Real-space Correlation Function Research Articles

Redshift-space distortions with the halo occupation distribution - I. Numerical simulations

We show how redshift-space distortions of the galaxy correlation function or power spectrum can constrain the matter density parameter Ω m and the linear matter fluctuation amplitude σ 8 . We improve on previous treatments by adopting a fully non-linear description of galaxy clustering and bias, which allows us to achieve the accuracy demanded by larger galaxy redshift surveys and to break parameter degeneracies by combining large-scale and small-scale distortions. Given an observationally motivated choice of the initial power spectrum shape, we consider different combinations of Ω m and σ 8 and find parameters of the galaxy halo occupation distribution (HOD) that yield nearly identical galaxy correlation functions in real space. We use these HOD parameters to populate the dark matter haloes of large N-body simulations, from which we measure redshift-space distortions on small and large scales. We include a velocity bias parameter α v that allows the velocity dispersions of satellite galaxies in haloes to be systematically higher or lower than those of dark matter. Large-scale distortions are determined by the parameter combination β ≡ Ω 0.6 m /b g , where bg is the bias factor defined by the ratio of galaxy and matter correlation functions, in agreement with the linear theory prediction of parameter degeneracy. However, linear theory does not accurately describe the distortions themselves on scales accessible to our simulations. We provide fitting formulas to estimate β from measurements of the redshift-space correlation function or power spectrum, and we show that these formulas are significantly more accurate than those in the existing literature. On small scales, the 'FOG' distortions at projected separations ∼0.1 h -1 Mpc depend on Ω m α 2 v but are independent of as, while at intermediate separations they depend on σ 8 as well. One can thus use measurements of redshift-space distortions over a wide range of scales to separately determine Ω m , σ 8 , and α v .

Large scale correlations in galaxy clustering from the two degree field galaxy redshift survey

We study galaxy correlations from samples extracted from the 2dFGRS final release. Statistical properties are characterized by studying the nearest neighbor probability density, the conditional density and the reduced two-point correlation function. The result is that the conditional density has a power-law behavior in redshift space described by an exponent \gamma=0.8 \pm 0.2 in the interval from about 1 Mpc/h, the average distance between nearest galaxies, up to about 40 Mpc/h, corresponding to radius of the largest sphere contained in the samples. These results are consistent with other studies of the conditional density and are useful to clarify the subtle role of finite-size effects on the determination of the two-point correlation function in redshift and real space

The Luminosity and Color Dependence of the Galaxy Correlation Function

We study the luminosity and color dependence of the galaxy two-point correlation function in the Sloan Digital Sky Survey, starting from a sample of ~200,000 galaxies over 2500 deg2. We concentrate our analysis on volume-limited subsamples of specified luminosity ranges, for which we measure the projected correlation function wp(rp), which is directly related to the real-space correlation function ξ(r). The amplitude of wp(rp) rises continuously with luminosity from Mr ≈ -17.5 to Mr ≈ -22.5, with the most rapid increase occurring above the characteristic luminosity L* (Mr ≈ -20.5). Over the scales 0.1 h-1 Mpc < rp < 10 h-1 Mpc, the measurements for samples with Mr > -22 can be approximated, imperfectly, by power-law three-dimensional correlation functions ξ(r) = (r/r0)-γ with γ ≈ 1.8 and r0(L*) ≈ 5.0 h-1 Mpc. The brightest subsample, -23 < Mr < -22, has a significantly steeper ξ(r). When we divide samples by color, redder galaxies exhibit a higher amplitude and steeper correlation function at all luminosities. The correlation amplitude of blue galaxies increases continuously with luminosity, but the luminosity dependence for red galaxies is less regular, with bright red galaxies exhibiting the strongest clustering at large scales and faint red galaxies exhibiting the strongest clustering at small scales. We interpret these results using halo occupation distribution (HOD) models assuming concordance cosmological parameters. For most samples, an HOD model with two adjustable parameters fits the wp(rp) data better than a power law, explaining inflections at rp ~ 1-3 h-1 Mpc as the transition between the one-halo and two-halo regimes of ξ(r). The implied minimum mass for a halo hosting a central galaxy more luminous than L grows steadily, with Mmin ∝ L at low luminosities and a steeper dependence above L*. The mass at which a halo has, on average, one satellite galaxy brighter than L is M1 ≈ 23Mmin(L), at all luminosities. These results imply a conditional luminosity function (at fixed halo mass) in which central galaxies lie far above a Schechter function extrapolation of the satellite population. The HOD model fits nicely explain the color dependence of wp(rp) and the cross correlation between red and blue galaxies. For galaxies with Mr < -21, halos slightly above Mmin have blue central galaxies, while more massive halos have red central galaxies and predominantly red satellite populations. The fraction of blue central galaxies increases steadily with decreasing luminosity and host halo mass. The strong clustering of faint red galaxies follows from the fact that nearly all of them are satellite systems in high-mass halos. The HOD fitting results are in good qualitative agreement with the predictions of numerical and semianalytic models of galaxy formation.

