Peaks in the cosmological density field: sensitivity to initial power spectrum, redshift distortions and galaxy halo occupation

We investigate the number density of maxima in the cosmological galaxy density field smoothed with a filter as a probe of clustering. In previous work it has been shown that this statistic is closely related to the slope of the linear power spectrum, even when the directly measured power spectrum is non-linear. In the present paper we investigate the sensitivity of the peak number density to various models with differing power spectra, including rolling index models, cosmologies with massive neutrinos and different baryon densities. We find that rolling index models which have given an improved fit to CMB/LSS (cosmic microwave background/large scale structure) data yield a ∼10 per cent difference in peak density compared to the scale invariant case. Models with 0.3 eV neutrinos have effects of similar magnitude and it should be possible to constrain them with data from current galaxy redshift surveys. Baryon oscillations in the power spectrum also give rise to distinctive features in the peak density. These are preserved without modification when measured from the peak density in fully non-linear N -body simulations. Using the simulations, we also investigate how the peak density is modified in the presence of redshift distortions. Redshift distortions cause a suppression of the number of peaks, largely due to fingers of God overlapping in redshift space. We find that this effect can be modelled by using a modification of the input power spectrum. We also study the results when the simulation density field is traced by galaxies obtained by populating haloes with a halo occupation distribution consistent with observations. The peak number density is consistent with that in the dark matter for filter scales  >4  h ⁻¹ Mpc  , for which we find good agreement with the linear theory predictions. In a companion paper we analyse data from the 2dF Galaxy Redshift Survey.     

Physical effects on the Lyα forest flux power spectrum: damping wings, ionizing radiation fluctuations and galactic winds

We explore several physical effects on the power spectrum of the Lyα forest transmitted flux. The effects we investigate here are not usually part of hydrodynamic simulations and so need to be estimated separately. The most important effect is that of high column density absorbers with damping wings, which add power on large scales. We compute their effect using the observational constraints on their abundance as a function of column density. Ignoring their effect leads to an underestimation of the slope of the linear theory power spectrum. The second effect we investigate is that of fluctuations in the ionizing radiation field. For this purpose we use a very large high-resolution N -body simulation, which allows us to simulate both the fluctuations in the ionizing radiation and the small-scale Lyα forest within the same simulation. We find an enhancement of power on large scales for quasars and a suppression for galaxies. The strength of the effect rapidly increases with increasing redshift, allowing it to be uniquely identified in cases where it is significant. We develop templates that can be used to search for this effect as a function of quasar lifetime, quasar luminosity function and attenuation length. Finally, we explore the effects of galactic winds using hydrodynamic simulations. We find the wind effects on the Lyα forest power spectrum to be degenerate with parameters related to the temperature of the gas that are already marginalized over in cosmological fits. While more work is needed to conclusively exclude all possible systematic errors, our results suggest that, in the context of data analysis procedures, where parameters of the Lyα forest model are properly marginalized over, the flux power spectrum is a reliable tracer of cosmological information.     

Tidal alignments as a contaminant of redshift space distortions

We investigate the effect of orientation-dependent selection effects on galaxy clustering in redshift space. It is found that if galaxies are aligned by large-scale tidal fields, then these selection effects give rise to a dependence of the observed galaxy density on the local tidal field, in addition to the well-known dependences on the matter density and radial velocity gradient. This alters the galaxy power spectrum in a way that is different for Fourier modes parallel to and perpendicular to the line of sight. These tidal galaxy alignments can thus mimic redshift space distortions (RSD), and thus result in a bias in the measurement of the velocity power spectrum. If galaxy orientations are affected only by the local tidal field, then the tidal alignment effect has exactly the same scale and angular dependence as the RSDs in the linear regime, so it cannot be projected out or removed by masking small scales in the analysis. We consider several toy models of tidal alignments and orientation-dependent selection, normalize their free parameter (an amplitude) to recent observations, and find that they could bias the velocity amplitude   f ( z ) G ( z )  by 5–10 per cent in some models, although most models give much smaller contamination. We conclude that tidal alignments may be a significant systematic error in RSD measurements that aim to test general relativity via the growth of large-scale structure. We briefly discuss possible mitigation strategies.     

