Measuring the galaxy power spectrum with multiresolution decomposition -- II. diagonal and off-diagonal power spectra of the LCRS galaxies

The power spectrum estimator based on the discrete wavelet transform (DWT) for 3-dimensional samples has been studied. The DWT estimator for multi-dimensional samples provides two types of spectra with respect to diagonal and off-diagonal modes, which are very flexible to deal with configuration-related problems in the power spectrum detection. With simulation samples and mock catalogues of the Las Campanas redshift survey (LCRS), we show (1) the slice-like geometry of the LCRS doesn't affect the off-diagonal power spectrum with ``slice-like'' mode; (2) the Poisson sampling with the LCRS selection function doesn't cause more than 1-$\sigma$ error in the DWT power spectrum; and (3) the powers of peculiar velocity fluctuations, which cause the redshift distortion, are approximately scale-independent. These results insure that the uncertainties of the power spectrum measurement are under control. The scatter of the DWT power spectra of the six strips of the LCRS survey is found to be rather small. It is less than 1-$\sigma$ of the cosmic variance of mock samples in the wavenumber range $0.1 < k < 2$ h Mpc$^{-1}$. To fit the detected LCRS diagonal DWT power spectrum with CDM models, we find that the best-fitting redshift distortion parameter $\beta$ is about the same as that obtained from the Fourier power spectrum. The velocity dispersions $\sigma_v$ for SCDM and $\Lambda$CDM models are also consistent with other $\sigma_v$ detections with the LCRS. A systematic difference between the best-fitting parameters of diagonal and off-diagonal power spectra has been significantly measured. This indicates that the off-diagonal power spectra are capable of providing information about the power spectrum of galaxy velocity field.Comment: AAS LaTeX file, 41 pages, 10 figures included, accepted for publication in Ap

Cluster Correlation in Mixed Models

We evaluate the dependence of the cluster correlation length r_c on the mean intercluster separation D_c, for three models with critical matter density, vanishing vacuum energy (Lambda = 0) and COBE normalized: a tilted CDM (tCDM) model (n=0.8) and two blue mixed models with two light massive neutrinos yielding Omega_h = 0.26 and 0.14 (MDM1 and MDM2, respectively). All models approach the observational value of sigma_8 (and, henceforth, the observed cluster abundance) and are consistent with the observed abundance of Damped Lyman_alpha systems. Mixed models have a motivation in recent results of neutrino physics; they also agree with the observed value of the ratio sigma_8/sigma_25, yielding the spectral slope parameter Gamma, and nicely fit LCRS reconstructed spectra. We use parallel AP3M simulations, performed in a wide box (side 360/h Mpc) and with high mass and distance resolution, enabling us to build artificial samples of clusters, whose total number and mass range allow to cover the same D_c interval inspected through APM and Abell cluster clustering data. We find that the tCDM model performs substantially better than n=1 critical density CDM models. Our main finding, however, is that mixed models provide a surprisingly good fit of cluster clustering data.Comment: 22 pages + 10 Postscript figures. Accepted for publication in Ap

Correlations in the Spatial Power Spectrum Inferred from Angular Clustering: Methods and Application to APM

We reconsider the inference of spatial power spectra from angular clustering data and show how to include correlations in both the angular correlation function and the spatial power spectrum. Inclusion of the full covariance matrices loosens the constraints on large-scale structure inferred from the APM survey by over a factor of two. We present a new inversion technique based on singular value decomposition that allows one to propagate the covariance matrix on the angular correlation function through to that of the spatial power spectrum and to reconstruct smooth power spectra without underestimating the errors. Within a parameter space of the CDM shape Gamma and the amplitude sigma_8, we find that the angular correlations in the APM survey constrain Gamma to be 0.19-0.37 at 68% confidence when fit to scales larger than k=0.2h Mpc^-1. A downturn in power at k<0.04h Mpc^-1 is significant at only 1-sigma. These results are optimistic as we include only Gaussian statistical errors and neglect any boundary effects.Comment: 37 pages, LaTex, 9 figures. Submitted to Ap

