Dynamics of pairwise motions

We derive a simple closed-form expression, relating \vs(r) -- the mean relative velocity of pairs of galaxies at fixed separation $r$ -- to the two-point correlation function of mass density fluctuations, $\xi(r)$. We compare our analytic model for \vs(r) with N-body simulations, and find excellent agreement in the entire dynamical range probed by the simulations (0.1 \lsim \xi \lsim 1000). Our results can be used to estimate the cosmological density parameter, \Om, directly from redshift-distance surveys, like Mark III.Comment: 10 pages 2 Figs., submitted to ApJ Let

Omega from the skewness of the cosmic velocity divergence

We propose a method for measuring the cosmological density parameter $\Omega$ from the statistics of the divergence field, $\theta \equiv H^{-1} \div v$, the divergence of peculiar velocity, expressed in units of the Hubble constant, $H \equiv 100 h km/s/Mpc$. The velocity field is spatially smoothed over $\sim 10 h^{-1} Mpc$ to remove strongly nonlinear effects. Assuming weakly-nonlinear gravitational evolution from Gaussian initial fluctuations, and using second-order perturbative analysis, we show that \propto -\Omega^{-0.6} ^2. The constant of proportionality depends on the smoothing window. For a top-hat of radius R and volume-weighted smoothing, this constant is $26/7-\gamma$, where $\gamma=-d\log / d\log R$. If the power spectrum is a power law, $P(k)\propto k^n$, then $\gamma=3+n$. A Gaussian window yields similar results. The resulting method for measuring $\Omega$ is independent of any assumed biasing relation between galaxies and mass. The method has been successfully tested with numerical simulations. A preliminary application to real data, provided by the POTENT recovery procedure from observed velocities favors $\Omega \sim 1$. However, because of an uncertain sampling error, this result should be treated as an assessment of the feasibility of our method rather than a definitive measurement of $\Omega$.Comment: 16 pages + 2 figures, uuencoded postscript file, also available by anonymous ftp from ftp.cita.utoronto.ca in directory /cita/francis/div_skewness, CITA 94-1

Streaming velocities as a dynamical estimator of Omega

It is well known that estimating the pairwise velocity of galaxies, v_{12}, from the redshift space galaxy correlation function is difficult because this method is highly sensitive to the assumed model of the pairwise velocity dispersion. Here we propose an alternative method to estimate v_{12} directly from peculiar velocity samples, which contain redshift-independent distances as well as galaxy redshifts. In contrast to other dynamical measures which determine beta = sigma_8 x Omega^{0.6}, our method can provide an estimate of (sigma_8)^2 x Omega^{0.6} for a range of sigma_8 (here Omega is the cosmological mass density parameter while sigma_8 is the standard normalization parameter for the spectrum of matter density fluctuations). We demonstrate how to measure this quantity from realistic catalogues.Comment: 8 pages of text, 4 figures Subject headings: Cosmology: theory - observation - peculiar velocities: large scale flows Last name of one of the authors was misspelled. It is now corrected. Otherwise the manuscript is identical to its original versio

Measuring Omega with Galaxy Streaming Velocities

The mean pairwise velocity of galaxies has traditionally been estimated from the redshift space galaxy correlation function. This method is notorious for being highly sensitive to the assumed model of the pairwise velocity dispersion. Here we propose an alternative method to estimate the streaming velocity directly from peculiar velocity samples, which contain redshift-independent distances as well as galaxy redshifts. This method can provide an estimate of $\Omega^{0.6}\sigma_8^2$ for a range of $\sigma_8$ where $\Omega$ is the cosmological density parameter, while $\sigma_8$ is the standard normalization for the power spectrum of density fluctuations. We demonstrate how to measure this quantity from realistic catalogues and identify the main sources of bias and errorsComment: Proceedings of New Worlds in Astroparticle Physics, 6 pages, 2 figure

Evidence for a low-density Universe from the relative velocities of galaxies

The motions of galaxies can be used to constrain the cosmological density parameter Omega and the clustering amplitude of matter on large scales. The mean relative velocity of galaxy pairs, estimated from the Mark III survey, indicates that Omega = 0.35 +0.35/-0.25. If the clustering of galaxies is unbiased on large scales, Omega = 0.35 +/- 0.15, so that an unbiased Einstein-de Sitter model (Omega = 1) is inconsistent with the data.Comment: 12 pages, 2 figures, to appear in the Jan.7 issue of ``Science''; In the original version, the title appeared twice. This problem has now been corrected. No other changes were mad

