Velocity Power Spectra Research Articles

The variance of the locally measured Hubble parameter explained with different estimators

We study the expected variance of measurements of the Hubble constant, H0, as calculated in either linear perturbation theory or using non-linear velocity power spectra derived from N-body simulations. We compare the variance with that obtained by carrying out mock observations in the N-body simulations, and show that the estimator typically used for the local Hubble constant in studies based on perturbation theory is different from the one used in studies based on N-body simulations. The latter gives larger weight to distant sources, which explains why studies based on N-body simulations tend to obtain a smaller variance than that found from studies based on the power spectrum. Although both approaches result in a variance too small to explain the discrepancy between the value of H0 from CMB measurements and the value measured in the local universe, these considerations are important in light of the percent determination of the Hubble constant in the local universe.

Kriging interpolating cosmic velocity field. II. Taking anistropies and multistreaming into account

Measuring the volume-weighted peculiar velocity statistics from inhomogeneously and sparsely distributed galaxies/halos, by existing velocity assignment methods, suffers from a significant sampling artifact. As an alternative, the Kriging interpolation based on Gaussian processes was introduced and evaluated [Y. Yu, J. Zhang, Y. Jing, and P. Zhang, Phys. Rev. D 92, 083527 (2015)]. Unfortunately, the most straightforward application of Kriging does not perform better than the existing methods in the literature. In this work, we investigate two physically motivated extensions. The first takes into account of the anisotropic velocity correlations. The second introduces the nugget effect, on account of multi-streaming of the velocity field. We find that the performance is indeed improved. For sparsely sampled data [$n_P\lesssim 6\times 10^{-3}(h^{-1} {\rm Mpc})^{-3}$] where the sampling artifact is the most severe, the improvement is significant and is two-fold: 1) The scale of reliable measurement of the velocity power spectrum is extended by a factor $\sim 1.6$, and 2) the dependence on the velocity correlation prior is weakened by a factor of $\sim 2$. We conclude that such extensions are desirable for accurate velocity assignment by Kriging.

Measuring the velocity field from type Ia supernovae in an LSST-like sky survey

In a few years, the Large Synoptic Survey Telescope will vastly increase the number of type Ia supernovae observed in the local universe. This will allow for a precise mapping of the velocity field and, since the source of peculiar velocities is variations in the density field, cosmological parameters related to the matter distribution can subsequently be extracted from the velocity power spectrum. One way to quantify this is through the angular power spectrum of radial peculiar velocities on spheres at different redshifts. We investigate how well this observable can be measured, despite the problems caused by areas with no information. To obtain a realistic distribution of supernovae, we create mock supernova catalogs by using a semi-analytical code for galaxy formation on the merger trees extracted from N-body simulations. We measure the cosmic variance in the velocity power spectrum by repeating the procedure many times for differently located observers, and vary several aspects of the analysis, such as the observer environment, to see how this affects the measurements. Our results confirm the findings from earlier studies regarding the precision with which the angular velocity power spectrum can be determined in the near future. This level of precision has been found to imply, that the angular velocity power spectrum from type Ia supernovae is competitive in its potential to measure parameters such as σ8. This makes the peculiar velocity power spectrum from type Ia supernovae a promising new observable, which deserves further attention.

Renormalization-group flow of the effective action of cosmological large-scale structures

Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically, the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input values at the UV scale. This allows for a self-contained computation of matter and velocity power spectra for which the sensitivity to UV modes is under control.

Field experiment and analysis of the wake behind a horizontal-axis wind turbine

Wind turbines work in a complex natural environment, where their flow field shows the characteristics of high turbulence levels. Due to the complexity and instability of the atmospheric boundary layer flow, as well as the influence of the scale effect, wind tunnel test cannot reflect the real working condition of wind turbine. So field experiments are very necessary to study wind turbine flow characteristics in actual wind field. In this investigation, field experiments of the wake behind a wind turbine were carried out to get velocity distribution in it. The field experiment system is composed of a 33 kW wind turbine, a 20 m high anemometer tower, a wake velocity measurement platform and the controlling device. The wind turbine is horizontal-axial, two-bladed, upwind-type, with variable pitch angles, 14.8 m in diameter. Wake velocity measurement platform is composed of an 18 m high hydraulic lift, anemometer installation platform and three sets of the US CSAT3 three-dimensional ultrasonic anemometer. Inflow parameters were gauged, such as wind speed, wind direction, atmospheric pressure, temperature and humidity. Besides, the operating conditions of the wind turbine were recorded, including pitch angle, yaw angle, rotor speed. It is discussed that the time domain and power spectrum characteristics of wake velocity at a measuring point located at one rotor diameter downwind from the rotor plane. The results show that there are larger velocity deficits in the wake. The axial velocity deficit rate at the measuring point is between 35.1% and 54.17%. The change of the velocity in vertical direction is small. The velocity in lateral direction is slightly larger than the velocity component of inflow, which reflects the expansion characteristics of the wake. Besides, the turbulent kinetic energy at the measuring point shows a periodic variation, and the vortex sheet passage frequency is similar to the rotation frequency of the wind turbine. Meanwhile, all of the power spectra of turbulent velocity in three directions at the measuring point show a characteristic of slope for –1 at the section of low frequency, which mean the turbulent flow is in the classical production subrange.

