Recovering the Primordial Density Fluctuations: A comparison of methods

We present a comparative study of six different methods for reversing the gravitational evolution of a cosmological density field to recover the primordial fluctuations: linear theory, the Gaussianization mapping scheme, two different quasi-linear dynamical schemes based on the Zel'dovich approximation, a Hybrid dynamical-Gaussianization method and the Path Interchange Zel'dovich Approximation (PIZA). The final evolved density field from an N-body simulation constitutes our test case. We use a variety of statistical measures to compare the initial density field recovered from it to the true initial density field, using each of the six different schemes. These include point-by-point comparisons of the density fields in real space, the individual modes in Fourier space, as well as global statistical properties such as the genus, the PDF of the density, and the distribution of peak heights and their shapes. We find linear theory to be the most inaccurate of all the schemes. The Gaussianization scheme is the least accurate after linear theory. The two quasi-linear dynamical schemes are more accurate than Gaussianization, although they break down quite drastically when used outside their range of validity - the quasi-linear regime. The complementary beneficial aspects of the dynamical and the Gaussianization schemes are combined in the Hybrid method. We find this Hybrid scheme to be more accurate and robust than either Gaussianization or the dynamical method alone. The PIZA scheme performs substantially better than the others in all point-by-point comparisons. However, it produces an oversmoothed initial density field, with a smaller number of peaks than expected, but recovers the PDF of the initial density with impressive accuracy on scales as small as 3Mpc/h.Comment: 39 pages, including 13 Figures, submitted to Ap

Dynamical flows through Dark Matter Haloes II: one and two points statistics at the virial radius

In a serie of three papers, the dynamical interplay between environments and dark matter haloes is investigated, while focussing on the dynamical flows through their virial sphere. Our method relies on both cosmological simulations, to constrain the environments, and an extension to the classical matrix method to derive the response of the halo (see Pichon & Aubert (2006), paper I). The current paper focuses on the statistical characterisation of the environments surrounding haloes, using a set of large scale simulations. Our description relies on a `fluid' halocentric representation where the interactions between the halo and its environment are investigated in terms of a time dependent external tidal field and a source term characterizing the infall. The method is applied to 15000 haloes, with masses between 5 x 10^12 Ms and 10^14 Ms evolving between z = 1 and z = 0. The net accretion at the virial radius is found to decrease with time, resulting from both an absolute decrease of infall and from a growing contribution of outflows. Infall is found to be mainly radial and occurring at velocities ~ 0.75 V200. Outflows are also detected through the virial sphere and occur at lower velocities ~ 0.6 V200 on more circular orbits. The external tidal field is found to be strongly quadrupolar and mostly stationnary, possibly reflecting the distribution of matter in the halo's near environment. The coherence time of the small scale fluctuations of the potential hints a possible anisotropic distribution of accreted satellites. The flux density of mass on the virial sphere appears to be more clustered than the potential while the shape of its angular power spectrum seems stationnary.Comment: 34 pages, 29 figures, accepted for publication in MNRA

Critical fluctuations and anomalous transport in soft Yukawa-Langevin systems

Simulation of a Langevin-dynamics model demonstrates emergence of critical fluctuations and anomalous grain transport which have been observed in experiments on "soft" quasi-two-dimensional dusty plasma clusters. It has been suggested that these anomalies derive from particular non-equilibrium physics, but our model does not contain such physics: the grains are confined by an external potential, interact via static Yukawa forces, and are subject to stochastic heating and dissipation from neutrals. One remarkable feature is emergence of leptokurtic probability distributions of grain displacements $\xi(\tau)$ on time-scales $\tau<\tau_{\Delta}$, where $\tau_{\Delta}$ is the time at which the standard deviation $\sigma(\tau)\equiv ^{1/2}$ approaches the mean inter-grain distance $\Delta$. Others are development of humps in the distributions on multiples of $\Delta$, anomalous Hurst exponents, and transitions from leptokurtic towards Gaussian displacement distributions on time scales $\tau>\tau_{\Delta}$. The latter is a signature of intermittency, here interpreted as a transition from bursty transport associated with hopping on intermediate time scales to vortical flows on longer time scales.Comment: 12 pages, 9 figure

