Rms Density Research Articles

Approximating Density Probability Distribution Functions Across Cosmologies

Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is well-described by a function of two parameters: n s , the spectral slope, and σ L , the linear rms density fluctuation. For redshift-space density and the geometric mean of real- and redshift-space densities, we introduce a third parameter, . We find that density PDFs for the LCDM cosmology is also well-parameterized by these three parameters. As a result, we are able to use a suite of self-similar cosmological simulations to approximate density PDFs for a range of cosmologies. We make the density PDFs publicly available and provide an analytical fitting formula for them.

Growth of structures and redshift-space distortion data in scale-dependent gravity

This study is devoted to the implications of scale-dependent gravity in Cosmology. Redshift-space distortion data indicate that there is a tension between $\Lambda$CDM and available observations as far as the value of the rms density fluctuation, $\sigma_8$, is concerned. It has been pointed out that this tension may be alleviated in alternative theories in which gravity is weaker at red-shift $z \sim 1$. We study the evolution of density perturbations for non-relativistic matter on top of a spatially flat FLRW Universe, and we compute the combination $A=f \sigma_8$ in the framework of scale-dependent gravity, where both Newton's constant and the cosmological constant are allowed to vary with time. Upon comparison between available observational data (supernovae data as well as redshift-space distortion data) and theoretical predictions of the model, we determine the numerical value of $\sigma_8$ that best fits the data.

Turbulence in the intracluster medium: simulations, observables, and thermodynamics

We conduct two kinds of homogeneous isotropic turbulence simulations relevant for the intracluster medium (ICM): (i) pure turbulence runs without radiative cooling; (ii) turbulent heating$+$radiative cooling runs with global thermal balance. For pure turbulence runs in the subsonic regime, the rms density and surface brightness (SB) fluctuations vary as the square of the rms Mach number ($\mathcal{M}_{\text{rms}}$). However, with thermal balance, the density and SB fluctuations $(\delta SB/SB)$ are much larger. These scalings have implications for translating SB fluctuations into a turbulent velocity, particularly for cool cores. For thermal balance runs with large (cluster core) scale driving, both the hot and cold phases of the gas are supersonic. For small scale (one order of magnitude smaller than the cluster core) driving, multiphase gas forms on a much longer timescale but $\mathcal{M}_{\text{rms}}$ is smaller. Both small and large scale driving runs have velocities larger than the Hitomi results from the Perseus cluster. Thus turbulent heating as the dominant heating source in cool cluster cores is ruled out if multiphase gas is assumed to condense out from the ICM. Next we perform thermal balance runs in which we partition the input energy into thermal and turbulent parts and tune their relative magnitudes. The contribution of turbulent heating has to be $\lesssim 10\%$ in order for turbulence velocities to match Hitomi observations. If the dominant source of multiphase gas is not cooling from the ICM (but say uplift from the central galaxy), the importance of turbulent heating cannot be excluded.

Density distribution of the cosmological matter field

The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering, massive production of mock galaxy catalogs, and testing predictions of cosmological models. Here we make a comprehensive analysis of the dark matter PDF using a suite of 7000 N-body simulations that covers a wide range of numerical and cosmological parameters. We find that the PDF has a simple shape: it declines with density as a power-law P~rho**(-2), which is exponentially suppressed on both small and large densities. The proposed double-exponential approximation provides an accurate fit to all our N-body results for small filtering scales R< 5Mpc/h with rms density fluctuations sigma>1. In combination with the spherical infall model that works well for small fluctuations sigma<1, the PDF is now approximated with just few percent errors over the range of twelve orders of magnitude -- a remarkable example of precision cosmology. We find that at 5-10% level the PDF explicitly depends on redshift (at fixed sigma) and on cosmological density parameter Omega_m. We test different existing analytical approximations and find that the often used log-normal approximation is always 3-5 times less accurate than either the double-exponential approximation or the spherical infall model.

