Power Spectrum Of Density Fluctuations Research Articles

X-ray surface brightness and gas density fluctuations in the Coma cluster

X-ray surface brightness fluctuations in the core ($650 \times 650$ kpc) region of the Coma cluster observed with XMM-Newton and Chandra are analyzed using a 2D power spectrum approach. The resulting 2D spectra are converted to 3D power spectra of gas density fluctuations. Our independent analyses of the XMM-Newton and Chandra observations are in excellent agreement and provide the most sensitive measurements of surface brightness and density fluctuations for a hot cluster. We find that the characteristic amplitude of the volume filling density fluctuations relative to the smooth underlying density distribution varies from 7-10% on scales of $\sim$500 kpc down to $\sim$5% at scales $\sim$ 30 kpc. On smaller spatial scales, projection effects smear the density fluctuations by a large factor, precluding strong limits on the fluctuations in 3D. On the largest scales probed (hundreds of kpc), the dominant contributions to the observed fluctuations most likely arise from perturbations of the gravitational potential by the two most massive galaxies in Coma, NGC4874 and NGC4889, and the low entropy gas brought to the cluster by an infalling group. Other plausible sources of X-ray surface brightness fluctuations are discussed, including turbulence, metal abundance variations, and unresolved sources. Despite a variety of possible origins for density fluctuations, the gas in the Coma cluster core is remarkably homogeneous on scales from $\sim$ 500 to $\sim$30 kpc.

Quantum Gravitational Contributions to the Cosmic Microwave Background Anisotropy Spectrum

We derive the primordial power spectrum of density fluctuations in the framework of quantum cosmology. For this purpose we perform a Born-Oppenheimer approximation to the Wheeler-DeWitt equation for an inflationary universe with a scalar field. In this way, we first recover the scale-invariant power spectrum that is found as an approximation in the simplest inflationary models. We then obtain quantum gravitational corrections to this spectrum and discuss whether they lead to measurable signatures in the cosmic microwave background anisotropy spectrum. The nonobservation so far of such corrections translates into an upper bound on the energy scale of inflation.

Revisiting a vector-tensor theory of gravitation

A certain vector-tensor theory of gravitation has been recently studied. In this theory, the zero-order energy density of the vector field could play the role of dark energy. In such a case, the question is: could the theory explain current cosmological observations as well as the so-called concordance model? Previous papers on the subject only consider a reduced number of current observations. We consider a wider set of observations including supernovae of type Ia, cosmic microwave background anisotropies, and the power spectrum of the energy density fluctuations. Results imply that, for negligible scalar perturbations of the vector field, the theory does not work.

Weak-lensing statistics from the Coyote Universe

Analyzing future weak lensing data sets from KIDS, DES, LSST, Euclid, WFIRST requires precise predictions for the weak lensing measures. In this paper we present a weak lensing prediction code based on the Coyote Universe emulator. The Coyote Universe emulator predicts the (non-linear) power spectrum of density fluctuations (P_delta) to high accuracy for k \in [0.002;3.4] h/Mpc within the redshift interval z \in [0;1], outside this regime we extend P_delta using a modified Halofit code. This pipeline is used to calculate various second-order cosmic shear statistics, e.g., shear power spectrum, shear-shear correlation function, ring statistics and COSEBIs (Complete Orthogonal Set of EB-mode Integrals), and we examine how the upper limit in k (and z) to which P_delta is known, impacts on these statistics. For example, we find that k_max~8 h/Mpc causes a bias in the shear power spectrum at l~4000 that is comparable to the statistical errors (intrinsic shape-noise and cosmic variance) of a DES-like survey, whereas for LSST-like errors k_max~15 h/Mpc is needed to limit the bias at l~4000. For the most recently developed second-order shear statistics, the COSEBIs, we find that 9 modes can be calculated accurately knowing P_delta to k_max=10 h/Mpc. The COSEBIs allow for an EB-mode decomposition using a shear-shear correlation function measured over a finite range, thereby avoiding any EB-mode mixing due to finite survey size. We perform a detailed study in a 5-dimensional parameter space in order to examine whether all cosmological information is captured by these 9 modes with the result that already 7-8 modes are sufficient.

