Astron. Astrophys. 335, 703–708 (1998) ASTRONOMYAND

ASTROPHYSICS

Whistler waves observed during an in-situ solar type III radio burst

O. Moullard 1, D. Burgess1, and S. D. Bale2

1 Astronomy Unit, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK (o.moullard@qmw.ac.uk, d.burgess@qmw.ac.uk)2 Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450, USA (bale@ssl.berkeley.edu)

Received 21 January 1998 / Accepted 14 April 1998

Abstract. On Dec. 24, 1996, the WIND spacecraft encoun-tered a solar type III source region at 1 AU, as indicated bya characteristic radio signature down to less than the secondharmonic of the local electron plasma frequency, the enhance-ment of the electron flux at high energies and the presence ofelectrostatic noise at the local plasma frequency. During thisinterval, electromagnetic wave activity was recorded below theelectron cyclotron frequency, by the Time Domain Sampler ofthe WAVES instrument. Analysis suggests that the observedwaves are whistler waves, propagating, approximately parallelor antiparallel to the interplanetary magnetic field, in the plasmaframe.

Key words: solar wind – Sun: radio radiation – interplanetarymedium

1. Introduction

The accepted picture for type III emission is that an electronbeam accelerated in the solar corona, for example from a flare,is guided along open magnetic field lines, and, as it goes awayfrom the sun, interacts with the solar wind plasma of decreasingdensity, thereby producing electromagnetic emission at propor-tionally decreasing frequency. Because of a time-of-flight effect,the local electron distribution function in the direction parallelto the interplanetary magnetic field (IMF) is expected to show abump at the beam speed (with positive slope in the parallel di-rection). This “bump-on-tail” distribution is unstable and drivesthe excitation of Langmuir waves (L) with a phase speed closeto the beam velocity, which can release some of their energyin conversion to an electromagnetic (e/m) wave at the plasmafrequencyfpe or its harmonics. The non-linear wave-wave in-teraction involved in that conversion, for example, three-wave(parametric decay) or four-wave (modulational instability), cre-ates various wave products. For example, in the standard theoryfor type III emission, it is expected that ion acoustic waves oflow frequency should appear (Gurnett et al. 1993, for a list ofreview articles).

Lin et al.’s observation of ion acoustic waves (IA) in anISEE3 in-situ type III (Lin et al. 1986) constitutes one of thebest pieces of evidence in favour of the standard type III

wave-wave interaction process. However instruments on boardUlysses and Gallileo did not observe any ion acoustic wave fullyconsistent with being the product of type III emission mech-anisms (Thejappa et al. 1993 and Hospodarsky et al. 1995).Cairns (1995) pointed out that this might be due to instrumentalresolution and sensitivity: either because the IA field strengthis too weak to be above the instrumental noise level existingduring an in-situ type III, or because the IA last too short a timeto be detected by instruments with low duty cycles.

In-situ type III observations are rare with less than 10 suchevents discussed in the literature of the past 15 years. Here wereview them and summarize what set of observations usuallyconstitutes an in-situ type III, based on both theoretical andobservational criteria.

What makes an in-situ type III observation? Firstly, type IIIradio-emission, e.g., on a radiospectrogram, should be observeddecreasing in frequency with time down to the local secondharmonic of the electron plasma frequency 2f†

pe († for local),and perhaps continuing further down to the limit off†

pe. In anideal solar wind model with density decreasing monotonicallywith radial distance, emission atf†

pe < f < 2f†pe is due to

remote emission at non-localfpe or 2fpe upstream, or at non-local 2fpe downstream. Secondly, fast electrons must be seen,i.e., the type III associated electron beam. Thirdly, Langmuirwaves should be detected. Other observational criteria could beadded, but that would introduce too many assumptions aboutthe type III emission mechanism.

Previously reported examples of in-situ Type III sourceevents and some references for their discussion are: HeliosDec. 11, 1978 (1 AU) (Kellogg 1986), ISEE3 Feb. 8 and Mar. 11,1979 (1 AU) (Lin et al. 1986 and Robinson et al. 1993), ISEE3Feb. 11, 1979 (1 AU) (Lin et al. 1981 and Robinson et al. 1993),Ulysses Dec. 11 and 23, 1990 (1.3, 1.4 AU) and Feb. 22, 1991(2.1 AU) (Reiner et al. 1992 and Thejappa et al. 1993), UlyssesMar. 7, 1991 (2.3 AU) (Thejappa et al. 1993), Ulysses Jan. 9,1991 (1.7 AU) (Thejappa et al. 1995), Galileo Dec. 10, 1990(1 AU) (Hospodarsky et al. 1995). In many events, not all thecriteria for an in-situ type III are satisfied. In some cases, notall the criteria can be verified (e.g., no spectrogram provided,or electron data missing).