MassiveNuS: cosmological massive neutrino simulations

The non-zero mass of neutrinos suppresses the growth of cosmic structure on small scales. Since the level of suppression depends on the sum of the masses of the three active neutrino species, the evolution of large-scale structure is a promising tool to constrain the total mass of neutrinos and possibly shed light on the mass hierarchy. In this work, we investigate these effects via a large suite of N-body simulations that include massive neutrinos using an analytic linear-response approximation: the Cosmological Massive Neutrino Simulations (MassiveNuS). The simulations include the effects of radiation on the background expansion, as well as the clustering of neutrinos in response to the nonlinear dark matter evolution. We allow three cosmological parameters to vary: the neutrino mass sum Mν in the range of 0–0.6 eV, the total matter density Ωm, and the primordial power spectrum amplitude As. The rms density fluctuation in spheres of 8 comoving Mpc/h (σ8) is a derived parameter as a result. Our data products include N-body snapshots, halo catalogues, merger trees, ray-traced galaxy lensing convergence maps for four source redshift planes between zs=1–2.5, and ray-traced cosmic microwave background lensing convergence maps. We describe the simulation procedures and code validation in this paper. The data are publicly available at http://columbialensing.org.

Intrinsic suppression of turbulence in linear plasma devices

Plasma turbulence is the dominant transport mechanism for heat and particles in magnetised plasmas in linear devices and tokamaks, so the study of turbulence is important in limiting and controlling this transport. Linear devices provide an axial magnetic field that serves to confine a plasma in cylindrical geometry as it travels along the magnetic field from the source to the strike point. Due to perpendicular transport, the plasma density and temperature have a roughly Gaussian radial profile with gradients that drive instabilities, such as resistive drift-waves and Kelvin–Helmholtz. If unstable, these instabilities cause perturbations to grow resulting in saturated turbulence, increasing the cross-field transport of heat and particles. When the plasma emerges from the source, there is a time, , that describes the lifetime of the plasma based on parallel velocity and length of the device. As the plasma moves down the device, it also moves azimuthally according to E × B and diamagnetic velocities. There is a balance point in these parallel and perpendicular times that sets the stabilisation threshold. We simulate plasmas with a variety of parallel lengths and magnetic fields to vary the parallel and perpendicular lifetimes, respectively, and find that there is a clear correlation between the saturated RMS density perturbation level and the balance between these lifetimes. The threshold of marginal stability is seen to exist where . This is also associated with the product , where is the drift-wave linear growth rate, indicating that the instability must exist for roughly 100 times the growth time for the instability to enter the nonlinear growth phase. We explore the root of this correlation and the implications for linear device design.

SUPERNOVA DRIVING. II. COMPRESSIVE RATIO IN MOLECULAR-CLOUD TURBULENCE

ABSTRACT The compressibility of molecular cloud (MC) turbulence plays a crucial role in star formation models, because it controls the amplitude and distribution of density fluctuations. The relation between the compressive ratio (the ratio of powers in compressive and solenoidal motions) and the statistics of turbulence has been previously studied systematically only in idealized simulations with random external forces. In this work, we analyze a simulation of large-scale turbulence (250 pc) driven by supernova (SN) explosions that has been shown to yield realistic MC properties. We demonstrate that SN driving results in MC turbulence with a broad lognormal distribution of the compressive ratio, with a mean value ≈0.3, lower than the equilibrium value of ≈0.5 found in the inertial range of isothermal simulations with random solenoidal driving. We also find that the compressibility of the turbulence is not noticeably affected by gravity, nor are the mean cloud radial (expansion or contraction) and solid-body rotation velocities. Furthermore, the clouds follow a general relation between the rms density and the rms Mach number similar to that of supersonic isothermal turbulence, though with a large scatter, and their average gas density probability density function is described well by a lognormal distribution, with the addition of a high-density power-law tail when self-gravity is included.

