of primordial non-Gaussianity on the development of large-scale cosmic structure using high-resolution N -body simulations. In particular, we focus on the topological properties of the 'cosmic web', quantitatively characterized by the Minkowski functionals (MFs), for models with quadratic non-linearities with different values of the usual non-Gaussianity parameter f _NL. In the weakly non-linear regime (the amplitude of mass density fluctuations σ₀ < 0.1), we find that analytic formulae derived from perturbation theory agree with the numerical results within a few per cent of the amplitude of each MF when | f _NL| < 1000. In the non-linear regime, the detailed behaviour of the MFs as functions of threshold density deviates more strongly from the analytical curves, while the overall amplitude of the primordial non-Gaussian effect remains comparable to the perturbative prediction. When smaller-scale information is included, the influence of primordial non-Gaussianity becomes increasingly significant statistically due to decreasing sample variance. We find that the effect of the primordial non-Gaussianity with  | f _NL| = 50  is comparable to the sample variance of mass density fields with a volume of 0.125( h ⁻¹ Gpc)³ when they are smoothed by Gaussian filter at a scale of 5  h ⁻¹ Mpc. The detectability of this effect in actual galaxy surveys will strongly depend on residual uncertainties in cosmological parameters and galaxy biasing.     

Multiple methods for estimating the bispectrum of the cosmic microwave background with application to the MAXIMA data

We describe different methods for estimating the bispectrum of cosmic microwave background data. In particular, we construct a minimum-variance estimator for the flat-sky limit and compare results with previously studied frequentist methods. Application to the MAXIMA data set shows consistency with primordial Gaussianity. Weak quadratic non-Gaussianity is characterized by a tunable parameter   f _NL  , corresponding to non-Gaussianity at a level of  ∼10⁻⁵ f _NL  (the ratio of non-Gaussian to Gaussian terms), and we find limits of   f _NL= 1500 ± 950  for the minimum-variance estimator and   f _NL= 2700 ± 1650  for the usual frequentist estimator. These are the tightest limits on primordial non-Gaussianity, which include the full effects of the radiation transfer function.     

Figure rotation of dark haloes in cold dark matter simulations

We investigate the figure rotation of dark matter haloes identified in Λ cold dark matter (CDM) simulations. We find that when strict criteria are used to select suitable haloes for study, five of the 222 haloes identified in our   z = 0  simulation output undergo coherent figure rotation over a  5 h ⁻¹ Gyr  period. We discuss the effects of varying the selection criteria and find that pattern speeds for a much larger fraction of the haloes can be measured when the criteria are relaxed. Pattern speeds measured over a  1 h ⁻¹ Gyr  period follow a lognormal distribution, centred at  Ω_p= 0.2 h rad Gyr⁻¹  with a maximum value of 0.94 h rad Gyr⁻¹. Over a  5 h ⁻¹ Gyr  period, the average pattern speed of a halo is about  0.1 h rad Gyr⁻¹  and the largest pattern speed found is  0.24 h rad Gyr⁻¹  . Less than half of the selected haloes showed alignment between their figure rotation axis and minor axis, the exact fraction being somewhat dependent on how one defines a halo. While the pattern speeds observed are lower than those generally thought capable of causing spiral structure, we note that coherent figure rotation is found over very long periods and argue that further simulations would be required before strong conclusions about spiral structure in all galaxies could be drawn. We find no correlation between halo properties such as total mass and the pattern speed.     

