Interstellar Sonic and Alfv\'enic Mach Numbers and the Tsallis Distribution

In an effort to characterize the Mach numbers of ISM magnetohydrodynamic (MHD) turbulence, we study the probability distribution functions (PDFs) of patial increments of density, velocity, and magnetic field for fourteen ideal isothermal MHD simulations at resolution 512^3. In particular, we fit the PDFs using the Tsallis function and study the dependency of fit parameters on the compressibility and magnetization of the gas. We find that the Tsallis function fits PDFs of MHD turbulence well, with fit parameters showing sensitivities to the sonic and Alfven Mach numbers. For 3D density, column density, and position-position-velocity (PPV) data we find that the amplitude and width of the PDFs shows a dependency on the sonic Mach number. We also find the width of the PDF is sensitive to global Alfvenic Mach number especially in cases where the sonic number is high. These dependencies are also found for mock observational cases, where cloud-like boundary conditions, smoothing, and noise are introduced. The ability of Tsallis statistics to characterize sonic and Alfvenic Mach numbers of simulated ISM turbulence point to it being a useful tool in the analysis of the observed ISM, especially when used simultaneously with other statistical techniques.Comment: 20 pages, 16 figures, ApJ submitte

What's Behind the Inequality we Measure: An Investigation Using Latin American Data

The use of income distribution indicators in the economics literature has increased considerably in recent years. This work relies on household surveys from 18 LAC countries to take a step back from the use of these indicators, and explore what`s behind the numbers, and what information they convey. We find: a) that the way countries rank according to inequality measured in a conventional way is to a large extent an illusion created by differences in characteristics of the data and on the particular ways in which the data is treated; b) Our ideas about the effect of inequality on economic growth are also driven by quality and coverage differences in household surveys and by the way in which the data is treated; c) Standard household surveys in LAC are unable to capture the incomes of the richest sectors of society; so, the inequality we are able to measure is most likely a gross underestimation. Our main conclusion is that there is an important story behind each number. This story influences our judgement about how unequal countries are and about the relation between inequality and other development indicators, but it is seldom told or known. Perhaps other statistics commonly used in economics also have their own interesting story, and it might be worth trying to find out what it is.

Magnetization of cloud cores and envelopes and other observational consequences of reconnection diffusion

Recent observational results for magnetic fields in molecular clouds reviewed by Crutcher (2012) seem to be inconsistent with the predictions of the ambipolar diffusion theory of star formation. These include the measured decrease in mass to flux ratio between envelopes and cores, the failure to detect any self-gravitating magnetically subcritical clouds, the determination of the flat PDF of the total magnetic field strengths implying that there are many clouds with very weak magnetic fields, and the observed scaling $B \propto \rho^{2/3}$ that implies gravitational contraction with weak magnetic fields. We consider the problem of magnetic field evolution in turbulent molecular clouds and discuss the process of magnetic field diffusion mediated by magnetic reconnection. For this process that we termed "reconnection diffusion" we provide a simple physical model and explain that this process is inevitable in view of the present day understanding of MHD turbulence. We address the issue of the expected magnetization of cores and envelopes in the process of star formation and show that reconnection diffusion provides an efficient removal of magnetic flux that depends only on the properties of MHD turbulence in the core and the envelope. As a result, the magnetic flux trapped during the collapse in the envelope is being released faster than the flux trapped in the core, resulting in much weaker fields in envelopes than in cores, as observed. We provide simple semi-analytical model calculations which support this conclusion and qualitatively agree with the observational results. We argue that magnetic reconnection provides a solution to the magnetic flux problem of star formation that agrees better with observations than the long-standing ambipolar diffusion paradigm.Comment: 22 pages, 11 figures, submitted to ApJ, revised version. arXiv admin note: substantial text overlap with arXiv:1111.069

Solar cycle dependence of scaling in solar wind fluctuations

In this review we collate recent results for the statistical scaling properties of fluctuations in the solar wind with a view to synthesizing two descriptions: that of evolving MHD turbulence and that of a scaling signature of coronal origin that passively propagates with the solar wind. The scenario that emerges is that of coexistent signatures which map onto the well known "two component" picture of solar wind magnetic fluctuations. This highlights the need to consider quantities which track Alfvénic fluctuations, and energy and momentum flux densities to obtain a complete description of solar wind fluctuations