Probing magnetic turbulence by synchrotron polarimetry: statistics and structure of magnetic fields from Stokes correlators

We describe a novel technique for probing the statistical properties of cosmic magnetic fields based on radio polarimetry data. Second-order magnetic field statistics like the power spectrum cannot always distinguish between magnetic fields with essentially different spatial structure. Synchrotron polarimetry naturally allows certain fourth-order magnetic field statistics to be inferred from observational data, which lifts this degeneracy and can thereby help us gain a better picture of the structure of the cosmic fields and test theoretical scenarios describing magnetic turbulence. In this work we show that a fourth-order correlator of specific physical interest, the tension force spectrum, can be recovered from the polarized synchrotron emission data. We develop an estimator for this quantity based on polarized emission observations in the Faraday rotation free frequency regime. We consider two cases: a statistically isotropic field distribution, and a statistically isotropic field superimposed on a weak mean field. In both cases the tension force power spectrum is measurable; in the latter case, the magnetic power spectrum may also be obtainable. The method is exact in the idealized case of a homogeneous relativistic electron distribution that has a power-law energy spectrum with a spectral index of   p = 3  , and assumes statistical isotropy of the turbulent field. We carry out numerical tests of our method using synthetic polarized emission data generated from numerically simulated magnetic fields. We show that the method is valid, that it is not prohibitively sensitive to the value of the electron spectral index p , and that the observed tension force spectrum allows one to distinguish between e.g. a randomly tangled magnetic field (a default assumption in many studies) and a field organized in folded flux sheets or filaments.     

Large-scale galactic turbulence: can self-gravity drive the observed H i velocity dispersions?

Observations of turbulent velocity dispersions in the H  i component of galactic discs show a characteristic floor in galaxies with low star formation rates and within individual galaxies the dispersion profiles decline with radius. We carry out several high-resolution adaptive mesh simulations of gaseous discs embedded within dark matter haloes to explore the roles of cooling, star formation, feedback, shearing motions and baryon fraction in driving turbulent motions. In all simulations the disc slowly cools until gravitational and thermal instabilities give rise to a multiphase medium in which a large population of dense self-gravitating cold clouds are embedded within a warm gaseous phase that forms through shock heating. The diffuse gas is highly turbulent and is an outcome of large-scale driving of global non-axisymmetric modes as well as cloud–cloud tidal interactions and merging. At low star formation rates these processes alone can explain the observed H  i velocity dispersion profiles and the characteristic value of  ∼10 km s⁻¹  observed within a wide range of disc galaxies. Supernovae feedback creates a significant hot gaseous phase and is an important driver of turbulence in galaxies with a star formation rate per unit area  ≳10⁻³ M_⊙ yr⁻¹ kpc⁻²  .     

The inner scale of the plasma turbulence towards PSR J1644−4559

By measuring the decaying shape of the scatter-broadened pulse from the bright distant pulsar PSR J1644−4559, we probe waves scattered at relatively high angles by very small spatial scales in the interstellar plasma, which allows us to test for a wavenumber cutoff in the plasma density spectrum. Under the hypothesis that the density spectrum is due to plasma turbulence, we can thus investigate the (inner) scale at which the turbulence is dissipated. We report observations carried out with the Parkes radio telescope at 660 MHz from which we find strong evidence for an inner scale in the range 70–100 km, assuming an isotropic Kolmogorov spectrum. By identifying the inner scale with the ion inertial scale, we can also estimate the mean electron density of the scattering region to be 5–10 cm⁻³. This is comparable with the electron density of H  ii region G339.1−0.4, which lies in front of the pulsar, and so confirms that this region dominates the scattering. We conclude that the plasma inside the region is characterized by fully developed turbulence with an outer scale in the range 1–20 pc and an inner scale of 70–100 km. The shape of the rising edge of the pulse constrains the distribution of the strongly scattering plasma to be spread over about 20 per cent of the 4.6 kpc path from the pulsar, but with similarly high electron densities in two or more thin layers, their thicknesses can only be 10–20 pc.     

