GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/,

SKR properties measured within its source region: local1

conditions, radio source location and emission pattern2

L. Lamy1, P. Schippers2, P. Zarka3, B. Cecconi3, C. Arridge4, M.K. Dougherty1, P.Louarn5, N. Andre5, W.S. Kurth2, A.J. Coates4

On 30 oct. 2008, the Cassini spacecraft crossed the south-3

ern sources of Saturn kilometric radiation (SKR), while fly-4

ing along high-latitude nightside magnetic field lines. In situ5

measurements allowed us to characterize for the first time6

the source region of an extra-terrestrial auroral radio emis-7

sion. Using radio, magnetic field and particles observations,8

we show that SKR sources are surrounded by a tenuous9

plasma, dominated by hot electrons, in a region of globally10

upward field-aligned currents. The beaming pattern of local11

and distant SKR sources reveals oblique emission at ∼7012

from the local magnetic field direction, decreasing with fre-13

quency above 100kHz. Magnetic field lines supporting radio14

sources map a continuous, high-latitude and spiral-shaped15

auroral oval observed on the dawnside, consistent with en-16

hanced auroral activity.17

1. IntroductionIn the past four decades, remote observations have iden-18

tified intense radio emissions from auroral regions of all ex-19

plored magnetized planets of the solar system [Zarka, 1998].20

However, the source region of the terrestrial auroral kilomet-21

ric radiation (AKR) was the only one studied so far with in22

situ measurements. First observations of ISIS 1 (1970’s),23

followed by extensive ones of Viking (1980’s) and FAST24

(1990’s) brought crucial constraints on the local plasma con-25

ditions and properties of emitted waves, leading to a com-26

prehensive picture of AKR and its generation mechanism.27

Signatures of AKR source crossings were identified in28

Viking dynamic spectra [Bahnsen et al., 1989] by both an29

enhanced amplitude of the low frequency envelope, reach-30

ing typically 10mV.m−1 [Roux et al., 1993], and a cutoff31

frequency fcut close to, and occasionally below, the local32

electron cyclotron frequency fce . The feature f ≤ fce was33

attributed to the effect of predominant weakly relativistic34

electrons on the frequency cutoff of AKR emitted on the35

extraordinary mode [Le Queau and Louarn, 1989]. Indeed,36

radio sources lie in auroral cavities depleted in cold plasma37

(≤1keV), where fpe/fce ≤0.1, corresponding to an acceler-38

ation region characterized by downward (upward) beams of39

electrons (ions) [Benson and Calvert , 1979]. The spatial ex-40

tent of AKR source region is narrow in latitude (typically41

a few tens of km), more extended in longitude, and time42

variable [Hilgers et al., 1991].43

1SPAT, Imperial College London, London, UK2University of Iowa, Iowa city, USA3LESIA, CNRS, Obs. Paris, Meudon, France4MSSL, UCL, London, UK5CESR, CNRS, Univ. Paul Sab., Toulouse, France

Copyright 2010 by the American Geophysical Union.0094-8276/10/$5.00

Attributed to the wave/electron interaction named Cy-44

clotron Maser Instability (CMI) [Wu and Lee, 1979], AKR is45

emitted quasi-perpendicularly from the local magnetic field46

[Hilgers et al., 1992] by trapped [Louarn et al., 1990], or47

shell-type [Ergun et al., 2000] electron distributions.48

The first crossing of the auroral Saturn Kilometric Radi-49

ation (SKR) sources was identified on day 291 of 2008, at a50

distance of 5RS and latitudes below -60 (fce ∼10kHz) near51

midnight local time (LT) [Kurth et al, submitted]. Here,52

we investigate simultaneous observations of the Radio and53

Plasma Wave Science (RPWS) experiment, the magnetome-54

ter (MAG) and the Cassini Plasma Electron Spectrometer55

(CAPS) instrument (datasets are described and discussed in56

auxiliary material). We focus on the characteristics of the57

source region (section 2), the SKR emission pattern (section58

3) and the location of its sources (section 4), compared to59

the terrestrial case. SKR polarization and modes of emission60

are addressed in a companion paper [Lamy et al, in prep.].61

2. Source region properties

RPWS, MAG and CAPS observations, for day 291 of year62

2008 between 0600 and 1100 UT, are displayed on Figure 1.63

Panel a shows a dynamic spectrum of electric power mea-64

sured on one RPWS monopole between 3.5 and 1500kHz.65

Except around 0848 and 0924 UT, where the antenna de-66

tected little signal (clear above 100kHz) due to its quasi-67

alignment with incoming wave vectors, the SKR pattern68

extends from ∼ fce to 1000kHz. A clear source crossing69

signature is seen at low frequencies. There, SKR power70

is enhanced. Indeed, once calibrated, corrected from the71

real distance to each source (see section 4) and normalized72

to 1 AU, SKR intensity reaches ∼10−18 W.m−2.Hz−1, i.e.73

the upper 1% quantile of SKR mid-latitudes observations at74

10kHz [Lamy et al., 2008a]. Also, the SKR spectrum shows75

a cutoff around fce (see also Figure A1). The SKR cutoff76

frequency, as well as fce , are quantitatively investigated in77

panel b. Whereas fcut approaches fce from 0748 to 1000 UT,78

it displays intense signal close to fce between 0812 and 091279

UT (orange shaded, hereafter called source region), with two80

unambiguous passes below fce (red shaded, labelled A and81

B). There, the SKR peaks at ∼10−9 V2.Hz−1 within the82

∼[fce−1kHz,fce+4kHz] bandwidth, corresponding to a field83

strength of ∼0.1mV.m−1 over the length of the antenna.84

Events A and B display negative (fcut -fce)/fce , as low as85

−3%, considered at Earth as the best indication of AKR86

source regions. This feature is related to a region domi-87

nated by weakly relativistic electrons (see below and [Lamy88

et al, in prep.]).89

1

X - 2 LAMY ET AL.:

