The Turbulence Spectrum of Molecular Clouds in the Galactic Ring Survey: A Density-Dependent PCA Calibration

Turbulence plays a major role in the formation and evolution of molecular clouds. The problem is that turbulent velocities are convolved with the density of an observed region. To correct for this convolution, we investigate the relation between the turbulence spectrum of model clouds, and the statistics of their synthetic observations obtained from Principal Component Analysis (PCA). We apply PCA to spectral maps generated from simulated density and velocity fields, obtained from hydrodynamic simulations of supersonic turbulence, and from fractional Brownian motion fields with varying velocity, density spectra, and density dispersion. We examine the dependence of the slope of the PCA structure function, alpha_PCA, on intermittency, on the turbulence velocity (beta_v) and density (beta_n) spectral indexes, and on density dispersion. We find that PCA is insensitive to beta_n and to the log-density dispersion sigma_s, provided sigma_s 2, alpha_PCA increases with sigma_s due to the intermittent sampling of the velocity field by the density field. The PCA calibration also depends on intermittency. We derive a PCA calibration based on fBms with sigma_s<2 and apply it to 367 CO spectral maps of molecular clouds in the Galactic Ring Survey. The average slope of the PCA structure function, =0.62\pm0.2, is consistent with the hydrodynamic simulations and leads to a turbulence velocity exponent =2.06\pm0.6 for a non-intermittent, low density dispersion flow. Accounting for intermittency and density dispersion, the coincidence between the PCA slope of the GRS clouds and the hydrodynamic simulations suggests beta_v~1.9, consistent with both Burgers and compressible intermittent turbulence

An improved SPH scheme for cosmological simulations

We present an implementation of smoothed particle hydrodynamics (SPH) with improved accuracy for simulations of galaxies and the large-scale structure. In particular, we combine, implement, modify and test a vast majority of SPH improvement techniques in the latest instalment of the GADGET code. We use the Wendland kernel functions, a particle wake-up time-step limiting mechanism and a time-dependent scheme for artificial viscosity, which includes a high-order gradient computation and shear flow limiter. Additionally, we include a novel prescription for time-dependent artificial conduction, which corrects for gravitationally induced pressure gradients and largely improves the SPH performance in capturing the development of gas-dynamical instabilities. We extensively test our new implementation in a wide range of hydrodynamical standard tests including weak and strong shocks as well as shear flows, turbulent spectra, gas mixing, hydrostatic equilibria and self-gravitating gas clouds. We jointly employ all modifications; however, when necessary we study the performance of individual code modules. We approximate hydrodynamical states more accurately and with significantly less noise than standard SPH. Furthermore, the new implementation promotes the mixing of entropy between different fluid phases, also within cosmological simulations. Finally, we study the performance of the hydrodynamical solver in the context of radiative galaxy formation and non-radiative galaxy cluster formation. We find galactic disks to be colder, thinner and more extended and our results on galaxy clusters show entropy cores instead of steadily declining entropy profiles. In summary, we demonstrate that our improved SPH implementation overcomes most of the undesirable limitations of standard SPH, thus becoming the core of an efficient code for large cosmological simulations.Comment: 21 figures, 2 tables, accepted to MNRA

Density Power Spectrum in Turbulent Thermally Bi-stable Flows

In this paper we numerically study the behavior of the density power spectrum in turbulent thermally bistable flows. We analyze a set of five three-dimensional simulations where turbulence is randomly driven in Fourier space at a fixed wave-number and with different Mach numbers M (with respect to the warm medium) ranging from 0.2 to 4.5. The density power spectrum becomes shallower as M increases and the same is true for the column density power spectrum. This trend is interpreted as a consequence of the simultaneous turbulent compressions, thermal instability generated density fluctuations, and the weakening of thermal pressure force in diffuse gas. This behavior is consistent with the fact that observationally determined spectra exhibit different slopes in different regions. The values of the spectral indexes resulting from our simulations are consistent with observational values. We do also explore the behavior of the velocity power spectrum, which becomes steeper as M increases. The spectral index goes from a value much shallower than the Kolmogorov one for M=0.2 to a value steeper than the Kolmogorov one for M=4.5.Comment: 16 pages, 11 figures. Accepted for publication in Ap

Solar wind turbulence at 0.72 AU and solar minimum

We investigate Venus Express (VEX) observations of magnetic field fluctuations performed systematically in the solar wind at 0.72 Astronomical Units (AU), between 2007 and 2009, during the deep minimum of the solar cycle 24. The Power Spectral Densities (PSD) of the magnetic field components have been computed for the time intervals that satisfy data integrity criteria and have been grouped according to the type of wind, fast and slow defined for speeds larger and respectively smaller than 450 km/s. The PSDs show higher levels of power for the fast than for the slow wind. The spectral slopes estimated for all PSDs in the frequency range 0.005-0.1 Hz exhibit a normal distribution. The average value of the trace of the spectral matrix is -1.60 for fast solar wind and -1.65 for slow wind. Compared to the corresponding average slopes at 1 AU, the PSDs are shallower at 0.72 AU for slow wind conditions suggesting a steepening of the solar wind spectra between Venus and Earth. No significant time variation trend is observed for the spectral behavior of both slow and fast wind

The spectrum of kink-like oscillations of solar photospheric magnetic elements

Recently, the availability of new high-spatial and -temporal resolution observations of the solar photosphere has allowed the study of the oscillations in small magnetic elements. Small magnetic elements have been found to host a rich variety of oscillations detectable as intensity, longitudinal or transverse velocity fluctuations which have been interpreted as MHD waves. Small magnetic elements, at or below the current spatial resolution achieved by modern solar telescopes, are though to play a relevant role in the energy budget of the upper layers of the Sun's atmosphere, as they are found to cover a significant fraction of the solar photosphere. Unfortunately, the limited temporal length and/or cadence of the data sets, or the presence of seeing-induced effects have prevented, so far, the estimation of the power spectra of kink-like oscillations in small magnetic elements with good accuracy. Motivated by this, we studied kink-like oscillations in small magnetic elements, by exploiting very long duration and high-cadence data acquired with the Solar Optical Telescope on board the Hinode satellite. In this work we present the results of this analysis, by studying the power spectral density of kink-like oscillations on a statistical basis. We found that small magnetic elements exhibit a large number of spectral features in the range 1-12 mHz. More interestingly, most of these spectral features are not shared among magnetic elements but represent a unique signature of each magnetic element itself.Comment: A&A accepted for publication. 8 pages, 5 figure