On the viability of a certain vector-tensor theory of gravitation

A certain vector-tensor theory is revisited. Our attention is focused on cosmology. Against previous suggestions based on preliminary studies, it is shown that, if the energy density of the vector field is large enough to play the role of the dark energy and its fluctuations are negligible, the theory is not simultaneously compatible with current observations on: supernovae, the cosmic microwave background (CMB) anisotropy, and the power spectrum of the energy density fluctuations. However, for small enough energy densities of the vector field, the theory becomes compatible with all the above observations and, moreover, it leads to an interesting evolution of the so-called vector cosmological modes. This evolution appears to be different from that of general relativity, and the difference might be useful to explain the anomalies in the low order CMB multipoles.

A slight excess of large-scale power from moments of the peculiar velocity field

The peculiar motions of galaxies can be used to infer the distribution of matter in the Universe. It has recently been shown that measurements of the peculiar velocity field indicates an anomalously high bulk flow of galaxies in our local volume. In this paper we find the implications of the high bulk flow for the power spectrum of density fluctuations. We find that analyzing only the dipole moment of the velocity field yields an average power spectrum amplitude which is indeed much higher than the LCDM value. However, by also including shear and octupole moments of the velocity field, and marginalizing over possible values for the growth rate, an average power spectrum amplitude which is consistent with LCDM is recovered. We attempt to infer the shape of the matter power spectrum from moments of the velocity field, and find a slight excess of power on scales ~ h-1 Gpc.

MEASUREMENTS OF RAPID DENSITY FLUCTUATIONS IN THE SOLAR WIND

The power spectrum of density fluctuations in the solar wind is inferred by tracking small timescale changes in the electron plasma frequency during periods of strong Langmuir wave activity. STEREO electric field waveform data are used to produce time profiles of plasma density from which the density power spectrum is derived. The power spectra obtained by this method extend the observed frequency range by an order of magnitude while remaining consistent with previous results near a few Hertz. Density power spectral indices are found to be organized by the angle between the local magnetic field and the solar wind direction, indicating significant anisotropy in solar wind high-frequency density turbulence.

Searching for signatures of cosmic superstrings in the CMB

Because cosmic superstrings generically form junctions and gauge theoreticstrings typically do not, junctions may provide a signature to distinguishbetween cosmic superstrings and gauge theoretic cosmic strings. Incosmic microwave background anisotropy maps, cosmic strings lead todistinctive line discontinuities. String junctions lead to junctionsin these line discontinuities. In turn, edge detection algorithms suchas the Canny algorithm can be used to search for signatures of stringsin anisotropy maps. We apply the Canny algorithm to simulated mapswhich contain the effects of cosmic strings with and without string junctions.The Canny algorithm produces edge maps. To distinguish betweenedge maps from string simulations with and without junctions, weexamine the density distribution of edges and pixels crossed by edges.We find that in string simulations without Gaussian noise (such asproduced by the dominant inflationary fluctuations) our analysisof the output data from the Canny algorithm can clearly distinguishbetween simulations with and without string junctions. In the presenceof Gaussian noise at the level expected from the current bounds on thecontribution of cosmic strings to the total power spectrum of densityfluctuations, the distinction between models with and without junctionsis more difficult. However, by carefully analyzing the data themodels can still be differentiated.

Acquired scaling relations in dark matter turbulence

Variety of scaling relations are observed in astronomical objects. We study a consistent understanding of them from a simple proposal that the collision-less dark matter fluid terns into a turbulent state, i.e. cosmic dark turbulence. This happens most likely when the density fluctuations cross the caustic surface toward the non-linear regime. Collision-less dark turbulence may not be eddy-dominant. We first derive Kolmogorov scaling laws from the gravitational Navier-Stokes equation by the method similar to the case in Smoluchowski coagulation equation. Then we apply this to several observations such as the scale-dependent velocity dispersion, mass-luminosity ratio, magnetic fields, and mass-angular momentum relation, power spectrum of density fluctuations. They all conclude a single value for a constant energy flow per mass: 0.3cm2/sec3. This value may deeply related with the speed of the hierarchical coalescence process in the cosmic structure formation.