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Figure 1. Multi-instruments observations during day 291 of year 2008 over [0600,1100] UT. Panel a displays the RPWS-HFR dynamic spectrum of electric voltage recorded by the Z monopole (rather than the Stokes parameter S, computedfrom simultaneous 2-antenna measurements, but noisier at low frequencies). The dashed line overplots local fce , as derivedfrom MAG observations. SKR lies between ∼fce and 1000kHz. Panel b superimposes fpeak (gray) and fcut (black) to fce

(dashed), with a time resolution of 32s. The typical uncertainty on fcut is less than 1%, and the one fce less than 0.05%.Orange shaded region maps the interval [0812,0912] UT, where SKR is enhanced below 30 kHz and its low frequencycutoff reaches fce . Red shaded events A and B mark unambiguous passes fcut ≤ fce . Panel c reproduces fcut and fce

with a log scale, together with the total electron density ne (expressed in

ne(cm−3), right, and fpe(kHz), left) derivedfrom CAPS-ELS observations (black dots). Colors reveal contributions of cold (blue, ≤50eV), warm (orange, 50-400eV)and hot (red, ≥50eV). Uncertainties on ne are discussed in auxiliary material. Panel d shows the azimuthal magneticfield component Bφ, measured by MAG with a a 1min resolution and a 0.1nT uncertainty. As a consequence of Ohm’slaw, its variations indicate field-aligned currents. A positive (negative) slope corresponds to an up-going (down-going) netcurrent. Panel e displays the CAPS-ELS electron spectrogram of differential energy flux (DEF), summed over all anodesat a 3min resolution. Three electron populations are detected: a hot component above 400eV, a cold one below 50eVand a sporadic warm one in between. Cold electrons are partially masked by S/C photoelectrons, and all field-aligneddown-going electrons were missed due to incomplete pitch angle coverage.