Constraining β(z) and Ω0mfrom redshift-space distortions inz∼ 3 galaxy surveys

We use a sample of 813 Lyman-break galaxies (LBGs) with 2.6 < z < 3.4 to perform a detailed analysis of the redshift-space (z-space) distortions in their clustering pattern, and from that derive confidence levels in the [� 0, β(z = 3)] plane. We model the z-space distortions in the shape of the correlation function measured in orthogonal directions, ξ (σ , π ). This modelling requires an accurate description of the real-space correlation function to be given as an input. From the projection of ξ (σ , π )i nthe angular direction, wp (σ ), we derive the best-fitting amplitude and slope for the LBG real-space correlation function: r 0 = 4.48 +0.17 −0.18 h −1 Mpc and γ = 1.76 +0.08 −0.09 [ξ (r ) = (r/r 0) −γ ]. A comparison between the shape of ξ (s) and wp (σ ) suggests that ξ (r )d eviates from a simple power-law model, with a break at ∼9 h −1 Mpc. This model is consistent with the observed projected correlation function. However, due to the limited size of the fields used, the w p(σ ) results are limited to σ 10 h −1 Mpc. Assuming this doublepower-law model, and by analysing the shape distortions in ξ (σ , π ), we find the following constraints: β(z = 3) = 0.15 +0.20

The 2dF QSO Redshift Survey- XV. Correlation analysis of redshift-space distortions

We analyse the redshift-space (z-space) distortions of QSO clustering in the 2dF QSO Redshift Survey (2QZ). To interpret the z-space correlation function, xi(sigma,pi), we require an accurate model for the QSO real-space correlation function, xi(r). Although a single power-law xi(r) model fits the projected correlation function (wp(sigma)) at small scales, it implies somewhat too shallow a slope for both wp(sigma) and the z-space correlation function, xi(s), at larger scales > 20 h^(-1) Mpc. Motivated by the form for xi(r) seen in the 2dF Galaxy Redshift Survey (2dFGRS) and in standard LCDM predictions, we use a double power-law model for xi(r) which gives a good fit to xi(s) and wp(sigma). The model is parametrized by a slope of gamma=1.45 for 1<r<10 h^(-1) Mpc and gamma=2.30 for 10<r<40 h^(-1) Mpc. As found for 2dFGRS, the value of beta determined from the ratio of xi(s)/xi(r) depends sensitively on the form of xi(r) assumed. With our double power-law form for xi(r), we measure beta(z=1.4)=0.32(+0.09)(-0.11). Assuming the same model for xi(r) we then analyse the z-space distortions in the 2QZ xi(sigma,pi) and put constraints on the values of Omega m and beta(z=1.4), using an improved version of the method of Hoyle et al. The constraints we derive are Omega m=0.35(+0.19)(-0.13), beta(z=1.4)=0.50(+0.13)(-0.15), in agreement with our xi(s)/\xi(r) results at the ~1 sigma level.

