A. Esquivel

VELOCITY CENTROIDS AS TRACERS OF THE TURBULENT VELOCITY STATISTICS

We use the results of magnetohydrodynamic (MHD) simulations to emulate spectroscopic observations and use maps of centroids to study their statistics. In order to assess under which circumstances the scaling properties of the velocity field can be retrieved from velocity centroids, we compare two-point statistics (structure functions and power spectra) of velocity centroids with those of the underlying velocity field and analytic predictions presented by us in a previous paper. We tested a criterion for recovering velocity spectral index from velocity centroids derived in our previous work and propose an approximation of the early criterion using only the variances of unnormalized velocity centroids and column density maps. It was found that both criteria are necessary, but not sufficient, to determine if the centroids recover velocity statistics. Both criteria are well fulfilled for subsonic turbulence. We find that for supersonic turbulence with sonic Mach numbers s 2.5, centroids fail to trace the spectral index of velocity. Asymptotically, however, we claim that recovery of velocity statistics is always possible provided that the density spectrum is steep and the observed inertial range is sufficiently extended. In addition, we show that velocity centroids are useful for anisotropy studies and determining the direction of the magnetic field, even if the turbulence is highly supersonic, but only if it is sub-Alfvenic. This provides a tool for mapping the magnetic field direction and for testing whether the turbulence is sub-Alfvenic or super-Alfvenic.

TSALLIS STATISTICS AS A TOOL FOR STUDYING INTERSTELLAR TURBULENCE

We used magnetohydrodynamic (MHD) simulations of interstellar turbulence to study the probability distribution functions (PDFs) of increments of density, velocity, and magnetic field. We found that the PDFs are well described by a Tsallis distribution, following the same general trends found in solar wind and electron MHD studies. We found that the PDFs of density are very different in subsonic and supersonic turbulence. In order to extend this work to ISM observations, we studied maps of column density obtained from three-dimensional MHD simulations. From the column density maps, we found the parameters that fit to Tsallis distributions and demonstrated that these parameters vary with the sonic and Alfven Mach numbers of turbulence. This opens avenues for using Tsallis distributions to study the dynamical and perhaps magnetic states of interstellar gas.

Velocity statistics from spectral line data: effects of density—velocity correlations, magnetic field and shear

In a previous work, Lazarian and Pogosyan suggested a technique to extract velocity and density statistics, of interstellar turbulence, by means of analysing statistics of spectral line data cubes. In this paper, we test that technique by studying the effect of correlation between velocity and density fields, providing a systematic analysis of the uncertainties arising from the numerics, and exploring the effect of a linear shear. We make use of both compressible magnetohydrodynamics simulations and synthetic data to emulate spectroscopic observations and to test the technique. With the same synthetic spectroscopic data, we have also studied anisotropies of the two point statistics and related those anisotropies with the magnetic field direction. This presents a new technique for magnetic field studies. The results show that the velocity and density spectral indices measured are consistent with the analytical predictions. We have identified the dominant source of error with the limited number of data points along a given line of sight. We decrease this type of noise by increasing the number of points and by introducing Gaussian smoothing. We argue that in real observations the number of emitting elements is essentially infinite and that the source of noise vanishes.

MIRROR AND POINT SYMMETRIES IN A BALLISTIC JET FROM A BINARY SYSTEM

Models of accretion disks around a star in a binary system predict that the disk will have a retrograde precession with a period a factor of ~10 times the orbital period. If the star+disk system ejects a bipolar outflow, this outflow will be subject to the effects of both the orbital motion and the precession. We present an analytic, ballistic model and a three-dimensional gasdynamical simulation of a bipolar outflow from a source in a circular orbit, and with a precessing outflow axis. We find that this combination results in a jet/counterjet system with a small spatial scale, reflection-symmetric spiral (resulting from the orbital motion) and a larger-scale, point-symmetric spiral (resulting from the longer period precession). These results provide interesting possibilities for modeling specific Herbig-Haro jets and bipolar planetary nebulae.

Interstellar cloud structure: the statistics of centroid velocities

Context. The statistical properties of maps of line centroids have been used for almost 50 years, but there is still no general agreement on their interpretation. Aims. We have tried to quantify which properties of underlying turbulent velocity fields can be derived from centroid velocity maps, and we tested conditions under which the scaling behaviour of the centroid velocities matches the scaling of the three-dimensional velocity field. Methods. Using fractal cloud models we systematically studied the relation between three-dimensional density and velocity fields and the statistical properties of the resulting line centroid maps. We paid special attention to cases with large density fluctuations resembling supersonic interstellar turbulence. Starting from the ∆-variance analysis, we derived a new tool to compute the scaling behaviour of the three-dimensional velocity field from observed intensity and centroid velocity maps. Results. We provide two criteria to decide whether the information from the centroid velocities directly reflects the properties of the underlying velocity field. Applying these criteria allows us to understand the different results found so far in the literature for interpreting the statistics of velocity centroids. The new iteration scheme can be used to derive the three-dimensional velocity scaling from centroid velocity maps for arbitrary density and velocity fields, but it requires accurate knowledge of the average density of the interstellar cloud under consideration.

