What do Scintillations tell us about the Ionized ISM ?

Barney Rickett

UC San DiegoSINS Socorro May 2006

For scales far from the inner and outer scales in an isotropic Kolmogorov spectrum

P3ne() = Cn2 inner > > outer { inner = 1/linner ; outer =1/louter}

Dne() with =5/3 linner < < louter

Electron density and its spectrumThe radio scintillation of pulsars and AGNs probe the fine structure in the interstellar electron density ne(s,z) versus transverse position s and

distance z from the Earth. From observations one can estimate the structure function of density versus a transverse separation

Dne() = ∫0

L< [ne(s,z) - ne(s+,z)]2 > dz (for a pulsar at distance L)

This is the density structure function (integrated over los). It’s related to the Power spectrum of density versus transverse wavenumber

Dne() = ∫ P3ne(z=0) {1-ei}d2

log( innerouter

P ()3ne -(3.67)

Notice that a Kolmogorov density spectrum only suggests turbulence (no V or B obs)The scales probed by ISS are 100km to 30 AUTiny for ISS is 100 kmlouter > 10AU

Structure Function with Inner scale

For scales smaller than the inner scale the structure function follows a square law. Thus scattering effects are still present on scales below the inner scale.

Note that there is not much difference between =1.667 and 2, so the ISS effects of an inner scale are subtle.

Log[ Dne() ]

Log[ ]

linner

What can we learn from ISS?

Scintillation can probe the form of the spectrum => inner & outer scales, anisotropy for one line of sightAnd explore its rms amplitude versus Galactic coords => Cn

2 or more accurately Scattering Measure SM = ∫Cn2 dz

versus latitude, longitude and scattered path length

The first order description is an isotropic Kolmogorov spectrum that is pervasive throughout the Galaxy - with some volume filling factor.

This is the conceit of ISS studies that the small scale structure of the ionized ISM could be decribed by three parameters: exponent (5/3), level (Cn

2) & filling factor

Pulsar dispersion measures combined with independent distance estimates suggest that the volume average <ne> ~

0.03 cm-3

Estimates of the volume filling factor are 0.1-0.25 and so imply local electron densities in the ionized regions 0.1-0.3 cm-3

Ramachandran et al 2006:

Variation of Dispersion Measure psr B1937+21

(2.2x1018 cm-2)

3x1014 cm-2

Slope = 1.66

Structure Function of phase at 1.4 GHz psr B1937+21

If extrapolated down to where D = 1 rad2 the diffractive scale is predicted to be 7x106 m.Compare with the scale estimated fromsc. It is 2 times larger which they suggest is due to an inner scale of 1.3x109 m (~0.01 AU) which is larger than the diffractive scale ~0.001 AU

The solid line gives the best fit line for the data in the time interval of 10 days to 5000 days. The derived values of the the power law index =1.66 ±0.04. Remarkably close to Kolmogorov value 5/3

Rickett MNRAS 1970

Pulse broadening vs DM

Ramachandran et al. MNRAS 1997Bhat et al. ApJ, 2004 (scaled to 1 GHz)

sc(msec) ~ Lkpc SM1.2 GHz-4.4 if uniform SM DM L => sc DM2.2

DM dependence 2The uniform Kolmogorov model predicts:sc DM2.2

But the observations show a much steeper dependence on DM. (first noticed by Sutton 1971). They imply that at larger DMs, (larger distances through the electron layer) there is an increasing chance of encountering regions of large density and large density variance ie higher turbulence (?).Note that SM is column of density-variance (it's related to emision measure). We expect ne ~ ne So ISS picks out the highest densities along a line of sight. We model this by a phase screen.

Boldyrev and Gwinn model the plot by proposing non-Gaussian statistics for the interstellar electron density ne - specifically a Levy flight distribution, in which its probability distribution has a power law tail ne

-. They find ~ 0.7, which is a rather extreme distribution for which both the mean and variance diverge.

This is a novel description of the extra scattering deep into the Galaxy. More traditionally….

DM dependence 3

Cordes & Lazio used their electron model to convert the observed d to SM. For

uniform turbulence we expect SM DM, but the observations are much steeper => an enormous increase in “plasma turbulence” toward the inner Galaxy.