The Intermediate‐Scale Clustering of Luminous Red Galaxies

We report the intermediate-scale (0.3-40 h-1 Mpc) clustering of 35,000 luminous early-type galaxies at redshifts 0.16-0.44 from the Sloan Digital Sky Survey. We present the redshift space two-point correlation function ξ(s), the projected correlation function wp(rp), and the deprojected real space correlation function ξ(r), for approximately volume-limited samples. As expected, the galaxies are highly clustered, with the correlation length varying from 9.8 ± 0.2 to 11.2 ± 0.2 h-1 Mpc, dependent on the specific luminosity range. For the -23.2 < Mg < -21.2 sample, the inferred bias relative to that of L* galaxies is 1.84 ± 0.11 for 1 h-1 Mpc < rp 10 h-1 Mpc, with yet stronger clustering on smaller scales. We detect luminosity-dependent bias within the sample but see no evidence for redshift evolution between z = 0.2 and z = 0.4. We find a clear indication for deviations from a power-law in the real space correlation function, with a dip at ~2 h-1 Mpc scales and an upturn on smaller scales. The precision measurements of these clustering trends offer new avenues for the study of the formation and evolution of these massive galaxies.

Galaxy-galaxy-galaxy lensing: Third-order correlations between the galaxy and mass distributions in the Universe

Galaxy-galaxy lensing (GGL) measures the 2-point cross-correlation between galaxies and mass in the Universe. In this work we seek to generalise this effect by considering the third-order correlations between galaxies and mass: galaxy-galaxy- galaxy lensing. Third-order correlations in the cosmic shear field have recently been reported in the VIRMOS-DESCART and CTIO surveys. Such data should also be ideal for measuring galaxy-galaxy-galaxy lensing. Indeed, the effects of these higher- order correlations may have already been detected in recent studies of galaxy-galaxy lensing. Higher-order cross-correlation functions contain invaluable information about the relationship between galaxies and their mass environments that GGL studies alone cannot detect. In this paper we lay out the basic relations for third-order cross correlations and their projections and introduce a new set of scale dependent third-order bias parameters. We define three new observables: two galaxy-shear-shear correlation functions, G±, and a galaxy-galaxy-shear correlation, G. We relate these to the various projected cross-bispectra and give practical estimators for their measurement. We note that the observational signature of these correlators is simply the excess shear-shear correlation measured about foreground galaxies (for G±) and the average tangential shear around foreground galaxy pairs (for G). These quantities are no more than second order in the shear and so should be more easily measurable than the shear 3-point correlation. Finally we derive expressions for the third order aperture mass statistics in terms of both the cross-bispectra and the real-space correlation functions. Such statistics provide a very localized measurement of the bispectra, thus encapsulating essentially all of the available third-order information, while remaining easily obtainable from observations of 3-point cross-correlation functions. In addition we find that utilising aperture statistics has the further benefit that they measure only the connected part of the third order correlation.

The spatial clustering of X-ray selected AGN and galaxies in the Chandra Deep Field South and North

We investigate the spatial clustering of X-ray selected sources in the two deepest X-ray fields to date, namely the 2 Ms Chandra Deep Field North (CDFN) and the 1 Ms Chandra Deep Field South (CDFS). The projected correlation function w(rp), measured on scales ∼0.2−10 h −1 Mpc for a sample of 240 sources with spectroscopic redshift in the CDFN and 124 sources in the CDFS at a median redshift of ¯ z ∼ 0.8 is used to constrain the amplitude and slope of the real space correlation function ξ(r) = (r/r0) −γ . The clustering signal is detected at high confidence (> 7σ) in both fields. The amplitude of the correlation is found to be significantly different in the two fields, the correlation length r0 being 8.6 ± 1.2 h −1 Mpc in the CDFS and 4.2 ± 0.4 h −1 Mpc in the CDFN, while the correlation slope γ is found to be flat in both fields: γ = 1.33 ± 0.11 in the CDFS and γ = 1.42 ± 0.07 in the CDFN (a flat Universe with Ωm = 0. 3a ndΩΛ = 0.7 is assumed; 1σ Poisson error estimates are considered). The correlation function also has been measured separately for sources classified as AGN or galaxies. In both fields AGN have a median redshift of ¯ ∼ 0. 9a nd am edian 0.5−10 keV luminosity of ¯ Lx ∼ 10 43 erg s −1 , i.e. they are generally in the Seyfert luminosity regime. As in the case of the total samples, we found a significant difference in the AGN clustering amplitude between the two fields, the best fit correlation parameters being r0 = 10.3 ± 1.7 h −1 Mpc, γ = 1.33 ± 0.14 in the CDFS, and r0 = 5.5 ± 0.6 h −1 Mpc, γ = 1.50 ± 0.12 in the CDFN. In the CDFN, where the statistics are sufficiently high, we were also able to measure the clustering of X-ray selected galaxies, finding r0 = 4.0 ± 0.7 h −1 Mpc and γ = 1.36 ± 0.15. Within each field no statistically significant difference is found between soft and hard X-ray selected sources or between type 1 and type 2 AGN. After having discussed and ruled out the possibility that the observed variance in the clustering amplitude is due to observational biases, we verified that the extra correlation signal in the CDFS is primarily due to the two prominent redshift spikes at z ∼ 0.7 reported by Gilli et al. (2003). The high (5−10 h −1 Mpc) correlation length measured for the X-ray selected AGN at z ∼ 1i n the twoChandra Ms fields is comparable to that of early type galaxies at the same redshift. This is consistent with the idea that, at z ∼ 1, AGN with Seyfert-like luminosities might be generally hosted by massive galaxies.