In the previous list there is only one report of observationof low-frequency e/m waves (below the electron cyclotron fre-

704 O. Moullard et al.: Whistler waves observed at a solar type III radio-source

quencyfce), inside what is probably a type III source regionon Jan. 9, 1991 (Ulysses), although no electron data confirmsthe solar wind conditions. In that event, Thejappa et al. (1995)identified lower-hybrid waves and rejected any non-linear wave-wave explanation in favour of a particle-wave interaction withelectrons originating from Langmuir wave scattering of the elec-tron beam.

Otherwise, low-frequency e/m waves have been often re-ported in conjunction with a type III source region, but thetype III was no longer apparent on the radiospectrogram at thetime the local wave activity, including Langmuir waves, wasrecorded. Presumably what was observed is wave activity re-lated to the electron beam associated with a type III. Exam-ples of such observations and a reference for their discussionare: Ulysses Nov. 26, 1990 (1 AU) and Jul. 14, 1991 (3.6 AU)(Kellogg et al. 1992). Kellogg et al. (1992) identified obliquelypropagating whistlers, and suggested they were part of a non-linear wave-wave process involving Langmuir waves. However,the lack of some wave field components makes the propagationangle determination ambiguous.

What is clear from the last type of event is that, at the timeof low frequency e/m wave activity, the type III radio-emissionis no longer detected. One possibility is that at such times, thelower frequency limit below which emission does not occurhas been reached. Unless great care is taken when discussingthe lower limit of detectable intensity of the electromagneticemission and proof given that type III emission might still occur,should one consider the possibility of wave-wave interaction of atype III in a region where no type III radio-signals is obvious? Ifone considers that such cases may represent the situation whereconditions are no longer met for type III emission to occur, thenthis might be fruitful. In other words, the low frequency e/memission might be a tracer of a “type III associated” electronbeam, that was for some reason, not producing any observabletype III radio-emission.

There exist many observations of whistler waves in the so-lar wind (generally, their generation is explained via an elec-tron heat-flux instability). The discussion here is concernedonly with low frequency e/m waves that are correlated witha type III source region or with a ”type III associated” elec-tron beam only. Until now, electromagnetic emission at lowfrequency (< fce) has been reported only once in a type IIIsource region (Thejappa et al. 1995) but many times in the casesof local wave activity correlated to a type III electron beam inthe absence of a local type III radio signature. Low frequencyelectrostatic emission (presumably IA) has been found in bothcases.

In this paper, we report observations, made by the WINDWAVES-TDS instrument, of low frequency monochromatic e/mwaves found in a type III source region. We believe that the lowfrequency waves are related to the in-situ type III. A thorough,if incomplete, identification of the waves as whistlers (W) isobtained, based on their frequency and polarization properties.The analysis includes the recovery of the direction of propaga-tion with respect to the IMF, by applying minimum varianceanalysis on the magnetic field waveforms. No IA were detected

during this event. We propose some possible mechanisms tojustify the presence of such whistler waves.

2. Data overview

On Dec. 24, 1996, the WIND spacecraft, situated at∼ 75 RE

from the Earth and around [14:00-16:00] UT, observed a type IIIsource region as indicated by a type III radio signature seen onthe WAVES radio-spectrogram (electric field swept frequencydetectors: RAD2, RAD1, TNR) from 13 MHz at 13:00 UT,down to the local plasma frequencyf†

pe = 40 kHz at 14:00 UT.There was also an intensification of electric wave activity aroundf†

pe during [14:00-15:20] UT, and a strong enhancement of theelectron flux at high energy in channels above 34 keV, startingfirst in the highest energy channel 176 keV at 13:25 UT (seeFig. 1).

