arXiv subjects

Blakesley Burkhart

Publications and source records attributed to Blakesley Burkhart.

139 records · Page 8Linked to original sources

arXiv2013

Characterizing the Turbulent Properties of the Starless Molecular Cloud MBM16

We investigate turbulent properties of the non-star-forming, translucent molecular cloud, MBM16 by applying the statistical technique of a two-dimensional spatial power spectrum (SPS) on the neutral hydrogen (HI) observations obtained by the Galactic Arecibo L-Band Feed Array HI (GALFA-HI) survey. The SPS, calculated over the range of spatial scales from 0.1 to 17 pc, is well represented with a single power-law function, with a slope ranging from -3.3 to -3.7 and being consistent over the velocity range of MBM16 for a fixed velocity channel thickness. However, the slope varies significantly with the velocity slice thickness, suggesting that both velocity and density contribute to HI intensity fluctuations. By using this variation we estimate the slope of 3D density fluctuations in MBM16 to be -3.7\pm0.2. This is significantly steeper than what has been found for HI in the Milky Way plane, the Small Magellanic Cloud, or the Magellanic Bridge, suggesting that interstellar turbulence in MBM16 is driven on scales >17 pc and that the lack of stellar feedback could be responsible for the steep power spectrum.

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arXiv2013

Observational Diagnostics for Two-Fluid Turbulence in Molecular Clouds As Suggested by Simulations

We present high resolution simulations of two-fluid (ion-neutral) MHD turbulence with resolutions as large as 512^3. The simulations are supersonic and mildly sub-Alfvenic, in keeping with the conditions present in molecular clouds. Such turbulence is thought to influence star formation processes in molecular clouds because typical cores form on length scales that are comparable to the dissipation scales of this turbulence in the ions. The simulations are motivated by the fact that recent studies of isophotologue lines in molecular clouds have found significant differences in the linewidth-size relationship for neutral and ion species. The goals of this paper are to explain those observations using simulations and analytic theory, present a new set of density-based diagnostics by drawing on similar diagnostics that have been obtained by studying single-fluid turbulence, and show that our two-fluid simulations play a vital role in reconciling alternative models of star formation. The velocity-dependent diagnostics display a complementarity with the density-dependent diagnostics. We find that the linewidth-size relationships show a prominent difference between ions and neutrals when the line of sight is orthogonal to the mean field. This is because the MHD waves in the ions differ from hydrodynamic waves in the neutrals. We also find that the density probability distribution functions (PDFs) show prominent differences between the ions and neutrals when the line of sight is parallel to the mean field. This is because the velocity fluctuations in the ions tend to produce column density fluctuations along field lines. When the magnetic field makes an angle to the line of sight, both observable differences should be visible. These diagnostics should be easy for observers to test. This analysis assumes optically thin lines and a mean magnetic field that is uniform in direction within a cloud.

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arXiv2013

The Turbulence Power Spectrum in Optically Thick Interstellar Clouds

The Fourier power spectrum is one of the most widely used statistical tools to analyze the nature of magnetohydrodynamic turbulence in the interstellar medium. Lazarian & Pogosyan (2004) predicted that the spectral slope should saturate to -3 for an optically thick medium and many observations exist in support of their prediction. However, there have not been any numerical studies to-date testing these results. We analyze the spatial power spectrum of MHD simulations with a wide range of sonic and Alfvénic Mach numbers, which include radiative transfer effects of the $^{13}$CO transition. We confirm numerically the predictions of Lazarian & Pogosyan (2004) that the spectral slope of line intensity maps of an optically thick medium saturates to -3. Furthermore, for very optically thin supersonic CO gas, where the density or CO abundance values are too low to excite emission in all but the densest shock compressed gas, we find that the spectral slope is shallower than expected from the column density. Finally, we find that mixed optically thin/thick CO gas, which has average optical depths on order of unity, shows mixed behavior: for super-Alfvénic turbulence, the integrated intensity power spectral slopes generally follow the same trend with sonic Mach number as the true column density power spectrum slopes. However, for sub-Alfvénic turbulence the spectral slopes are steeper with values near -3 which are similar to the very optically thick regime.

