Steven R. Spangler

Evidence for an inner scale to the density turbulence in the interstellar medium

The form of the density power spectrum is studied. The relationship between the visibility and the properties of density turbulence is discussed. Observational determinations of the power-law index of the interstellar density power spectrum are presented. An inner scale is derived, and the effect of an inner scale in the interstellar plasma turbulence is examined. It is concluded that the host plasma for the density irregularities must be similar to the warm ionized medium in the Mckee-Ostriker model (1979) of the interstellar medium or the low-density envelopes of H II regions. 32 refs.

Weakly Compressible Magnetohydrodynamic Turbulence in the Solar Wind and the Interstellar Medium

A new four-field system of equations is derived from the compressible magnetohydrodynamic (MHD) equations for low Mach number turbulence in the solar wind and the interstellar medium, permeated by a spatially varying magnetic field. The plasma beta is assumed to be of order unity or less. It is shown that the full MHD equations can be reduced rigorously to a closed system for four fluctuating field variables: magnetic flux, vorticity, pressure, and parallel flow. Although the velocity perpendicular to the magnetic field is shown to obey a two-dimensional incompressibility condition (analogous to the Proudman-Taylor theorem in hydrodynamics), the three-dimensional dynamics exhibit the effects of compressibility. In the presence of spatial inhomogeneities, the four dynamical equations are coupled to each other, and pressure fluctuations enter the weakly compressible dynamics at leading order. If there are no spatial inhomogeneities and or if the plasma beta is low, the four-field equations reduce to the well-known equations of reduced magnetohydrodynamics (RMHD). For pressure-balanced structures, the four-field equations undergo a remarkable simplification which provides insight on the special nature of the fluctuations driven by these structures. The important role of spatial inhomogeneities is elucidated by 2.5-dimensional numerical simulations. In the presence of inhomogeneities, the saturated pressure and density fluctuations scale with the Mach number of the turbulence, and the system attains equipartition with respect to the kinetic, magnetic, and thermal energy of the fluctuations. The present work suggests that if heliospheric and interstellar turbulence exists in a plasma with large-scale, nonturbulent spatial gradients, one expects the pressure and density fluctuations to be of significantly larger magnitude than suggested in nearly incompressible models such as pseudosound.

Heating of the Interstellar Diffuse Ionized Gas via the Dissipation of Turbulence

We have recently published observations that specify most of the turbulent and mean plasma characteristics for a region of the sky containing the interstellar diffuse ionized gas (DIG). These observations have provided virtually all of the information necessary to calculate the heating rate from dissipation of turbulence. We have calculated the turbulent dissipation heating rate employing two models for the interstellar turbulence. The first is a customary modeling as a superposition of magnetohydrodynamic waves. The second is a fluid-turbulence-like model based on the ideas of Higdon. This represents the first time that such calculations have been carried out with full and specific interstellar turbulence parameters. The wave model of interstellar turbulence encounters the severe difficulty that plausible estimates of heating by Landau damping exceed the radiative cooling capacity of the interstellar DIG by 3-4 orders of magnitude. Clearly interstellar turbulence does not behave like an ensemble of obliquely propagating fast magnetosonic waves. The heating rate due to two other wave dissipation mechanisms, ion-neutral collisional damping and the parametric decay instability, are comparable to the cooling capacity of the diffuse ionized medium. We find that the fluid-like turbulence model is an acceptable and realistic model of the turbulence in the interstellar medium once the effects of ion-neutral collisions are included in the model. This statement is contingent on an assumption that the dissipation of such turbulence because of Landau damping is several orders of magnitude less than that from an ensemble of obliquely propagating magnetosonic waves with the same energy density. Arguments as to why this may be the case are made in the paper. Rough parity between the turbulent heating rate and the radiative cooling rate in the DIG also depends on the hydrogen ionization fraction being in excess of 90% or on a model-dependent lower limit to the heating rate being approximately valid. We conclude that the dissipation of turbulence is capable of providing a substantial and perhaps major contribution to the energy budget of the diffuse ionized medium.