THE COYOTE UNIVERSE. II. COSMOLOGICAL MODELS AND PRECISION EMULATION OF THE NONLINEAR MATTER POWER SPECTRUM

The power spectrum of density fluctuations is a foundational source of cosmological information. Precision cosmological probes targeted primarily at investigations of dark energy require accurate theoretical determinations of the power spectrum in the nonlinear regime. To exploit the observational power of future cosmological surveys, accuracy demands on the theory are at the one percent level or better. Numerical simulations are currently the only way to produce sufficiently error-controlled predictions for the power spectrum. The very high computational cost of (precision) N-body simulations is a major obstacle to obtaining predictions in the nonlinear regime, while scanning over cosmological parameters. Near-future observations, however, are likely to provide a meaningful constraint only on constant dark energy equation of state 'wCDM' cosmologies. In this paper we demonstrate that a limited set of only 37 cosmological models -- the "Coyote Universe" suite -- can be used to predict the nonlinear matter power spectrum at the required accuracy over a prior parameter range set by cosmic microwave background observations. This paper is the second in a series of three, with the final aim to provide a high-accuracy prediction scheme for the nonlinear matter power spectrum for wCDM cosmologies.

Signatures of dark energy on LSS

This review surveys the signatures of dark energy on large-scale structures (LSS) at low redshift, focusing on observables relying on the evolution of matter perturbations, i.e. on the growth of structures. We discuss in particular galaxy clustering, weak-gravitational lensing by LSS, also called cosmic-shear, and Lyman-α forest, which respectively describe the 3D, 2D, and 1D power spectrum of matter density fluctuations. We illustrate some example of data analysis for each these observables.

A SEARCH FOR COSMIC MICROWAVE BACKGROUND ANISOTROPIES ON ARCMINUTE SCALES WITH BOLOCAM

We have surveyed two science fields totaling one square degree with Bolocam at 2.1 mm to search for secondary CMB anisotropies caused by the Sunyaev- Zel'dovich effect (SZE). The fields are in the Lynx and Subaru/XMM SDS1 fields. Our survey is sensitive to angular scales with an effective angular multipole of l_eff = 5700 with FWHM_l = 2800 and has an angular resolution of 60 arcseconds FWHM. Our data provide no evidence for anisotropy. We are able to constrain the level of total astronomical anisotropy, modeled as a flat bandpower in C_l, with frequentist 68%, 90%, and 95% CL upper limits of 590, 760, and 830 uKCMB^2. We statistically subtract the known contribution from primary CMB anisotropy, including cosmic variance, to obtain constraints on the SZE anisotropy contribution. Now including flux calibration uncertainty, our frequentist 68%, 90% and 95% CL upper limits on a flat bandpower in C_l are 690, 960, and 1000 uKCMB^2. When we instead employ the analytic spectrum suggested by Komatsu and Seljak (2002), and account for the non-Gaussianity of the SZE anisotropy signal, we obtain upper limits on the average amplitude of their spectrum weighted by our transfer function of 790, 1060, and 1080 uKCMB^2. We obtain a 90% CL upper limit on sigma8, which normalizes the power spectrum of density fluctuations, of 1.57. These are the first constraints on anisotropy and sigma8 from survey data at these angular scales at frequencies near 150 GHz.

Peculiar velocities into the next generation: cosmological parameters from large surveys without bias from non-linear structure

We investigate methods to best estimate the normalization of the mass density fluctuation power spectrum (σ8) using peculiar velocity data from a survey like the six-degree Field Galaxy Velocity Survey (6dFGSv). We focus on two potential problems: (i) biases from non-linear growth of structure and (ii) the large number of velocities in the survey. Simulations of ΛCDM-like models are used to test the methods. We calculate the likelihood from a full covariance matrix of velocities averaged in grid cells. This simultaneously reduces the number of data points and smoothes out non-linearities which tend to dominate on small scales. We show how the averaging can be taken into account in the predictions in a practical way, and show the effect of the choice of cell size. We find that a cell size can be chosen that significantly reduces the non-linearities without significantly increasing the error bars on cosmological parameters. We compare our results with those from a principal components analysis following Watkins et al. and Feldman et al. to select a set of optimal moments constructed from linear combinations of the peculiar velocities that are least sensitive to the non-linear scales. We conclude that averaging in grid cells performs equally well. We find that for a survey such as 6dFGSv we can estimate σ8 with less than 3 per cent bias from non-linearities. The expected error on σ8 after marginalizing over Ωm is approximately 16 per cent.