Cosmic evolution of quasar clustering: implications for the host haloes

We present detailed clustering measurements from the 2dF Quasi-Stellar Object Redshift Survey (2QZ) in the redshift range 0.8 < z < 2.1. Using a flux-limited sample of ∼14 000 objects with effective redshift z eff = 1.47, we estimate the quasar projected correlation function for separations 1 < r/ h −1 Mpc < 20. We find that the two-point correlation function in real space is well approximated by a power law with slope γ = 1.5 ± 0.2 and comoving correlation length r 0 = 4.8 +0.9 h −1 Mpc. Splitting the sample into three subsets based on redshift, we find evidence for an increase of the clustering amplitude with look-back time. For a fixed γ ,e v olution of r0 is detected at the 3.6σ confidence level. The ratio between the quasar correlation function and the mass autocorrelation function (derived adopting the concordance cosmological model) is found to be scale-independent. For a linear mass-clustering amplitude σ 8 = 0.8, the ‘bias parameter’ decreases from b � 3.9 at z eff = 1.89 to b � 1.8 at z eff = 1.06. From the observed abundance and clustering, we infer how quasars populate dark matter

Projected Three‐Point Correlation Functions and Galaxy Bias

The three-point correlation function (3PCF) can now be measured in large galaxy redshift surveys, but in three dimensions its interpretation is complicated by the presence of redshift-space distortions. I investigate the projected 3PCF, where these distortions are eliminated by integrating over the redshift dimension, as is commonly done for the two-point correlation function. The calculation of the projected 3PCF from the real-space, three-dimensional bispectrum is greatly simplified by expanding both quantities in Fourier components, analogous to Szapudi's expansion of the three-dimensional quantities in multipole components. In the weakly nonlinear regime, the bispectrum can be well represented by the first few Fourier components. There is a well-known relation between the reduced 3PCFs of matter and galaxies in the weakly nonlinear regime, which can be used to infer galaxy bias factors if the real-space three-dimensional galaxy correlation functions (two-point and three-point) can be measured. I show that the same relation holds for the reduced projected 3PCFs if these are properly defined. These results should aid determinations of galaxy bias from large redshift surveys by eliminating the complication of redshift-space distortions.

Structural investigation of liquid formic acid by neutron diffraction. II: Isotopic substitution for DCOO[H/D

New measurements of neutron diffraction data for four samples involving H/D isotopic substitution on the hydroxyl hydrogen of liquid formic acid at 20 °C are reported. The results are combined with earlier measurements on [H/D]COOD to provide a full range of data. The determination of molecular conformation and bond-lengths has been made with a partial form-factor formalism and also using the “Monte Carlo determination of g(r)” technique. The partial real-space correlation functions, RR, RH and HH are evaluated in each case and compared with existing computer simulations.

