Evidence for Anisotropy and Intermittencyin the Turbulent Interstellar Plasma

Bill Coles, University of California, San Diego

1. It had been thought that turbulence in the WIM was more or lessisotropic. This view was based on a few VLBI observations ofhighly scattered sources. However highly scattered sources areatypical. Evidence is accumulating that anisotropy may be actuallyrelatively common.

2. There is no doubt that the warm interstellar plasma (WIM) ishighly sporadic, but it is not clear that it is intermittent in the senseused in hydrodynamics. However the tiny structures observed byDan and discussed by Barney may be evidence for intermittency.

Key Plasma Parameters for Radio ScatteringInner Scale: Li = dissipation scale.

Dissipation via ion-neutral collisions (neutral viscosity)which occurs about Li = 10 AU decouples scaleslarger than this from scales smaller. In fact twoturbulent spectra can exist supported by differentenergy sources.

The small scale process suffers ion cyclotron damping atLi = the ion inertial scale = VA/ωci = 622km/(NEcm-3)1/2

Thermal pressure/Magnetic pressure: β = NEkT/B2

β < 1 -> magnetic fields dominate -> anisotropy likely

Astrophysical PlasmasIonosphere F region at 400 km;

Li = 500 m; β = 4 x 10-6

always highly anisotropic

Solarwind at distance RS;

Li = RS km; β < 1 for RS < 20;

anisotropic for RS < 20WIM: NE = 0.1 cm-3; B = 5 µg; T = 104 K.

Li = 2200 km; β = 0.15

Solar Wind Anisotropy vs Solar Distance

Model AR(R) of plasma

expected AR(R) for radio wave

The vertical bars indicatevariation not statistical error

β < 1 β > 1

Radio Parameters1. Weak Scattering: spatial scale = Rf = (λz/2π)0.5

WIM @ 5 GHz; 500 pc; Rf = 4 x 105 km; Rf/Li = 200This is why parabolic arcs are so clear in ISS!

Solarwind @ 1 GHz; 1 AU; Rf = 85 km; Rf/Li = 4

Ionosphere@100 MHz; 400 km; Rf = 400 m; Rf/Li = 0.8

2. Strong Scattering: small spatial scale = S0 ∝ λ-6/5 << Rflarge spatial scale = SR where SRS0=Rf

2

WIM 100 MHz; S0/Li = 2; so arcs are always visible

SR = 4 x 107 km, so even the largest scales remain below theion-neutral cutoff scale.

More Radio ParametersRefractive Scale: Nan Dieter was probably the first personto observe refractive scintillation when she reported timevariation in OH sources, notably NGC6334.

Temporal broadening must exceed the pulse width to bevisible. Thus it has always been measured in very strongscattering where S0 < Li.

We should make more effort to understand the broadeningof Crab giant pulses for S0 > Li. It may be possible toobserve temporal broadening in the inertial subrange.

Ulyssesspacecraft

VLBA

Grall et al., VLA par

Harmon and Coles

Paetzold & Birdphase scintillation

VLA perp

ωci/VA

Anisotropic Range -intensity scintillationand angular scattering

Spectra Measured in the Fast Polar Solar Wind

Large Scale StructuresIt is difficult to probe scales larger than Rf using radioscattering, so one is driven to use other observations such asdispersion measure fluctuations in the WIM, or white lightbrightness in the Solar corona. However

Thus dispersion and scattering can be dominated bydifferent structures. Small dense structures may dominatethe scattering yet be invisible in dispersion, and largestructures which dominate dispersion may be invisible inscattering. This occurs in the solar wind, and probably inthe WIM

Aug. 2 3 4

Mercury

Ramachandran et al 2006:

Timing vs Scattering for B1937+21 from Ramachandran et al.

AnisotropyIt is hard to measure anisotropy in the WIM directly becausethe spatial scales are much larger than our interferometersunless the scattering is very strong. Of course very strongscattering implies more distant pulsars and less likelihood ofthe scattering being dominated by a single compact region.