Modification of Velocity Power Spectra by Thermal Plasma Instrumentation

The upcoming Solar Probe Plus mission (Launch 2018) will launch with the newest and fastest space plasma instrumentation to date. The Solar Wind Electrons, Alphas, and Protons (SWEAP) instrument suite, which measures thermal plasma, will make measurements faster than the local gyro-frequency and proton plasma frequency. By developing an end-to-end computer model of a SWEAP instrument, this work explores the specific instrumental effects of thermal space plasma measurement, particularly in the reproduction of velocity power spectra, or Power Spectral Densities (PSDs). This model reproduces the slowest measurement cadence of the Solar Probe Cup (SPC), a Faraday cup (FC) style instrument on that will measure thermal plasma density, velocity, and temperature on SPP. By using the calibrated model to model measurement of fully determined and synthetic turbulent time series data, a consistent underestimation of the velocity power spectral indices has been quantified, with possible implications for previous missions flying similar instrumentation.

Stroboscopic two-dimensional ultrasonic velocity profiling for measuring flow transition in Taylor Couette systems

Flow characterization in a Taylor Couette system was made by investigating the radial velocity component with Ultrasonic Doppler Velocimetry based flow mapping. With the technique presented in this work, it is possible to measure the radial velocity components for variable axial position in a Couette cell within Taylor vortex flow (TVF), wavy vortex flow (WVF), modulated vortex flow (MVF) as well as spiral vortex domains in a conical shaped gap. The resulting maps for the different flow states show the location of vortices in the annular gap between the inner and outer cylinder. Cylindrical and conical concentrically rotating inner bodies were applied and respective flow patterns were analyzed. The method uses a stroboscopic triggering to synchronize flow measurements and rotational motion. The oscillation frequency f of unsteady motion in WVF, MVF, and spirals can be obtained from the power spectrum of velocity. The UVP transducer was preferably positioned in radial direction, perpendicular to the surface of the inner rotating body for measuring the radial velocity component. At the same time, the transducer was moved with constant velocity vertically along the outer cylinder height.

Cosmological forecasts for combined and next-generation peculiar velocity surveys

Peculiar velocity surveys present a very promising route to measuring the growth rate of large-scale structure and its scale dependence. However, individual peculiar velocity surveys suffer from large statistical errors due to the intrinsic scatter in the relations used to infer a galaxy's true distance. In this context we use a Fisher Matrix formalism to investigate the statistical benefits of combining multiple peculiar velocity surveys. We find that for all cases we consider there is a marked improvement on constraints on the linear growth rate $f\sigma_{8}$. For example, the constraining power of only a few peculiar velocity measurements is such that the addition of the 2MASS Tully-Fisher survey (containing only $\sim2,000$ galaxies) to the full redshift and peculiar velocity samples of the 6-degree Field Galaxy Survey (containing $\sim 110,000$ redshifts and $\sim 9,000$ velocities) can improve growth rate constraints by $\sim20\%$. Furthermore, the combination of the future TAIPAN and WALLABY+WNSHS surveys has the potential to reach a $\sim3\%$ error on $f\sigma_{8}$, which will place tight limits on possible extensions to General Relativity. We then turn to look at potential systematics in growth rate measurements that can arise due to incorrect calibration of the peculiar velocity zero-point and from scale-dependent spatial and velocity bias. For next generation surveys, we find that neglecting velocity bias in particular has the potential to bias constraints on the growth rate by over $5\sigma$, but that an offset in the zero-point has negligible impact on the velocity power spectrum.