Constraints on Radial Migration in Spiral Galaxies - II. Angular momentum distribution and preferential migration

The orbital angular momentum of individual stars in galactic discs can be permanently changed through torques from transient spiral patterns. Interactions at the corotation resonance dominate these changes and have the further property of conserving orbital circularity. We derived in an earlier paper an analytic criterion that an unperturbed stellar orbit must satisfy in order for such an interaction to occur i.e. for it to be in a trapped orbit around corotation. We here use this criterion in an investigation of how the efficiency of induced radial migration for a population of disc stars varies with the angular momentum distribution of that population. We frame our results in terms of the velocity dispersion of the population, this being an easier observable than is the angular momentum distribution. Specifically, we investigate how the fraction of stars in trapped orbits at corotation varies with the velocity dispersion of the population, for a system with an assumed flat rotation curve. Our analytic results agree with the finding from simulations that radial migration is less effective in populations with 'hotter' kinematics. We further quantify the dependence of this trapped fraction on the strength of the spiral pattern, finding a higher trapped fraction for higher amplitude perturbations.Comment: 28 pages, 15 figure, accepted for publication in MNRA

On the streaming model for redshift-space distortions

The streaming model describes the mapping between real and redshift space for 2-point clustering statistics. Its key element is the probability density function (PDF) of line-of-sight pairwise peculiar velocities. Following a kinetic-theory approach, we derive the fundamental equations of the streaming model for ordered and unordered pairs. In the first case, we recover the classic equation while we demonstrate that modifications are necessary for unordered pairs. We then discuss several statistical properties of the pairwise velocities for DM particles and haloes by using a suite of high-resolution $N$-body simulations. We test the often used Gaussian ansatz for the PDF of pairwise velocities and discuss its limitations. Finally, we introduce a mixture of Gaussians which is known in statistics as the generalised hyperbolic distribution and show that it provides an accurate fit to the PDF. Once inserted in the streaming equation, the fit yields an excellent description of redshift-space correlations at all scales that vastly outperforms the Gaussian and exponential approximations. Using a principal-component analysis, we reduce the complexity of our model for large redshift-space separations. Our results increase the robustness of studies of anisotropic galaxy clustering and are useful for extending them towards smaller scales in order to test theories of gravity and interacting dark-energy models.Comment: 22 pages, 20 figures, accepted for publication in MNRA

Super-Sonic Turbulence in the Perseus Molecular Cloud

We compare the statistical properties of J=1-0 13CO spectra observed in the Perseus Molecular Cloud with synthetic J=1-0 13CO spectra, computed solving the non-LTE radiative transfer problem for a model cloud obtained as solutions of the three dimensional magneto-hydrodynamic (MHD) equations. The model cloud is a randomly forced super-Alfvenic and highly super-sonic turbulent isothermal flow. The purpose of the present work is to test if idealized turbulent flows, without self-gravity, stellar radiation, stellar outflows, or any other effect of star formation, are inconsistent or not with statistical properties of star forming molecular clouds. We present several statistical results that demonstrate remarkable similarity between real data and the synthetic cloud. Statistical properties of molecular clouds like Perseus are appropriately described by random super-sonic and super-Alfvenic MHD flows. Although the description of gravity and stellar radiation are essential to understand the formation of single protostars and the effects of star formation in the cloud dynamics, the overall description of the cloud and of the initial conditions for star formation can apparently be provided on intermediate scales without accounting for gravity, stellar radiation, and a detailed modeling of stellar outflows. We also show that the relation between equivalent line width and integrated antenna temperature indicates the presence of a relatively strong magnetic field in the core B1, in agreement with Zeeman splitting measurements.Comment: 20 pages, 8 figures included, ApJ (in press