There are two indirect methods which work in relativelyweak scattering: (1) intensity correlations; (2) the secondaryspectrum.

1. The shape of the auto-correlation in weak-scatteringbecomes very angle-dependent when the medium isanisotropic.

Isotropic intensity autocorrelation

Anisotropic autocorrelation with AR = 3

Observational EvidenceThere are several ways one can make use of this correlation.

1. If a cut through the intensity correlation shows strongoscillation then the AR > 3 is likely.

2. If the system cuts through the correlation at differentangles then the time constant will change with angle. Thisoccurs in two situations: (a) due to changes in the Earth’svelocity; (b) due to changes in the pulsar velocity.

“Intra-day” variability in the quasar J1819+3845

Secondary SpectraSecondary spectra provide even more direct evidence for

anisotropy. In weak scattering the secondary spectrum canactually be inverted to obtain the two-dimensional phasespectrum, so anisotropy can be observed directly. Instrong scattering an inversion is not possible but the effectof anisotropy is clear.

This is best seen on full-electromagnetic simulations.

Isotropic strong scattering simulation

Anisotropic strong scattering simulation AR = 3

Why do we care about anisotropy anyway?So we have evidence that anisotropy is more common than

had been thought. So what?

1. Analysis of IDV and binary pulsar observations dependsstrongly on anisotropy and failure to include it will leadto serious errors.

2. Observation of anisotropic turbulence suggests that theplasma β < 1, which may provide an interesting boundon the magnetic field and/or the temperature.

3. The refractive scale size is considerably larger when theturbulence is anisotropic. The simple concept of the“scattering disc” = “refractive scale” breaks down.

Isotropic Anisotropic

scatteringdisc

refractivescale

scattering disc = θz ≡ refractive scale

Spatial Variation in Level of TurbulenceScattering observations of different pulsars, even closeneighbours, show radically different scattering strengths.This can be seen most directly in a plot of the effective pulsebroadening vs dispersion measure.

Spatial Variations of Level of TurbulenceOne can model this variation using a random population ofpc sized structures with Ne = 0.1 to 10 cm-3. The meanseparation needed is 10’s of pc.

These objects are large compared with the scattering discand the drift time is very long. However they are smallcompared with the distance to the Earth - thus they can bemodeled by a Thin Screen, and they will show arcs.

Secondary spectra show well-defined arcs which persist fordecades apparently unchanged. Sometimes they showseveral persistent well-defined arcs, suggesting that severalscattering objects may be involved.

Double Pulsar ScintillationsStrong scattering spatial scale = 40,000 km @ 1400 MHzRf = 5.6 x 105 km; Scattering disc = 2 x 107 km; drift timefor scattering disc = 8 days; Orbital period = 2.4 hrs.Orbital diameter = 9 x 105 km -> during an orbit one doesnot see refractive scintillation.

Phase gradients are obvious at some times but not at others.The gradient must persist for at least 2 x 107 km but cannotlast longer than 108 km. They cause asymmetrical arcs.

Dynamic Spectrum of Double Pulsar

We thought that these gradients required an excess of phaseover a Kolmogorov spectrum and might be related to TinyStructures. However we (recently) have been able tosimulate them with a Kolmogorov spectrum - alas.

So these phase gradients are unremarkable…

IntermittencyHowever secondary spectra also show much smallerstructures which cross the line of sight on a time scale ofmonths. There is also evidence for such structures in the ISSof extra-galactic IDV sources.

These Tiny Structures have sub-AU diameters, yet theymust be common. It is reasonable to imagine that they are“intermittent plumes” of turbulence within the pc-sizedstructures.

A suitable generating mechanism might be the shear-instabilities. Colliding clouds would certainly generate suchplumes close to the contact surface, and they would stopgrowing in size and persist as “fossil” plumes after theclouds moved apart.