LAMY ET AL.: X - 3

Frequencies fcut and fce are reproduced in the logarith-91

mic plot of panel c, together with the plasma frequency92

fpe (density) and its contributions from cold, warm, and93

hot electrons, derived from CAPS measurements. The un-94

certainty on the above values, discussed in auxiliary ma-95

terial, is mainly due to the underestimation of cold elec-96

trons masked by the S/C positive potential, and electrons97

missed by incomplete and time variable pitch angle cover-98

age. The obtained values do not display any terrestrial-like99

cavity devoid of cold electrons surrounded by a denser cold100

medium. We rather observe a large tenuous region, with a101

sporadic warm component, and dominated by hot electrons102

after 0700 UT, corresponding to high latitudes λsc ≤-50103

and distances 4.5≤ rsc ≤5.8RS . Within the source region,104

the total electron plasma frequency fpe roughly varies over105

400-900Hz, leading to ratio fpe/fce ∼0.05-0.09, in agreement106

with requirements for generation by the CMI and observed107

AKR generation conditions. Contrary to Earth, the kro-108

nian auroral plasma environment appears to be naturally109

tenuous/magnetized enough to generate SKR, as soon as110

CMI-unstable electrons are present.111

Panel d investigates the azimuthal component of the mag-112

netic field Bφ. Whereas its sudden variations indicate field-113

aligned currents (FAC), the sign of their slope gives the114

sense of the local net current. Here, the source region (or-115

ange shaded) roughly correspond to a positive slope (start-116

ing from 0748 UT), and events A and B nearly match the117

highest positive slopes. This trend suggests a globally up-118

ward current, associated with downward electrons [Bunce119

et al, in prep.], and upward ions [Kurth et al, submitted],120

similar to observations within AKR sources.121

MAG measurements thus complement CAPS observa-122

tions shown by the electron spectrogram of panel e, where123

incomplete pitch angle coverage prevented to observe down-124

going electrons within the range [0,15]. The phase plane125

density of detected electrons reveals two sporadic distribu-126

tions [Schippers et al, in prep]: a partial shell-like distribu-127

tion for 1-10keV electrons, that displays part of expected128

down-going electrons, consequently accelerated at higher al-129

titudes, and up-going field-aligned beams of a few 100eV.130

Both distributions, possible candidates for SKR generation131

[Mutel et al, in prep], are observed during and out of events132

A and B. They might thus complete criteria used to identify133

source regions. Finally, no loss cone was observed within the134

11 CAPS angular resolution, consistent with an expected135

value around 5.136

3. Diagram of emission

RPWS-HFR 3-antenna observations enable to derive un-137

ambiguously the full polarization state and the wave vector138

k of each time-frequency measurement [Cecconi and Zarka,139

2005]. The analytical inversion used here assumes trans-140

verse waves and point sources, discussed in auxiliary mate-141

rial. Under the hypothesis of SKR generation at f = fce ,142

Cecconi et al. [2009] used the SPV magnetic field model (and143

a simple current sheet) to derive the intersection of each k di-144

rection with the corresponding isosurface-f=fce , giving the145

3D spatial source location, its associated field line, and its146

aperture angle θ=(k,B) between the wave direction and the147

local magnetic field vector.148

In this section, we focus on the SKR emission pattern.149

The distribution of beaming angles (Figure 2) θ was com-150

puted within the source region using both the SPV model151

(black) and in situ MAG observations (blue), only valid lo-152

cally. Histograms of Figure 2a organize the results in suc-153

cessive ranges of f − fce . The difference between black and154

blue distributions is related to the angle between the mod-155

eled field vector at the source and the one measured in situ156

ce ce ce ce

ce ce ce ce

Cou

nts

Cou

nts

b - Average beaming angle

a - Local beaming angle

ce

Figure 2. SKR beaming pattern for local (panel a) and distant (panel b) sources, expressed in beaming angle θ be-tween the incoming wave direction and the magnetic field vector at the source. RPWS data were selected as describedin auxiliary material. Panel a focuses on the source region ([0812,0912] UT and f close to fce). Each time-frequencyk-vector direction is derived from goniopolarimetric analysis, whereas the magnetic field at the source is either computedfrom the SPV model (and a simple current sheet), or from in situ MAG measurements. The two resulting beaming angledistributions are displayed in black and blue respectively, with a frequency scale expressed in f − fce for more accuracy onthe Cassini-source distance. All directions of arrival were used in blue histograms, whereas black distributions only usedthe ones giving reliable θ, i.e. that intersect their iso-fce [Cecconi et al., 2009]. In spite a few noisy events below fce , theydisplay similar average values (dashed lines) below fce+3kHz and diverge above. Panel b investigates the average apparentemission pattern for distant sources (i.e. assuming a straight line wave propagation), computed from SPV model, alongthe extended time-frequency interval UT=[0700,1100] and f=[7,1000kHz] (data collected between 0600 and 0700 UT weretoo noisy). In spite of scattered measurements (∆θ ∼ ±15), the average (gray line) displays a clear trend, with a plateauat θ(f) ∼70 below 100kHz, followed by a decrease with frequency until θ(1000kHz)∼50.

X - 4 LAMY ET AL.:

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Figure 3. Location of radio sources in Cassini’s field of view, or FOV, (panel a) and magnetically projected down tothe planet (panel b). The radio data selection is the same as the one used for Figure 2. The time-frequency interval isrestricted to UT=[0812,0912] UT (source region) and f=[7,40kHz] (highest spatial resolution). Crosses (diamonds) refer todirections of arrival that cross (do not cross) their associated isosurface-f = fce [Cecconi et al., 2009]. Most of frequencies(plotted in blue scale for increasing ranges of f − fce) display distant sources, clustered along high-latitude magnetic fieldlines in panel a (dashed, with footprint coordinates LTB=[0400,0600] and λB=[-80,-75]), quantitatively identified on thedawnside in panel b. Red frequencies (f ≤ fce+1kHz) reveal local sources, detected through the entire observation planein panel a, and mapping the ionospheric footprint of the field lines crossed by Cassini in panel b, the green (black) lineshowing the projected S/C trajectory for [0812,0912] UT ([0600,1100]). Panel c displays the radio map [Lamy et al., 2009]integrated along the extended time interval UT=[0700,1100] and frequency range f=[7,1000kHz]. The global distribution ofSKR sources follows an unusual spiral shape starting from narrow very high latitude ∼-80±2 at LTB=0100, then evolvingto broad lower latitudes toward noon until λB=-75±6 at LTB=1300.