A DWT Power Spectrum Analysis of PSCz Galaxies

The power spectrum estimator based on the Discrete Wavelet Transformation (DWT) is applied to detect the clustering power in the IRAS Point Source Catalog Redshift Survey(PSCz). Comparison with mock samples extracted from N-body simulation shows that the DWT power spectrum estimator could provide a robust measurement of banded fluctuation power over a range of wavenumbers 0.1-2.0h Mpc^-1. We have fitted three typical CDM models (SCDM, TCDM and ACDM) using the Peacock-Dodds formula including non-linear evolution and redshift distortion. We find that, our results are in good agreement with other statistical measurements of the PSCz.     

Modification of the 21-cm power spectrum by quasars during the epoch of reionization

We assess the effect of a population of high-redshift quasars on the 21-cm power spectrum during the epoch of reionization. Our approach is to implement a seminumerical scheme to calculate the three-dimensional structure of ionized regions surrounding massive haloes at high redshift. We include the ionizing influence of luminous quasars by populating a simulated overdensity field with quasars using a Monte Carlo Markov Chain algorithm. We find that quasars modify both the amplitude and shape of the power spectrum at a level which is of the same order as the fractional contribution to reionization. The modification is found both at constant redshift and at constant global neutral fraction, and arises because ionizing photons produced by quasars are biased relative to the density field at a level that is higher than stellar ionizing photons. The modification of the power spectrum is likely to be small, rendering the effect of quasars difficult to isolate. However, we find the modification of the power spectrum by quasars to be at a level that is comparable to the precision expected for future low-frequency telescopes. Correct interpretation of observations will therefore require the effect of quasars to be considered, and our results imply that quasar ionization will need to be included in detailed modelling of observed 21-cm power spectra.     

Sunyaev–Zel'dovich distortion from early galactic winds

We consider the distortion in the cosmic microwave background (CMB) resulting from galactic winds at high redshift. Winds outflowing from galaxies have been hypothesized to be possible sources of metals in the intergalactic medium, which is known to have been enriched to 10^−2.5 Z_⊙ at z ∼3. We model these winds as functions of mass of the parent galaxy and redshift, assuming that they activate at a common initial redshift, z _in, and calculate the mean y -distortion and the angular power spectrum of the distortion in the CMB. We find that the thermal Sunyaev–Zel'dovich (SZ) effect resulting from the winds is consistent with previous estimates. The distortion arising from the kinetic SZ (kSZ) effect is, however, found to be more important than the thermal SZ (tSZ) effect. We find that the distortion resulting from galactic winds is an important contribution to the power spectrum of distortion at very small angular scales ( l ∼10⁴). We also find that the power spectrum resulting from clustering dominates the Poisson power spectrum for l ≤(4–5)×10⁵. We show explicitly how the combined power spectrum from wind dominates over that of clusters at 217 GHz, relevant for PLANCK . We also show how these constraints change when the efficiency of the winds is varied.     

The non-linear redshift-space power spectrum of galaxies

We study the power spectrum of galaxies in redshift space, with third-order perturbation theory to include corrections that are absent in linear theory. We assume a local bias for the galaxies: i.e., the galaxy density is sampled from some local function of the underlying mass distribution. We find that the effect of the non-linear bias in real space is to introduce two new features: first, there is a contribution to the power which is constant with wavenumber, whose nature we reveal as essentially a shot-noise term. In principle this contribution can mask the primordial power spectrum, and could limit the accuracy with which the latter might be measured on very large scales. Secondly, the effect of second- and third-order bias is to modify the effective bias (defined as the square root of the ratio of galaxy power spectrum to matter power spectrum). The effective bias is almost scale-independent over a wide range of scales. These general conclusions also hold in redshift space. In addition, we have investigated the distortion of the power spectrum by peculiar velocities, which may be used to constrain the density of the Universe. We look at the quadrupole-to-monopole ratio, and find that higher order terms can mimic linear theory bias, but the bias implied is neither the linear bias, nor the effective bias referred to above. We test the theory with biased N -body simulations, and find excellent agreement in both real and redshift space, providing the local biasing is applied on a scale whose fractional rms density fluctuations are < 0.5.     