Faraday Rotation and Models for the Plasma Structure of the Solar Corona

Faraday rotation observations of polarized radiation from natural radio sources are unique among remote diagnostics of the solar corona in that they provide information on the coronal magnetic field. Dual frequency radio polarization measurements yield the rotation measure, a quantity that is proportional to the integral along the line of sight of the product of the electron density and the line-of-sight component of the magnetic field. We made linear polarization observations with the NRAO Very Large Array of 13 polarized radio sources occulted by the solar corona. The observations were made at frequencies of 1465 and 1665 MHz on four days in 1997 May and cover a 20 day period, sampling elongations ranging from about 5 to 14 R☉. The magnitudes of the rotation measures observed range from about 11 to 0 rad m-2. The relatively low values for the rotation measures are due to the solar minimum configuration of the corona at the time of the observations, with the lines of sight to the sources generally not crossing sector boundaries. The largest rotation measure was observed for the extended radio source 3C 79 on 1997 May 11 and corresponds to a case in which the line of sight passed next to the streamer belt at small solar elongations. We have developed a three-dimensional model of the solar corona that is in excellent agreement with the observed rotation measures, as well as being completely consistent with other coronal diagnostics such as coronagraph images. In particular, our observations support the coronal magnetic field model of Patzold et al. (1987); they would be inconsistent with coronal magnetic fields significantly weaker or stronger than this model. The plasma density distribution in the corona is successfully modeled by a dense streamer belt component and a more tenuous coronal hole component. Details of these models are given in § 3 of this paper. The principal disagreement between the model and observations occurs for three lines of sight for which the model predicts nearly zero rotation measure but for which we measure small but significant values of -1 to -2 rad m-2. These lines of sight passed over the solar polar regions. We discuss the possibility that these residual rotation measures are due to static coronal plasma structures, not described by global coronal models, or to very long wavelength coronal Alfven waves. Fluctuations in the rotation measure on timescales of a few hours were observed for some sources and not others. When detected, they were of order 1-2 rad m-2 and occurred on timescales of several hours.

Kinetic effects of Alfvén wave nonlinearity. I: Ponderomotive density fluctuations

The Vlasov theory is used to study kinetic corrections to fluid descriptions of Alfven wave nonlinearity. The method is to obtain an expression for the second‐order perturbed distribution function produced by a nonlinear Alfven wave. From this distribution function a kinetically correct expression is obtained for δn, the plasma density perturbation associated with an envelope‐modulated Alfven wave. This kinetic theory result differs substantially from the fluid expression when the plasma β≳1, and the electron and ion temperatures are approximately equal. This result is of interest because density fluctuations are an observationally accessible indicator of wave nonlinearity in solar system Alfven waves. It also will assist in the determination of properties of Alfven waves in the interstellar medium. Finally, this analysis also yields a kinetically correct expression for u, the magnetic field‐aligned component of the plasma fluid velocity. For parallel‐propagating wave packets, this field‐aligned flow is a...

Kinetic effects on Alfvén wave nonlinearity. II , The modified nonlinear wave equation

The study of kinetic effects on Alfven wave nonlinearity is continued. Previously obtained expressions for the perturbed (by an Alfven wave) ion and electron distribution functions are used to obtain a nonlinear wave equation for parallel‐propagating, circularly polarized waves. The results are cast in the form of a modified version of the familiar derivative nonlinear Schrodinger equation. The approach in obtaining this equation is a hybrid one; fluid theory is used to the greatest extent possible, and kinetic theory is introduced where the correction is believed to be most important. Fluid theory at two levels of sophistication is employed. The first uses a simple scalar pressure term. This approach yields physical insight and illuminates the field‐aligned fluid flow and the associated plasma density perturbation as a major contributor to Alfven wave nonlinearity. The second approach employs a tensor pressure term that in general will be necessary. The results indicate that kinetic effects in general pr...

VLBI observations of a complete sample of radio galaxies. 4: The radio galaxies NGC 2484, 3C 109, and 3C 382

We present here new Very Long Base Interferometry (VLBI) observations of one Fanaroff and Riley (F-R) I radio galaxy (NGC 2484) and two broad-line F-R II radio galaxies (3C 109 and 3C 382). For 3C 109 new Very Large Array (VLA) maps are also shown. These sources belong to a complete sample of radio galaxies under study for a better knowledge of their structures at parsec resolution. The parsec structure of these three objects is very similar: asymmetric emission, which we interpret as the core plus a one-side jet. The parsec-scale jet is always on the same side of the main kiloparsec-scale jet. The limit on the jet to counterjet brightness ratio, the ratio of the core radio power to the total radio power and the synchrotron-self Compton model allow us to derive some constraints on the jet velocity and orientation with respect to the line of sight. From these data and from those published on two other sources of our sample, we suggest that parsec-scale jets are relativistic in both F-R I and F-R II radio galaxies and that parsec scale properties in F-R I and F-R II radio galaxies are very similar despite the large difference between these two classes of radio galaxies on the kiloparsec scale.