(the wave direction remaining unchanged), and to the data157

selection (black histograms only use directions intercepting158

their iso-fce). In spite of the limited number of events below159

fce , both techniques give similar average θ(f) ∼ 70±15 be-160

low fce+3kHz. Above this limit, MAG-derived θ(f) shifts161

toward lower values, when the local magnetic field becomes162

irrelevant. In other words, this sets an upper frequency limit163

for local radio sources.164

Computed with an accuracy of 2, obtained directions165

of arrival are very variable, whatever the frequency. Below166

fce+3kHz (local sources), the angular uncertainty on the167

modeled field is thus negligible compared to the scattering168

on k directions. This justifies a posteriori the choice of a169

field model for remote radio localization technique [Cecconi170

et al., 2009; Lamy et al., 2009]. Among other possible fac-171

tors (listed in section 4), observations close to, or within, the172

source region may be primarily affected by mixed emissions173

from several intense sources. Nevertheless, typical angles174

θ ∼70 at the source have been confirmed using a differ-175

ent technique based on SKR polarization properties varying176

with the spacecraft location [Lamy et al, in prep.]. Those177

results support oblique emission, different from the quasi-178

perpendicularly radiated AKR. Possible origins, like refrac-179

tion close to the source, or direct oblique emission driven180

by loss-cone or ring electron distributions, must be investi-181

gated.182

The diagram of emission of distant sources is investigated183

in Figure 2b, along the extended time-frequency interval184

UT=[0700,1100] and f=[7,1000kHz]. The average beaming185

angle is approximately constant at θ(f)∼70 below 100kHz186

and then decreases with frequency toward θ(1000kHz)∼50.187

The broad scattering in Figure 2b results from instanta-188

neous k directions highly variable with time, that might be189

explained by multiple instrumental/physical causes. First,190

S/C rotation motions affect goniopolarimetric results be-191

tween 0748 and 0924 UT (see auxiliary material). Then, er-192

ror on θ increases with frequency (i.e. distance to the source)193

as expected. Finally, apart from wrong directions result-194

ing from the mixing of multiple sources mentioned above, θ195

might also be variable with time, position and/or azimuth196

w.r.t the magnetic field, as well as additionally affected by197

refraction along the ray path, expected to play a non negli-198

gible role below 100kHz.199

Below 500Hz, the median behavior (gray line) differs from200

the [60,50] range previously derived in both hemispheres201

by [Cecconi et al., 2009] from close mid-latitude distances.202

The present measurements were however acquired from very203

high latitudes, where the tenuous medium along the ray path204

may lead to less refraction than for close mid-latitude ob-205

servations. Moreover, Figure 2b is in good agreement with206

the oblique frequency-decreasing beaming angle computed207

by Lamy et al. [2008b] to model features in SKR dynamic208

spectra observed from equatorial, but large, distances.209

4. Source locationThe instantaneous 3D location of radio sources was never210

directly derived for AKR source regions at Earth. The spa-211

tial distribution of low frequency SKR sources is shown over212

the interval [0812,0912] UT in Figure 3a,b, on the Cassini’s213

field of view (FOV, plotted with a 126 aperture) and af-214

ter magnetic polar projection. The radio localization tech-215

nique yields more accurate location for sources closer to216

the spacecraft, i.e. lowest frequencies. Radio emissions at217

f ≥ fce+1kHz reveal distant sources (blue), organized along218

dawnside high-latitudes magnetic field lines in the FOV219

(dashed lines), with, as expected, sources closer to the planet220

for increasing frequencies. Footprints of associated field lines221

are identified in the polar view to vary from λB=-80±2222

at LTB=0100 to -75±5 at 0700. Low frequency emissions223

f ≤ fce+1kHz (red) appear as local sources, simultaneously224

filling in the S/C FOV, while strikingly matching the iono-225

spheric footprint of the field lines crossed by Cassini on the226

polar view (green line).227

LAMY ET AL.: X - 5

Derived from the S/C velocity, the dimension of the228

source region, approximately along the latitudinal direction,229

is estimated to be 51000km, much larger than at Earth.230

Events A and B, previously identified as probable traversed231

sources, display similar widths of 1800km for event A, and232

then two times 900km for event B. This suggests successive233

(≥3) encounters of SKR curtains, consistent with sub-ovals234

observed in UV aurorae. The accuracy on the radio source235

location is not enough here to confirm it.236

The unusual distribution of sources in Figure 3b is con-237

firmed and expanded along an extended time-frequency in-238

terval by the radio image of Figure 3c, that maps SKR239

intensity. It reveals half of the entire radio auroral oval240

[Lamy et al., 2009], with most intense emissions correspond-241

ing to lowest frequencies within the source region shown by242

Figures 1a and 3a,b. This distribution also lies along an243

extended spiral shape, whose latitude, and latitudinal ex-244

tent, decreases, and broadens, with LT until λB=-75±6 at245

LTB=1300.246

The detection of intense SKR at very low frequencies247

(that made possible the present source crossing in spite of248

a 5RS distance), associated with a global filling of the po-249

lar cap (whose spiral distribution starts from nightside very250

high latitudes), indicate a high level of auroral activity, pos-251

sibly triggered by a nightside injection, and reminding the252

known picture of active UV aurorae. This enhancement is253

discussed by Bunce et al (in prep.), that identify its origin254

as a solar wind compression.255

5. ConclusionCassini crossed the first source region of exo-terrestrial256

radio auroral emissions, evidenced by intense low frequency257

SKR and fcut ≤ fce . The auroral plasma does not re-258

veal any terrestrial-like cavity. It is dominated by hot259

electrons, with fpe/fce ≤0.1, low enough to enable CMI-260

driven SKR generation. Local sources, lying at frequen-261

cies below, or close to, fce , are detected on the field lines262

crossed by Cassini, in a region of upward field-aligned cur-263

rent. The diagram of emission at the sources is found oblique264

(θ ∼70±15) and decreasing with frequency above 100kHz265

until θ(1000kHz) ∼50. The source crossing was made pos-266

sible by the sudden extension of the SKR spectrum toward267

lower frequencies (higher altitudes) with intense high lati-268

tude dawnside emissions, characteristic of enhanced auroral269

activity. More crossings of the SKR source region, planned270

at the end of the Cassini mission, are needed to check those271

characteristics, possibly varying with time and hemisphere.272

Acknowledgments. We thank Cassini RPWS, MAG and273

CAPS engineers for support on instrumental questions. The274

French co-authors acknowledge support from the Centre National275

d’Etudes Spatiales (CNES). LL thanks A. Roux, M. Dekkali, R.276

Prange, F. Mottez and S. Hess for inspiring discussions.277

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source of auroral kilometric radiation, Geophys. Res. Lett., ,282

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GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/,

Auxiliary material for ”SKR properties measured within its

source region: local conditions, radio source location and

emission pattern”

L. Lamy1, P. Schippers2, P. Zarka3, B. Cecconi3, C. Arridge4, M.K. Dougherty1, P.Louarn5, N. Andre5, W.S. Kurth2, A.J. Coates4

The present auxiliary material describes how radio, mag-netic field and particles observations, acquired during thecrossing of the SKR source region on day 291 of year 2008,were processed to derive results and Figures 1,2 and 3 dis-played in the main article. Section A1 details specific RPWSdata processing and selection, as well as the technique usedto compute SKR low frequency cutoff, and discusses assump-tions used in radio localization technique. Section A2 spec-ifies accuracy on MAG measurements. Finally, section A3presents CAPS data processing and moment calculation.

”corrected for the distance to the center of the planet(rather than the real distance to each source). This repre-sentation is thus underestimating the flux density for sourcesclose to the spacecraft.” pourquoi ”not accurate for lowSNR” ? pourquoi ”to be normalized to 1 AU” ?