Dynamical Masses in Modified Gravity

Differences in masses inferred from dynamics, such as velocity dispersions or X-rays, and those inferred from lensing are a generic prediction of modified gravity theories. Viable models however must include some non-linear mechanism to restore General Relativity (GR) in dense environments, which is necessary to pass Solar System constraints on precisely these deviations. In this paper, we study the dynamics within virialized structures in the context of two modified gravity models, f(R) gravity and DGP. The non-linear mechanisms to restore GR, which f(R) and DGP implement in very different ways, have a strong impact on the dynamics in bound objects; they leave distinctive signatures in the dynamical mass-lensing mass relation as a function of mass and radius. We present measurements from N-body simulations of f(R) and DGP, as well as semi-analytical models which match the simulation results to surprising accuracy in both cases. The semi-analytical models are useful for making the connection to observations. Our results confirm that the environment- and scale-dependence of the modified gravity effects have to be taken into account when confronting gravity theories with observations of dynamics in galaxies and clusters.Comment: 18 pages, 16 figures; submitted to PRD; v2: typos corrected, references added, minor additions (Sec. IID

The Angular Power Spectrum of EDSGC Galaxies

We determine the angular power spectrum, C_l, of the Edinburgh/Durham Southern Galaxy Catalog (EDSGC) and use this statistic to constrain cosmological parameters. Our methods for determining C_l, and the parameters that affect it are based on those developed for the analysis of cosmic microwave background maps. We expect them to be useful for future surveys. Assuming flat cold dark matter models with a cosmological constant (constrained by COBE/DMR and local cluster abundances), and a scale--independent bias, b, we find good fits to the EDSGC angular power spectrum with 1.11 < b < 2.35 and 0.2 < Omega_m < 0.55 at 95% confidence. These results are not significantly affected by the ``integral constraint'' or extinction by interstellar dust, but may be by our assumption of Gaussianity.Comment: 11 pages, 9 figures, version to appear in Ap

Measuring the galaxy power spectrum with future redshift surveys

Precision measurements of the galaxy power spectrum P(k) require a data analysis pipeline that is both fast enough to be computationally feasible and accurate enough to take full advantage of high-quality data. We present a rigorous discussion of different methods of power spectrum estimation, with emphasis on the traditional Fourier method, the linear (Karhunen-Loeve; KL), and quadratic data compression schemes, showing in what approximations they give the same result. To improve speed, we show how many of the advantages of KL data compression and power spectrum estimation may be achieved with a computationally faster quadratic method. To improve accuracy, we derive analytic expressions for handling the integral constraint, since it is crucial that finite volume effects are accurately corrected for on scales comparable to the depth of the survey. We also show that for the KL and quadratic techniques, multiple constraints can be included via simple matrix operations, thereby rendering the results less sensitive to galactic extinction and mis-estimates of the radial selection function. We present a data analysis pipeline that we argue does justice to the increases in both quality and quantity of data that upcoming redshift surveys will provide. It uses three analysis techniques in conjunction: a traditional Fourier approach on small scales, a pixelized quadratic matrix method on large scales and a pixelized KL eigenmode analysis to probe anisotropic effects such as redshift-space distortions.Comment: Major revisions for clarity. Matches accepted ApJ version. 23 pages, with 2 figs included. Color figure and links at http://www.sns.ias.edu/~max/galpower.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/galpower.html (faster from Europe) or from [email protected]