Wave breaking in the surf zone and deep-water in a non-hydrostatic RANS model. Part 1: Organized wave motions

We examine wave-breaking predictions ranging from shallow- to deep-water conditions using a non-hydrostatic σ-coordinate RANS model NHWAVE as described in Derakhti et al. (2016a), comparing results both with corresponding experiments and with the results of a volume-of-fluid (VOF)/Navier-Stokes solver (Ma et al., 2011; Derakhti and Kirby, 2014a,b). Our study includes regular and irregular depth-limited breaking waves on planar and barred beaches as well as steepness-limited unsteady breaking focused wave packets in intermediate and deep water. In Part 1 of this paper, it is shown that the model resolves organized wave motions in terms of free-surface evolution, spectral evolution, organized wave velocity evolution and wave statistics, using a few vertical σ-levels. In addition, the relative contribution of modeled physical dissipation and numerical dissipation to the integral breaking-induced wave energy loss is discussed. In steepness-limited unsteady breaking focused wave packets, the turbulence model has not been triggered, and all the dissipation is imposed indirectly by the numerical scheme. Although the total wave-breaking-induced energy dissipation is underestimated in the unsteady wave packets, the model is capable of predicting the dispersive and nonlinear properties of different wave packet components before and after the break point, as well as the overall wave height decay and the evolution of organized wave velocity field and power spectrum density over the breaking region. In Part 2 (Derakhti et al., 2016b), model reproduction of wave-breaking-induced turbulence and mean circulation is examined in detail. The same equations and numerical methods are used for the various depth regimes, and no ad-hoc treatment, such as imposing hydrostatic conditions, is involved in triggering breaking. Vertical grid resolution in all simulated cases is at least an order of magnitude coarser than that of typical VOF-based simulations.

A GLOBAL VIEW OF VELOCITY FLUCTUATIONS IN THE CORONA BELOW 1.3 R⊙ WITH CoMP

ABSTRACT The Coronal Multi-channel Polarimeter (CoMP) has previously demonstrated the presence of Doppler velocity fluctuations in the solar corona. The observed fluctuations are thought to be transverse waves, i.e., highly incompressible motions whose restoring force is dominated by the magnetic tension, some of which demonstrate clear periodicity. We aim to exploit CoMP’s ability to provide high cadence observations of the off-limb corona to investigate the properties of velocity fluctuations in a range of coronal features, providing insight into how (whether) the properties of the waves are influenced by the varying magnetic topology in active regions, quiet Sun and open field regions. An analysis of Doppler velocity time-series of the solar corona from the 10747 Å Iron xiii line is performed, determining the velocity power spectrum and using it as a tool to probe wave behavior. Further, the average phase speed and density for each region are estimated and used to compute the spectra for energy density and energy flux. In addition, we assess the noise levels associated with the CoMP data, deriving analytic formulae for the uncertainty on Doppler velocity measurements and providing a comparison by estimating the noise from the data. It is found that the entire corona is replete with transverse wave behavior. The corresponding power spectra indicate that the observed velocity fluctuations are predominately generated by stochastic processes, with the spectral slope of the power varying between the different magnetic regions. Most strikingly, all power spectra reveal the presence of enhanced power occurring at ∼3 mHz, potentially implying that the excitation of coronal transverse waves by p-modes is a global phenomenon.

Turbulence in the ionized gas of the Orion nebula

In order to study the nature, origin, and impact of turbulent velocity fluctuations in the ionized gas of the Orion Nebula, we apply a variety of statistical techniques to observed velocity cubes. The cubes are derived from high resolving power ($R \approx 40,000$) longslit spectroscopy of optical emission lines that span a range of ionizations. From Velocity Channel Analysis (VCA), we find that the slope of the velocity power spectrum is consistent with predictions of Kolmogorov theory between scales of 8 and 22 arcsec (0.02 to 0.05 pc). The outer scale, which is the dominant scale of density fluctuations in the nebula, approximately coincides with the autocorrelation length of the velocity fluctuations that we determine from the second order velocity structure function. We propose that this is the principal driving scale of the turbulence, which originates in the autocorrelation length of dense cores in the Orion molecular filament. By combining analysis of the non-thermal line widths with the systematic trends of velocity centroid versus ionization, we find that the global champagne flow and smaller scale turbulence each contribute in equal measure to the total velocity dispersion, with respective root-mean-square widths of 4-5 km/s. The turbulence is subsonic and can account for only one half of the derived variance in ionized density, with the remaining variance provided by density gradients in photoevaporation flows from globules and filaments. Intercomparison with results from simulations implies that the ionized gas is confined to a thick shell and does not fill the interior of the nebula.