Measurements of ICRF wave-induced density fluctuations in LHD by a microwave reflectometer

An O-mode microwave reflectometer has been developed to measure ICRF wave induced electron density fluctuations in LHD plasmas. The system has two probing frequencies (28.8 and 30.1 GHz) to measure two spatial points simultaneously. The rms density fluctuation levels are typically 0.01%. The linearity between the measured density fluctuation amplitude and the square root of the RF power is discussed. The decay length of the RF field was estimated to be 1 to 7 m under the operational condition investigated. A typical spatial distance between the two measurement points corresponding to the two probing frequencies is a few centimeters, and the fluctuation amplitudes at the two points are similar in amplitude. The phase difference between the two fluctuations show in-phase relationship on average. Out-of phase relationships, which implies a standing wave structure, are often observed when the wave absorption is expected to be poor.

Free-stream density perturbations in a reflected-shock tunnel

Focused laser differential interferometry is used to quantify the free-stream density perturbations in the T5 reflected-shock tunnel. The investigation of reflected-shock tunnel disturbances is motivated by the study of hypervelocity boundary-layer instability and transition. Past work on hypersonic wind-tunnel noise is briefly reviewed. New results are reported for hypervelocity air flows at reservoir enthalpies between 5 and 18 MJ/kg at Mach ≈ 5.5. Statistical analysis finds no correlation of RMS density perturbations with tunnel run parameters (reservoir pressure, reservoir mass-specific enthalpy, free-stream unit Reynolds number, free-stream Mach number, and shot number). Spectrograms show that the free-stream disturbance level is constant throughout the test time. Power spectral density estimates of each of the experiments are found to collapse upon each other when the streamwise disturbance convection velocity is used to eliminate the time scale. Furthermore, the disturbance level depends strongly on wavelength. If the disturbance wavelength range of interest is between 700 μm and 10 mm, the tunnel noise is measured to be less than 0.5 % with the focused laser differential interferometer.

Is there seismic attenuation in the mantle?

The small scale heterogeneity of the mantle is mostly due to the mixing of petrological heterogeneities by a smooth but chaotic convection and should consist in a laminated structure (marble cake) with a power spectrum S(k) varying as 1/k, where k is the wavenumber of the anomalies. This distribution of heterogeneities during convective stirring with negligible diffusion, called Batchelor regime is documented by fluid dynamic experiments and corresponds to what can be inferred from geochemistry and seismic tomography. This laminated structure imposes density, seismic velocity and potentially, anisotropic heterogeneities with similar 1/k spectra. A seismic wave of wavenumber k0 crossing such a medium is partly reflected by the heterogeneities and we show that the scattered energy is proportional to k0S(2k0). The reduction of energy for the propagating wave appears therefore equivalent to a quality factor 1/Q∝k0S(2k0). With the specific 1/k spectrum of the mantle, the resulting apparent attenuation should therefore be frequency independent. We show that the total contribution of 6–9% RMS density, velocity and anisotropy would explain the observed S and P attenuation of the mantle. Although these values are large, they are not unreasonable and we discuss how they depend on the range of frequencies over which the attenuation is explained. If such a level of heterogeneity were present, most of the attenuation of the Earth would be due to small scale scattering by laminations, not by intrinsic dissipation. Intrinsic dissipation must certainly exist but might correspond to a larger, yet unobserved Q. This provocative result would explain the very weak frequency dependence of the attenuation, and the fact that bulk attenuation seems negligible, two observations that have been difficult to explain for 50 years.

