The Nonlinear Redshift Space Power Spectrum: Omega from Redshift Surveys

We examine the anisotropies in the power spectrum by the mapping of real to redshift space. Using the Zel'dovich approximation, we obtain an analytic expression for the nonlinear redshift space power spectrum in the distant observer limit. For a given unbiased galaxy distribution in redshift space, the anisotropies in the power spectrum depend on the parameter $f(\Omega)\approx \Omega^{0.6}$, where $\Omega$ is the density parameter. We quantify these anisotropies by the ratio, $R$, of the quadrupole to monopole angular moments of the power spectrum. In contrast to linear theory, the Zel'dovich approximation predicts a decline in $R$ with decreasing scale. This departure from linear theory is due to nonlinear dynamics and not a result of incoherent random velocities. The rate of decline depends strongly on $\Omega$ and the initial power spectrum. However, we find a {\it universal} relation between the quantity $R/R_{lin}$ (where $R_{lin}$ the linear theory value of $R$) and the dimensionless variable $k/k_{nl}$, where $k_{nl}$ is a wavenumber determined by the scale of nonlinear structures. The universal relation is in good agreement with a large N-body simulation. This universal relation greatly extends the scales over which redshift distortions can be used as a probe of $\Omega$. A preliminary application to the 1.2 Jy IRAS yields $\Omega\sim 0.4$ if IRAS galaxies are unbiased.Comment: uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

The Small Scale Velocity Dispersion of Galaxies: A Comparison of Cosmological Simulations

The velocity dispersion of galaxies on small scales ($r\sim1h^{-1}$ Mpc), $\sigma_{12}(r)$, can be estimated from the anisotropy of the galaxy-galaxy correlation function in redshift space. We apply this technique to ``mock-catalogs'' extracted from N-body simulations of several different variants of Cold Dark Matter dominated cosmological models to obtain results which may be consistently compared to similar results from observations. We find a large variation in the value of $\sigma_{12}(1 h^{-1} Mpc)$ in different regions of the same simulation. We conclude that this statistic should not be considered to conclusively rule out any of the cosmological models we have studied. We attempt to make the statistic more robust by removing clusters from the simulations using an automated cluster-removing routine, but this appears to reduce the discriminatory power of the statistic. However, studying $\sigma_{12}$ as clusters with different internal velocity dispersions are removed leads to interesting information about the amount of power on cluster and subcluster scales. We also compute the pairwise velocity dispersion directly and compare this to the values obtained using the Davis-Peebles method, and find that the agreement is fairly good. We evaluate the models used for the mean streaming velocity and the pairwise peculiar velocity distribution in the original Davis-Peebles method by comparing the models with the results from the simulations.Comment: 20 pages, uuencoded (Latex file + 8 Postscript figures), uses AAS macro

Maximum-Likelihood Comparisons of Tully-Fisher and Redshift Data: Constraints on Omega and Biasing

We compare Tully-Fisher (TF) data for 838 galaxies within cz=3000 km/sec from the Mark III catalog to the peculiar velocity and density fields predicted from the 1.2 Jy IRAS redshift survey. Our goal is to test the relation between the galaxy density and velocity fields predicted by gravitational instability theory and linear biasing, and thereby to estimate $\beta_I = \Omega^{0.6}/b_I,$ where $b_I$ is the linear bias parameter for IRAS galaxies. Adopting the IRAS velocity and density fields as a prior model, we maximize the likelihood of the raw TF observables, taking into account the full range of selection effects and properly treating triple-valued zones in the redshift-distance relation. Extensive tests with realistic simulated galaxy catalogs demonstrate that the method produces unbiased estimates of $\beta_I$ and its error. When we apply the method to the real data, we model the presence of a small but significant velocity quadrupole residual (~3.3% of Hubble flow), which we argue is due to density fluctuations incompletely sampled by IRAS. The method then yields a maximum likelihood estimate $\beta_I=0.49\pm 0.07$ (1-sigma error). We discuss the constraints on $\Omega$ and biasing that follow if we assume a COBE-normalized CDM power spectrum. Our model also yields the 1-D noise noise in the velocity field, including IRAS prediction errors, which we find to be be 125 +/- 20 km/sec.Comment: 53 pages, 20 encapsulated figures, two tables. Submitted to the Astrophysical Journal. Also available at http://astro.stanford.edu/jeff

Redshift-Space Distortions and the Real-Space Clustering of Different Galaxy Types

We study the distortions induced by peculiar velocities on the redshift-space correlation function of galaxies of different morphological types in the Pisces-Perseus redshift survey. Redshift-space distortions affect early- and late-type galaxies in different ways. In particular, at small separations, the dominant effect comes from virialized cluster cores, where ellipticals are the dominant population. The net result is that a meaningful comparison of the clustering strength of different morphological types can be performed only in real space, i.e., after projecting out the redshift distortions on the two-point correlation function xi(r_p,pi). A power-law fit to the projected function w_p(r_p) on scales smaller than 10/h Mpc gives r_o = 8.35_{-0.76}^{+0.75} /h Mpc, \gamma = 2.05_{-0.08}^{+0.10} for the early-type population, and r_o = 5.55_{-0.45}^{+0.40} /h Mpc, \gamma = 1.73_{-0.08}^{+0.07} for spirals and irregulars. These values are derived for a sample luminosity brighter than M_{Zw} = -19.5. We detect a 25% increase of r_o with luminosity for all types combined, from M_{Zw} = -19 to -20. In the framework of a simple stable-clustering model for the mean streaming of pairs, we estimate sigma_12(1), the one-dimensional pairwise velocity dispersion between 0 and 1 /h Mpc, to be 865^{+250}_{-165} km/s for early-type galaxies and 345^{+95}_{-65} km/s for late types. This latter value should be a fair estimate of the pairwise dispersion for ``field'' galaxies; it is stable with respect to the presence or absence of clusters in the sample, and is consistent with the values found for non-cluster galaxies and IRAS galaxies at similar separations.Comment: 17 LaTeX pages including 3 tables, plus 11 PS figures. Uses AASTeX macro package (aaspp4.sty) and epsf.sty. To appear on ApJ, 489, Nov 199

