Observational quantification of three-dimensional anisotropies and scalings of space plasma turbulence at kinetic scales

A statistical survey of spectral anisotropy of space plasma turbulence is performed using five years measurements from MMS in the magnetosheath. By measuring the five-point second-order structure functions of the magnetic field, we have for the first time quantified the three-dimensional anisotropies and scalings at sub-ion-scales ($<$ 100 km). In the local reference frame $(\hat L_{\perp}, \hat l_{\perp}, \hat l_{\parallel})$ defined with respect to local mean magnetic field $\boldsymbol {B}_0$ (Chen et al. 2012), the "statistical eddies" are found to be mostly elongated along $\boldsymbol {B}_0$ and shortened in the direction perpendicular to both $\boldsymbol {B}_0$ and local field fluctuations. From several $d_i$ (ion inertial length) toward $\sim$ 0.05 $d_i$, the ratio between eddies' parallel and perpendicular lengths features a trend of rise then fall, whereas the anisotropy in the perpendicular plane appears scale-invariant. Specifically, the anisotropy relations for the total magnetic field at 0.1-1.0 $d_i$ are obtained as $l_{\parallel} \simeq 2.44 \cdot l_{\perp}^{0.71}$, and $L_{\perp} \simeq 1.58 \cdot l_{\perp}^{1.08}$, respectively. Our results provide new observational evidence to compare with phenomenological models and numerical simulations, which may help to better understand the nature of kinetic scale turbulence.Comment: Accepte

Cosmic velocity--gravity relation in redshift space

We propose a simple way to estimate the parameter beta = Omega_m^(0.6)/b from three-dimensional galaxy surveys. Our method consists in measuring the relation between the cosmological velocity and gravity fields, and thus requires peculiar velocity measurements. The relation is measured *directly in redshift space*, so there is no need to reconstruct the density field in real space. In linear theory, the radial components of the gravity and velocity fields in redshift space are expected to be tightly correlated, with a slope given, in the distant observer approximation, by g / v = (1 + 6 beta / 5 + 3 beta^2 / 7)^(1/2) / beta. We test extensively this relation using controlled numerical experiments based on a cosmological N-body simulation. To perform the measurements, we propose a new and rather simple adaptive interpolation scheme to estimate the velocity and the gravity field on a grid. One of the most striking results is that nonlinear effects, including `fingers of God', affect mainly the tails of the joint probability distribution function (PDF) of the velocity and gravity field: the 1--1.5 sigma region around the maximum of the PDF is *dominated by the linear theory regime*, both in real and redshift space. This is understood explicitly by using the spherical collapse model as a proxy of nonlinear dynamics. Applications of the method to real galaxy catalogs are discussed, including a preliminary investigation on homogeneous (volume limited) `galaxy' samples extracted from the simulation with simple prescriptions based on halo and sub-structure identification, to quantify the effects of the bias between the galaxy and the total matter distibution, and of shot noise (ABRIDGED).Comment: 24 pages, 10 figures. Matches the version accepted for publication in MNRAS. The definitive version is available at http://www.blackwell-synergy.co