The 2dF galaxy redshift survey: clustering properties of radio galaxies

The clustering properties of local, S_{1.4 GHz} > 1 mJy, radio sources are investigated for a sample of 820 objects drawn from the joint use of the FIRST and 2dF Galaxy Redshift surveys. To this aim, we present 271 new bj < 19.45 spectroscopic counterparts of FIRST radio sources to be added to those already introduced in Magliocchetti et al. (2002). The two-point correlation function for the local radio population is found to be entirely consistent with estimates obtained for the whole sample of 2dFGRS galaxies. We estimate the parameters of the real-space correlation function xi(r)=(r/r_0)^{-\gamma}, r_0=6.7^{+0.9}_{-1.1} Mpc and \gamma=1.6\pm 0.1, where h=0.7 is assumed. Different results are instead obtained if we only consider sources that present signatures of AGN activity in their spectra. These objects are shown to be very strongly correlated, with r_0=10.9^{+1.0}_{-1.2} Mpc and \gamma=2\pm 0.1, a steeper slope than has been claimed in other recent works. No difference is found in the clustering properties of radio-AGNs of different radio luminosity. These results show that AGN-fuelled sources reside in dark matter halos more massive than \sim 10^{13.4} M_{\sun}},higher the corresponding figure for radio-quiet QSOs. This value can be converted into a minimum black hole mass associated with radio-loud, AGN-fuelled objects of M_{BH}^{min}\sim 10^9 M_{\sun}. The above results then suggest -at least for relatively faint radio objects -the existence of a threshold black hole mass associated with the onset of significant radio activity such as that of radio-loud AGNs; however, once the activity is triggered, there appears to be no evidence for a connection between black hole mass and level of radio output. (abridged)

The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe

We present a detailed analysis of the two-point correlation function, from the 2dF Galaxy Redshift Survey (2dFGRS). We estimate the redshift-space correlation function, xi(s), from which we measure the redshift-space clustering length, s_0=6.82+/-0.28 Mpc/h. We also estimate the projected correlation function, Xi(sigma), and the real-space correlation function, xi(r), which can be fit by a power-law, with r_0=5.05+/-0.26Mpc/h, gamma_r=1.67+/-0.03. For r>20Mpc/h, xi drops below a power-law as is expected in the popular LCDM model. The ratio of amplitudes of the real and redshift-space correlation functions on scales of 8-30Mpc/h gives an estimate of the redshift-space distortion parameter beta. The quadrupole moment of xi on scales 30-40Mpc/h provides another estimate of beta. We also estimate the distribution function of pairwise peculiar velocities, f(v), including rigorously the effect of infall velocities, and find that it is well fit by an exponential. The accuracy of our xi measurement is sufficient to constrain a model, which simultaneously fits the shape and amplitude of xi(r) and the two redshift-space distortion effects parameterized by beta and velocity dispersion, a. We find beta=0.49+/-0.09 and a=506+/-52km/s, though the best fit values are strongly correlated. We measure the variation of the peculiar velocity dispersion with projected separation, a(sigma), and find that the shape is consistent with models and simulations. Using the constraints on bias from recent estimates, and taking account of redshift evolution, we conclude that beta(L=L*,z=0)=0.47+/-0.08, and that the present day matter density of the Universe is 0.3, consistent with other 2dFGRS estimates and independent analyses.

On the angular correlation function of SZ clusters: Extracting cosmological information from a 2D catalog

We discuss the angular correlation function of Sunyaev-Zel'dovich (SZ)-detected galaxy clusters as a cosmological probe. As a projection of the real-space cluster correlation function, the angular function samples the underlying SZ catalog redshift distribution. It offers a way to study cosmology and cluster evolution directly with the two-dimensional catalog, even before extensive follow-up observations, thereby facilitating the immediate scientific return from SZ surveys. As a simple illustration of the information content of the angular function, we examine its dependence on the parameter pair Om_m, sigma_8 in flat cosmologies. We discuss sources of modeling uncertainty and consider application to the future Planck SZ catalog, showing how these two parameters and the normalization of the SZ flux-mass relation can be simultaneously found when the local X-ray cluster abundance constraint is included.

