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Karl B. Fisher

Publications and source records attributed to Karl B. Fisher.

13 recordsLinked to original sources
arXiv1998

Filaments and Pancakes in the IRAS 1.2 Jy Redshift Catalogue

We explore shapes of clusters and superclusters in the IRAS 1.2 Jy redshift survey with three reconstructions spanning the range β= 0.1, 0.5, 1.0, where β= Ω^{0.6}/b, b is the bias factor and Ωthe present value of the dimensionless matter density. Comparing our results to Gaussian randomized reconstructions of the IRAS catalogue, we find structures having both planar and filamentary properties. For β= 0.5, 1.0 the largest structures in the survey have a distinct tendency to be filament-like} in general agreement with the results of N-body simulations.

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arXiv1998

Skewed exponential pairwise velocities from Gaussian initial conditions

Using an Eulerian perturbative calculation, we show that the distribution of relative pairwise velocities which arises from gravitational instability of Gaussian density fluctuations has asymmetric (skewed) exponential tails. The negative skewness is induced by the negative mean streaming velocity of pairs (the infall prevails over expansion), while the exponential tails arise because the relative pairwise velocity is a number, not volume weighted statistic. The derived probability distribution is compared with N-body simulations and shown to provide a reasonable fit.

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arXiv1997

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, γ= 2.05_{-0.08}^{+0.10} for the early-type population, and r_o = 5.55_{-0.45}^{+0.40} /h Mpc, γ= 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.

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arXiv1996

Percolation Analysis of a Wiener Reconstruction of the IRAS 1.2 Jy Redshift Catalog

We present percolation analyses of Wiener Reconstructions of the IRAS 1.2 Jy Redshift Survey. There are ten reconstructions of galaxy density fields in real space spanning the range $β= 0.1$ to $1.0$, where $β={Ω^{0.6}}/b$, $Ω$ is the present dimensionless density and $b$ is the bias factor. Our method uses the growth of the largest cluster statistic to characterize the topology of a density field, where Gaussian randomized versions of the reconstructions are used as standards for analysis. For the reconstruction volume of radius, $R {\approx} 100 h^{-1} $ Mpc, percolation analysis reveals a slight `meatball' topology for the real space, galaxy distribution of the IRAS survey. cosmology-galaxies:clustering-methods:numerical

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arXiv1996

The Signature of a Correlation between $>10^{19}{\rm eV}$ Cosmic Ray Sources and Large Scale Structure

We analyze the anisotropy signature expected if the high energy (above $10^{19}$eV) cosmic ray (CR) sources are extra-Galactic and trace the distribution of luminous matter on large scales. We investigate the dependence of the anisotropy on both the relative bias between the CR sources and the galaxy distribution and on the (unknown) intrinsic CR source density. We find that the expected anisotropy associated with the large scale structure (LSS) should be detected once the number of CR events observed above $10^{19}{\rm eV}$ is increased by a factor of $\sim10$. This would require $\sim30$ observation-years with existing experiments, but less then $1$ year with the proposed $\sim5000\ {\rm km}^2$ Auger detectors. We find that the recently reported concentration of the Haverah Park CR events towards the super-galactic plane is not consistent with the known LSS. If real, the Haverah Park result suggests that the CR sources are much more concentrated towards the super-galactic plane than the known LSS. Our results are not sensitive to the number density of CR sources. We show that once the number of detected events is increased by a factor of $\sim10$, the number density would be strongly constrained by considering the probability for having repeating sources.

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arXiv1996

Galaxy Clustering Around Nearby Luminous Quasars

We examine the clustering of galaxies around a sample of 20 luminous low redshift (z<0.30) quasars observed with the Wide Field Camera-2 on the Hubble Space Telescope. The HST resolution makes possible galaxy identification brighter than V=23.5 and as close as 2'' to the quasar. We find a significant enhancement of galaxies within a projected separation of < 100 kpc/h of the quasars. If we model the qso/galaxy correlation function as a power law with a slope given by the galaxy/galaxy correlation function, we find that the ratio of the qso/galaxy to galaxy/galaxy correlation functions is $3.8\pm 0.8$. The galaxy counts within r<15 kpc/h of the quasars are too high for the density profile to have an appreciable core radius ( > 100 kpc). Our results reinforce the idea that low redshift quasars are located preferentially in groups of 10-20 galaxies rather than in rich clusters. We see no significant difference in the clustering amplitudes derived from radio-loud and radio-quiet subsamples.

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arXiv1994

On The Validity of the Streaming Model for the Redshift-Space Correlation Function in the Linear Regime

The relation between the galaxy correlation function in real and redshift-space is derived in the linear regime by an appropriate averaging of the joint probability distribution of density and velocity. The derivation recovers the familiar linear theory result on large scales but has the advantage of clearly revealing the dependence of the redshift distortions on the underlying peculiar velocity field; streaming motions give rise to distortions of ${\cal O}(Ω^{0.6}/b)$ while variations in the anisotropic velocity dispersion yield terms of order ${\cal O}(Ω^{1.2}/b^2)$. This probabilistic derivation of the redshift-space correlation function is similar in spirit to the derivation of the commonly used ``streaming'' model, in which the distortions are given by a convolution of the real-space correlation function with a velocity distribution function. The streaming model is often used to model the redshift-space correlation function on small, highly non-linear, scales. There have been claims in the literature, however, that the streaming model is not valid in the linear regime. Our analysis confirms this claim, but we show that the streaming model can be made consistent with linear theory {\it provided} that the model for the streaming has the functional form predicted by linear theory and that velocity distribution is chosen to be a Gaussian with the correct linear theory dispersion.