A1. RPWS-HFR data

Together with the three electrical antennas +X, -X and Z(monopoles also noted u, v and w), the RPWS experimentincludes a High Frequency Receiver (HFR) which measuresthe wave electric power spectral density between 3.5 kHzand 16.125 MHz [Gurnett et al., 2004]. The receiver recordstwo auto-correlations and cross-correlation of input signalssensed on a pair of antennas. Hence, for the +XZ pair ofantennas, are obtained A+XX , AZZ (one autocorrelation ofeach antenna signal), Cr

+XZ and Ci+XZ (real and imaginary

parts of the cross-correlation between both antenna signals).During the time interval investigated in this study, the HFRwas set up in the 3-antenna operating mode, consisting oftwo consecutive sets of measurements of the above 4 quan-tities using the +XZ and -XZ pairs of monopoles, resultingin a total of 8 measurements (among which only 7 are inde-pendent, AZZ being measured twice).

Under the assumptions of transverse electromagneticwaves (k.E = 0) and instantaneous point sources, a go-niopolarimetric inversion (or direction-finding and polariza-tion analysis) applied to each 3-antenna measurement set[Cecconi and Zarka, 2005] enables one to directly retrieve

1Space and Atmospheric Physics, Blackett Laboratory,Imperial College London, London, UK

2Department of Physics and Astronomy, University ofIowa, Iowa City, Iowa, USA

3Laboratoire d’Etudes et d’Instrumentation enAstrophysique, Observatoire de Paris, CNRS, Meudon,France

4Mullard Space Science Laboratory, University CollegeLondon, London, UK

5Centre d’Etude Spatiale des Rayonnements, UniversitePaul Sabatier, CNRS, Toulouse, France

Copyright 2010 by the American Geophysical Union.0094-8276/10/$5.00

the six physical parameters of the observed wave, namelyits k-vector direction, defined by two angular coordinates,and its full state of polarization, defined by the four Stokesparameters S, Q, U and V [Kraus, 1966].

As shown by Figure A1, RPWS observations were con-tinuous on day 291 of year 2008 with 3-antenna measure-ments most of the time, and all the time between 0600 and1100 UT. The SKR spectrum reached frequencies as low asa few kHz around 1700, and a sharp clow-frequency cutoffshows up between 0800 and 0900 around fce (see Figure 1of main paper).

A1.1. Calibration of autocorrelations on radio

antennas measured over ABC spectral bands

Over the [3.5,1500kHz] spectral range, where the SKRis detected, HFR measurements were acquired on logarith-mically spaced frequency channels distributed within threebands (named A, B, C) from 3.5 to 325 kHz, with a spectralresolution of ∆f/f = 5%, and linearly spaced channels withinthe high frequency band HF1 above 325 kHz, with a fixedresolution of 25 kHz.

During observations of day 291, RPWS measurementsof AZZ displayed a systematic and unexpected discon-tinuity between the last frequency channel of band C,f1 = 320.43 kHz, and the first one of band HF1,f2 = 325 kHz (separated by 5 kHz only), with higher in-tensities below f1, as displayed in Figure A2.

We consequently determined a gain offset (in dB), i.e.a multiplicative correction computed on the median signalover [0600,1100] UT (black line in Figure A2), in order toensure spectrum continuity from band C (channel f1) toband HF1 (channel f2) (blue line). The correction factorcomputed for AZZ over [0600,1100] UT is c = 0.74.

Then, we checked the relevance of this correction ondirection-finding results (tried by correcting either bandC only, either all bands ABC together, either band HF1only). Indeed, uncorrected directions of arrival, once pro-jected onto the observation plane as observed from Cassinirevealed the discontinuity observed in Figure A2 (below andabove 325 kHz) in terms of source location, as shown by Fig-ure A3. We found that only the correction of all bands ABCproduces a consistent continuous source region in Cassini’sFOV (Figure A3c) corresponding to a better organization ofthe data once magnetically projected (Figure A3d).

We attribute the above effect to contamination of low fre-quency bands by a positive offset in the gain applied to theZ antenna (resulting in a multiplicative correction factor)caused by high intensity signals. The reason why AZZ ismost affected remains to be determined. Finally, we notedthat the C/HF1 discontinuity in autocorrelations appearsto slightly vary with time, for all antennas. This effect willhave to be taken into account in further goniopolarimetricstudies.

A1.2. Radio data selection

Several parameters, described in [Cecconi and Zarka,2005; Cecconi et al., 2009; Lamy et al., 2009], affect go-niopolarimetric results. They consist of Radio Frequency

1

X - 2 LAMY ET AL.: SKR SOURCE REGION: LOCAL PLASMA AND RADIO PROPERTIES

0 5

fce

10 15 20DOY 2008-291 (h)

10

100

1000

Freq

uenc

y (k

Hz)

dB

-230

-220

-210

-200

-190

W.m-2.Hz-1

Figure A1. RPWS-HFR dynamic spectrum over day 291 of year 2008 of the Stokes parameter S, computed from 2-antennameasurements, corrected for the distance to the planet (rather than the real distance to each source, not available for alltime-frequency measurements) and normalized to 1AU. The dashed line displays fce . White arrows indicate 3-antennamode observations.

Interferences (RFI) at fixed frequencies, the Signal-to-NoiseRatio (SNR) measured on each monopole of one 2-antennameasurement, the angle β between the direction of arrivaland the antenna plane, as well as the degree of circular po-larization V.

