What do Scintillations tell us about
the Ionized ISM ?
Barney Rickett
UC San Diego
SINS Socorro May 2006
Electron density and its spectrum
The 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 s
L
Dne(s) = ∫0 < [ne(s,z) - ne(s+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 k
Dne(s) = ∫ P3ne(k,kz=0) {1-eik.s}d2k
For scales far from the inner and outer scales in an isotropic Kolmogorov spectrum
P3ne(k) = Cn2 k-(2+a) ;
Dne(s)  sa with a=5/3
kinner > k > kouter
{ kinner = 1/linner ; kouter =1/louter}
linner < s < louter
P (k)
Notice that a Kolmogorov density spectrum
only suggests turbulence (no V or B obs)
The scales probed by ISS are 100km to 30
AU
Tiny for ISS is 100 km
louter > 10AU
k-(3.67)
3ne
kouter
log(k)
kinner
Structure Function with Inner scale
Log[ Dne(s) ]
sa
s2
Log[ s ]
linner
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 a=1.667 and 2, so the ISS
effects of an inner scale are subtle.
What can we learn from ISS?
Scintillation can probe the form of the spectrum
=> inner & outer scales, anisotropy for one line of sight
And explore its rms amplitude versus Galactic coords
=> Cn2 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 (Cn2) & 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
Variation of Dispersion Measure psr B1937+21
Ramachandran et al 2006:
3x1014 cm-2
(2.2x1018 cm-2)
Structure Function of phase at 1.4 GHz psr B1937+21
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 a =1.66 ±0.04.
Remarkably close to
Kolmogorov value 5/3
If extrapolated down to
where Df = 1 rad2 the
diffractive scale is
predicted to be 7x106 m.
Compare with the scale
estimated from tsc. 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
Slope = 1.66
Pulse broadening vs DM
Rickett MNRAS 1970
g
Bhat et al. ApJ, 2004 (scaled to 1 GHz)
Ramachandran et al. MNRAS 1997
tsc(msec) ~ Lkpc SM1.2 nGHz-4.4
if uniform SM  DM  L =>
tsc  DM2.2
DM dependence 2
The uniform Kolmogorov model predicts: tsc  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 dne ~ 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-b. They find
b ~ 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
DM dependence 3
SMDM
3
Cordes & Lazio used their electron model to
convert the observed td 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.
SM  DM
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 ~ (dne2/<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.
Local Density Spectrum
(Armstrong Rickett & Spangler, ApJ 1995)
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.
k-4
k-11/3
However, note the relatively
minor difference between the
Kolmogorov spectrum k-11/3
and k-4 , which corresponds to
a random superposition of
abrupt density steps such as
due to shocks, discontinuities
etc.
1 pc
1 AU
100km
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] 0.3pc
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
AGN ISS versus Ha 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 Ha
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 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 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 Parkes
Rickett, Johnston and Tomlinson, 2004
x
x
Cauchy-Levy dist
x
 t-1.5
x
x
Inner scale < 10km
Inner scale > 1000km
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
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”
•
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
B0405-385 => 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
Scintillation Arcs
PSR B1133+16
at Arecibo
(Stinebring et al.)
dtd
dnd
Primary Dynamic Spectrum
“Secondary Spectrum” (S2) with
three 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
Predicted for plasma refraction
The right plot shows how the ft values vary
The left plot shows the angular position of with observing frequency. Open circles at
334 MHz and filled circles at 321 MHz.
the structures (in mas) responsible for
each reverse arclet, mapped from the
Remarkably this shows that the spatial
Doppler frequency ft . The lines have the
location of the scatterers is independent of
slope expected for the known pulsar
frequency. They DO NOT show the
proper motion.
expected shift due to the dispersive nature
of 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 s decreases as s -1/6).
P
Lp
D
Lo
r1
r2
O
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 r ~ (l/2p) f
Roughly f ~ f/a ~ rel nea which is independent of scale a
Substituting 10 mas for r gives nea ~ 2pr re-1l-2 ~ 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
dnea ~ nea with an outer scale ~ a.