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arXiv1994

Constraints onOmega from the IRAS Redshift Surveys

We measure the anisotropy of the redshift-space power spectrum in the 1.2-Jy and QDOT redshift surveys of IRAS-selected galaxies. On large scales, this anisotropy is caused by coherent peculiar motions, and gravitational instability theory predicts a distortion of the power spectrum that depends only on the ratio $β\equiv f(Ω)/b \approx Ω^{0.6}/b$, where Omega is the cosmological density parameter and $b$ is the bias parameter. On small scales, the distortion is dominated by the random velocity dispersion in non-linear structures. We fit the observed anisotropy with an analytic model that incorporates two parameters, beta, and a small-scale velocity dispersion sigma_v. Tests on N-body simulations show that this model recovers beta quite accurately on the scales accessible to the existing IRAS redshift surveys. Applying our procedure to the 1.2-Jy and QDOT surveys, we find beta=0.52 +/- 0.13 and beta=0.54 +/- 0.3, respectively. These results imply Omega approximately 0.35 if galaxies trace mass, or a bias factor of about 2 if Omega=1.

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arXiv1994

Wiener Filtering of the COBE DMR Data

We derive an optimal linear filter to suppress the noise from the COBE DMR sky maps for a given power spectrum. We then apply the filter to the first-year DMR data, after removing pixels within $20^\circ$ of the Galactic plane from the data. The filtered data have uncertainties 12 times smaller than the noise level of the raw data. We use the formalism of constrained realizations of Gaussian random fields to assess the uncertainty in the filtered sky maps. In addition to improving the signal-to-noise ratio of the map as a whole, these techniques allow us to recover some information about the CMB anisotropy in the missing Galactic plane region. From these maps we are able to determine which hot and cold spots in the data are statistically significant, and which may have been produced by noise. In addition, the filtered maps can be used for comparison with other experiments on similar angular scales.

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arXiv1993

A Spherical Harmonic Approach to Redshift Distortion: Implications for $Ω$ and the Power Spectrum

We examine the nature of galaxy clustering in redshift space using a method based on an expansion of the galaxian density field in Spherical Harmonics and linear theory. We derive a compact and self-consistent expression for the distortion when applied to flux limited redshift surveys. The amplitude of the distortion is controlled by the combination of the density and bias parameters, $β\equivΩ_\circ^{0.6}/b$ as well as the shape of the real space power spectrum, $P(k)$ (characterized by a shape parameter $Γ$), and its normalization, $σ_8$; we exploit this fact to derive a maximum likelihood estimator for $β$, $Γ$, and $σ_8$. We check our formalism using $N$-body simulations and demonstrate it provides an unbiased estimate of $β$ when the amplitude and shape of the galaxy power spectrum is known. Application of the technique to the 1.2 Jy \iras\ redshift survey yields $β=0.94\pm 0.17$ and $Γ=0.17\pm0.05$ (1-$σ$) when $σ_8$ is held fixed at its best value as determined from the real space correlation function. Allowing $σ_8$ to be a free parameter, we find $β=0.47\pm 0.25$, $Γ=0.15\pm0.05$, and $σ_8=0.81\pm0.06$.

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arXiv1993

Fourier Analysis of Redshift Space Distortions and the Determination of Omega

The peculiar velocities of galaxies distort the pattern of galaxy clustering in redshift space, making the redshift space power spectrum anisotropic. In the linear regime, the strength of this distortion depends only on the ratio $β\equiv f(Ω)/b \approx Ω^{0.6}/b$, where $Ω$ is the cosmological density parameter and $b$ is the bias parameter. We derive a linear theory estimator for $β$ based on the harmonic moments of the redshift space power spectrum. Using N-body simulations, we examine the impact of non-linear gravitational clustering on the power spectrum anisotropy and on our $β$-estimator. Non-linear effects can be important out to wavelengths $λ\sim 50$Mpc/h or larger; in most cases, they lower the quadrupole moment of the power spectrum and thereby depress the estimate of $β$ below the true value. With a sufficiently large redshift survey, the scaling of non-linear effects may allow separate determinations of $Ω$ and $b$. We describe a practical technique for measuring the anisotropy of the power spectrum from galaxy redshift surveys, and we test the technique on mock catalogues drawn from the N-body simulations. Preliminary application of our methods to the 1.2 Jy IRAS galaxy survey yields $β_{est} \sim 0.3-0.4 $ at wavelengths $λ\sim 30-40$Mpc/h . Non-linear effects remain important at these scales, so this estimate of $β$ is probably lower than the true value.

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arXiv1993

Clustering in the 1.2 Jy IRAS Galaxy Redshift Survey I: The Redshift and Real Space Correlation Functions

We present analyses of the two-point correlation function derived from an all-sky redshift survey of 5313 galaxies extracted from the Infrared Astronomical Satellite (IRAS) database. The redshift space correlation function ξ(s) is well described by a power law, $ξ(s) = (s/4.53h^{-1}{\rm Mpc})^{-1.28}$, on scales \simlt 20\mpc; on larger scales ξ(s) drops below the extension of this power law. We examine the effect of redshift space distortions on the correlation function and compute the full two dimensional correlation function ξ(r_p,π). From this, we derive the real space correlation function, which is well described by $ξ(r) = (r/3.76h^{-1}{\rm Mpc})^{-1.66}$ on scales \simlt 20\mpc. The derived correlation functions are found to be consistent with previous determinations in the literature, and seem to show more power on large scales than predicted by the standard Cold Dark Matter (CDM) model. Comparison of the derived ξ(r) with the correlation function of optical galaxies implies an optical to IRAS bias ratio of $b_O/b_I = 1.38\pm 0.12$ on a scale of $\sim 8$\mpc . The variances in cubical cells inferred from ξ(s) appear discrepant with the previously reported results of Efstathiou et al. (1990).

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