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arXiv2013

Hierarchical Structure of Magnetohydrodynamic Turbulence In Position-Position-Velocity Space

Magnetohydrodynamic turbulence is able to create hierarchical structures in the interstellar medium that are correlated on a wide range of scales via the energy cascade. We use hierarchical tree diagrams known as dendrograms to characterize structures in synthetic Position-Position-Velocity (PPV) emission cubes of optically thin isothermal magnetohydrodynamic turbulence. We show that the structures and degree of hierarchy observed in PPV space are related to the physics of the gas, i.e. self-gravity and the global sonic and Alfvenic Mach number. Simulations with higher Alfvenic Mach number, self-gravity and supersonic flows display enhanced hierarchical structure. We observed a strong sonic and Alfvenic dependency when we apply the the statistical moments (i.e. mean, variance, skewness, kurtosis) to the dendrogram distribution. Larger magnetic field and sonic Mach number correspond to larger values of the moments. Application of the dendrogram to 3D density cubes, also known as Position-Position-Position cubes (PPP), reveals that the dominant emission contours in PPP and PPV are related for supersonic gas but not for subsonic. We also explore the effects of smoothing, thermal broadening and velocity resolution on the dendrograms in order to make our study more applicable to observational data. These results all point to hierarchical tree diagrams as being a promising additional tool for studying ISM turbulence and star forming regions in the direction of obtaining information on the degree of self-gravity, the Mach numbers and the complicated relationship between PPV and PPP.

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arXiv2013

The Effects of Radiative Transfer on the PDFs of Molecular MHD Turbulence

We study the effects of radiative transfer on the Probability Distribution Functions (PDFs) of simulations of magnetohydrodynamic turbulence in the widely studied $^{13}$CO 2-1 transition. We find that the integrated intensity maps generally follow a log-normal distribution, with the cases that have $τ\approx 1$ best matching the PDF of the column density. We fit a 2D variance-sonic Mach number relationship to our logarithmic PDFs of the form $σ_{ln(Σ/Σ_0)}^2=A\times ln(1+b^2{\cal M}_s^2)$ and find that, for parameter $b=1/3$, parameter $A$ depends on the radiative transfer environment. We also explore the variance, skewness, and kurtosis of the linear PDFs finding that higher moments reflect both higher sonic Mach number and lower optical depth. Finally, we apply the Tsallis incremental PDF function and find that the fit parameters depend on both Mach numbers, but also are sensitive to the radiative transfer parameter space, with the $τ\approx 1$ case best fitting the incremental PDF of the true column density. We conclude that, for PDFs of low optical depth cases, part of the gas is always sub-thermally excited so that the spread of the line intensities exceeds the spread of the underlying column densities and hence the PDFs do not reflect the true column density. Similarly, PDFs of optically thick cases are dominated by the velocity dispersion and therefore do not represent the true column density PDF. Thus, in the case of molecules like carbon monoxide, the dynamic range of intensities, structures observed and consequently, the observable PDFs, are less determined by turbulence and more-often determined by radiative transfer effects.

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arXiv2012

The Column Density Variance-Sonic Mach Number Relationship

Although there are a wealth of column density tracers for both the molecular and diffuse interstellar medium, there are very few observational studies investigating the relationship between the density variance ($σ^2$) and the sonic Mach number (${\cal M}_s$). This is in part due to the fact that the $σ^2$-${\cal M}_s$ relationship is derived, via MHD simulations, for the 3D density variance only, which is not a direct observable. We investigate the utility of a 2D column density $σ_{Σ/Σ_0}^2$-${\cal M}_s$ relationship using solenoidally driven isothermal MHD simulations and find that the best fit follows closely the form of the 3D density $σ_{ρ/ρ_0}^2$-${\cal M}_s$ trend but includes a scaling parameter $A$ such that: $σ_{ln(Σ/Σ_0)}^2=A\times ln(1+b^2{\cal M}_s^2)$, where $A=0.11$ and $b=1/3$. This relation is consistent with the observational data reported for the Taurus and IC 5146 molecular clouds with $b=0.5$ and $A=0.16$ and $b=0.5$ and $A=0.12$, respectively. These results open up the possibility of using the 2D column density values of $σ^2$ for investigations of the relation between the sonic Mach number and the PDF variance in addition to existing PDF sonic Mach number relations.

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arXiv2011

Properties of Interstellar Turbulence from Gradients of Linear Radio Polarization Maps

Faraday rotation of linearly polarized radio signals provides a very sensitive probe of fluctuations in the interstellar magnetic field and ionized gas density resulting from magnetohydrodynamic (MHD) turbulence. We used a set of statistical tools to analyze images of the spatial gradient of linearly polarized radio emission ($|\nabla \textbf{P}|$) from the ISM for both observational data from a test image of the Southern Galactic Plane Survey (SGPS) and isothermal simulations of MHD turbulence. We compared the observational data with results of synthetic observations obtained with the simulations of 3D turbulence. Visually, in both data sets, a complex network of filamentary structures is seen. Our analysis shows that the filaments in the gradient can be produced by shocks as well as random fluctuations characterizing the non-differentiable field of MHD turbulence. The latter dominates for subsonic turbulence, while the former dominates for supersonic turbulence. In order to quantitatively characterize these differences we use the topology tool known as a genus curve as well as the moments of the image distribution. We find that higher values for the moments correspond to cases of $|\nabla \textbf{P}|$ with larger Mach numbers, but the strength of the dependency is connected to the telescope angular resolution. In regards to the topology, the supersonic filaments observed in $|\nabla \textbf{P}|$ have a positive genus shift, which indicates a "swisscheese" like topology, while the subsonic cases show a negative genus, indicating a "clump" like topology. In the case of the genus, the dependency on the telescope resolution is not as strong. The SGPS test region data has a distribution and morphology that matches subsonic to transsonic type turbulence, which independently confirms what is now expected for the WIM.