Line ratios from shocked cloudlets in planetary nebulae

Context. Some PNe and PPNe show compact knots, travelling at high velocities away from the central sources. Aims. We compute a number of models from which we obtain predictions of the emission-line spectrum, which can be compared with the spectra of the observed knots. Methods. We completed a series of 11 axisymmetric simulations of an initially spherical cloudlet, travelling away from a photoionizing source, into a uniform medium. The simulations included a multi-frequency transfer of the ionizing radiation, and a 33 species non-equilibrium ionization network. Results. From our simulations, we computed emission maps and spatially-integrated emission-line spectra. The predictions show a transition from spectra similar to those of shock wave models (for simulations with lower photoionization rates) to spectra similar to those of photoionized regions (for simulations with higher photoionization rates). Conclusions. The spectra from our photoionized cloudlet models have a range of line ratios that agree approximately with the observed spectra when shown in two-line ratio diagnostic diagrams. The predicted and observed spatial distributions of the emission (with high ionization lines extending more towards the source than lower ionization lines) agree in a qualitative way.

Measuring the Alfvénic nature of the interstellar medium: Velocity anisotropy revisited

The dynamics of the interstellar medium (ISM) are strongly affected by turbulence, which shows increased anisotropy in the presence of a magnetic field. We expand upon the Esquivel & Lazarian method to estimate the Alfven Mach number using the structure function anisotropy in velocity centroid data from position-position-velocity maps. We utilize 3D magnetohydrodynamic (MHD) simulations of fully developed turbulence, with a large range of sonic and Alfvenic Mach numbers, to produce synthetic observations of velocity centroids with observational characteristics such as thermal broadening, cloud boundaries, noise, and radiative transfer effects of carbon monoxide. In addition, we investigate how the resulting anisotropy-Alfven Mach number dependency found in Esquivel & Lazarian (2011) might change when taking the second moment of the position-position-velocity cube or when using different expressions to calculate the velocity centroids. We find that the degree of anisotropy is related primarily to the magnetic field strength (i.e. Alfven Mach number) and the line-of-sight orientation, with a secondary effect on sonic Mach number. If the line-of-sight is parallel to up to ~45 deg off of the mean field direction, the velocity centroid anisotropy is not prominent enough to distinguish different Alfvenic regimes. The observed anisotropy is not strongly affected by including radiative transfer, although future studies should include additional tests for opacity effects. These results open up the possibility of studying the magnetic nature of the ISM using statistical methods in addition to existing observational techniques.

Magnetohydrodynamic Turbulent Mixing Layers: Equilibrium Cooling Models

We present models of turbulent mixing at the boundaries between hot (T ∼ 10 6 7 K) and warm material (T ∼ 10 4 K) in the interstellar medium, using a three-dimensional magnetohydrodynamical code, with radiative cooling. The source of turbulence in our simulations is a Kelvin-Helmholtz instability, produced by shear between the two media. We found, that because the growth rate of the large scale modes in the instability is rather slow, it takes a significant amount of time (∼ 1 Myr) for turbulence to produce effective mixing. We find that the total column densities of the highly ionized species (C IV, N V, and O VI) per interface (assuming ionization equilibrium) are similar to previous steady-state non-equilibrium ionization models, but grow slowly from logN ∼ 10 11 to a few ×10 12 cm 2 as the interface evolves. However, the column density ratios can differ significantly from previous estimates, with an order of magnitude variation in N(C IV)/N(O VI) as the mixing develops. Subject headings: ISM: general — ISM: structure — magnetohydrodynamics: MHD — turbulence

A wind–shell interaction model for multipolar planetary nebulae

We explore the formation of multipolar structures in planetary and pre-planetary nebulae from the interaction of a fast post-AGB wind with a highly inhomogeneous and filamentary shell structure assumed to form during the final phase of the high density wind. The simulations were performed with a new hydrodynamics code integrated in the interactive framework of the astrophysical modeling package SHAPE. In contrast to conventional astrophysical hydrodynamics software, the new code does not require any programming intervention by the user for setting up or controlling the code. Visualization and analysis of the simulation data has been done in SHAPE without external software. The key conclusion from the simulations is that secondary lobes in planetary nebulae, such as Hubble 5 and K3-17, can be formed through the interaction of a fast low-density wind with a complex high density environment, such as a filamentary circumstellar shell. The more complicated alternative explanation of intermittent collimated outflows that change direction, in many cases may therefore not be necessary. We consider that the wind-shell interaction scenario is more likely since the bow-shock shape expected from a strongly cooling bow-shock from jets is different from that of the observed bubbles. Furthermore, the timescales of the wind-wind interaction suggest that the progenitor star was rather massive.

A precessing jet model for the PN K 3 − 35: simulated radio-continuum emission

The bipolar morphology of the planetary nebula (PN) K 3 - 35 observed in radio-continuum images was modelled with 3D hydrodynamic simulations with the adaptive grid code YGUAZU-A. We find that the observed morphology of this PN can be reproduced considering a precessing jet evolving in a dense AGB circumstellar medium, given by a mass-loss rate M csm = 5 x 10 -5 M ⊙ yr -1 and a terminal velocity v w = 10 km s -1 . Synthetic thermal radio-continuum maps were generated from numerical results for several frequencies. Comparing the maps and the total fluxes obtained from the simulations with the observational results, we find that a model of precessing dense jets, where each jet injects material into the surrounding CSM at a rate M j = 2.8 x 10 -4 M ⊙ yr -1 (equivalent to a density of 8 x 10 4 cm -3 ), a velocity of 1500 km s -1 , a precession period of 100 yr and a semi-aperture precession angle of 20° agrees well with the observations.