The matter power spectrum from the Lyα forest: an optical depth estimate

We measure the matter power spectrum from 31 Lyα spectra spanning the redshift range of 1.6–3.6. The optical depth, τ, for Lyα absorption of the intergalactic medium is obtained from the flux using the inversion method of Nusser & Haehnelt. The optical depth is converted to density by using a simple power-law relation,  τ∝ (1 +δ)^α  . The non-linear 1D power spectrum of the gas density is then inferred with a method that makes simultaneous use of the one- and two-point statistics of the flux and compared against theoretical models with a likelihood analysis. A cold dark matter model with standard cosmological parameters fits the data well. The power-spectrum amplitude is measured to be (assuming a flat Universe),  σ₈= (0.92 ± 0.09) × (Ω_m/0.3)^−0.3  , with α varying in the range of 1.56–1.8 with redshift. Enforcing the same cosmological parameters in all four redshift bins, the likelihood analysis suggests some evolution in the temperature–density relation and the thermal smoothing length of the gas. The inferred evolution is consistent with that expected if reionization of He  ii occurred at   z ∼ 3.2  . A joint analysis with the Wilkinson Microwave Anisotropy Probe results together with a prior on the Hubble constant as suggested by the Hubble Space Telescope key project data, yields values of Ω_m and σ₈ that are consistent with the cosmological concordance model. We also perform a further inversion to obtain the linear 3D power spectrum of the matter density fluctuations.     

Cosmic microwave background constraints on the epoch of reionization

We use a compilation of cosmic microwave anisotropy data to constrain the epoch of reionization in the Universe, as a function of cosmological parameters. We consider spatially flat cosmologies, varying the matter density Ω₀ (the flatness being restored by a cosmological constant), the Hubble parameter h and the spectral index n of the primordial power spectrum. Our results are quoted both in terms of the maximum permitted optical depth to the last-scattering surface, and in terms of the highest allowed reionization redshift assuming instantaneous reionization. For critical-density models, significantly tilted power spectra are excluded as they cannot fit the current data for any amount of reionization, and even scale-invariant models must have an optical depth to last scattering of below 0.3. For the currently favoured low-density model with Ω₀=0.3 and a cosmological constant, the earliest reionization permitted to occur is at around redshift 35, which roughly coincides with the highest estimate in the literature. We provide general fitting functions for the maximum permitted optical depth, as a function of cosmological parameters. We do not consider the inclusion of tensor perturbations, but if present they would strengthen the upper limits that we quote.     

A primordial feature at the scale of superclusters of galaxies

We investigate a spatially flat cold dark matter model (with the matter density parameter     with a primordial feature in the initial power spectrum. We assume that there is a bump in the power spectrum of density fluctuations at wavelengths     , which corresponds to the scale of superclusters of galaxies . There are indications for such a feature in the power spectra derived from redshift surveys and also in the power spectra derived from peculiar velocities of galaxies. We study the mass function of clusters of galaxies, the power spectrum of the cosmic microwave background (CMB) temperature fluctuations, the rms bulk velocity and the rms peculiar velocity of clusters of galaxies. The baryon density is assumed to be consistent with the big bang nucleosynthesis value. We show that with an appropriately chosen feature in the power spectrum of density fluctuations at the scale of superclusters, the mass function of clusters, the CMB power spectrum, the rms bulk velocity and the rms peculiar velocity of clusters are in good agreement with the observed data.     

Large scale magnetic fields: Density power spectrum in redshift space

We compute the density redshift-space power spectrum in the presence of tangled magnetic fields and compare it with existing observations. Our analysis shows that if these magnetic fields originated in the early universe then it is possible to construct models for which the shape of the power spectrum agrees with the large scale slope of the observed power spectrum. However requiring compatibility with observed CMBR anisotropies, the normalization of the power spectrum is too low for magnetic fields to have significant impact on the large scale structure at present. Magnetic fields of a more recent origin generically give density power spectrumα k ⁴which doesn’t agree with the shape of the observed power spectrum at any scale. Magnetic fields generate curl modes of the velocity field which increase both the quadrupole and hexadecapole of the redshift space power spectrum. For curl modes, the hexadecapole dominates over quadrupole. So the presence of curl modes could be indicated by an anomalously large hexadecapole, which has not yet been computed from observation. It appears difficult to construct models in which tangled magnetic fields could have played a major role in shaping the large scale structure in the present epoch. However if they did, one of the best ways to infer their presence would be from the redshift space effects in the density power spectrum.     