A comparison of the galaxy peculiar velocity field with the PSCz gravity field - a Bayesian hyper-parameter method

We constructed a Bayesian hyper-parameter statistical method to quantify the difference between predicted velocities derived from the observed galaxy distribution in the IRAS-PSCz (Point Source Catalogue Redshift) survey and peculiar velocities measured using different distance indicators. In our analysis, we find that the model–data comparison becomes unreliable beyond 70 h−1 Mpc because of the inadequate sampling by the IRAS survey of prominent, distant superclusters, like the Shapley Concentration. On the other hand, the analysis of the velocity residuals shows that the PSCz gravity field provides an adequate model to the local, ≤70 h−1 Mpc, peculiar velocity field. The hyper-parameter combination of ENEAR, SN, A1SN and SFI++ catalogues in the Bayesian framework constrains the amplitude of the linear flow to be β = 0.53 ± 0.014. For an rms density fluctuation in the PSCz galaxy number density , we obtain an estimate of the growth rate of density fluctuations fσ8(z ∼ 0) = 0.42 ± 0.033, which is in excellent agreement with independent estimates based on different techniques.

ON RADIATION PRESSURE IN STATIC, DUSTY H II REGIONS

Radiation pressure acting on gas and dust causes H ii regions to have central densities that are lower than the density near the ionized boundary. H ii regions in static equilibrium comprise a family of similarity solutions with three parameters: β, γ, and the product Q0nrms; β characterizes the stellar spectrum, γ characterizes the dust/gas ratio, Q0 is the stellar ionizing output (photons/s), and nrms is the rms density within the ionized region. Adopting standard values for β and γ, varying Q0nrms generates a one-parameter family of density profiles, ranging from nearly uniform density (small Q0nrms) to shell-like (large Q0nrms). When Q0nrms ≳ 1052 cm−3 s−1, dusty H ii regions have conspicuous central cavities, even if no stellar wind is present. For given β, γ, and Q0nrms, a fourth quantity, which can be Q0, determines the overall size and density of the H ii region. Examples of density and emissivity profiles are given. We show how quantities of interest—such as the peak-to-central emission measure ratio, the rms-to-mean density ratio, the edge-to-rms density ratio, and the fraction of the ionizing photons absorbed by the gas—depend on β, γ, and Q0nrms. For dusty H ii regions, compression of the gas and dust into an ionized shell results in a substantial increase in the fraction of the stellar photons that actually ionize H (relative to a uniform-density H ii region with the same dust/gas ratio and density n = nrms). We discuss the extent to which radial drift of dust grains in H ii regions can alter the dust-to-gas ratio. The applicability of these solutions to real H ii regions is discussed.

Neutral Density and Crosswind Determination from Arbitrarily Oriented Multiaxis Accelerometers on Satellites

An iterative algorithm for determining density and crosswind from multiaxis accelerometer measurements on satellites is presented, which works independently of the orientation of the instrument in space. The performance of the algorithm is compared with previously published algorithms using simulated data for the challenging minisatellite payload. Without external error sources, the algorithm reduces rms density errors from 0.7 to 0.03% andrmswinderrorsfrom38to1 m=sinthistest.However,theeffectsoftheerrorsintheinstrumentcalibrationand the external models that are used in the density and wind retrieval are dominant for the challenging minisatellite payload. These lead to mostly systematic density errors of the order of 10–15%. The accuracy of the wind results whenusingthenewalgorithmisalmostfullydeterminedbythesensitivityofthecross-trackaccelerationcomponent to the calibration and radiation pressure modeling errors. The applicability of the iterative algorithm and the accuracyofits resultsaredemonstrated bypresenting challenging minisatellite payload datafromaperiodin which thesatellitewascommandedto flysidewaysandbycomparingthedensityandwindresultswiththosefromadjacent days for which the satellite was in its nominal attitude mode. These investigations result in recommendations for the design of future satellite accelerometer missions for thermosphere research.

Nonlinearities in modified gravity cosmology: Signatures of modified gravity in the nonlinear matter power spectrum

A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter \zeta, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution (\zeta = 1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance to include the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size and initial redshift). We find that, the nonlinear power spectra can differ by ~30% for 10% deviation from GR (|\zeta-1| = 0.1) where the rms density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.