Stochastic Biasing and Weakly Non-linear Evolution of Power Spectrum

Distribution of galaxies may be a biased tracer of the dark matter distribution and the relation between the galaxies and the total mass may be stochastic, non-linear and time-dependent. Since many observations of galaxy clustering will be done at high redshift, the time evolution of non-linear stochastic biasing would play a crucial role for the data analysis of the future sky surveys. In this paper, we develop the weakly non-linear analysis and attempt to clarify the non-linear feature of the stochastic biasing. We compute the one-loop correction of the power spectrum for the total mass, the galaxies and their cross correlation. Assuming the local functional form for the initial galaxy distribution, we investigate the time evolution of the biasing parameter and the correlation coefficient. On large scales, we first find that the time evolution of the biasing parameter could deviate from the linear prediction in presence of the initial skewness. However, the deviation can be reduced when the initial stochasticity exists. Next, we focus on the quasi-linear scales, where the non-linear growth of the total mass becomes important. It is recognized that the scale-dependence of the biasing dynamically appears and the initial stochasticity could affect the time evolution of the scale-dependence. The result is compared with the recent N-body simulation that the scale-dependence of the halo biasing can appear on relatively large scales and the biasing parameter takes the lower value on smaller scales. Qualitatively, our weakly non-linear results can explain this trend if the halo-mass biasing relation has the large scatter at high redshift.Comment: 29pages, 7 postscript figures, submitted to Ap

The influence of physical exercise on alterations in concentrations of neuropeptide Y, leptin and other selected hormonal and metabolic parameters in sportspeople

The aim of this study was to evaluate the behaviour and relationships between hormones, and metabolic blood parameters essential for energetic balance control during rest, exercise and restitution. Two groups of young boys (17 cyclists and 11 canoeists) were tested twice. Tests were performed on a cycloergometer. During the first study, anaerobic threshold was determined by a non-invasive method and in the second one - cyclists performed prolonged 2-hour exercise below anaerobic threshold and canoeists - 20-min effort above anaerobic threshold. Neuropeptide Y (NPY), leptin, insulin, C-peptide, metabolic clearance of insulin, growth hormone (GH), somatomedin C (IGF1) and glycaemia were analysed. Values of NPY and GH measured directly after exercise were significantly higher than the values of these parameters at rest, in both groups. However, effort did not cause significant changes in leptin concentration and insulin clearance in both groups. Besides, it was shown that 20-min exercise had no influence on insulin concentration in canoeists blood. In these studies significantly lower IGF1 value during restitution than directly after exercise was also noted in the cyclists group. Relations between measured hormonal parameters indicate that some mechanisms, which supply the organism with necessary energetic substrates during the effort, and accelerate the restitution are activated

Skewness as a probe of non-Gaussian initial conditions

We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate analytically the ratio between the skewness due to non-linear clustering and the part due to the intrinsic non-Gaussianity of the models. We finally extend our estimates to higher moments.Comment: 5 pages, 2 ps-figs., accepted for publication in PRD, rapid com

Galaxy clustering constraints on deviations from Newtonian gravity at cosmological scales II: Perturbative and numerical analyses of power spectrum and bispectrum

We explore observational constraints on possible deviations from Newtonian gravity by means of large-scale clustering of galaxies. We measure the power spectrum and the bispectrum of Sloan Digital Sky Survey galaxies and compare the result with predictions in an empirical model of modified gravity. Our model assumes an additional Yukawa-like term with two parameters that characterize the amplitude and the length scale of the modified gravity. The model predictions are calculated using two methods; the second-order perturbation theory and direct N-body simulations. These methods allow us to study non-linear evolution of large-scale structure. Using the simulation results, we find that perturbation theory provides reliable estimates for the power spectrum and the bispectrum in the modified Newtonian model. We also construct mock galaxy catalogues from the simulations, and derive constraints on the amplitude and the length scale of deviations from Newtonian gravity. The resulting constraints from power spectrum are consistent with those obtained in our earlier work, indicating the validity of the previous empirical modeling of gravitational nonlinearity in the modified Newtonian model. If linear biasing is adopted, the bispectrum of the SDSS galaxies yields constraints very similar to those from the power spectrum. If we allow for the nonlinear biasing instead, we find that the ratio of the quadratic to linear biasing coefficients, b_2/b_1, should satisfy -0.4 < b_2/b_1<0.3 in the modified Newtonian model.Comment: 12 pages, 7 figure