In some detail, the type III e/m emission sweeps all thefrequency range of the TNR detector down tof†

pe, but en-hancement atf†

pe is due to local type III emission or possiblyelectrostatic emission (L). The variation of the electron plasmafrequency inferred fromne follows very closely the variationof the plasma line; using it as a guide to delimit the varyingfrequency range of the plasma line, one finds that the radio-emission in betweenf†

pe and 2f†pe, during the local type III

activity [14:00-15:20] UT, is typically 50 times weaker thanthe plasma line emission, which averages at approximately10 µV/m

√Hz. For comparison, the type III emission, before

the onset atf†pe is about 0.02µV/m

√Hz. The sharp peaks of

intensity observed on the TNR spectrum aroundf†pe present a

maximum at 22.9µV/m√

Hz at 14:32 UT. The first burst ob-served, that marks the onset of the local type III emission atf†

pe

occurs at 13:55 UT; a five-minute long quiet period follows.Wave activity below the electron cyclotron frequency (fce =

280 Hz ) was recorded by the WAVES-TDS instrument during[14:30-15:08] UT, whereas the WAVES-FFT instrument de-tected no IA. The FFT instrument usually returns, at regularinterval, on board Fast Fourier Transforms of electric and mag-netic measurements in 3 frequency bands, L(ow), M(edium),H(igh), ranging [0.3 Hz-10.4 kHz]. Noise apparent in the TNRspectrogram belowf†

pe is due to instrumental effects rather thanDoppler shifted ion acoustic waves (fIA ≤ fpi <1 kHz). It isattributed to an increase of the instrument’s noise level at allfrequencies in the band containing possibly Langmuir waves(although the TNR is not saturated by the intense waves), thatalso leaks into the lower frequency band of the TNR. Confir-mation comes from the absence of any signal in FFTH-Ex andFFTH-Ey channels, at that time.

The solar wind parameters varied little during the in-situtype III period, the IMF being particularly constant (VSW =(−358.9,−9.5, 21.1) kms−1 andB0 = (−5.63, 6.59, 4.95) nTin GSE,VSW = 360 kms−1, B0 = 10.0 nT, ne = 17.0 cm−3).There was a significant density increase relative to the previ-ously quiet solar wind (ne = 10.6 cm−3). All quantities areaverages over one-hour periods: [14:00-15:00] UT and [09:00-10:00] UT; data comes from WIND ISTP Key Parameters.

O. Moullard et al.: Whistler waves observed at a solar type III radio-source 705

Fig. 1.The TNR spectrogram, over the period [10:00-22:00] UT, illustrating the type III burst, together with the electron flux in 3 energy channels.Electron data comes from 3DP Key Parameters. The lower panel shows the TDSS events occurences and waveforms during [10:00-22:00] UT.Waveforms amplitude are plotted along the time axis. Inner time ticks mark the occurences of TDSS events.

The low frequency wave data described herein are sampledelectric and magnetic measurements coming from the TDS in-strument (Time Domain Sampler), part of the radio and plasmawave experiment WAVES, on board of the spacecraft WIND(Bougeret et al. 1995). The TDS gathers fast waveform data di-rectly from the WAVES sensors (three electric dipolar antennaeand three magnetic search coils), and shares its 6 input chan-nels between the TDSF (2 channels with a higher sampling fre-quency, for this period 120 ksamples/s) and the TDSS (4 chan-nels with a lower sampling frequency, for this period 7.5 kS/s).The TDS instrument has a dynamic range of 90 dB. It triggerson TDSF fast channels, i.e. in practice, often when Langmuirwaves are detected. A TDSS event is telemetered, if its qualityis higher than the TDSF one. Since the TDSS event’s qualityusually depends on the signal’s amplitude found in the ExDCchannel, which contains spacecraft interference, the capture ofa TDSS event seems rather statistically random.

On Dec. 24, 1996, there were 73 TDSS events, each com-prising ofEx, Bx, By, Bz waveforms, each consisting of 2048samples over a period of 0.27 s. Fifteen such events were foundduring the in-situ type III (see Fig. 1 and Fig. 2). There is a

spate of TDSS events with a very high signal to noise ratio dur-ing [14:30-15:08] UT, in the type III source region. As seenin WAVES-TDS frame of reference, they consist of 9 low fre-quency quasi-monochromatic waves at about 30 Hz (magneticcomponents only) with little modulation apparent at this timescale. The highest magnetic field strength is around 0.5 nT.Those quasi-monochromatic waves contrast with waveformsrecorded before the in-situ type III, that consist only of noise.In order to obtain the best amplitude and phase values, cali-bration taking account of the instrument transfer function wasused, which introduced a low-frequency trend which was laterremoved via low-order polynomial curve fitting. Confirmationthat the capture of those TDSS events is not fortuitous, but more-over temporally correlated to the in-situ type III, comes fromthe detection, by the FFTL instrument (in Bx, By, Bz mode), ofsome weak magnetic signal in [20-40] Hz at [14:30-16:15] UT.