Microlensing in dark matter haloes

Using eight dark matter haloes extracted from fully self-consistent cosmological N -body simulations, we perform microlensing experiments. A hypothetical observer is placed at a distance of 8.5 kpc from the centre of the halo measuring optical depths, event durations and event rates towards the direction of the Large Magellanic Cloud. We simulate 1600 microlensing experiments for each halo. Assuming that the whole halo consists of massive astronomical compact halo objects (MACHOs),   f = 1.0  , and a single MACHO mass is   m _M= 1.0 M_⊙  , the simulations yield mean values of  τ= 4.7^+5.0_−2.2× 10⁻⁷  and  Γ= 1.6^+1.3_−0.6× 10⁻⁶  events star⁻¹ yr⁻¹. We find that triaxiality and substructure can have major effects on the measured values so that τ and Γ values of up to three times the mean can be found. If we fit our values of τ and Γ to the MACHO collaboration observations, we find   f = 0.23^+0.15_−0.13  and   m _M= 0.44^+0.24_−0.16  . Five out of the eight haloes under investigation produce f and m _M values mainly concentrated within these bounds.     

The real-space power spectrum of the PSCz survey from 0.01 to 300 h Mpc−1

We report a measurement of the real-space (not redshift-space) power spectrum of galaxies over four and a half decades of wavenumber, 0.01 to 300  h  Mpc⁻¹, from the IRAS Point Source Catalog Redshift Survey (PSC z ). Since estimates of power are highly correlated in the non-linear regime, we also report results for the pre-whitened power spectrum, which is less correlated. The inferred bias between optically selected APM and IRAS -selected PSC z galaxies is about 1.15 at linear scales ≲0.3  h  Mpc⁻¹, increasing to about 1.4 at non-linear scales ≳1  h  Mpc⁻¹. The non-linear power spectrum of PSC z shows a near power-law behaviour to the smallest scales measured, with possible mild upward curvature in the broad vicinity of   k ∼2  h  Mpc⁻¹  . Contrary to the prediction of unbiased dark matter models, there is no prominent inflection at the linear to non-linear transition scale, and no turnover at the transition to the virialized regime. The non-linear power spectrum of PSC z requires scale-dependent bias: all Dark Matter models without scale-dependent bias are ruled out with high confidence.     

The distribution of ejected subhaloes and its implication for halo assembly bias

Using a high-resolution cosmological N -body simulation, we identify the ejected population of subhaloes, which are haloes at redshift   z = 0  but were once contained in more massive 'host' haloes at high redshifts. The fraction of the ejected subhaloes in the total halo population of the same mass ranges from 9 to 4 per cent for halo masses from  ∼10¹¹  to  ∼10¹²  h ⁻¹ M_⊙  . Most of the ejected subhaloes are distributed within four times the virial radius of their hosts. These ejected subhaloes have distinct velocity distribution around their hosts in comparison to normal haloes. The number of subhaloes ejected from a host of given mass increases with the assembly redshift of the host. Ejected subhaloes in general reside in high-density regions, and have a much higher bias parameter than normal haloes of the same mass. They also have earlier assembly times, so that they contribute to the assembly bias of dark matter haloes seen in cosmological simulations. However, the assembly bias is not dominated by the ejected population, indicating that large-scale environmental effects on normal haloes are the main source for the assembly bias.     

Dark matter subhaloes in numerical simulations

We use cosmological Λ cold dark matter (CDM) numerical simulations to model the evolution of the substructure population in 16 dark matter haloes with resolutions of up to seven million particles within the virial radius. The combined substructure circular velocity distribution function (VDF) for hosts of 10¹¹ to  10¹⁴ M_⊙  at redshifts from zero to two or higher has a self-similar shape, is independent of host halo mass and redshift, and follows the relation  d n /d v = (1/8)( v _cmax/ v _cmax,host)⁻⁴  . Halo to halo variance in the VDF is a factor of roughly 2 to 4. At high redshifts, we find preliminary evidence for fewer large substructure haloes (subhaloes). Specific angular momenta are significantly lower for subhaloes nearer the host halo centre where tidal stripping is more effective. The radial distribution of subhaloes is marginally consistent with the mass profile for   r ≳ 0.3 r _vir  , where the possibility of artificial numerical disruption of subhaloes can be most reliably excluded by our convergence study, although a subhalo distribution that is shallower than the mass profile is favoured. Subhalo masses but not circular velocities decrease towards the host centre. Subhalo velocity dispersions hint at a positive velocity bias at small radii. There is a weak bias towards more circular orbits at lower redshift, especially at small radii. We additionally model a cluster in several power-law cosmologies of   P ∝ kⁿ   , and demonstrate that a steeper spectral index, n , results in significantly less substructure.     