IRAS versus POTENT Density Fields on Large Scales: Biasing and Omega

The galaxy density field as extracted from the IRAS 1.2 Jy redshift survey is compared to the mass density field as reconstructed by the POTENT method from the Mark III catalog of peculiar velocities. The reconstruction is done with Gaussian smoothing of radius 12 h^{-1}Mpc, and the comparison is carried out within volumes of effective radii 31-46 h^{-1}Mpc, containing approximately 10-26 independent samples. Random and systematic errors are estimated from multiple realizations of mock catalogs drawn from a simulation that mimics the observed density field in the local universe. The relationship between the two density fields is found to be consistent with gravitational instability theory in the mildly nonlinear regime and a linear biasing relation between galaxies and mass. We measure beta = Omega^{0.6}/b_I = 0.89 \pm 0.12 within a volume of effective radius 40 h^{-1}Mpc, where b_I is the IRAS galaxy biasing parameter at 12 h^{-1}Mpc. This result is only weakly dependent on the comparison volume, suggesting that cosmic scatter is no greater than \pm 0.1. These data are thus consistent with Omega=1 and b_I\approx 1. If b_I>0.75, as theoretical models of biasing indicate, then Omega>0.33 at 95% confidence. A comparison with other estimates of beta suggests scale-dependence in the biasing relation for IRAS galaxies.Comment: 35 pages including 10 figures, AAS Latex, Submitted to The Astrophysical Journa

Pulsed versus DC I-V characteristics of resistive manganites

We report on pulsed and DC I-V characteristics of polycrystalline samples of three charge-ordered manganites, Pr_{2/3}Ca_{1/3}MnO_3, Pr_{1/2}Ca_{1/2}MnO_3, Bi_{1/2}Sr_{1/2}MnO_3 and of a double-perovskite Sr_2MnReO_6, in a temperature range where their ohmic resistivity obeys the Efros-Shklovskii variable range hopping relation. For all samples, the DC I(V) exhibits at high currents negative differential resistance and hysteresis, which mask a perfectly ohmic or a moderately nonohmic conductivity obtained by pulsed measurements. This demonstrates that the widely used DC I-V measurements are usually misleading.Comment: 6 pages, 4 figures. Accepted for publication to AP

Inter-grain tunneling in the half-metallic double-perovskites Sr2_2BB'O6_6 (BB'-- FeMo, FeRe, CrMo, CrW, CrRe

The zero-field conductivities ($\sigma$) of the polycrystaline title materials, are governed by inter-grain transport. In the majority of cases their $\sigma$(T) can be described by the "fluctuation induced tunneling" model. Analysis of the results in terms of this model reveals two remarkable features: 1. For \emph{all} Sr$_2$FeMoO$_6$ samples of various microstructures, the tunneling constant (barrier width $\times$ inverse decay-length of the wave-function) is $\sim$ 2, indicating the existence of an intrinsic insulating boundary layer with a well defined electronic (and magnetic) structure. 2. The tunneling constant for \emph{all} cold-pressed samples decreases linearly with increasing magnetic-moment/formula-unit.Comment: 10 pages, 2 tables, 3 figure

Radial Redshift Space Distortions

The radial component of the peculiar velocities of galaxies cause displacements in their positions in redshift space. We study the effect of the peculiar velocities on the linear redshift space two point correlation function. Our analysis takes into account the radial nature of the redshift space distortions and it highlights the limitations of the plane parallel approximation. We consider the problem of determining the value of \beta and the real space two point correlation function from the linear redshift space two point correlation function. The inversion method proposed here takes into account the radial nature of the redshift space distortions and can be applied to magnitude limited redshift surveys that have only partial sky coverage.Comment: 26 pages including 11 figures, to appear in Ap

Overconstrained dynamics in galaxy redshift surveys

The least-action principle (LAP) method is used on four galaxy redshift surveys to measure the density parameter Omega_m and the matter and galaxy-galaxy power spectra. The datasets are PSCz, ORS, Mark III and SFI. The LAP method is applied on the surveys simultaneously, resulting in an overconstrained dynamical system that describes the cosmic overdensities and velocity flows. The system is solved by relaxing the constraint that each survey imposes upon the cosmic fields. A least-squares optimization of the errors that arise in the process yields the cosmic fields and the value of Omega_m that is the best fit to the ensemble of datasets. The analysis has been carried out with a high-resolution Gaussian smoothing of 500 km/s and over a spherical selected volume of radius 9,000 km/s. We have assigned a weight to each survey, depending on their density of sampling, and this parameter determines their relative influence in limiting the domain of the overall solution. The influence of each survey on the final value of Omega_m, the cosmographical features of the cosmic fields and the power spectra largely depends on the distribution function of the errors in the relaxation of the constraints. We find that PSCz and Mark III are closer to the final solution than ORS and SFI. The likelihood analysis yields Omega_m= 0.37\pm 0.01 to 1sigma level. PSCz and SFI are the closest to this value, whereas ORS and Mark III predict a somewhat lower Omega_m. The model of bias employed is a scale-dependent one, and we retain up to 42 bias coefficients b_{rl} in the spherical harmonics formalism. The predicted power spectra are estimated in the range of wavenumbers 0.02-0.49h Mpc^{-1}, and we compare these results with measurements recently reported in the literature.Comment: 10 pages, no figure