Simulated Extragalactic Observations with a Cryogenic Imaging Spectrophotometer

In this paper we explore the application of cryogenic imaging spectrophotometers. Prototypes of this new class of detector, such as superconducting tunnel junctions (STJs) and transition edge sensors (TESs), currently deliver low resolution imaging spectrophotometry with high quantum efficiency (70-100%) and no read noise over a wide bandpass in the visible to near-infrared. In order to demonstrate their utility and the differences in observing strategy needed to maximize their scientific return, we present simulated observations of a deep extragalactic field. Using a simple analytic technique, we can estimate both the galaxy redshift and spectral type more accurately than is possible with current broadband techniques. From our simulated observations and a subsequent discussion of the expected migration path for this new technology, we illustrate the power and promise of these devices.Comment: 30 pages, 10 figures, accepted for publication in the Astronomical Journa

Gravitational lens magnification by Abell 1689: Distortion of the background galaxy luminosity function

Gravitational lensing magnifies the luminosity of galaxies behind the lens. We use this effect to constrain the total mass in the cluster Abell 1689 by comparing the lensed luminosities of background galaxies with the luminosity function of an undistorted field. Since galaxies are assumed to be a random sampling of luminosity space, this method is not limited by clustering noise. We use photometric redshift information to estimate galaxy distance and intrinsic luminosity. Knowing the redshift distribution of the background population allows us to lift the mass/background degeneracy common to lensing analysis. In this paper we use 9 filters observed over 12 hours with the Calar Alto 3.5m telescope to determine the redshifts of 1000 galaxies in the field of Abell 1689. Using a complete sample of 151 background galaxies we measure the cluster mass profile. We find that the total projected mass interior to 0.25h^(-1)Mpc is (0.48 +/- 0.16) * 10^(15)h^(-1) solar masses, where our error budget includes uncertainties from the photometric redshift determination, the uncertainty in the off-set calibration and finite sampling. This result is in good agreement with that found by number count and shear-based methods and provides a new and independent method to determine cluster masses.Comment: 13 pages, 10 figures. Submitted to MNRAS (10/99); Replacement with 1 page extra text inc. new section, accepted by MNRA

The Axiverse Extended: Vacuum Destabilisation, Early Dark Energy and Cosmological Collapse

A model is presented in the philosophy of the "String Axiverse" of Arvanitaki et al (arXiv:0905.4720v2 [hep-th]) that incorporates a coupling of ultralight axions to their corresponding moduli through the mass term. The light fields roll in their potentials at late times and contribute to the dark sector energy densities in the cosmological expansion. The addition of a coupling and extra field greatly enrich the possible phenomenology of the axiverse. There are a number of interesting phases where the axion and modulus components behave as Dark Matter or Dark Energy and can have considerable and distinct effects on the expansion history of the universe by modifying the equation of state in the past or causing possible future collapse of the universe. In future such a coupling may help to alleviate fine tuning problems for cosmological axions. We motivate and present the model, and briefly explore its cosmological consequences numerically.Comment: 13 pages, 17 figures, published in PRD. v3: corrected SUSY interpretation of axion potential scal

The Power Spectrum of Clusters of Galaxies and the Press-Schechter Approximation

We examine the power spectrum of clusters in the Press-Schechter (PS) theory and in N-body simulations to see how the power spectrum of clusters is related to the power spectrum of matter density fluctuations in the Universe. An analytic model for the power spectrum of clusters for their given number density is presented, both for real space and redshift space. We test this model against results from N-body simulations and find that the agreement between the analytic theory and the numerical results is good for wavelengths $\lambda >60h^{-1}$ Mpc. On smaller scales non-linear processes that are not considered in the linear PS approximation influence the result. We also use our analytic model to study the redshift-space power spectrum of clusters in cold dark matter models with a cosmological constant ($\Lambda$CDM) and with a scale-invariant Harrison-Zel'dovich initial spectrum of density fluctuations. We find that power spectra of clusters in these models are not consistent with the observed power spectra of the APM and Abell-ACO clusters. One possible explanation for the observed power spectra of clusters is an inflationary scenario with a scalar field with the potential that has a localized steplike feature. We use the PS theory to examine the power spectrum of clusters in this model.Comment: 16 pages, 5 figures. Accepted by Ap