Dynamical Variable of Bi<sub>50</sub>Zn<sub>50</sub> Bulk Metallic Glass at Various Temperature

The theoretical study of dynamical variables: velocity autocorrelation function (VACF), power spectrum (PS) and mean square displacement (MSD) of Bi50Zn50 bulk metallic glass at T= 793K, 873K, 1023K and 1123K have been calculated based on the static harmonic well approximation. The effective interatomic potential for bulk metallic glass is computed using our established model potential with the exchange correlation functions due to Farid et al. It is observed that negative dip in velocity auto correlation function decreases as the temperature increases. In the power spectrum as temperature increases, the peak of power spectrum shifts toward lower ω. The obtained result of MSD concludes that the vibrating component in the atomic motion is decreases as increases the temperatures.

Goodness-of-fit analysis of the Cosmicflows-2 data base of velocities

The goodness-of-fit (GoF) of the Cosmicflows-2 (CF2) database of peculiar velocities with the LCDM standard model of cosmology is presented. Standard application of the Chi^2 statistics of the full database, of its 4,838 data points, is hampered by the small scale nonlinear dynamics which is not accounted for by the (linear regime) velocity power spectrum. The bulk velocity constitutes a highly compressed representation of the data which filters out the small scales non-linear modes. Hence the statistics of the bulk flow provides an efficient tool for assessing the GoF of the data given a model. The particular approach introduced here is to use the (spherical top-hat window) bulk velocity extracted from the Wiener filter reconstruction of the 3D velocity field as a linear low pass filtered highly compressed representation of the CF2 data. An ensemble 2250 random linear realizations of the WMAP/LCDM model has been used to calculate the bulk velocity auto-covariance matrix. We find that the CF2 data is consistent with the WMAP/LCDM model to better than the 2 sigma confidence limits. This provides a further validation that the CF2 database is consistent with the standard model of cosmology.

Understanding redshift space distortions in density-weighted peculiar velocity

Observations of the kinetic Sunyaev-Zel'dovich (kSZ) effect measure the density-weighted velocity field, a potentially powerful cosmological probe. This paper presents an analytical method to predict the power spectrum and two-point correlation function of the density-weighted velocity in redshift space, the direct observables in kSZ surveys. We show a simple relation between the density power spectrum and the density-weighted velocity power spectrum that holds for both dark matter and halos. Using this relation, we can then extend familiar perturbation expansion techniques to the kSZ power spectrum. One of the most important features of density-weighted velocity statistics in redshift space is the change in sign of the cross-correlation between the density and density-weighted velocity at mildly small scales due to nonlinear redshift space distortions. Our model can explain this characteristic feature without any free parameters. As a result, our results can precisely predict the non-linear behavior of the density-weighted velocity field in redshift space up to ∼ 30 h−1 Mpc for dark matter particles at the redshifts of z=0.0, 0.5, and 1.0.

The effects of bar–spiral coupling on stellar kinematics in the Galaxy

We investigate models of the Milky Way disc taking into account simultaneously the bar and a two-armed quasi-static spiral pattern. Away from major resonance overlaps, the mean stellar radial motions in the plane are essentially a linear superposition of the isolated effects of the bar and spirals. Thus, provided the bar is strong enough, even in the presence of spiral arms, these mean radial motions are predominantly affected by the Galactic bar for large scale velocity fluctuations. This is evident when comparing the peculiar line-of-sight velocity power spectrum of our coupled models with bar-only models. However, we show how forthcoming spectroscopic surveys could disentangle bar-only non-axisymmetric models of the Galaxy from models in which spiral arms have a significant amplitude. We also point out that overlaps of low-order resonances are sufficient to enhance stellar churning within the disc, even when the spirals amplitude is kept constant. Nevertheless, for churning to be truly non-local, stronger or (more likely) transient amplitudes would be needed: otherwise the disc is actually mostly unaffected by churning in the present models. Finally, regarding vertical breathing modes, the combined effect of the bar and spirals on vertical motions is a clear non-linear superposition of the isolated effects of both components, significantly superseding the linear superposition of modes produced by each perturber separately, thereby providing an additional effect to consider when analysing the observed breathing mode of the Galactic disc in the extended Solar neighbourhood.

Systematic renormalization of the effective theory of Large Scale Structure

A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast δ and momentum density π(k) scale as k2 and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of δ is indeed valid to all orders.

