We present a number of statistical tools that show promise for obtaining information on turbulence in molecular clouds and diffuse interstellar medium. For our tests we make use of three-dimensional 512 3 compressible MHD isothermal simulations performed for different sonic, i.e. M s ≡ V L /V s , where V L is the injection velocity, V s is the sound velocity, and Alfvénic M A ≡ V L /V A , where V A is the Alfvén velocity, Mach numbers. We introduce the bispectrum, a new tool for statistical studies of the interstellar medium which, unlike an ordinary power spectrum of turbulence, preserves the phase information of the stochastic field. We show that the bispectra of the 3D stochastic density field and of column densities, available from observations, are similar. This opens good prospects for studies of molecular clouds and diffuse media with the new tool. We use the bispectrum technique to define the role of non-linear wave-wave interactions in the turbulent energy cascade. We also obtained the bispectrum function for density and column densities with varying magnetic field strength. As expected, a strong correlation is obtained for wave modes k 1 = k 2 for all models. Larger values of M s result in increased correlations for modes with k 1 = k 2 . This effect becomes more evident with increasing magnetic field intensity. We believe that the different MHD wave modes, e.g. Alfvén and magneto-acoustic, which arise in strongly magnetized turbulence, may be responsible for the increased correlations compared to purely hydrodynamical perturbations. In addition to the bispectrum, we calculated the 3rd and 4th statistical moments of density and column density, namely, skewness and kurtosis, respectively. We found a strong dependence of skewness and kurtosis with M s . In particular, as M s increases, so does the Gaussian asymmetry of the density distribution. We also studied the correlations of 2D column density with dispersion of velocities and magnetic field, as well as the correlations of 3D density with magentic and kinetic energy and M A for comparison. Our results show that column density is linearly correlated with magnetic field for high M s . This trend is independent of the turbulent kinetic energy and can be used to characterize inhomogeneities of physical properties in low density clumps in the ISM.

Polarimetry is extensively used as a tool to trace the interstellar magnetic field projected on the plane of sky. Moreover, it is also possible to estimate the magnetic field intensity from polarimetric maps based on the ChandrasekharFermi method. In this work, we present results for turbulent, isothermal, three-dimensional simulations of sub/supersonic and sub/super-Alfvénic cases. With the cubes, assuming perfect grain alignment, we created synthetic polarimetric maps for different orientations of the mean magnetic field with respect to the line of sight (LOS). We show that the dispersion of the polarization angle depends on the angle of the mean magnetic field regarding the LOS and on the Alfvénic Mach number. However, the second-order structure function of the polarization angle follows the relation SF / l , being dependent exclusively on the Alfvénic Mach number. The results show an anticorrelation between the polarization degree and the column density, with exponent $ À0:5, in agreement with observations, which is explained by the increase in the dispersion of the polarization angle along the LOS within denser regions. However, this effect was observed exclusively on supersonic, but sub-Alfvénic, simulations. For the super-Alfvénic, and the subsonic model, the polarization degree showed to be independent of the column density. Our major quantitative result is a generalized equation for the CF method, which allowed us to determine the magnetic field strength from the polarization maps with errors <20%. We also account for the role of observational resolution on the CF method.

A deep survey of the Large Magellanic Cloud at ∼ 0.1−100 TeV photon energies with the Cherenkov Telescope Array is planned. We assess the detection prospects based on a model for the emission of the galaxy, comprising the four known TeV emitters, mock populations of sources, and interstellar emission on galactic scales. We also assess the detectability of 30 Doradus and SN 1987A, and the constraints that can be derived on the nature of dark matter. The survey will allow for fine spectral studies of N 157B, N 132D, LMC P3, and 30 Doradus C, and half a dozen other sources should be revealed, mainly pulsar-powered objects. The remnant from SN 1987A could be detected if it produces cosmic-ray nuclei with a flat power-law spectrum at high energies, or with a steeper index 2.3 − 2.4 pending a flux increase by a factor > 3 − 4 over ∼ 2015 − 2035. Large-scale interstellar emission remains mostly out of reach of the survey if its > 10 GeV spectrum has a soft photon index ∼ 2.7, but degree-scale 0.1 − 10 TeV pion-decay emission could be detected if the cosmic-ray spectrum hardens above >100 GeV. The 30 Doradus star-forming region is detectable if acceleration efficiency is on the order of 1 − 10% of the mechanical luminosity and diffusion is suppressed by two orders of magnitude within < 100 pc. Finally, the survey could probe the canonical velocity-averaged cross section for self-annihilation of weakly interacting massive particles for cuspy Navarro-Frenk-White profiles.