The effects of crustal heterogeneity on ray-based teleseismic imaging

SUMMARY We evaluate the efficacy of crustal scale receiver function imaging in the presence of crustal scattering. First, we show that the resolution of an image is not appreciably affected by geologically realistic crustal scattering. Rather, we show that the image contrast is reduced: the image of actual targets get ‘buried’ in the noise created by arrivals arising from crustal scattering. Then, we construct three classes of models in which we simulate a flat Moho, a Moho with topography, and a subduction zone. For all the models, we simulate the Moho as a finite-thickness velocity transition zone and the crust with a three-layer heterogeneous zone that contains binary von-Karman statistics with varying degrees of rms density and velocity contrasts. We use finite-difference simulations to generate a suite of varying-slowness seismograms, which we then image with pre-stack 2-D Kirchhoff migration and CCP stacking. We find that for a small degree of rms density/velocity contrasts, both imaging methodologies faithfully image the models, but for rms density/velocity variations greater than approximately 5 per cent per cent, we observed distortion and/or artefacts to the images. For migration, the distortion takes the form of amplitude variations for horizontal model features, whereas for the CCP imaging, the main affect is the enhancement of any horizontal feature in the model.

PLANETESIMAL AND PROTOPLANET DYNAMICS IN A TURBULENT PROTOPLANETARY DISK: IDEAL UNSTRATIFIED DISKS

The dynamics of planetesimals and planetary cores may be strongly influenced by density perturbations driven by magneto-rotational turbulence in their natal protoplanetary gas disks. Using the local shearing box approximation, we perform numerical simulations of planetesimals moving as massless particles in a turbulent, magnetized, unstratified gas disk. Our fiducial disk model shows turbulent accretion characterized by a Shakura-Sunyaev viscosity parameter of α ~ 10^-2, with rms density perturbations of ~10%. We measure the statistical evolution of particle orbital properties in our simulations including mean radius, eccentricity, and velocity dispersion. We confirm random walk growth in time of all three properties, the first time that this has been done with direct orbital integration in a local model. We find that the growth rate increases with the box size used at least up to boxes of eight scale heights in horizontal size. However, even our largest boxes show velocity dispersions sufficiently low that collisional destruction of planetesimals should be unimportant in the inner disk throughout its lifetime. Our direct integrations agree with earlier torque measurements showing that type I migration dominates over diffusive migration by stochastic torques for most objects in the planetary core and terrestrial planet mass range. Diffusive migration remains important for objects in the mass range of kilometer-sized planetesimals. Discrepancies in the derived magnitude of turbulence between local and global simulations of magneto-rotationally unstable disks remains an open issue, with important consequences for planet formation scenarios. (Less)

The size distribution of void filaments in a ΛCDM cosmology

The size distribution of mini-filaments in voids has been derived from the Millennium Run halo catalogs at redshifts z=0,0.5,1 and 2. It is assumed that the primordial tidal field originated the presence of filamentary substructures in voids and that the void filaments have evolved only little, keeping the initial memory of the primordial tidal field. Applying the filament-finding algorithm based on the minimal spanning tree (MST) technique to the Millennium voids, we identify the mini-filaments running through voids and measure their sizes at each redshift. Then, we calculate the comoving number density of void filaments as a function of their sizes in the logarithmic interval and determine an analytic fitting function for it. It is found that the size distribution of void mini-filaments in the logarithmic interval has an almost universal shape, insensitive to the redshift: In the short-size section it is well approximated as a power-law, while in the long-size section it decreases exponentially. We expect that the universal size distribution of void filaments may provide a useful cosmological probe without resorting to the rms density fluctuations.