X-ray spectral analysis of optically faint sources in the Chandra deep fields

We present the results of a detailed spectral analysis of optically faint hard X-ray sources in the Chandra deep fields selected on the basis of their high X-ray to optical flux ratio (X/O). The stacked spectra of high X/O sources in both Chandra deep fields, fitted with a single power-law model, are much harder than the spectrum of the X-ray background (XRB). The average slope is also insensitive to the 2–8 keV flux, being approximately constant around Γ≃ 1 over more than two decades, strongly indicating that high X/O sources represent the most obscured component of the XRB. For about half of the sample, a redshift estimate (in most of the cases a photometric redshift) is available from the literature. Individual fits of a few of the brightest objects and of stacked spectra in different redshift bins imply column densities in the range  10²²–10^23.5 cm⁻²  . A trend of increasing absorption towards higher redshifts is suggested.     

Looking Down the Light Cone: Can Deep Redshift Surveys Alone Measure the Power Spectrum?

We analyse the window functions for the spherical harmonic mode estimators of all-sky, volume-limited surveys, considering evolutionary effects along the past light-cone which include the deviation of the distance scale from a linear relationship with redshift, linear peculiar velocity corrections, and linear evolution of the density perturbations. The spherical harmonic basis functions are considered, because they correspond most closely to the symmetries of typical survey geometries and of the light-cone effects we consider. Our results show substantial broadening of the windows over that expected by ignoring light-cone effects, indicating the difficulty of measuring the power spectrum independently from cosmology. We suggest that because of light-cone effects, deep redshift surveys should be analysed either in conjunction with CMBR data which determines the cosmological parameters, or by using a Bayesian likelihood scheme in which varying cosmological parameters and a simple parametrization of the primordial power spectrum are assumed as the priors, so that observed data can be mapped from redshift to real space. The derived power spectrum can then be compared with underlying models of fluctuation generation and growth in structure formation to evaluate both these models and the cosmological priors.     

Constraining the nature of dark energy using the Square Kilometer Array Telescope

We investigate the potential of the Square Kilometer Array Telescope (SKA) to constrain the sound speed of dark energy. The Integrated Sachs Wolfe (ISW) effect results in a significant power spectrum signal when Cosmic Microwave Background (CMB) temperature anisotropies are cross-correlated with galaxies detectable with the SKA in H  i . We consider using this measurement, the autocorrelation of H  i galaxies and the CMB temperature power spectrum to derive constraints on the sound speed. We study the contributions to the cross-correlation signal made by galaxies at different redshifts and use redshift tomography to improve the signal-to-noise. We use a  χ²  analysis to estimate the significance of detecting a sound speed different from that expected in quintessence models, finding that there is potential to distinguish very low sound speeds from the quintessence value.     

The association between gas and galaxies – I. CFHT spectroscopy and pair analysis

We investigate the relative distribution of the gaseous contents of the Universe (as traced by a sample of Lyα absorbers), and the luminous baryonic matter (as traced by a redshift survey of galaxies in the same volume searched for Lyα absorbers), along 16 lines of sight (LOS) between redshifts 0 and 1. Our galaxy redshift survey was made with the multi-object spectrograph on the Canada–France–Hawaii Telescope and, when combined with galaxies from the literature in the same LOS, gives us a galaxy sample of 636 objects. By combining this with an absorption-line sample of 406 absorbing systems drawn from published works, we are able to study the relationship between gas and galaxies over the latter half of the age of the Universe. A correlation between absorbers and galaxies is detected out to separation of 1.5 Mpc. This correlation is weaker than the galaxy–galaxy correlation. There is also some evidence that the absorbing systems seen in C  iv are more closely related to galaxies, although this correlation could be with column density rather than metallicity. The above results are all consistent with the absorbing gas and the galaxies coexisting in dark matter filaments and knots as predicted by current models where the column density of the absorbing gas is correlated with the underlying matter density.     