Cordes et al 1991 describe this as electron “clouds” which fill a fraction of the volume and are turbulent internally (with a Kolmogorov spectrum) such that contributions to SM are:

dSM F ne2 dz, where ne is local average density and F is a

fluctuation parameter. NE2001 models have mean density increasing by 3 and F increasing from 0.2 to 110 toward the inner (thinner) Galactic electron disk.Here F ~ (ne

2/<ne>2 ) /(f louter2/3) where f is the volume filling factor for

ionized ISM and louter is the outer scale. The 550 factor increase in F implies a 23 times increase in the fractional fluctuations of density or a 550 times decrease in filling factor or a 104 decrease in outer scale… or more reasonably some combination of these.We have not found what are these sparsely distributed dense ionized regions

SM DM

SMDM3

Local Density Spectrum(Armstrong Rickett & Spangler, ApJ 1995)

1 AU 1 pc 100km

-11/3

-4

However, note the relatively minor difference between the Kolmogorov spectrum -11/3 and -4 , which corresponds to a random superposition of abrupt density steps such as due to shocks, discontinuities etc.

Note that PSR B1937+21 confirms the Kolmogorov spectrum over scales from 0.001AU to 100AU => a remarkable confirmation of the Kolmogorov model all on one sight line.

Discontinuity model(Lambert & Rickett 2000)

We tested the discontinuity model against observations of refractive scintillation index (mR) [especially

610 MHz data from Stinebring et al. 1998] relative to the observed diffractive decorrelation bandwidth.

The solid lines are predictions for the discontinuity model for various “outer scales” (0.1 AU TO 0.3 pc). They do not follow the 610 MHz data for either a screen or an extended medium calculation. The dashed line is for a simple Kolmogorov model. It does better in the trend but shows an excess in mR. => could be due an inner

scale.

0.1AU

0.3pc

AGN ISS versus H emission

NRL monitored 150 AGNs for 10-year project using the Green Bank interferometer at 2 & 8 GHz. 121 of them exhibited ISS at 2 GHz on time scales of 5-50 days. Their scintillation index (rms/mean) m2 is plotted vs the WHAM brightness

of H emission (in Rayleighs). Dashed line has the expected slope

assuming that the brightness is proportional to the emission measure.m2 is strongly limited by angular diameters of the AGNs

Flatter spectrum (smaller diameter) sources are shown by squares.

WHAM Haffner Reynolds et al, 2003 ApJS, 149,405

Inner Scale EstimatesSpangler & Gwinn ApJ 1990:Angular broadening measurements of strongly scattered extra-galactic sources.They measured the precise shape of the visibility function Found inner scales ~ 100 kmSuggested the ion inertial scale as the cut-off for the density spectrum

lioninertial = Alfven speed/(ion larmor frequency)

= (ne cm-3 )-0.5 230 km => ne ~ 5 cm-3

If ISS occurs where ne ~ 0.2 cm-3 we expect inner scale ~ 500

km

The shape of the far-out tail of scatter-broadened pulses provides another diagnostic.

Scattered pulse shape for PSR J1644-45 observed at 660 MHz at ParkesRickett, Johnston and Tomlinson, 2004

Isotropic Kolmogorov models (with inner scale) fitted from 1/e point outward;

Conclude for screen: linner < 100 km or for extended scattering medium: linner ~ 76 km

Allowing for possible anisotropy makes these values lower limits

Inner scale < 10km

Inner scale > 1000km

x

xx

xx

Cauchy-Levy dist t-1.5

Anisotropy

There has been increasing evidence in recent years that the scattering plasma often shows evidence for anisotropy.

• Scattered images can appear elongated Axial ratio A~1.2-2

• Rapid ISS of quasars (IHV) appears to be “oscillatory” B0405-385 => A>4

• Quasar J1819+38 has annual changes in its ISS timescale with a 6-mo and 12-mo periods that require anisotropy A~6 (maybe source influence)

• Scintillation arcs are prominent A ~2-5

• Correlated ISS of the two pulsars in J0737-3039 requires anisotropy A>4

Scintillation in local ISM

The variation of a few very compact radio sources on times of 1 hour or shorter (IHV) must be caused by scintillation at a distance of 3-30 pc.

• There are only 4 IHV sources. (MASIV scintillating time scales are 1day or more)=> The local turbulent regions must have a low covering

fraction.

• It will be important to find which of the local interstellar clouds are responsible

• The turbulence in these local clouds is anisotropic

“Secondary Spectrum” (S2) with three scintillation arcs

PSR B1133+16 at Arecibo

(Stinebring et al.)

d

td

Primary Dynamic Spectrum

Scintillation Arcs

The Puzzle of the “Arc-lets”

Hill, Stinebring et al. (2005) showed this example of the arcs observed for pulsar B0834+06. In addition to the main forward arc (following the dotted curve) there are “reverse arclets”. Those labelled a-d are particularly striking. They followed these over 25 days and found that they moved in the secondary spectrum plots, and that the movement was due to the known pulsar proper motion and was consistent with scattering from isolated structures that were stationary in the ISM and survived for at least 20 days.