Use of two-line element data for thermosphere neutral density model calibration

Traditional empirical thermospheric density models are widely used in orbit determination and prediction of low-Earth satellites. Unfortunately, these models often exhibit large density errors of up to around 30% RMS. Density errors translate into orbit errors, adversely affecting applications such as re-entry operations, manoeuvre planning, collision avoidance and precise orbit determination for geodetic missions. The extensive database of two-line element (TLE) orbit data contains a wealth of information on satellite drag, at a sufficiently high spatial and temporal resolution to allow a calibration of existing neutral density models with a latency of one to two days. In our calibration software, new TLE data for selected objects is converted to satellite drag data on a daily basis. The resulting drag data is then used in a daily adjustment of density model calibration parameters, which modify the output of an existing empirical density model with the aim of increasing its accuracy. Two different calibration schemes have been tested using TLE data for about 50 objects during the year 2000. The schemes involve either height-dependent scale factors to the density or corrections to CIRA-72 model temperatures, which affect the density output based on a physical model. Both schemes have been applied with different spherical harmonic expansions of the parameters in latitude and local solar time. Five TLE objects, varying in perigee altitude between 280 and 530 km, were deliberately not used during calibration, in order to provide independent validation. Even with a single daily parameter, the RMS density model error along their tracks can already be reduced from the 30% to the 15% level. Adding additional parameters results in RMS errors lower than 12%.

Modeling of filtered heat release for large eddy simulation of compressible infinitely fast reacting flows

A priori and a posteriori studies for large eddy simulation of the compressible turbulent infinitely fast reacting shear layer are presented. The filtered heat release appearing in the energy equation is unclosed and the accuracy of different models for the filtered scalar dissipation rate and the conditional filtered scalar dissipation rate of the mixture fraction in closing this term is analyzed. The effect of different closures of the subgrid transport of momentum, energy and scalars on the modeling of the filtered heat release via the resolved fields is also considered. Three explicit models of these subgrid fluxes are explored, each with an increasing level of reconstruction and all of them regularized by a Smagorinsky-type term. It is observed that a major part of the error in the prediction of the conditional filtered scalar dissipation comes from the unsatisfactory modeling of the filtered dissipation itself. The error can be substantial in the turbulent fluctuation (rms) of the dissipation fields. It is encouraging that all models give good predictions of the mean and rms density in a posteriori LES of this flow with realistic heat release corresponding to large density change. Although a posteriori results show a small sensitivity to subgrid modeling errors in the current problem, extinction–reignition phenomena involving finite-rate chemistry would demand more accurate modeling of the dissipation rates. A posteriori results also show that the resolved fields obtained with the approximate reconstruction using moments (ARM) agree better with the filtered direct numerical simulation since the level of reconstruction in the modeled subfilter fluxes is increased.

Galaxy groups in the 2dF Galaxy Redshift Survey: the number density of groups

The abundance of galaxy clusters as a function of mass is determined from the 2dF Galaxy Redshift Survey (2dFGRS) Percolation-Inferred Galaxy Group (2PIGG) catalogue. This is used to estimate the amplitude of the matter fluctuation spectrum, parametrized by the linear theory rms density fluctuations in spheres of radius 8h -1 Mpc, σ 8 . The best-fitting value for this parameter is highly correlated with the mean matter density in the Universe, Ω m , and is found to satisfy σ 8 = 0.25 Ω -0.92-4.5(Ω m -0.22)2 m ± 10 per cent (statistical) ±20 per cent (systematic) for 0.18 ≤ Ω m ≤ 0.50, assuming that Ω m + Ω ^ = 1. This gives σ 8 = 0.89 when evaluated at Ω m = 0.25. A ∼20 per cent correction has been applied to undo the systematic bias inherent in the measurement procedure. Mock catalogues, constructed from large cosmological N-body simulations, are used to help understand and model these systematic errors. The abundance of galaxy groups as a function of group b J -band luminosity is also determined. This is used in conjunction with the halo mass function, determined from simulations, to infer the variation of halo mass-to-light ratio over four orders of magnitude in halo mass. The mass-to-light ratio shows a minimum value of 100 h M ⊙ /L ⊙ in the bj band at a total group luminosity of L bJ ≈ 5×10 9 h -2 L ⊙ . Together with the observed Tully-Fisher (TF) relation, this implies that the observed rotation speed of TF galaxies with L bJ 10 10 h -2 L ⊙ is within ∼10 per cent of the typical circular speed of the haloes that host them.