In the particular case of 3-antenna measurements, a sup-plementary effect has to be taken into account. Each 3-antenna observation indeed consists of two successive 2-antenna measurements (+XZ and -XZ). In other words, itsimulates a real 3-antenna instantaneous observation whenthe observed signal does not vary significantly between bothmeasurements. An estimation of this variation can be quan-tified from the two consecutive measurements of AZZ on+XZ and -XZ pairs of antennas (measurements 1 and 2) as:

z =A1

ZZ −A2ZZ

A1ZZ + A2

ZZ

(1)

Figure 1 used all available data over the interval [6,11h],once RFI removed. Figures 2 and 3 used the following selec-tion: 0.05 ≤ |V| ≤ 1.1 (to remove unpolarized or aberrantmeasurements), SNR ≥ 20 dB simultaneously on each an-tenna of the full 3-antenna measurement, |V| ≥ 0.7 when20 ≤ SNR ≤ 45 dB (to remove specifically low frequencyvariable background as well as high SNR and polarized lowfrequency narrowband emissions), and |z| ≤ 0.05 (corre-sponding to a tolerance of signal variation of 10 % between2 consecutive sets of measurements, see equation 1).

No selection on β was applied because most of 3-antennaresults above 30 kHz did not satisfy the criterion β ≥ 20

(to be applied for each of the +XZ and -XZ antenna planes)indicated by Cecconi and Zarka [2005]. This absence of se-lection contributed to the large scattering observed in Figure2b. Nevertheless, we checked that goniopolarimetric analy-sis of the same set of data used as 2-antenna measurements,when including the additional selection β ≥ 20 (less se-vere for 2-antenna measurements, since applied only on oneantenna plane) gave consistent results with 3-antenna ones.

A1.3. Computation of peak and cutoff frequencies

Accurate knowledge of the real cutoff frequency of emis-sion of SKR is of particular importance to investigate itsgeneration mechanism. In particular, the initial HFR spec-tral resolution of 5% was not sufficient to determine unam-

biguously if the SKR real cutoff frequency lied below, at, orabove fce within the identified source region.

To improve the accuracy on the determination of the peakand cutoff frequencies fpeak and fcut , shown in Figures 1b and1c, we simulated the instrumental response of the HFR toa model of input (unfiltered) signal in order to fit each ob-served (filtered) spectrum separately, as illustrated by Fig-ure A4.

The spectral response of the HFR is given by gray lines,each representing the transfer function of the filter associ-ated with one frequency channel.

The observed spectrum of AZZ (black line), acquiredwithin the source region, displays a typical abrupt step froma background level to a peak level, followed by a plateau overa few kHz. We consequently chose a step function as a sim-ple model of initial spectrum, with background and peaklevels fixed by the observed ones (dotted blue line). Indeed,this step function, once convoluted by the HFR response(solid blue line), approaches remarkably well the shape ofthe observed spectrum.

We then simulated step functions continuously shiftedover the interval [fbg ,fpeak ] to determine the best fit withthe observed spectrum (solid blue line), and therefore ob-tain an accurate determination of fcut . The uncertainty onfcut was less than ∼1% for well defined spectra within thesource region.

A1.4. Point source assumption for goniopolarimetric

analysis

The validity of the goniopolarimetric analysis essentiallylies on the point source assumption, discussed below in thecase of observations of radio waves close to their source re-gion.

Investigating the effect of extended sources on RPWS-HFR goniopolarimetric results, Cecconi [2007] showed thatthe induced bias is not significant for an extended sourcewhose angular size Ω is less than 5. However, the fractionof the extended source that illuminates the spacecraft (i.e.the apparent extended source) depends on the beaming pat-tern associated to each point source, hereafter assumed tobe an axisymetric hollow cone, defined by an aperture angleθ ± ∆θ/2 with respect to the local magnetic field vector.

The SKR being generated at f ∼ fce, the locus of in-dividual point sources along auroral magnetic field lines isdirectly given by their frequency of emission. Then, ob-served from close enough distances, a single active magnetic

LAMY ET AL.: SKR SOURCE REGION: LOCAL PLASMA AND RADIO PROPERTIES X - 3

10 100 1000

f (kHz)

a

b

10-10

10-9

10-11

10-12

10-13

10-14

10-11

10-12

10-13

10-14

10-15

260 280 300

f1

f2

320 340 360 380 400

f (kHz)

C band HF1 band

Azz (

V .

Hz

)2

-1

Azz (

V .

Hz

)2

-1

A, B and C bands HF1 band

Figure A2. Spectra of AZZ over the interval [6,11h]. Panel b displays a zoom of panel a with a linear frequency scale.Black dots show individual measurements for each frequency channel. The black line marked by triangles indicates themedian signal, that shows a discontinuity between 320 and 325 kHz. The blue line displays the corrected median signalbelow 325 kHz. Peaks at high frequencies correspond to frequency channels contaminated by RFI.

field line can be approximated by an infinite straight line,continuously populated with individual radio sources, eachemitting along the cone of emission described above. Wecan compute that the fraction of the source region detectedby the spacecraft is subtended by the angle Ω = ∆θ. Model-ing arc-shaped features observed in dynamic spectra, Lamyet al. [2008] set an upper limit on Ω with ∆θ ≤ 5. In thecase of a source extended along a single magnetic field lineobserved by a close observer, the point source assumption isconsequently valid whatever the value of θ.

Along longitudinal and latitudinal directions, the extentof SKR source region remain unknown and prevent to inferthe solid angle subtended by their visible fraction, possiblyexceeding the 5 limit when observed from close enough dis-tances. Nevertheless, this source of uncertainty is includedwithin the more general case of the mix of spatially sepa-rated sources of similar intensities, invoked in the discussionof Figure 2 as the primary source of error on goniopolari-metric results within the source region over [0812,0912] UT.

