Microstructure in the Ionized ISM from radio scattering observations. Barney Rickett UC San Diego O’Dell Symposium Lake Geneva WI April 2007

Radio Probing of the ionized ISM At radio frequencies the ionized ISM is dispersive - in that its refractive index varies strongly with frequency µ = 1 - f p 2 /f 2. Since f p 2  n e we have a probe of the electron density in the ISM The simplest observable is from measuring the dispersion in pulse arrival times from pulsars at different frequencies. This gives the column density of n e - called the dispersion measure: DM = ∫ 0 L n e dl accurately known over 1000 lines of sight toward each pulsar. Other observables include: Rotation Measure RM = ∫ 0 L n e B.dl from Faraday Rotation Emission Measure EM = ∫ 0 L n e 2 dl from H  emission and radio free-free absorption Scattering Measure SM = ∫ 0 L C n 2 dl from radio scintillation and scattering - which is the topic of my talk. C n 2 gives the strength of variations in n e

For scales far from the inner and outer scales in an isotropic Kolmogorov spectrum P 3ne (  ) = C n 2        inner >  >  outer {  inner = 1/l inner ;  outer =1/l outer } D ne (  )     with  =5/3 l inner <  < l outer  n e 2 = ∫ P 3ne (  ) d 3 k  C n 2 l outer (2/3)  2 ? Electron density and its spectrum The radio scintillation of pulsars and AGNs probe the fine structure in the interstellar electron density n e (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  D ne (  ) = ∫ 0 L dz ( for a pulsar at distance L) This is related to the Power spectrum of density versus transverse wavenumber  D ne (  ) = ∫ 0 L ∫ P 3ne (  z =0) {1-e i  }d 2  dz log (   inner  outer P (  ) 3ne  -(3.67) Tiny for ISS is 100 km The scales probed by ISS are 100km to 30 AU

What can we learn from ISS? Interstellar Scintillation (ISS) can probe the form of the spectrum => inner & outer scales, anisotropy for one line of sight And explore its rms amplitude versus Galactic coords => C n 2 or more accurately Scattering Measure SM = ∫C n 2 dz versus latitude, longitude and scattered path length Scattering Measure should be closely related to the Emission Measure The first order description is an isotropic Kolmogorov spectrum that is pervasive throughout the Galaxy - with some volume filling factor. Pulsar dispersion measures combined with independent distance estimates suggest that the local volume average ~ 0.03 cm -3 Estimates of the volume filling factor are and so imply local electron densities in the ionized regions cm -3

Local Density Spectrum (Armstrong Rickett & Spangler, ApJ 1995) 1 AU1 pc100km  -11/3  -4 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.

ensity Spectrum (Armstrong Rickett & Spangler, ApJ 1995)

Ramachandran et al 2006: Variation of Dispersion Measure psr B Slope = 1.66 When extrapolated down to the diffractive scale ~ AU, this is within a factor 2 of independent ISS observations. Giving evidence of a Kolmogorov spectrum over range to 10 2 AU (with a possible inner scale at AU) The solid line gives the best fit line for the data in the time interval of 5 days to 2000 days. The derived values of the the power law index  =1.66 ±0.04 Remarkably close to Kolmogorov value 5/3

Angular Broadening and Temporal Broadening  d is related to the diffractive scale s d which is the transverse separation for an observer over which there is an rms difference of 1 radian in propagation phase.  d = /(2πs d ) <<1radian 11 dd z1z1 z2z2 Waves from a point source are scattered by density inhomogeneities and appear to arrive from a range of angles This can be seen as a scattered brightness function of whose width is the diffractive scattering angle  d, which is a very small angle. There is an extra travel time for each scattered path. Hence an ideal impulse is broadened into a one-sided pulse with decay like an exponential of width  d  d = (L scatt -L)/c = (z 1  z 2  d 2 )/2c = L  d 2 z 2 /(2z 1 c) which is called the diffractive pulse broadening time Formally s d is defined via the structure function of the propagation phase  (r) at transverse coordinate r, which is: D  (  ) =  D ne (  ) For isotropic Kolmogorov model D  (  ) => (  s d )   with  =5/3

Pulse Broadening If the receiver bandwidth B Scattering time  d If  d > 1/B the pulse is broadened by scattering, its width  d  4.4 If  d < 1/B the pulse does not appear to be broadened, but its amplitude becomes variable. We call this scintillation, which can also be studied as a probe of the ISM. Then the bandwidth over which the scintillations are correlated provides an another way to estimate  d.