Stochastic wobble of accretion discs and jets from turbulent rocket torques

Models of accretion discs and their associated outflows often incorporate assumptions of axisymmetry and symmetry across the disc plane. However, for turbulent discs these symmetries only apply to averaged quantities and do not apply locally. The local asymmetries can induce local imbalances in outflow power across the disc mid-plane, which can in turn induce local tilting torques. Here we calculate the effect of the resulting stochastic torques on disc annuli that are a consequence of standard mean field accretion disc models. The torques induce a random walk of the vector perpendicular to the plane of each averaged annulus. This random walk is characterized by a radially dependent diffusion coefficient which we calculate for small angle tilt. We use the coefficient to calculate a radially dependent time-scale for annular tilt and associated jet wobble. The wobble time depends on the square of the wander angle so the age of a given system determines the maximum wobble angle. We apply this to examples of blazars, young stellar objects and binary engines of pre-planetary nebulae and microquasars. It is noteworthy that for an averaging time   t _w∼ 3 d  , we estimate a wobble angle for jets in SS 433 of  θ∼ 0.8°  , not inconsistent with observational data. In general the non-periodic nature of the stochastic wobble could distinguish it from faster periodic jet precession.     

Suppression of the large‐scale Lorentz force by turbulence

The components of the total stress tensor (Reynolds stress plus Maxwell stress) are computed within the quasilinear approximation for a driven turbulence influenced by a large‐scale magnetic background field. The conducting fluid has an arbitrary magnetic Prandtl number and the turbulence without the background field is assumed as homogeneous and isotropic with a free Strouhal number St. The total large‐scale magnetic tension is always reduced by the turbulence with the possibility of a ‘catastrophic quenching’ for large magnetic Reynolds number Rm so that even its sign is reversed. The total magnetic pressure is enhanced by turbulence in the high‐conductivity limit but it is reduced in the low‐conductivity limit. Also in this case the sign of the total pressure may reverse but only for special turbulences with sufficiently large St > 1. The turbulence‐induced terms of the stress tensor are suppressed by strong magnetic fields. For the tension term this quenching grows with the square of the Hartmann number of the magnetic field. For microscopic (i.e. small) diffusivity values the magnetic tension term becomes thus highly quenched even for field amplitudes much smaller than their equipartition value. In the opposite case of large‐eddy simulations the magnetic quenching is only mild but then also the turbulence‐induced Maxwell tensor components for weak fields remain rather small (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Development of the Automatic Seeing Monitor for the Site Testing of Dome A

The Antarctic site-testing campaigns have shown that Dome C is an excellent astronomical site on the earth, it is better than any of existing mid-latitude astronomical sites in the world, because of its cold and dry weather, low infrared background radiation, continuously observable time as long as 3–4 months, clear and highly transparent atmosphere, low wind speed, and the absence of dust and light pollution. And in the international astronomical community it is generally believed that Dome A with a higher altitude may be better than Dome C as a potential excellent astronomical site. In the past 3 years, although held by the Center for Antarctic Astronomy of Chinese Academy of Sciences, the site testing at Dome A has preliminarily con?rmed the many advantages of Dome A as an excellent astronomical site, but the data about the atmospheric seeing, which is an important parameter for assessing the site quality for optical observations, have not been obtained until now. Hence, on the basis of a commercial telescope with the diameter of 35 cm, we have made the hardware reformation and software development to have it operate as a DIMM (Differential Image Motion Monitor), which can simultaneously monitor both the seeing and isoplanatic angle at Dome A automatically. At present this instrument has been shipped to Antarctica by the “Xuelong” exploration ship, and will be installed at Dome A, and begin to work in early 2011. Before the shipment, by through the comparative measurements together with an existing seeing monitor at the Xinglong astronomical station, the software, hardware, as well as the installation and adjustment of the instrument, are further veri?ed by testing.     

Relating millimeter-scale turbulence to meter-scale subtidal erosion and accretion across the fringe of a coastal mangrove forest

Within a wave-exposed mangrove forest, novel field observations are presented, comparing millimeter-scale turbulent water velocity fluctuations with contemporaneous subtidal bed elevation changes. High-resolution velocity and bed level measurements were collected from the unvegetated mudflat, at the mangrove forest fringe, and within the forest interior over multiple tidal cycles (flood–ebb) during a 2-week period. Measurements demonstrated that the spatial variability in vegetation density is a control on sediment transport at sub-meter scales. Scour around single and dense clusters of pneumatophores was predicted by a standard hydraulic engineering equation for wave-induced scour around regular cylinders, when the cylinder diameter in the equations was replaced with the representative diameter of the dense pneumatophore clusters. Waves were dissipated as they propagated into the forest, but dissipation at infragravity periods (> 30 s) was observed to be less than dissipation at shorter periods (< 30 s), consistent with the predictions of a simple model. Cross-wavelet analysis revealed that infragravity-frequency fluctuations in the bed level were occasionally coherent with velocity, possibly indicating scour upstream of dense pneumatophore patches when infragravity waves reinforced tidal currents. Consequently, infragravity waves were a likely driver of sediment transport within the mangrove forest. Near-bed turbulent kinetic energy, estimated from the turbulent dissipation rate, was also correlated with bed level changes. Specifically, within the mangrove forest and over the unvegetated mudflat, high-energy events were associated with erosion or near-zero bed level change, whereas low-energy events were associated with accretion. In contrast, no single relationship between bed level changes and mean current velocity was applicable across both vegetated and unvegetated regions. These observations support the theory that sediment mobilization scales with turbulent energy, rather than mean velocity, a distinction that becomes important when vegetation controls the development of turbulence.     