SPACE: the spectroscopic all-sky cosmic explorer

We describe the scientific motivations, the mission concept and the instrumentation of SPACE, a class-M mission proposed for concept study at the first call of the ESA Cosmic-Vision 2015–2025 planning cycle. SPACE aims to produce the largest three-dimensional evolutionary map of the Universe over the past 10 billion years by taking near-IR spectra and measuring redshifts for more than half a billion galaxies at 0 < z < 2 down to AB~23 over 3π sr of the sky. In addition, SPACE will also target a smaller sky field, performing a deep spectroscopic survey of millions of galaxies to AB~26 and at 2 < z < 10 +. These goals are unreachable with ground-based observations due to the ≈500 times higher sky background (see e.g. Aldering, LBNL report number LBNL-51157, 2001). To achieve the main science objectives, SPACE will use a 1.5 m diameter Ritchey-Chretien telescope equipped with a set of arrays of Digital Micro-mirror Devices covering a total field of view of 0.4 deg2, and will perform large-multiplexing multi-object spectroscopy (e.g. ≈6000 targets per pointing) at a spectral resolution of R~400 as well as diffraction-limited imaging with continuous coverage from 0.8 to 1.8 μm. Owing to the depth, redshift range, volume coverage and quality of its spectra, SPACE will reveal with unique sensitivity most of the fundamental cosmological signatures, including the power spectrum of density fluctuations and its turnover. SPACE will also place high accuracy constraints on the dark energy equation of state parameter and its evolution by measuring the baryonic acoustic oscillations imprinted when matter and radiation decoupled, the distance-luminosity relation of cosmological supernovae, the evolution of the cosmic expansion rate, the growth rate of cosmic large-scale structure, and high-z galaxy clusters. The datasets from the SPACE mission will represent a long lasting legacy for the whole astronomical community whose data will be mined for many years to come.

New constraints on dark energy from the observed growth of the most X-ray luminous galaxy clusters

We present constraints on the mean matter density, Omega_m, the normalization of the density fluctuation power spectrum, sigma_8, and the dark-energy equation-of-state parameter, w, obtained from measurements of the X-ray luminosity function of the largest known galaxy clusters at redshifts z<0.7, as compiled in the Massive Cluster Survey (MACS) and the local BCS and REFLEX galaxy cluster samples. Our analysis employs an observed mass-luminosity relation, calibrated by hydrodynamical simulations, including corrections for non-thermal pressure support and accounting for the presence of intrinsic scatter. Conservative allowances for all known systematic uncertainties are included, as are standard priors on the Hubble constant and mean baryon density. We find Omega_m=0.28 +0.11 -0.07 and sigma_8=0.78 +0.11 -0.13 for a spatially flat, cosmological-constant model, and Omega_m=0.24 +0.15 -0.07, sigma_8=0.85 +0.13 -0.20 and w=-1.4 +0.4 -0.7 for a flat, constant-w model. Future work improving our understanding of redshift evolution and observational biases affecting the mass--X-ray luminosity relation have the potential to significantly tighten these constraints. Our results are consistent with those from recent analyses of type Ia supernovae, cosmic microwave background anisotropies, the X-ray gas mass fraction of relaxed galaxy clusters, baryon acoustic oscillations and cosmic shear. Combining the new X-ray luminosity function data with current supernova, cosmic microwave background and cluster gas fraction data yields the improved constraints Omega_m=0.269 +- 0.016, sigma_8=0.82 +- 0.03 and w=-1.02 +- 0.06. (Abridged)

BARYONIC ACOUSTIC OSCILLATIONS VIA THE RENORMALIZATION GROUP

Renormalization Group techniques, successfully employed in quantum field theory and statistical physics, are applied to study the dynamics of structure formation in the Universe. A semi-analytic approach to the computation of the nonlinear power-spectrum of dark matter density fluctuations is proposed. The method can be applied down to zero redshift and to length scales where perturbation theory fails. Our predictions accurately fit the results of numerical simulations in reproducing the "acoustic oscillations" features of the power spectrum, which will be accurately measured in future galaxy surveys and will provide a probe to distinguish among different dark energy models.