Pulse broadening vs DM Bhat et al. ApJ, 2004 (scaled to 1 GHz) For a Kolmogorov spectrum over a path length L we predict:  d(msec) ~ L kpc SM 1.2 GHz -4.4 if the inhomogeneities are uniformly distributed, SM  DM  L And we predict  d  DM 2.2 Observations of many pulsars show that  d ( scaled to 1 GHz) depends strongly on DM. The observed  d increases much more steeply with DM. The large DM pulsars are at low Galactic latitudes and mostly toward the inner Galactic disk. Since DM measures the mean n e, we conclude that the ratio  n e /n e increases toward the inner Galactic disk by a factor of more than 20

DM dependence 2 So there is an enormous increase in “plasma turbulence” toward the inner Galaxy.  n e /n e can be greater than one if the filling factor is less than one - that is the turbulence is sparsely distributed (or “intermittent”) In recent papers Boldyrev and Gwinn characterize this higher turbulence by proposing non-Gaussian statistics for the interstellar electron density - specifically a Levy flight distribution, in which its probability distribution has a power law tail n e - . They find  ~ 0.7, which is a rather extreme distribution for which both the mean and variance diverge. Boldyrev and Konigl have further shown that such a distribution can arise from lines of sight passing through randomly distributed thin shells of enhanced electron density (~100 cm -2 ) and/or enhanced turbulence. Cordes et al 1991 describe this as electron “clouds” which fill a fraction f of the volume and are turbulent internally (with a Kolmogorov spectrum). They show that the turbulence parameter F ~ (  n e 2 / 2 ) /(f l outer 2/3 ) increases by a factor 550 in the inner Galactic plane. l outer is the outer scale which could be no larger than the size of the turbulent regions. 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 10 4 decrease in outer scale… or more reasonably some combination of these.

Inner Scale Estimates Spangler & 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 km Suggested the ion inertial scale as the scale where turbulence is dissipated (cutting off the density spectrum) l ioninertial = Alfven speed/(ion Larmor frequency) = (n e cm -3 ) km => n e ~ 5 cm -3 If ISS occurs where n e ~ 0.2 cm -3 we expect inner scale ~ 500 km The shape of the far-out tail of scatter-broadened pulses provides another diagnostic. For observations of pulsar J at Parkes I found l inner ≥ ~100 km in agreement with Spangler and Gwinn.

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” B => A>4 Quasar J 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 (not modeled quantitatively) Correlated ISS of the two pulsars in J requires anisotropy A>4

Intra-Hour Variables ISS is normally observed in pulsars, but it can also be seen as a low level variation of 1-10% in some compact extra-galactic AGN jet sources. These are called intra-day variables since their flux density varies on time-scales of a day. There are about 5 AGNs which vary on times of I hr or less at 5 GHz and are called intra-hour variables. It has been established that these are due to scintillation in the local ISM - within 1-30 pc of the Earth.

Source Diameter / Screen Distance trade-off 8.6 GHz: modulation index 0.08 < m c < 0.37  c constant m c constant and time scale 0.31hr <  c < 0.51hr ISS of PKS B observed with ATCA ( Rickett, Kedziora-Chudczer & Jauncey ApJ 2002) T b constant 4.8 GHz Conclude that scattering region is between 3-30 pc from Earth. This suggests a relationship with local interstellar clouds.

ISS Time scale for quasar B from Bignall et al. Transverse velocities for local clouds from Linsky and Redfield Aura and Gem clouds match the ISS data Linsky has proposed that collisions between clouds may drive the plasma turbulence responsible for the ISS. Their relative velocities are ~10 km/s. (see Linsky & Redfield poster)

“Secondary Spectrum” (S 2 ) with three scintillation arcs PSR B at Arecibo (Stinebring et al.) Primary Dynamic Spectrum Scintillation Arcs Pulsar intensity varies with time and frequency due to interstellar Scintillation (ISS). When this “image” is Fourier analyzed the arcs are revealed when the Fourier amplitude is plotted on a log scale. The arcs follow a parabolic curve that relates delay and Doppler shift of the scattered waves. These imply discrete scattering “screens” (here 3 screens) along the line of sight - occupying a small fraction of the path.