A1.5. Ambiguity on k-vector direction

Goniopolarimetric analysis of one 3-antenna measure-ment gives the k-vector direction of the detected wave,but does not constrain its sense of arrival along this direc-tion. Each 3-antenna measurement consequently providestwo possible solutions (θ,φ) and (π − θ,π + φ) for the k-vector coordinates, among which routine goniopolarimetricanalysis systematically retains the wave direction the closestto the planet. This choice is valid most of the time, whenobserving distant sources.

However, it may be questioned when observing localsources. Considering that a given radio wave emitted at

f ∼ fce cannot propagate toward more intense magneticfields (f ≥ fce), but that the magnetic field gradient is notstrictly perpendicular to the local magnetic field vector, pos-sible aperture angles slightly higher than 90 may be possi-ble. However, Figure 2a shows a similar number of eventsbetween black and blue distributions (the blue one consider-ing all directions, and the black one only those interceptingtheir iso-fce surface), with a similar average, close to 70, forlocal sources. If existing, the number of waves propagatingtoward the planet is thus negligible.

A2. MAG data

The components of the local magnetic field vector Bwere measured by the Flux Gate Magnetometer (FGM) ofthe MAG experiment [Dougherty et al., 2004]. They wereexpressed in kronocentric spherical coordinates (Br,Bθ,Bφ)with a 1 minute resolution.

The uncertainty on the field magnitude B was typically0.1 nT. Over the interval [0600,1100] UT, the relative un-certainty on B, and following, on the determination of fce,lied between 0.02 % and 0.05 %.

A3. CAPS-ELS data

The ELectron Spectrometer of the CAssini Plasma Spec-trometer (CAPS-ELS) [Linder et al., 1998; Young et al.,2004] is an electrostatic analyzer that measures elec-tron count rates from 0.56 eV to 28 keV in 63 quasi-logarithmically spaced energy channels. The eight anodes

X - 4 LAMY ET AL.: SKR SOURCE REGION: LOCAL PLASMA AND RADIO PROPERTIES

Before calibration

discontinuity

wrong projections

a b

c dAfter calibration

0

2

2

4

6

4

6R

S

0 22 44 66

0

2

2

4

6

4

6

RS

RS

Error ellipse: 2°

Error ellipse: 2°

24:00

12:00

06:0

0 18:00

24:00

12:00

06:0

0 18:00

f ! 320.43 kHzf " 325 kHz

wrong directions

Figure A3. Location of radio sources in Cassinis FOV, (panels a,c) and magnetically projected down to the planet (panelb,d) in the same format, and with the same data selection than Figure 3. The time interval is [06:42,06:48] UT and thespectral range [fce ,1000kHz]. Data are displayed before (panels a,b) and after (panels c,d) calibration of HFR frequenciesbelow 320.43 kHz (blue symbols). The calibration process removes the discontinuity shown in panel a, and corrects wrongprojections shown in panel b.

of the instrument are mounted on a turntable partially ro-tating around the z axis of the spacecraft, which allows aspatial coverage of 160 in elevation and 208 in azimuth.The energy resolution of the instrument is ∆E/E = 16.7%.

A3.1. Data processing

Raw CAPS-ELS data were converted into physical unitsof Differential Energy Flux (DEF) using the following ex-pression:

DEF =counts/acc

∆t×GF(2)

where counts/acc is the number of counts per accumu-lation time, ∆t the accumulation time corrected from deadtime (23.44 ms), and GF the geometric factor of the instru-

ment, which incorporates detector efficiency, given by Lewiset al. [2008]. Figure 1e shows the electron DEF, as a func-tion of time and energy, summed over the eight anodes ofELS.

There are two main sources of instrument backgroundfor ELS. The first is produced by radiation sources inCassini’s heater and radioisotope thermoelectric genera-tor units, and produces an look-direction-dependent back-ground count rate. To correct for this effect in the momentcalculation (see section A3.2), we applied the correction de-scribed in [Arridge et al., 2009]. The second instrumentbackground is produced by energetic particles in Saturn’s ra-diation belts, and also produces a look-direction-dependentbackground. However, this did not affect the data consid-ered in this study.

Spacecraft charging (positive or negative) also affects themeasured distribution function of the particles by either re-tarding or accelerating the incoming charged particles as

LAMY ET AL.: SKR SOURCE REGION: LOCAL PLASMA AND RADIO PROPERTIES X - 5

fpeak

fce

fbg

HFR Filters

Spec

tral p

ower

den

sity

(V .

Hz )

2

-1

Rela

tive

powe

r

6 7 8 9 10 11 120

0.2

0.6

0.4

1.4

1.2

1.0

0.8

f (kHz)

10-14

10-13

10-12

10-11

10-10

10-9

Step function(modeled fcut)

Filtered signalObserved spectrum

Figure A4. Spectra of AZZ at 0855 UT. The observed spectrum is by the black line, where each time-frequency mea-surement corresponds to two values of AZZ , displayed by crosses. Dashed lines indicate the frequencies fbg and fpeak

corresponding to background and peak levels. Transfer functions of each individual RPWS-HFR filter are shown by graycurves, expressed in relative power (right scale). The initial step function (dotted blue line), once filtered by the HFR(solid blue line) fits well the observed spectrum between fbg and fpeak . Left of the peak frequency fpeak of the SKR, fcut

is found to lie between ∼250 Hz below fce (black dashed line), i.e. (fcut − fce/fcut ∼ 3%, with an uncertainty on fcut

estimated to less than ∼1%.

they pass through the spacecraft potential well. Generally,photoemission and secondary electron emission cause thespacecraft to charge to a positive potential (as high as 50 Vin the kronian environment). However, in Saturn’s innermagnetosphere the large plasma density and thermal elec-tron current cause the spacecraft to charge to a negative po-tential. In the present event, trapped spacecraft photoelec-trons were visible in individual CAPS-ELS spectra, indicat-ing a positive potential, and their maximum energy/chargewas used to determine the value of the potential. CAPS-ELSspectra were then corrected for the presence of this poten-tial by shifting the distribution in energy, by the value ofthe potential, in accordance with Liouville’s theorem. Mo-ments (see section A3.2)were calculated on the basis of thosecorrected spectra.