Fast and accurate mock catalogue generation for low-mass galaxies

We present an accurate and fast framework for generating mock catalogues including low-mass halos, based on an implementation of the COmoving Lagrangian Acceleration (COLA) technique. Multiple realisations of mock catalogues are crucial for analyses of large-scale structure, but conventional N-body simulations are too computationally expensive for the production of thousands of realisations. We show that COLA simulations can produce accurate mock catalogues with a moderate computation resource for low- to intermediate- mass galaxies in $10^{12} M_\odot$ haloes, both in real and redshift space. COLA simulations have accurate peculiar velocities, without systematic errors in the velocity power spectra for k < 0.15 h/Mpc, and with only 3-per-cent error for k < 0.2 h/Mpc. We use COLA with 10 time steps and a Halo Occupation Distribution to produce 600 mock galaxy catalogues of the WiggleZ Dark Energy Survey. Our parallelized code for efficient generation of accurate halo catalogues is publicly available at github.com/junkoda/cola_halo.

Cosmological non-linear density and velocity power spectra including non-linear vector and tensor modes

We present the leading order non-linear density and velocity power spectra in the complete form; previous studies have omitted the vector- and tensor-type perturbations simultaneously excited by the scalar-type perturbation in nonlinear order. These additional contributions are comparable to the scalar-type purely relativistic perturbations, and thus negligible in the current paradigm of concordance cosmology: i.e., concerning density and velocity perturbations of the pressureless matter in perturbation regime well inside of matter-dominated epoch, we show that pure Einstein's gravity contributions appearing from the third order are entirely negligible (five orders of magnitude smaller than the Newtonian contributions) in all scales. We thus prove that Newtonian perturbation theory is quite reliable in calculating the amplitude of matter fluctuations even in the precision era of cosmology. Therefore, besides the ones imprinted as the initial condition generated in the earlier phase, the other relativistic effect relevant for interpreting observational data must be the projection effect that occurs when mapping galaxies on to the observed coordinate.

Laser Heating of 2-D Dusty Plasmas Using a Random Arc Pattern

A laser heating method for 2-D dusty plasmas is improved so that particle motion better resembles thermal motion in a liquid. Laser beams are rastered in a pattern of arcs with three randomly varying parameters: curvature, initial angle, and the speed of the laser footprint as it follows an arc. An experimental test is performed using particle tracking to generate power spectra of velocities. Peaks in these spectra indicate coherence in the particle motion, which is a discrepancy when compared with the stochastic nature of molecular motion in a liquid. We find that spectral peaks are diminished tenfold by rastering with random arcs as compared with a previously used pattern in which beams moved in straight lines at constant speeds.

Searching for modified gravity: scale and redshift dependent constraints from galaxy peculiar velocities

We present measurements of both scale- and time-dependent deviations from the standard gravitational field equations. These late-time modifications are introduced separately for relativistic and non-relativistic particles, by way of the parameters $G_{\rm matter}(k,z)$ and $G_{\rm light}(k,z)$ using two bins in both scale and time, with transition wavenumber $0.01$ Mpc$^{-1}$ and redshift 1. We emphasize the use of two dynamical probes to constrain this set of parameters, galaxy power spectrum multipoles and the direct peculiar velocity power spectrum, which probe fluctuations on different scales. The multipole measurements are derived from the WiggleZ and BOSS Data Release 11 CMASS galaxy redshift surveys and the velocity power spectrum is measured from the velocity sub-sample of the 6-degree Field Galaxy Survey. We combine with additional cosmological probes including baryon acoustic oscillations, Type Ia SNe, the cosmic microwave background (CMB), lensing of the CMB, and the temperature--galaxy cross-correlation. Using a Markov Chain Monte Carlo likelihood analysis, we find the inferred best-fit parameter values of $G_{\rm matter}(k,z)$ and $G_{\rm light}(k,z)$ to be consistent with the standard model at the $95\%$ confidence level. Furthermore, accounting for the Alcock-Paczynski effect, we perform joint fits for the expansion history and growth index gamma; we measure $\gamma = 0.665 \pm 0.0669$ ($68\%$ C.L) for a fixed expansion history, and $\gamma = 0.73^{+0.08}_{-0.10}$ ($68\%$ C.L) when the expansion history is allowed to deviate from $\Lambda$CDM. With a fixed expansion history the inferred value is consistent with GR at the $95\%$ C.L; alternatively, a $2\sigma$ tension is observed when the expansion history is not fixed, this tension is worsened by the combination of growth and SNe data.