Primordial non-Gaussianities in the intergalactic medium

We present results from the first high-resolution hydrodynamical simulations of non-Gaussian cosmological models. We focus on the statistical properties of the transmitted Lyman-α flux in the high-redshift intergalactic medium. Imprints of non-Gaussianity are present and are larger at high redshifts. Differences larger than 20 per cent at   z > 3  in the flux probability distribution function for high-transmissivity regions (voids) are expected for values of the non-linearity parameter   f _NL=±100  when compared to a standard Λ cold dark matter cosmology with   f _NL= 0  . We also investigate the one-dimensional flux bispectrum: at the largest scales (corresponding to tens of Mpc), we expect deviations in the flux bispectrum up to 20 per cent at   z ∼ 4  (for   f _NL=±100  ), significantly larger than deviations of ∼3 per cent in the flux power spectrum. We briefly discuss possible systematic errors that can contaminate the signal. Although challenging, a detection of non-Gaussianities in the interesting regime of scales and redshifts probed by the Lyman-α forest could be possible with future data sets.     

On the distribution of haloes, galaxies and mass

The stochasticity in the distribution of dark haloes in the cosmic density field is reflected in the distribution function   P _V ( N _h| δ _m)  , which gives the probability of finding N _h haloes in a volume V with mass density contrast δ _m. We study the properties of this function using high-resolution N -body simulations, and find that   P _V ( N _h| δ _m)  is significantly non-Poisson. The ratio between the variance and the mean goes from ∼1 (Poisson) at  1+ δ _m≪1  to <1 (sub-Poisson) at  1+ δ _m∼1  to >1 (super-Poisson) at  1+ δ _m≫1  . The mean bias relation is found to be well described by halo bias models based on the Press–Schechter formalism. The sub-Poisson variance can be explained as a result of halo exclusion, while the super-Poisson variance at high δ _m may be explained as a result of halo clustering. A simple phenomenological model is proposed to describe the behaviour of the variance as a function of δ _m. Galaxy distribution in the cosmic density field predicted by semi-analytic models of galaxy formation shows similar stochastic behaviour. We discuss the implications of the stochasticity in halo bias to the modelling of higher order moments of dark haloes and of galaxies.     

The three-dimensional power spectrum of dark and luminous matter from the VIRMOS-DESCART cosmic shear survey

We present the first optimal power spectrum estimation and three-dimensional deprojections for the dark and luminous matter and their cross-correlations. The results are obtained using a new optimal fast estimator, deprojected using minimum variance and Singular Value Decomposition (SVD) techniques. We show the resulting 3D power spectra for dark matter and galaxies, and their covariance for the VIRMOS-DESCART weak lensing shear and galaxy data. The survey is most sensitive to non-linear scales   k _NL∼ 1 h Mpc⁻¹  . On these scales, our 3D power spectrum of dark matter is in good agreement with the RCS 3D power spectrum found by Tegmark & Zaldarriaga. Our galaxy power is similar to that found by the 2MASS survey, and larger than that of SDSS, APM and RCS, consistent with the expected difference in galaxy population.
We find an average bias   b = 1.24 ± 0.18  for the I -selected galaxies, and a cross-correlation coefficient   r = 0.75 ± 0.23  . Together with the power spectra, these results optimally encode the entire two point information about dark matter and galaxies, including galaxy–galaxy lensing. We address some of the implications regarding galaxy haloes and mass-to-light ratios. The best-fitting 'halo' parameter   h ≡ r / b = 0.57 ± 0.16  , suggesting that dynamical masses estimated using galaxies systematically underestimate total mass.
Ongoing surveys, such as the Canada–France–Hawaii Telescope Legacy Survey, will significantly improve on the dynamic range, and future photometric redshift catalogues will allow tomography along the same principles.     