A numerical study of nonlinear Alfvén waves and solitons

Finite‐amplitude Alfven waves can be modeled by a nonlinear wave equation termed the derivative nonlinear Schrodinger equation. A computer program has been developed that solves the derivative nonlinear Schrodinger equation via the ‘‘split‐step’’ Fourier method. This program has been used to investigate a number of topics in the area of nonlinear Alfven waves. When analytic envelope solitons are used as initial conditions, the wave packets propagate without distortion and with the expected speed–amplitude relation. When an arbitrary, amplitude‐modulated wave is used as an initial condition, the results depend strongly on the β of the plasma and the polarization of the wave. For a left circularly polarized wave in a β 1, a collapse instability has been observed in which the wave amplitude increases and modulation scale decreases. For other combinations of polarization and value of β, the wave packet tends to broaden, eliminating the initial modulation.

Two-dimensional Magnetohydrodynamics and Interstellar Plasma Turbulence

This paper is concerned with a physical understanding of the main features of interstellar plasma turbulence. Our observational knowledge of this turbulence is provided by radio-wave propagation observations, generically referred to as interstellar scintillations. Distinctive features of the observations are the nearly omnipresent anisotropy of scattering, revealed by elliptical rather than circular scattering disks, drastic differences in the magnitude of scattering between closely spaced lines of sight through the interstellar medium, evidence from Faraday rotation observations that the interstellar vector magnetic field changes markedly on small spatial scales, and the existence of a power-law spectrum of density irregularities over a wide range of spatial scales. This power-law density spectrum strongly suggests the existence of similar spatial power spectra for the other magnetohydrodynamic (MHD) variables such as flow velocity and magnetic field. In this paper, it is pointed out that the aforementioned features arise or may naturally be explained by an approximate theory of magnetohydrodynamic turbulence, two-dimensional magnetohydrodynamics. In this theory, the plasma turbulence is described by two scalar functions (a velocity stream function and one component of the magnetic vector potential) that are coupled by nonlinear partial differential equations. These equations are physically transparent, possess some relevant analytic results, and are easily solved numerically. Arguments for the relevance of this reduced plasma description are presented. Although obviously an incomplete description of the interstellar plasma, these equations provide plausible explanations for the observational features described above. Anisotropy of scattering arises as an obvious consequence of the conditions for validity of the two-dimensional MHD description, i.e., that spatial gradients along a large-scale magnetic field are much smaller than those perpendicular to the field. The equations of two-dimensional MHD predict the formation of intense electrical current and vorticity sheets from broad classes of initial conditions. It is highly plausible that these sheets are the loci of elevated turbulence, which could explain the variations of radio-wave scattering and provide a physical explanation for intermittency in interstellar turbulence. The strong current sheets would also produce localized reversals in the turbulent component of the interstellar magnetic field. Finally, the equations of two-dimensional MHD produce spectral flattening of initial conditions with steep spatial power spectra. The calculations presented here, as well as elsewhere in the literature, indicate that the equilibrium magnetic field and velocity spectra may be power laws with indices close to those observed for the density fluctuations. In summary, the equations of two-dimensional magnetohydrodynamics are proposed as a simplified theoretical tool for use in understanding interstellar plasma turbulence.

The evolution of nonlinear Alfvén waves subject to growth and damping

Results of a numerical study of Alfven waves are presented subject to nonlinearity, dispersion, growth, and damping. The model presented is the derivative nonlinear Schrodinger equation, modified to include linear growth and damping processes. The processes that are considered are wave amplification by streaming particle distributions, and damping resulting from ion‐cyclotron resonance absorption. These growth and damping mechanisms are dominant in different portions of wavenumber space. The primary role of nonlinearity is the transfer of wave energy from growing or amplified wavenumbers to those which are damped. A nonlinear saturation mechanism thereby results, in which instability of low wavenumber modes may be quenched. A simple phenomenological model is developed, which accounts for many of the salient features of the numerical calculations. The application of these results to observations of Alfven waves upstream of the Earth’s bow shock is briefly considered. It is suggested that the short waveleng...