The finite size effect of galaxies on the cosmic virial theorem and the pairwise peculiar velocity dispersions

We discuss the effect of the finite size of galaxies on estimating small-scale relative pairwise peculiar velocity dispersions from the cosmic virial theorem (CVT). Specifically we evaluate the effect by incorporating the finite core radius $r_c$ in the two-point correlation function of mass, i.e. $\xi_\rho(r) \propto (r+r_c)^{-\gamma}$ and the effective gravitational force softening $r_s$ on small scales. We analytically obtain the lowest-order correction term for $\gamma <2$ which is in quantitative agreement with the full numerical evaluation. With a nonzero $r_s$ and/or $r_c$ the cosmic virial theorem is no longer limited to the case of $\gamma<2$. We present accurate fitting formulae for the CVT predicted pairwise velocity dispersion for the case of $\gamma>2$. Compared with the idealistic point-mass approximation ($r_s=r_c=0$), the finite size effect can significantly reduce the small-scale velocity dispersions of galaxies at scales much larger than $r_s$ and $r_c$. Even without considering the finite size of galaxies, nonzero values for $r_c$ are generally expected, for instance, for cold dark matter (CDM) models with a scale-invariant primordial spectrum. For these CDM models, a reasonable force softening r_s\le 100 \hikpc would have rather tiny effect. We present the CVT predictions for the small-scale pairwise velocity dispersion in the CDM models normalized by the COBE observation. The implication of our results for confrontation of observations of galaxy pair-wise velocity dispersions and theoretical predictions of the CVT is also discussed.Comment: 18 pages. LaTeX text and 8 postcript figures. submitted to Ap

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

The Gravitational Lensing in Redshift-space Correlation Functions of Galaxies and Quasars

The gravitational lensing, as well as the velocity field and the cosmological light-cone warp, changes the observed correlation function of high-redshift objects. We present an analytical expression of 3D correlation function, simultaneously including those three effects. When two objects are separated over several hundreds Mpc along a line of sight, the observed correlation function is dominated by the effect of gravitational lensing rather than the intrinsic clustering. For a canonical lambda-CDM model, the lensing signals in the galaxy-galaxy and galaxy-QSO correlations are beyond noise levels in large-scale redshift surveys like the Sloan Digital Sky Survey.Comment: 10 pages, 1 figure, submitted to ApJ

An Inversion Method for Measuring Beta in Large Redshift Surveys

A precision method for determining the value of Beta= Omega_m^{0.6}/b, where b is the galaxy bias parameter, is presented. In contrast to other existing techniques that focus on estimating this quantity by measuring distortions in the redshift space galaxy-galaxy correlation function or power spectrum, this method removes the distortions by reconstructing the real space density field and determining the value of Beta that results in a symmetric signal. To remove the distortions, the method modifies the amplitudes of a Fourier plane-wave expansion of the survey data parameterized by Beta. This technique is not dependent on the small-angle/plane-parallel approximation and can make full use of large redshift survey data. It has been tested using simulations with four different cosmologies and returns the value of Beta to +/- 0.031, over a factor of two improvement over existing techniques.Comment: 16 pages including 6 figures Submitted to The Astrophysical Journa

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]

The Correlation Function in Redshift Space: General Formula with Wide-angle Effects and Cosmological Distortions

A general formula for the correlation function in redshift space is derived in linear theory. The formula simultaneously includes wide-angle effects and cosmological distortions. The formula is applicable to any pair with arbitrary angle $\theta$ between lines of sight, and arbitrary redshifts, $z_1$, $z_2$, which are not necessarily small. The effects of the spatial curvature both on geometry and on fluctuation spectrum are properly taken into account, and thus our formula holds in a Friedman-Lema\^{\i}tre universe with arbitrary cosmological parameters $\Omega_0$ and $\lambda_0$. We illustrate the pattern of the resulting correlation function with several models, and also show that validity region of the conventional distant observer approximation is $\theta \le 10^\circ$.Comment: 45 pages including 9 figures, To Appear in Astrophys. J. 535 (2000

Exploring Large-scale Structure with Billions of Galaxies

We consider cosmological applications of galaxy number density correlations to be inferred from future deep and wide multi-band optical surveys. We mostly focus on very large scales as a probe of possible features in the primordial power spectrum. We find the proposed survey of the Large Synoptic Survey Telescope may be competitive with future all-sky CMB experiments over a broad range of scales. On very large scales the inferred power spectrum is robust to photometric redshift errors, and, given a sufficient number density of galaxies, to angular variations in dust extinction and photometric calibration errors. We also consider other applications, such as constraining dark energy with the two CMB-calibrated standard rulers in the matter power spectrum, and controlling the effect of photometric redshift errors to facilitate the interpretation of cosmic shear data. We find that deep photometric surveys over wide area can provide constraints that are competitive with spectroscopic surveys in small volumes.Comment: 11 pages, 7 figures, ApJ accepted, references added, expanded discussion in Sec. 3.

Kinetic and Thermodynamic Bases to Resolve Issues Regarding Conditioning of Uranium Metal Fuels

Numerous uranium - bearing fuels are corroding in fuel storage pools in several countries. At facilities where reprocessing is no longer available, dry storage is being evaluated to preclude aqueous corrosion that is ongoing. It is essential that thermodynamic and kinetic factors are accounted for in transitions of corroding uranium-bearing fuels to dry storage. This paper addresses a process that has been proposed to move Hanford N-Reactor fuel from wet storage to dry storage

Estimating Combined Effects of Climate Change and Land Cover Change on Water Regulation Services of Urban Wetlands in Valdivia, Chile

The relationship between cities and wetland cover varies across the globe, with some cities converting wetlands to low‐ and high‐density urban cover and others preserving, conserving, or restoring wetlands, or constructing new ones. However, the scientific literature lacks studies relating changes in systemic flood risk in an urban stormwater management systems to changes in wetland cover. Furthermore, whether and how such relationships are affected by changing storm intensity under climate change is unknown. We present a case study on the effects of changes in urban wetland extent and storm intensity on flooding in an urban drainage system in Valdivia, Chile, under several co‐produced future scenarios and historical trends of development. We used data derived from stakeholder workshops and historical landcover to determine four plausible scenarios of urban development, plus one business‐as‐usual scenario, in Valdivia through the year 2080. Additionally, we used historical precipitation data and downscaled climate data to estimate event rainfall from extreme storms in the year 2080. We found that system flood volume and time the system was flooded increased with increasing wetland loss and rainfall volume. Mean rate and hour of peak discharge were unaffected by wetland loss. Infiltration\u27s relative role in reducing flooding diminished as wetland loss increased. Cities may still experience dangerous and/or unacceptable flooding even with extensive wetland coverage and will likely need to pair conservation with additional improvements in their stormwater management systems and contributing watersheds