The 2dF Galaxy Redshift Survey: galaxy clustering per spectral type

We have calculated the two-point correlation functions in redshift space, xi(sigma,pi), for galaxies of different spectral types in the 2dF Galaxy Redshift Survey. Using these correlation functions we are able to estimate values of the linear redshift-space distortion parameter, beta = Omega_m^0.6/b, the pairwise velocity dispersion, a, and the real-space correlation function, xi(r), for galaxies with both relatively low star-formation rates (for which the present rate of star formation is less than 10% of its past averaged value) and galaxies with higher current star-formation activity. At small separations, the real-space clustering of passive galaxies is very much stronger than that of the more actively star-forming galaxies; the correlation-function slopes are respectively 1.93 and 1.50, and the relative bias between the two classes is a declining function of radius. On scales larger than 10 h^-1 Mpc there is evidence that the relative bias tends to a constant, b(passive)/b(active) ~ 1. This result is consistent with the similar degrees of redshift-space distortions seen in the correlation functions of the two classes -- the contours of xi(sigma,pi) require beta(active)=0.49+/-0.13, and beta(passive)=0.48+/-0.14. The pairwise velocity dispersion is highly correlated with beta. However, despite this a significant difference is seen between the two classes. Over the range 8-20 h^-1 Mpc, the pairwise velocity dispersion has mean values 416+/-76 km/s and 612+/-92 km/s for the active and passive galaxy samples respectively. This is consistent with the expectation from morphological segregation, in which passively evolving galaxies preferentially inhabit the cores of high-mass virialised regions.

Disordered Materials by P. M. Ossi. Springer-Verlag, 2003. Price Euros 59.95 + VAT, SFR 99.50, GBP 42.00, US$ 64.95. ISBN 3-540-41328-6.

This book is an outgrowth of lecture notes from the Politecnico in Milan. Contrary to what the title might suggest, ®ve out of its six chapters deal almost exclusively with structural aspects of disordered matter; this term is interpreted to include liquid and amorphous systems, and atomic clusters and quasicrystals, but not chemically or structurally disordered crystals, which have previously been extensively studied as models of disorder. ch. 1 basically rehearses the fundamentals of crystallography while ch. 2 contains a short overview of some measures of disorder. A succinct description of the glass transition is contained in ch. 3, which includes the basic thermodynamic concepts and facts. The unprepared reader may experience problems here in trying to understand what kinetic theories for the glass transition of the mode-coupling family really do predict. Time-dependent quantities such as the intermediate dynamic structure factor are introduced here without previous reference to the van-Hove real-space correlation functions. This makes it dif®cult to grasp what such functions really represent in terms of atomic motions. Compared with some of its predecessors in the ®eld, this textbook offers a somewhat more formal treatment of the structure of disordered systems (ch. 4) as well as an enjoyable chapter on atomic clusters, a sub®eld enlarged to accommodate the fullerenes and nanostructured materials. In contrast, some parts of ch. 4, dealing with experimental techniques such as vibrational spectroscopy, leave out many of the advances from the last couple of decades relating to our understanding of the spectrum of excitations of amorphous solids (or even liquids). Finally, ch. 6 on the structure and stability properties of quasicrystals contains a useful introduction to the ®eld for a newcomer. The book is primarily addressed to practitioners using X-ray scattering techniques as the basic tool. In fact, very few references are made to other radiation scattering techniques such as neutron scattering using isotopic substitution (which may offer obvious advantages over techniques such as EXAFS for the study of multicomponent systems). All in all, this new addition to the literature on disordered materials complements the existing literature, but falls short of being a standalone textbook.

Correlations in the isotropic phases of chiral liquid crystals: The role of helicity modes

The phenomenological theory of chiral liquid crystals is further developed by generalizing the model of self-consistent correlations [J. Englert, L. Longa, H. Stark, and H.-R. Trebin, Phys. Rev. Lett. 81, 1457 (1998)]. In the present approach, not only a leading helicity mode of the tensor order parameter is retained but also the remaining four modes. By considering a full fluctuating spectrum of the order parameter, the role of correlations between helicity modes in the isotropic phases is studied. Additionally, an exact form of the two-point correlation function in real space is derived and its properties are thoroughly discussed. It is shown that for chiral isotropic liquids purely chiral modes could be identified that do not exist for an ordinary liquid. Detailed results of the numerical calculations are compared with those obtained from the earlier model and these show regions where the coupling between the modes becomes important, in agreement with the available experimental data. Though the analysis up to first-order cumulant expansion does not predict a direct phase transition between the blue phase III and the isotropic phase, it is fairly easy to identify two differently correlated regions in a temperature-chirality plane. Various structural quantities, such as optical activity and specific heat, also reveal a behavior characteristic of two isotropic phases with different correlation lengths.