Evaluation of Webb Correction on CO2 Flux by Eddy Covariance Technique Using Open-Path Gas Analyzer over Asphalt Surface

Webb correction is indispensable when evaluating trace gas flux by the eddy covariance technique using an open-path gas analyzer. In the present study, direct measurements of CO2 flux by the eddy covariance technique using an open-path CO2/H2O gas analyzer were carried out over an asphalt surface where CO2 and latent heat fluxes were considered almost zero. The power spectrum of CO2 density fluctuation had similar frequency structure to those of vertical wind velocity, sound virtual temperature, and water vapor density fluctuations. The cospectrum of raw CO2 flux was negatively correlated with that of sensible heat flux. The cospectrum of latent heat flux was almost zero and poorly correlated with that of raw CO2 or sensible heat fluxes. Raw CO2 flux was apparently downward from the atmosphere to the asphalt surface during this observation period. The Webb CO2 correction term for sensible heat flux was upward and larger than the raw CO2 flux, although the Webb CO2 correction term for latent heat flux was almost zero. Total latent heat and CO2 fluxes were evaluated as significant upward fluxes. This result shows that Webb correction may cause an overestimated correction to CO2 flux by the eddy covariance technique using an open-path CO2/H2O gas analyzer over surfaces, especially where small CO2 flux by soil respiration or air-sea exchange process is observed.

Reconstruction method of local density fluctuation for heavy ion beam probe measurements

Heavy ion beam probe (HIBP) is an excellent diagnostic to measure the density and potential fluctuations simultaneously in magnetically confined plasmas. However, it has been well known that the density fluctuation measured with the HIBP is not local but contains the fluctuations along the beam orbits. In this article, a method is proposed to evaluate local density fluctuation in the HIBP measurements by removing the well-known path integral effects. The reconstructed density fluctuation amplitude and power spectrum are shown, for example, by applying the proposed method on the density fluctuation measurement data obtained in a toroidal helical plasma, Compact Helical System.

Dark matter clustering: A simple renormalization group approach

I compute a renormalization group (RG) improvement to the standard beyond-linear-order Eulerian perturbation theory (PT) calculation of the power spectrum of large-scale density fluctuations in the Universe. At $z=0$, for a power spectrum matching current observations, lowest order RGPT appears to be as accurate as one can test using existing numerical simulation-calibrated fitting formulas out to at least $k\ensuremath{\simeq}0.3h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$; although inaccuracy is guaranteed at some level by approximations in the calculation (which can be improved in the future). In contrast, standard PT breaks down virtually as soon as beyond-linear corrections become non-negligible, on scales even larger than $k=0.1h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$. This extension in range of validity could substantially enhance the usefulness of PT for interpreting baryonic acoustic oscillation surveys aimed at probing dark energy, for example. I show that the predicted power spectrum converges at high $k$ to a power law with index given by the fixed-point solution of the RG equation. I discuss many possible future directions for this line of work. The basic calculation of this paper should be easily understandable without any prior knowledge of RG methods, while a rich background of mathematical physics literature exists for the interested reader.

Gravitational dynamics of an infinite shuffled lattice of particles

We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static Euclidean space, starting from a simple class of infinite "shuffled lattice" initial conditions. These are obtained by applying independently to each particle on an infinite perfect lattice a small random displacement, and are characterized by a power spectrum (structure factor) of density fluctuations which is quadratic in the wave number k, at small k. For a specified form of the probability distribution function of the "shuffling" applied to each particle, and zero initial velocities, these initial configurations are characterized by a single relevant parameter: the variance delta(2) of the "shuffling" normalized in units of the lattice spacing l. The clustering, which develops in time starting from scales around l, is qualitatively very similar to that seen in cosmological simulations, which begin from lattices with applied correlated displacements and incorporate an expanding spatial background. From very soon after the formation of the first nonlinear structures, a spatiotemporal scaling relation describes well the evolution of the two-point correlations. At larger times the dynamics of these correlations converges to what is termed "self-similar" evolution in cosmology, in which the time dependence in the scaling relation is specified entirely by that of the linearized fluid theory. Comparing simulations with different delta, different resolution, but identical large scale fluctuations, we are able to identify and study features of the dynamics of the system in the transient phase leading to this behavior. In this phase, the discrete nature of the system explicitly plays an essential role.