The “slip law” of the free surface

A “slip law” connects the excess velocity or “slip” of a wind-blown water surface, relative to the motion in the middle of the mixed layer, to the wind stress, the wind-wave field, and buoyancy flux. An inner layer-outer layer model of the turbulent shear flow in the mixed layer is appropriate, as for a turbulent boundary layer or Ekman layer over a solid surface, allowing, however, for turbulent kinetic energy transfer from the air-side via breaking waves, and for Stokes drift. Asymptotic matching of the velocity distributions in inner and outer portions of the mixed layer yields a slip law of logarithmic form, akin to the drag law of a turbulent boundary layer. The dominant independent variable is the ratio of water-side roughness length to mixed layer depth or turbulent Ekman depth. Convection due to surface cooling is also an important influence, reducing surface slip. Water-side roughness length is a wind-wave property, varying with wind speed similarly to air-side roughness. Slip velocity is typically 20 times water-side friction velocity or 3% of wind speed, varying within a range of about 2 to 4.5%. A linearized model of turbulent kinetic energy distribution shows much higher values near the surface than in a wall layer. Nondimensional dissipation peaks at a value of about eight, a short distance below the surface.     

Dimensionless measures of turbulent magnetohydrodynamic dissipation rates

The magnetic Reynolds number, R _M, is defined as the product of a characteristic scale and associated flow speed divided by the microphysical magnetic diffusivity. For laminar flows, R _M also approximates the ratio of advective to dissipative terms in the total magnetic energy equation, but for turbulent flows this latter ratio depends on the energy spectra and approaches unity in a steady state. To generalize for flows of arbitrary spectra we define an effective magnetic dissipation number,   R _M,e  , as the ratio of the advection to microphysical dissipation terms in the total magnetic energy equation, incorporating the full spectrum of scales, arbitrary magnetic Prandtl numbers, and distinct pairs of inner and outer scales for magnetic and kinetic spectra. As expected, for a substantial parameter range   R _M,e∼ O (1) ≪ R _M  . We also distinguish   R _M,e  from     where the latter is an effective magnetic Reynolds number for the mean magnetic field equation when a turbulent diffusivity is explicitly imposed as a closure. That   R _M,e  and     approach unity even if   R _M≫ 1  highlights that, just as in hydrodynamic turbulence, energy dissipation of large-scale structures in turbulent flows via a cascade can be much faster than the dissipation of large-scale structures in laminar flows. This illustrates that the rate of energy dissipation by magnetic reconnection is much faster in turbulent flows, and much less sensitive to microphysical reconnection rates compared to laminar flows.     

LOLAS: an optical turbulence profiler in the atmospheric boundary layer with extreme altitude resolution

We report the development and first results of an instrument called Low Layer SCIDAR (Scintillation Detection and Ranging) (LOLAS) which is aimed at the measurement of optical-turbulence profiles in the atmospheric boundary layer with high altitude resolution. The method is based on the Generalized SCIDAR (GS) concept, but unlike the GS instruments which need a 1-m or larger telescope, LOLAS is implemented on a dedicated 40-cm telescope, making it an independent instrument. The system is designed for widely separated double-star targets, which enables the high altitude resolution. Using a 200-arcsec-separation double star, we have obtained turbulence profiles with unprecedented 12-m resolution. The system incorporates necessary novel algorithms for autoguiding, autofocus and image stabilization. The results presented here were obtained at Mauna Kea Observatory. They show LOLAS capabilities but cannot be considered as representative of the site. A forthcoming paper will be devoted to the site characterization. The instrument was built as part of the Ground Layer Turbulence Monitoring Campaign on Mauna Kea for Gemini Observatory.