Pairwise velocities in the halo model: luminosity and scale dependence

We investigate the properties of the pairwise velocity dispersion as a function of galaxy luminosity in the context of a halo model. We derive the distribution of velocities of pairs at a given separation taking into account both one- and two-halo contributions. We show that pairwise velocity distribution in real space is a complicated mixture of host–satellite, satellite–satellite (sat–sat) and two-halo pairs. The peak value is reached at around  1  h ⁻¹ Mpc  and does not reflect the velocity dispersion of a typical halo hosting these galaxies, but is instead dominated by the sat–sat pairs in high-mass clusters. This is true even for cross-correlations between bins separated in luminosity. As a consequence, the velocity dispersion at a given separation can decrease with luminosity, even if the underlying typical halo host mass is increasing, in agreement with recent observations. We compare our findings to numerical simulations and find a good agreement. Numerical simulations also suggest a luminosity-dependent velocity bias, which depends on the subhalo mass. We develop models of the auto- and cross-correlation functions of luminosity subsamples of galaxies in the observable   r _proj–π  space and calculate the inferred velocity dispersion as a function of wavevector if dispersion model is fit to the redshift-space power spectrum. We find that so-derived pairwise velocity dispersion also exhibits a bump at   k ∼ 1  h  Mpc⁻¹  .     

Redshift-space bias and β from the halo model

We analyse scale dependence of redshift-space bias b and β  ≡ Ω_m^0.6/ b in the context of the halo model. We show that linear bias is a good approximation only on large scales, for k <0.1  h  Mpc⁻¹ . On intermediate scales the virial motions of galaxies cause a suppression of the power spectrum relative to the linear one and the suppression differs from the same effect in dark matter. This can potentially mimic the effect of massive neutrinos, and the degeneracy can only be broken if the power spectrum is measured for k ≪0.1  h  Mpc⁻¹ . Different methods to determine β converge for k <0.1  h  Mpc⁻¹ , but give drastically different results on smaller scales, which explains some of the trends observed in the real data. We also assess the level of stochasticity by calculating the cross-correlation coefficient between the reconstructed velocity field divergence and the galaxies, and show that the two fields decorrelate for k >0.1  h  Mpc⁻¹ . Most problematic are galaxies predominantly found in groups and clusters, such as bright, red or elliptical galaxies, where we find poor convergence to a constant bias or β even on large scales.     

Resolving cosmic structure formation with the Millennium-II Simulation

We present the Millennium-II Simulation (MS-II), a very large N -body simulation of dark matter evolution in the concordance Λ cold dark matter (ΛCDM) cosmology. The MS-II assumes the same cosmological parameters and uses the same particle number and output data structure as the original Millennium Simulation (MS), but was carried out in a periodic cube one-fifth the size  (100  h ⁻¹ Mpc)  with five times better spatial resolution (a Plummer equivalent softening of  1.0  h ⁻¹ kpc  ) and with 125 times better mass resolution (a particle mass of  6.9 × 10⁶  h ⁻¹ M_⊙  ). By comparing results at MS and MS-II resolution, we demonstrate excellent convergence in dark matter statistics such as the halo mass function, the subhalo abundance distribution, the mass dependence of halo formation times, the linear and non-linear autocorrelations and power spectra, and halo assembly bias. Together, the two simulations provide precise results for such statistics over an unprecedented range of scales, from haloes similar to those hosting Local Group dwarf spheroidal galaxies to haloes corresponding to the richest galaxy clusters. The 'Milky Way' haloes of the Aquarius Project were selected from a lower resolution version of the MS-II and were then resimulated at much higher resolution. As a result, they are present in the MS-II along with thousands of other similar mass haloes. A comparison of their assembly histories in the MS-II and in resimulations of 1000 times better resolution shows detailed agreement over a factor of 100 in mass growth. We publicly release halo catalogues and assembly trees for the MS-II in the same format within the same archive as those already released for the MS.     