Its scattering angle will be sc ~ l2.2 (re nea)1.2 a0.2 A0.6
Hence nea ~ 2psc re-1l-2 {l/(2psca)}1/6 A-.5 =>
with10 mas for sc 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
http://akpc.ucsd.edu/ThermalInstability/
Kritsuk &
Norman 2002
Distribution
of
temperatures
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Summary
1.
2.
3.
4.
5.
6.
7.
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.
ISS picks out the dense regions => The medium is very clumpy => denser
and more turbulent regions becoming more common toward the inner
Galactic Plane
Local (<30pc) regions with small covering fraction need to be identified in
other tracers of the ISM
Inner scales consistent with the ion inertial scale are in the range 100500km
Isolated regions may often be anisotropic with axial ratios A>2. Presumably
this implies that the magnetic field controls the plasma
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
Are these the ionized equivalents of the TSAS n ~ 105 cm-3 ?? Ionization
fraction 10-4 ???
ISS Geometry
ISS of PKS B0405-385 observed with ATCA
Rickett, Kedziora-Chudczer & Jauncey (ApJ 2002)
Source Dia / Screen Dist trade-off
8.6 GHz:
modulation index
0.08 < mc < 0.37
and time scale
0.31hr <tc< 0.51hr
Tb constant
4.8 GHz
mc constant
tc constant
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.
From Ramachandran et al
2006:
Refractive Scintillation
J0737-3039A&B just after eclipse of A
A
B
=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
fn = dt1- dt2 = [12- 12] (z/2c) relative delay
ft = dn1- dn2 = (1x- 2x)V/l fringe frequency
With 2 = 0 we get 1x = ft l/V and 12 = 2cfn/z
so 1y = ± [(2cfn/z - (ft l/V)]2
Then S2(fn, ft) is bounded by a parabolic "arc"
fn ≥ ft2 [zl2/2cV2]
Scattered Brightness
B(1x, 1y)
1y
ft

Anisotropic scattered
brightness
1x
Secondary spectrum theory 2
Secondary Spectrum
S2(fn, ft)
fn
Secondary spectrum theory 1
scattering screen
2
z
1
V
I = |E1 + E2|2
if E1 and E2 are coherent:
= |E1|2 + |E2|2 + 2E1E2cos(Df)
where Df = 2π(n1t1-n2t2+f01-f02)
t1 = t+dt1
, n1 = n+dn1
Df = 2π[Df0+n(dt1- dt2)+(dn1- dn2)t .. + ..O(dn,dt)]
dt1 = z12/2c is the relative time delay
dn1 = n(V.1)/c is the relative Doppler frequency (ie fringe frequency)
So interference term is:
Cos[Df0 + 2πfn(n-n0) + 2πft(t-t0)]
fn = dt1- dt2 = [12- 12] (z/2c)
ft = dn1- dn2 = (1x- 2x)V/l
ft
t-t0
2DFT
x
x
S1
n-n0
S2
fn
Dynamic spectrum
pulsar B1929+10
Screen Simulation AR=1:1
Kolmogorov spectrum
Medium strong ISS mborn2 = 10
Screen Simulation AR=4:1
0 deg
Fringe rate
30 deg
60 deg
90 deg
Delay
Dynamic
Spectrum
Relationships
t
n
DI(t,n)
2d acf
2
|G2D(s,dn)|
s=Vdt
RDI(dt,dn)
dt
dn
squared
2d FT
DI†(ft,fn)
squared
2d FT
P2(ft,fn)
ft
Secondary
Spectrum
fn
Integrate over ft
fn=dt
RP(dt)
1d acf
G2D(s,dn)
Diffractive
2nd moment
at spatial offset s
frequency offset dn
G2D(0,dn)
1d FT
Scattered pulse
P(t)
t
t=ze2/2c
G2D(s,0)
visibility
2d FT
B(x,y)
Scattered
brightness