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arXiv2011

Low-Mach-number turbulence in interstellar gas revealed by radio polarization gradients

The interstellar medium of the Milky Way is multi-phase, magnetized and turbulent. Turbulence in the interstellar medium produces a global cascade of random gas motions, spanning scales ranging from 100 parsecs to 1000 kilometres. Fundamental parameters of interstellar turbulence such as the sonic Mach number (the speed of sound) have been difficult to determine because observations have lacked the sensitivity and resolution to directly image the small-scale structure associated with turbulent motion. Observations of linear polarization and Faraday rotation in radio emission from the Milky Way have identified unusual polarized structures that often have no counterparts in the total radiation intensity or at other wavelengths, and whose physical significance has been unclear. Here we report that the gradient of the Stokes vector (Q,U), where Q and U are parameters describing the polarization state of radiation, provides an image of magnetized turbulence in diffuse ionized gas, manifested as a complex filamentary web of discontinuities in gas density and magnetic field. Through comparison with simulations, we demonstrate that turbulence in the warm ionized medium has a relatively low sonic Mach number, M_s <~ 2. The development of statistical tools for the analysis of polarization gradients will allow accurate determinations of the Mach number, Reynolds number and magnetic field strength in interstellar turbulence over a wide range of conditions.

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arXiv2011

Statistical Tools of Interstellar Turbulence: Bridging the Gap Between Numerics and Observations

MHD Turbulence is a critical component of the current paradigms of star formation, particle transport, magnetic reconnection and evolution of the ISM. Progress on this difficult subject is made via numerical simulations and observational studies. However, due to limitations of resolution, scale discrepancies, and complexity of the observations, the best approach for connecting numerics to observations is not always obvious. Here we advocate for a approach that invokes statistical techniques to understand the underlying physics of turbulent astrophysical systems. The wealth of numerical and observational data calls for new statistical tools to be developed in order to study turbulence in the interstellar medium. We briefly review some of the recently developed statistics that focus on characterizing gas compressibility and magnetization and their uses to interstellar studies.

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arXiv2011

Interstellar Sonic and Alfvénic 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.

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arXiv2011

Statistical Tools of ISM turbulence

MHD Turbulence is a critical component of the current paradigms of star formation, particle transport, magnetic reconnection and evolution of the ISM, to name just a few. Progress on this difficult subject is made via numerical simulations and observational studies, however in order to connect these two, statistical methods are required. This calls for new statistical tools to be developed in order to study turbulence in the interstellar medium. Here we briefly review some of the recently developed statistics that focus on characterizing gas compressibility and magnetization and their uses to interstellar studies.

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arXiv2009

Characterizing Magnetohydrodynamic Turbulence in the Small Magellanic Cloud

We investigate the nature and spatial variations of turbulence in the Small Magellanic Cloud (SMC) by applying several statistical methods on the neutral hydrogen (HI) column density image of the SMC and a database of isothermal numerical simulations. By using the 3rd and 4th statistical moments we derive the spatial distribution of the sonic Mach number (M_s) across the SMC. We find that about 90% of the HI in the SMC is subsonic or transonic. However, edges of the SMC `bar' have M_s=4 and may be tracing shearing or turbulent flows. Using numerical simulations we also investigate how the slope of the spatial power spectrum depends on both sonic and Alfven Mach numbers. This allows us to gauge the Alfven Mach number of the SMC and conclude that its gas pressure dominates over the magnetic pressure. The super-Alfvenic nature of the HI gas in the SMC is also highlighted by the bispectrum, a three-point correlation function which characterizes the level of non-Gaussianity in wave modes. We find that the bispectrum of the SMC HI column density displays similar large-scale correlations as numerical simulations, however it has localized enhancements of correlations. In addition, we find a break in correlations at a scale of 160 pc. This may be caused by numerous expanding shells of a similar size.

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arXiv2008

Density Studies of MHD Interstellar Turbulence: Statistical Moments, Correlations and Bispectrum

We present a number of statistical tools for obtaining studying turbulence in molecular clouds and diffuse interstellar medium. For our tests we used of three-dimensional 512 cube compressible MHD isothermal simulations performed for different sonic and Alfvenic 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. 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. Larger values of sonic Mach number result in increased correlations for modes with different wavenumbers. This effect becomes more evident with increasing magnetic field intensity. 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 the sonic Mach number. In particular, as this number increases, so does the 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 Alfven Mach number for comparison. Our results show that column density is linearly correlated with magnetic field for high sonic Mach number. 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.

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