Scale-dependent galaxy bias in the Sloan Digital Sky Survey as a function of luminosity and colour

It has been known for a long time that the clustering of galaxies changes as a function of galaxy type. This galaxy bias acts as a hindrance to the extraction of cosmological information from the galaxy power spectrum or correlation function. Theoretical arguments show that a change in the amplitude of the clustering between galaxies and mass on large scales is unavoidable, but cosmological information can be easily extracted from the shape of the power spectrum or correlation function if this bias is independent of scale. Scale-dependent bias is generally small on large scales,   k < 0.1  h  Mpc⁻¹  , but on smaller scales can affect the recovery of  Ω_m h   from the measured shape of the clustering signal, and have a small effect on the Baryon Acoustic Oscillations. In this paper, we investigate the transition from scale-independent to scale-dependent galaxy bias as a function of galaxy population. We use the Sloan Digital Sky Survey Data Release 5 sample to fit various models, which attempt to parametrize the turn-off from scale-independent behaviour. For blue galaxies, we find that the strength of the turn-off is strongly dependent on galaxy luminosity, with stronger scale-dependent bias on larger scales for more luminous galaxies. For red galaxies, the scale dependence is a weaker function of luminosity. Such trends need to be modelled in order to optimally extract the information available in future surveys, and can help with the design of such surveys.     

Dark matter haloes within clusters

We examine the properties of dark matter haloes within a rich galaxy cluster using a high-resolution simulation that captures the cosmological context of a cold dark matter universe. The mass and force resolution permit the resolution of 150 haloes with circular velocities larger than 80 km s⁻¹ within the cluster virial radius of 2 Mpc (with Hubble constant H ₀ = 50 km s⁻¹ Mpc⁻¹). This enables an unprecedented study of the statistical properties of a large sample of dark matter haloes evolving in a dense environment. The cumulative fraction of mass attached to these haloes varies from close to zero per cent at 200 kpc to 13 per cent at the virial radius. Even at this resolution the overmerging problem persists; haloes that pass within 100–200 kpc of the cluster centre are tidally disrupted. Additional substructure is lost at earlier epochs within the massive progenitor haloes. The median ratio of apocentric to pericentric radii is 6:1, so that the orbital distribution is close to isotropic, circular orbits are rare and radial orbits are common. The orbits of haloes are unbiased with respect to both position within the cluster and the orbits of the smooth dark matter background, and no velocity bias is detected. The tidal radii of surviving haloes are generally well-fitted using the simple analytic prediction applied to their orbital pericentres. Haloes within clusters have higher concentrations than those in the field. Within the cluster, halo density profiles can be modified by tidal forces and individual encounters with other haloes that cause significant mass loss —'galaxy harassment'. Mergers between haloes do not occur inside the cluster virial radius.     

Recovering the initial conditions of our local Universe from NOG and PSCz catalogues

We apply the ztrace algorithm to the optical NOG and infrared PSC z galaxy catalogues to reconstruct the pattern of primordial fluctuations that have generated our local Universe. We check that the density fields traced by the two catalogues are well correlated, and consistent with a linear relation [either in δ or in  log (1 +δ)  ] with relative bias (of NOG with respect to PSC z )   b _rel= 1.1 ± 0.1  . The relative bias relation is used to fill the optical zone of avoidance at  | b | < 20°  using the PSC z galaxy density field.
We perform extensive testing on simulated galaxy catalogues to optimize the reconstruction. The quality of the reconstruction is predicted to be good at large scales, up to a limiting wavenumber   k _lim≃ 0.4 h Mpc⁻¹  beyond which all information is lost. We find that the improvement arising from the denser sampling of the optical catalogue is compensated by the uncertainties connected to the larger zone of avoidance.
The initial conditions reconstructed from the NOG catalogue are found (analogously to those from the PSC z ) to be consistent with a Gaussian paradigm. We use the reconstructions to produce sets of initial conditions ready to be used for constrained simulations of our local Universe.