Irradiation pressure effects in close binary systems

We test an analytic model for the two-point correlations of galaxy clusters in redshift space using the Hubble volume N -body simulations. The correlation function of clusters shows no enhancement along the line of sight, owing to the lack of any virialized structures in the cluster distribution. However, the distortion of the clustering pattern arising from coherent bulk motions is clearly visible. The distribution of cluster peculiar motions is well described by a Gaussian, except in the extreme high-velocity tails. The simulations produce a small but significant number of clusters with large peculiar motions. The form of the redshift-space power spectrum is strongly influenced by errors in measured cluster redshifts in extant surveys. When these errors are taken into account, the model reproduces the power spectrum recovered from the simulation to an accuracy of 15 per cent or better over a decade in wavenumber. We compare our analytic predictions with the power spectrum measured from the APM cluster redshift survey. The cluster power spectrum constrains the amplitude of density fluctuations, as measured by the linear rms variance in spheres of radius 8  h ⁻¹ Mpc, denoted by σ ₈. When combined with the constraints on σ ₈ and the density parameter Ω derived from the local abundance of clusters, we find a best-fitting cold dark matter model with     and     , for a power spectrum shape that matches that measured for galaxies. However, for the best-fitting value of Ω and given the value of Hubble's constant from recent measurements, the assumed shape of the power spectrum is incompatible with the most readily motivated predictions from the cold dark matter paradigm.     

Fluctuations of non-point mass galaxy distribution

We examine cosmic energy equation for extended galaxy structures on the basis of different models of universe. We also extend the power spectrum and density fluctuations for extended structure by introducing softening parameter both for linear and non-linear regimes. The results are compared with earlier results of point mass structures. It is found that softening parameters introduced in the theory influence the thermodynamic fluctuation theory. Results obtained with spectrum analysis are also compared with Riemannian geometric approach (Ruppeiner in Rev. Mod. Phys. 67:605, 1995) to the galaxy clustering. The singular solutions of thermodynamic fluctuation results can be interpreted on the basis of power spectrum analysis in terms of power index law of two point correlation function.     

Galaxy formation and evolution: low-surface-brightness galaxies

We investigate in detail the hypothesis that low-surface-brightness galaxies (LSBs) differ from ordinary galaxies simply because they form in haloes with large spin parameters. We compute star formation rates using the Schmidt law, assuming the same gas infall dependence on surface density as used in models of the Milky Way. We build stellar population models, predicting colours, spectra and chemical abundances. We compare our predictions with observed values of metallicity and colours for LSBs, and find excellent agreement with all observables. In particular, integrated colours, colour gradients, surface brightness and metallicity match very well to the observed values of LSBs for models with ages larger than 7 Gyr and high values (λ > 0.05) for the spin parameter of the haloes. We also compute the global star formation rate (SFR) in the Universe due to LSBs, and show that it has a flatter evolution with redshift than the corresponding SFR for normal discs. We furthermore compare the evolution in redshift of [ Zn / H ] for our models to those observed in damped Lyman α systems by Pettini et al. and show that damped Lyman α system abundances are consistent with the predicted abundances at different radii for LSBs. Finally, we show how the required late redshift of collapse of the halo may constrain the power spectrum of fluctuations.     

Angular cross-correlation of galaxies: a probe of gravitational lensing by large-scale structure

The angular cross-correlation between two galaxy samples separated in redshift is shown to be a useful measure of weak lensing by large-scale structure. Angular correlations in faint galaxies arise as a result of spatial clustering of the galaxies as well as gravitational lensing by dark matter along the line of sight. The lensing contribution to the two-point autocorrelation function is typically small compared with the gravitational clustering. However, the cross-correlation between two galaxy samples is almost unaffected by gravitational clustering provided that their redshift distributions do not overlap. The cross-correlation is then induced by magnification bias resulting from lensing by large-scale structure. We compute the expected amplitude of the cross-correlation for popular theoretical models of structure formation. For two populations with mean redshifts of ≃0.3 and 1, we find a cross-correlation signal of ≃1 per cent on arcmin scales and ≃3 per cent on scales of a few arcsec. The dependence on the cosmological parameters Ω and Λ, the dark matter power spectrum and the bias factor of the foreground galaxy population is explored.