The Puzzle of the “Arc-lets” Hill, Stinebring et al. (2005) showed this example of the arcs observed for pulsar B 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 f t. The lines have the slope expected for the known pulsar proper motion. The right plot shows how the f t 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 ). 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. Instead 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.

PSR B VLBI GB-Arecibo at 314 MHz We detect many “reverse arclets” one at a delay of 1 msec, which requires scattering ~40 mas from the pulsar direction. Differential Doppler frequency Differential Delay Amplitude Phase The observations confirm our basic arc interpretation since the fringe phase changes sign with the Doppler frequency.

Interferometry of the Arcs W.F. Brisken, J.-P. Macquart, A.T. Deller, C. West, B.J. Rickett, W.A. Coles & S.J. Tingay We can use the interferometer phase to determine the discrete scattering positions that constitute a scattered image. The result is a remarkably elongated image (axial ratio > 10:1) AND an offset feature separated by ~5 times the half-width (7 mas) of the main feature. What is the corresponding spatial structure of the electron density ? (On this scale the electrons still follow the protons) RA (mas) Dec (mas) Two possibilities: The image maps the location of extremely fine structure in the electron density, which scatters the radiation by angles larger than their angular extent (otherwise they could not be detected). => Filaments parallel to image axis OR Fine filamentary structure transverse to the image axis, causing the elongated image, but which has strong modulations that cause the offset feature. This is a preliminary estimate of the scattered image.

Cartoons of Scattering Geometry The structures must be narrower than 0.5 AU and have internal fine structure down to scale of 2x10 6 m What confines it to 0.5 AU? B-field? But this would favor scattering transverse to the elongated image B- field transverse to elongated image, creating fine density structure which scatters perpendicular to B-Field (causing the elongated image). Strong modulation in turbulence transverse to B-field.

Cygnus and Cirrus Nebula NGC 6992

The Puzzle of the “Arc-lets” 4 20 mas at 300pc => 6 AU from the pulsar line of sight; but the ionized “cloud” is 10 times smaller -- 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 n ea ( see Hill et al. 2005) It refracts by an angle  r ~ ( /2  )  Roughly  ~  /a ~ r e n ea which is independent of scale a Substituting 10 mas for  r gives n ea ~ 2  r r e   ~ 200 cm -3 ! If cloud is elongated along the propagation path by an axial ratio R => n ea ~ 200/R cm -3 Even if R~10 n ea ~ 20 cm -3 is uncomfortably high for a structure only ~0.5 AU Now consider an elliptical scatterer of width a and length Ra with mean electron density n ea Let it have a well developed Kolmogorov turbulence interior to a such that  n ea ~ n ea with an outer scale ~ a. Its scattering angle will be  sc ~ 2.2 (r e n ea ) 1.2 a 0.2 R 0.6 Hence n ea ~ 2  sc r e   { /(2  sc a)} 1/6 R -.5 With 20 mas for  sc and a = 0.5 AU n ea ~ 40 /R 0.5 cm -3 Even for R=10 n ea ~ 12 cm -3 still uncomfortably high for a structure only ~0.5 AU.

H-alpha map Composite H  map compiled by Finkbeiner from WHAM, VTSS & SHASSA.

Simulations of Turbulence Kritsuk, Norman et al, 2002 Box is 5 pc grid points (400AU steps) Starts at 10 6 K => cools and fragments into regions near 300 and 2x10 4 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, cm -3 is yellow to brown; Low-density gas, including the stable warm phase <1.2 cm -3, is a transparent red

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. The medium is very clumpy => denser and more turbulent regions becoming more common toward the inner Galactic Plane 3. Inner scales consistent with the ion inertial scale are in the range km 4. Isolated regions may often be anisotropic with axial ratios A>2. Presumably this implies that the magnetic field controls the plasma (ie  < 1) 5. Reverse arclets imply discrete anisotropic structures on sub-AU scales, that have very high electron densities cm Suggested geometry is magnetically-controlled filaments of plasma, where the scattering is predominantly perpendicular to B-field and is highly modulated in that direction