The Puzzle of the “Arc-lets” 2

The left plot shows the angular position of the structures (in mas) responsible for each reverse arclet, mapped from the Doppler frequency ft . The lines have the slope

expected for the known pulsar proper motion.

The right plot shows how the ft values vary with observing frequency. Open circles at 334 MHz and filled circles at 321 MHz.

Remarkably this shows that the spatial location of the scatterers is independent of frequency. They DO NOT show the expected shift due to the dispersive nature of plasma refraction.

Predicted for plasma refraction

The Puzzle of the “Arc-lets” 3

My first thought on seeing these arclets was that they are due to a multipath condition in which four extra ray-paths through the irregular plasma exist at angular offsets further from the unscattered path than the angular width of the scattering disk. Such a multi-path could exist if there are large scale gradients and curvature across the scattering disk, with an amplitude higher than expected from a Kolmogorov medium ( in which the rms phase gradient on a scale decreases as -1/6).

D

θr1 θ

r2

P

O

L

o

Lp

In other words the plasma could have an excess of power on scales larger than the scattering disk (~ AU). Such structures have been proposed previously in order to explain ESEs and fringes in pulsar dynamic spectra, which appear as “islands” in the arc plots Excess power on AU scales has also been invoked for the higher than expected scintillation index for refractive scintillations mR.

The Puzzle of the “Arc-lets” 4

BUT this idea is entirely incompatible with Dan’s result that the reverse arclets come from a fixed position in space - one that does not scale with frequency as do the stationary phase points that would govern multiple ray-paths in a plasma.I conclude that there must be isolated “tiny” structures that scatter or refract the waves through angles of the order of 10 mas at 330 MHz. But they must subtend an angle several times smaller than 10 mas or their signatures would overlap in the secondary spectrum.

10 mas at 300pc => 3 AU; so the ionized “clouds” have dimension a ≤ 0.5 AU say.As for ESEs there are two possibilities: pseudo-lens or scatterers:

Consider a spherical lens of radius a and electron density nea ( see Hill

et al. 2005)It refracts by an angle θr ~ (/2) Roughly ~ /a ~ re nea which is independent of scale a

Substituting 10 mas for θr gives nea ~ 2θr re ~ 100 cm-3 !

If cloud is elongated along the propagation path by an axial ratio A => nea ~ 100/A cm-3

Even if A~10 nea ~ 10 cm-3 is uncomfortably high for a structure only

~0.5 AU

The Puzzle of the “Arc-lets” 5

Now consider an elliptical scatterer of width a and length Aa with mean electron density nea

Let it have a well developed Kolmogorov turbulence interior to a such that nea ~ nea with an outer scale ~ a.

Its scattering angle will be θsc ~ 2.2 (re nea)1.2 a0.2 A0.6

Hence nea ~ 2θsc re {/(2θsca)}1/6 A-.5 =>

with10 mas for θsc and a = 0.5 AU

nea ~ 18 A-.5 cm-3

So for A=10 we need electron density ~ 6 cm-3

Are such small ionized dense (and turbulent) structures likely and what could they be?Stellar winds could be that small. But the chance of a 600pc line of sight passing within 3 AU of 4 stars is very small (~10-8). ie the space density of such clouds needs to be 108 times that of visible stars !

The Puzzle of the “Arc-lets” 6

My best guess is that the arclets are caused by a random foam-like geometry when the line of sight happens to be tangential to a surface in the “foam” (preferentially picking out large A values favourably aligned).

But what is this ionized foam with thin ionized walls with electron densities far above the equilibrium pressure at 104 K?

Here’s where I truly step beyond my field of competence….

I hear talks about thermal instabilities in the heating/cooling of the ISM, such that ionized warm regions can cool and recombine. The instability may lead to sheet-like or filamentary cool condensations (whose life times I don’t know). These might reach neutral densities of 10 per cc. Is it possible that there could be thin "Stromgren skins" on these structures that would be sheet-like and that it is the rare edge-on alignment of these with a line of sight that cause the arclets ?