Turbulent Velocity Structure in Molecular Clouds

We compare velocity structure in the Polaris Flare molecular cloud at scales ranging from 0.015 pc to 20 pc to simulations of supersonic hydrodynamic and MHD turbulence computed with the ZEUS MHD code. We use several different statistical methods to compare models and observations. The Delta-variance wavelet transform is most sensitive to characteristic scales and scaling laws, but is limited by a lack of intensity weighting. The scanning-beam size-linewidth relation is more robust with respect to noisy data. Obtaining the global velocity scaling behaviour requires that large-scale trends in the maps not be removed but treated as part of the turbulent cascade. We compare the true velocity PDF in our models to velocity centroids and average line profiles in optically thin lines, and find that the line profiles reflect the true PDF better unless the map size is comparable to the total line-of-sight thickness of the cloud. Comparison of line profiles to velocity centroid PDFs can thus be used to measure the line-of-sight depth of a cloud. The observed density and velocity structure is consistent with supersonic turbulence with a driving scale at or above the size of the molecular cloud and dissipative processes below 0.05 pc. Ambipolar diffusion could explain the dissipation. The velocity PDFs exclude small-scale driving such as that from stellar outflows as a dominant process in the observed region. In the models, large-scale driving is the only process that produces deviations from a Gaussian PDF shape consistent with observations. Strong magnetic fields impose a clear anisotropy on the velocity field, reducing the velocity variance in directions perpendicular to the field. (abridged)Comment: 21 pages, 24 figures, accepted by A&A, with some modifications, including change of claimed direct detection of dissipation scale to an upper limi

A Portrait of Cold Gas in Galaxies at 60pc Resolution and a Simple Method to Test Hypotheses That Link Small-Scale ISM Structure to Galaxy-Scale Processes

The cloud-scale density, velocity dispersion, and gravitational boundedness of the interstellar medium (ISM) vary within and among galaxies. In turbulent models, these properties play key roles in the ability of gas to form stars. New high fidelity, high resolution surveys offer the prospect to measure these quantities across galaxies. We present a simple approach to make such measurements and to test hypotheses that link small-scale gas structure to star formation and galactic environment. Our calculations capture the key physics of the Larson scaling relations, and we show good correspondence between our approach and a traditional "cloud properties" treatment. However, we argue that our method is preferable in many cases because of its simple, reproducible characterization of all emission. Using, low-J 12CO data from recent surveys, we characterize the molecular ISM at 60pc resolution in the Antennae, the Large Magellanic Cloud, M31, M33, M51, and M74. We report the distributions of surface density, velocity dispersion, and gravitational boundedness at 60pc scales and show galaxy-to-galaxy and intra-galaxy variations in each. The distribution of flux as a function of surface density appears roughly lognormal with a 1sigma width of ~0.3 dex, though the center of this distribution varies from galaxy to galaxy. The 60pc resolution line width and molecular gas surface density correlate well, which is a fundamental behavior expected for virialized or free-falling gas. Varying the measurement scale for the LMC and M31, we show that the molecular ISM has higher surface densities, lower line widths, and more self-gravity at smaller scales.Comment: Accepted for publication in the Astrophysical Journal, 36 pages (24+appendix), 21 figures (12+appendix), until publication high resolution version at http://www.astronomy.ohio-state.edu/~leroy.42/cloudscale.pd

Proton imaging of stochastic magnetic fields

Recent laser-plasma experiments report the existence of dynamically significant magnetic fields, whose statistical characterisation is essential for understanding the physical processes these experiments are attempting to investigate. In this paper, we show how a proton imaging diagnostic can be used to determine a range of relevant magnetic field statistics, including the magnetic-energy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the image-flux distribution created upon imaging that field. We conclude that features of the beam's final image-flux distribution often display a universal character determined by a single, field-scale dependent parameter - the contrast parameter - which quantifies the relative size of the correlation length of the stochastic field, proton displacements due to magnetic deflections, and the image magnification. For stochastic magnetic fields, we establish the existence of four contrast regimes - linear, nonlinear injective, caustic and diffusive - under which proton-flux images relate to their parent fields in a qualitatively distinct manner. As a consequence, it is demonstrated that in the linear or nonlinear injective regimes, the path-integrated magnetic field experienced by the beam can be extracted uniquely, as can the magnetic-energy spectrum under a further statistical assumption of isotropy. This is no longer the case in the caustic or diffusive regimes. We also discuss complications to the contrast-regime characterisation arising for inhomogeneous, multi-scale stochastic fields, as well as limitations currently placed by experimental capabilities on extracting magnetic field statistics. The results presented in this paper provide a comprehensive description of proton images of stochastic magnetic fields, with applications for improved analysis of given proton-flux images.Comment: Main paper pp. 1-29; appendices pp. 30-84. 24 figures, 2 table