The DEEP2 Galaxy Redshift Survey: Clustering of Galaxies in Early Data

We measure the two-point correlation function ξ(rp, π) in a sample of 2219 galaxies between z = 0.7 and 1.35 to a magnitude limit of RAB = 24.1 from the first season of the DEEP2 Galaxy Redshift Survey. From ξ(rp, π) we recover the real-space correlation function, ξ(r), which we find can be approximated within the errors by a power law, ξ(r) = (r/r0)-γ, on scales ~0.1-10 h-1 Mpc. In a sample with an effective redshift of zeff = 0.82, for a ΛCDM cosmology we find r0 = 3.53 ± 0.81 h-1 Mpc (comoving) and γ = 1.66 ± 0.12, while in a higher redshift sample with zeff = 1.14 we find r0 = 3.12 ± 0.72 h-1 Mpc and γ = 1.66 ± 0.12. These errors are estimated from mock galaxy catalogs and are dominated by the cosmic variance present in the current data sample. We find that red, absorption-dominated, passively evolving galaxies have a larger clustering scale length, r0, than blue, emission-line, actively star-forming galaxies. Intrinsically brighter galaxies also cluster more strongly than fainter galaxies at z 1. Our results imply that the DEEP2 galaxies have an effective bias b = 0.96 ± 0.13 if σ8DM = 1 today or b = 1.19 ± 0.16 if σ8DM = 0.8 today. This bias is lower than that predicted by semianalytic simulations at z 1, which may be the result of our R-band target selection. We discuss possible evolutionary effects within our survey volume, and we compare our results with galaxy-clustering studies at other redshifts, noting that our star-forming sample at z 1 has selection criteria very similar to the Lyman break galaxies at z 3 and that our red, absorption-line sample displays a clustering strength comparable to the expected clustering of the Lyman break galaxy descendants at z 1. Our results demonstrate that galaxy-clustering properties as a function of color, spectral type, and luminosity seen in the local universe were largely in place by z 1.

Anelastic compression of nanometer-sized silica particles under high pressure: A high-energy x-ray diffraction measurement

We compressed nanometer-sized silica particles, fumed silica, using a cubic-anvil-type apparatus up to pressures of 8 GPa at room temperature. The high-energy (61.7 keV) x-ray diffraction measurements of the recovered samples were carried out to determine the x-ray structure factor and in the real space correlation functions. These results indicate that anelastic compression occurs in silica nanoparticles in the pressure range from 4 to 8 GPa, which is well below the pressure regime of the anelastic compression (\ensuremath{\sim}10 to \ensuremath{\sim}20 GPa) observed for bulk amorphous silica.

One‐Point Statistics of the Cosmic Density Field in Real and Redshift Spaces with a Multiresolutional Decomposition

In this paper, we develop a method of performing the one-point statistics of a perturbed density field with a multiresolutional decomposition based on the discrete wavelet transform (DWT). We establish the algorithm of the one-point variable and its moments in considering the effects of Poisson sampling and selection function. We also establish the mapping between the DWT one-point statistics in redshift space and real space, i.e. the algorithm for recovering the DWT one-point statistics from the redshift distortion of bulk velocity, velocity dispersion, and selection function. Numerical tests on N-body simulation samples show that this algorithm works well on scales from a few hundreds to a few Mpc/h for four popular cold dark matter models. Taking the advantage that the DWT one-point variable is dependent on both the scale and the shape (configuration) of decomposition modes, one can design estimators of the redshift distortion parameter (beta) from combinations of DWT modes. When the non-linear redshift distortion is not negligible, the beta estimator from quadrupole-to-monopole ratio is a function of scale. This estimator would not work without adding information about the scale-dependence, such as the power-spectrum index or the real-space correlation function of the random field. The DWT beta estimators, however, do not need such extra information. Numerical tests show that the proposed DWT estimators are able to determine beta robustly with less than 15% uncertainty in the redshift range 0 < z < 3.