Simulations of Turbulence

Kritsuk, Norman et al, 2002

Box is 5 pc 2563 grid points (400AU steps)Starts at 106 K => cools and fragments into regions near 300 and 2x104 K

The color coding is log particle density: Dense blobs at the intersections of the filaments, >60 cm-3 , are light blue;

Stable cold phase, 6-60 cm-3 , is blue;

Unstable density regime, 1.2-6 cm-3 is yellow to brown;

Low-density gas, including the stable warm phase <1.2 cm-3, is a transparent red

Simulations of Turbulence

Kritsuk & Norman 2002

Distribution of temperatures

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

http://akpc.ucsd.edu/ThermalInstability/

Summary

1. Kolmogorov spectrum for the interstellar electron density is only a first approximation for the various ISS phenomena. This suggests Plasma Turbulence but does not require it.

2. ISS picks out the dense regions => The medium is very clumpy => denser and more turbulent regions becoming more common toward the inner Galactic Plane

3. Local (<30pc) regions with small covering fraction need to be identified in other tracers of the ISM

4. Inner scales consistent with the ion inertial scale are in the range 100-500km

5. Isolated regions may often be anisotropic with axial ratios A>2. Presumably this implies that the magnetic field controls the plasma

6. Reverse arclets imply discrete structures (as do ESEs) that have very high electron densities on sub AU scales

• Lens-like ne > 100/A cm-3.

• Scatterers ne > 6 A-.5 cm-3

7. Are these the ionized equivalents of the TSAS n ~ 105 cm-3 ?? Ionization fraction 10-4 ???

ISS Geometry

Source Dia / Screen Dist trade-off

8.6 GHz:modulation index

0.08 < mc < 0.37

c constant

mc constantand time scale

0.31hr <c< 0.51hr

ISS of PKS B0405-385 observed with ATCARickett, Kedziora-Chudczer & Jauncey (ApJ 2002)

Tb constant

4.8 GHz

From Ramachandran et al 2006:Refractive Scintillation

Variation of pulse broadening psr B1937+21

From Ramachandran et al 2006:

Variation of pulse broadening time at 327 MHz

± 20% variations uncorrelated with refractive ISS but with similar timescale. Uncorrelated with DM variations.

J0737-3039A&B just after eclipse of A

A

BxB

yB

=Origin at position of A at eclipse

Including VCM

A and B follow spiral paths through the ISM

At some point those paths cross

Raw correlation coefficient

θ1x

θ1y

θ

Scattered BrightnessB(θ1x, θ1y)

Anisotropic scattered brightness

f= t1- t2 = [θ12- θ1

2] (z/2c) relative delay

ft = 1- 2 = (θ1x- θ2x)V/ fringe frequency

With θ2 = 0 we get θ1x = ft /V and θ = 2cf/z

so θ1y = ± [(2cf/z - (ft /V)]2

Then S2(fft) is bounded by a parabolic "arc"

f ≥ ft2 [z2/2cV2]

ft

f

Secondary Spectrum S2(fft)

Secondary spectrum theory 2

I = |E1 + E2|2 if E1 and E2 are coherent:

= |E1|2 + |E2|2 + 2E1E2cos()

where = 2π(1t1-2t2+01-02)

t1 = t+t1 , 1 = 1

= 2π[0+(t1- t2)+(1- 2)t .. + ..O(t)]

θ

θ1

2

z

t1 = zθ12/2c is the relative time delay

1 = (V.θ1)/c is the relative Doppler frequency (ie fringe frequency)

V

scattering screen

ft

fx

x

2DFT

S2

So interference term is:

Cos[0 + 2πf(0) + 2πft(t-t0)]

f= t1- t2 = [θ12- θ1

2] (z/2c)

ft = 1- 2 = (θ1x- θ2x)V/ -0

t-t0

S1

Secondary spectrum theory 1

Dynamic spectrumpulsar B1929+10

Screen Simulation AR=1:1Kolmogorov spectrum Medium strong ISS mborn

2 = 10

Screen Simulation AR=4:1

Delay

Fri

nge

rate

0 deg30 deg

60 deg90 deg

t

I(t,)

RI(t,)t

2d acf

2d FT

I†(ft,f)

ft

f

P2(ft,f)

squared

Integrate over ft

f=t

RP(t)

P(t)

Dynamic Spectrum

SecondarySpectrum

Scattered pulse1d acf

|2D(,)|2 Vt

2D(,)

Diffractive 2nd momentat spatial offset frequency offset

squared

2D(0,)t

2D(,) B(θx,θy)Scattered brightness

2d FT

1d FT

2d FT

visibility

t=zeθ2/2c

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