A3.2. Moment calculation

In this paper, we used the numerically integrated tech-nique [Lewis et al., 2008] to derive a set of electron bulk/fluidparameters (density n, temperature T ) for each electronpopulation (cold, warm and hot).

The moment of order r of the distribution function f(v)is defined as:

Mr =

vrf(x, v, t)d3v (3)

To calculate moments from this integral, we made the as-sumption that the distribution is isotropic in the spacecraftframe [Lewis et al., 2008], which implicitly assumes that thebulk plasma velocity is zero in the spacecraft frame. This isgenerally a good approximation as the typical thermal elec-tron energy is more than a factor of 100 larger than the bulkkinetic energy [Arridge et al., 2009], although this is not agood approximation for cold populations with large bulk ve-locities (they are subsonic in the spacecraft frame). It thenfollows that the vector and tensor moments from the aboveintegral are scalars by definition.

The density and temperature are obtained by taking thezeroth (r = 0) and second (r = 2) order moments.

Considering the measured electron distribution functionf(v) to be constant across each energy bin, the density fora population j can be written as:

ne,j =4π3

i=imax,j

i=imin,j

f(vi)(v3i − v3

i−1) (4)

where imin, j and imax, j respectively correspond to theminimum and maximum index of CAPS-ELS correspondingto the energy limits of each electron population.

Correspondingly, the temperature of population j is ob-tained from:

Te,j =4πme

15kBne

i=imax,j

i=imin,j

f(vi)(v5i − v5

i−1) (5)

where me is the electron mass and kB the Boltzmannconstant.

Results derived from this technique generally agree withthose calculated from forward modeling techniques [Schip-pers et al., 2008] to within the errors of the numerically-integrated moments [Arridge et al., 2009].

A3.3. Limits to the estimation of electron density

Uncertainties on the density and temperature have beenobtained through simulation [Arridge et al., 2009] and arepresented in Figure A5. One can see that for populationswith densities less than ∼ 103 m−3 the density error is gen-erally more than 50 %, although this displays some energydependence, partly due to the energy-dependent efficiency ofthe CAPS-ELS instrument, where the noise level for colderpopulations is somewhat higher. The large error in the den-sity of low density cold populations is also caused by thedistribution being under-resolved and hence represents anunderestimate of the density. At higher energies, above sev-eral keV, the density is similarly underestimated due to miss-ing part of the distribution which appears above the 28 keVupper energy limit of ELS.

The density of very cold electron populations, with char-acteristic energies less than a few eV are greatly underesti-mated by the CAPS-ELS instrument. The primary reason

X - 6 LAMY ET AL.: SKR SOURCE REGION: LOCAL PLASMA AND RADIO PROPERTIES

b - Cold

c- Warm

d- Hot

6 7 8 9 10 11

Time (h)

a - Total

101

102

103

104

105

106

e(c

m )

-3

e(c

m )

-3

e(c

m )

-3

e(c

m )

-3

0.4

0.2

0

0.6

0.8

1

ee

101

102

103

104

105

106

0.4

0.2

0

0.6

0.8

1

ee

101

102

103

104

105

106

0.4

0.2

0

0.6

0.8

1

ee

101

102

103

104

105

106

0.4

0.2

0

0.6

0.8

1

ee

Figure A5. Electron density and relative uncertainty derived from CAPS-ELS observations for all (a), cold (b, ≤50eV),warm (c, 50-400eV) and hot (d, ≥50eV) electrons.

for this underestimate is that they exist at energies close tothe lower energy limit of the detectors. In the presence ofpositive spacecraft charging, these low energy distributionswill be shifted to higher energies but will then be unresolveddue to the larger energy bin widths compared to the width ofthe distribution. [Schippers et al., in prep.] have estimatedthe errors associated with this unresolving effect and con-clude that the densities of distributions with temperaturesaround 1 eV will be underestimated by a factor of around2, and, below 0.1 eV, the density is essentially uncorrelatedwith the actual density. So, based on purely instrumentalconcerns, there could be a dense population of cold electrons

that are not measured by CAPS-ELS. However, dense dis-tributions of cold electrons tend to drive the spacecraft po-tential towards zero or to negative values (e.g. [Lewis et al.,2008]). In the source region, the spacecraft potential is pos-itive by more than 5 V, thus suggesting that no such highdensity cold electron population is present, but hidden fromthe ELS detectors.

Furthermore, since Saturn is a rapidly rotating magneto-sphere, magnetic field-aligned electrostatic potentials existto maintain charge neutrality along field lines (e.g. [Mauriceet al., 1997]). Typically the potential difference betweenthe equator and the high latitude region is a few 10 V, and

LAMY ET AL.: SKR SOURCE REGION: LOCAL PLASMA AND RADIO PROPERTIES X - 7

so, cold electron distribution with energies less than a few10 eV should be confined to the equatorial regions. Hence,one would not expect to see large densities of cold electronsat high latitudes in a rapidly rotating magnetosphere. Thesearguments lead us to consider that the majority of the im-portant electron distributions have been captured by theCAPS/ELS instrument, apart from the high energy tail ofthe hot electron population.

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