During the day, TDS also recorded 164 TDSF events (Ex,Ey waveforms each comprising of 2048 samples over a periodof 0.017 s, corresponding to a Nyquist frequency of 60kHz).There are 25 TDSF events during [14:30-15:46] UT, duringthe in-situ type III, probably these are intense Langmuir waves

706 O. Moullard et al.: Whistler waves observed at a solar type III radio-source

Fig. 2.TDSS events with respect to the TNR spectrogram during the period of intensification of the electric wave activity atf†pe [14:00-15:20] UT,

and later, in correlation with an enhanced plasma line and apparently ion acoustic wave activity. No waveform is shown when the signal isinterpreted as mere noise (weak white noise); 6 such noisy events were recorded during the type III period.

(|Exy|max = 27 mVm−1), of frequency∼ 40 kHz and stronglymodulated (envelope∼ 400 Hz). Observations in the fore-shock and in this type III event, show that these waves aretransverse and may well be small wavenumber z-mode waves(Bale et al. 1998).

Note that some intense low-frequency e/m waves, at about60 Hz, with less regular waveforms than the TDSS events of[14:00-15:20] UT, are found later that day around 20:00 UT,in correlation with an enhanced plasma line (but no Langmuirbursts) and apparently ion acoustic wave activity (see Fig. 2).These TDSS wave events are also accompanied by FFTL mea-surements in the band [40-100] Hz at [20:00-21:30] UT.

3. Analysis of TDSS data

According to the cold plasma waves classification, whenfce <fpe, waves of frequencyf in the rangefci < f < fce andf � fpi < fpe (the case here) are whistler wave modes. OnDec. 24, 1996, the TDSS data gives us the completeB fieldwaveform, so that we can apply minimum variance analysis for

determining the direction of minimum field variation, by diag-onalizing< BB > − < B >< B > (Sonnerup et al. 1967).Preliminary despinning of the data was necessary because theTDSS waveforms last about one tenth of the spacecraft’s spinperiod (∼ 3 s). Once despun, the data were transformed into theGSE coordinates system, in order to facilitate comparison withdata from other instruments. The minimum variance analysisshows that for all the quasi-monochromatic TDSS events foundduring the in-situ type III period, the eigenvalue in the directionof minimum field variation (u0) is smaller by a factor of 50 thanthe eigenvalues corresponding to the two other directions (u1,u2). The maximum and intermediate eigenvalues are similarso that the wave are planar and quasi-circularly polarized (seeFig. 3).

The wave vectork is either parallel or anti-parallel to theaxis of minimum varianceu0, i.e., perpendicular to the plane ofvariation of the wave magnetic field. One can deduce the wave’sangle of propagation with respect to the IMF from the transfor-mation matrix to GSE, that is the direct angle betweenu0 andthe IMF. For all the TDSS events during the in-situ type III,

O. Moullard et al.: Whistler waves observed at a solar type III radio-source 707

the propagation angleθkB0 = cos−1(|k · B0|), is at most20◦

(average is15◦). Therefore, the polarization with respect to theIMF is approximately either the same or the opposite to the onewith respect tou0, depending on the sign of the IMF projectionon u0. For all the TDSS events during the in-situ type III, thepolarization with respect toB0 was found to be right-handed inthe spacecraft frame.

Thus, we have observed right-handed (with respect toB0

in the spacecraft frame) near circularly polarized waves, prop-agating approximately parallel or antiparallel to the IMF.

For θkB0 ≤ 20◦, the dependence of the whistler index ofrefraction from cold plasma theory is small since,

n2 =f2

pe

f(fce cos θkB0 − f)

We can assume thatn is the same as for parallel propaga-tion n ∼ n(θkB0 = 0) ≡ n‖. Taking, fpe = 37 kHz,fce = 280 Hz, and the observed frequencyfobs = 27 Hz,one obtainsn‖ ∼ 447 (with fpe inferred from the inflexionpoint of positive slope in the TNR plasma line spectrum). Overthe set of TDSS events,n‖ ranges [414-462]±30 (fobs aver-ages to 31.5 Hz). We can then estimate the Doppler effect usingthe wavenumber amplitudek inferred from the theoreticaln‖,k = n‖2πf/c ∼ 2.6 10−4 m−1 (for the typical values), and

the observed angleθkVSW= cos−1(|k · VSW|), which is at

least64◦ for all the TDSS events (average is70◦). The abso-lute value for the Doppler shift gives12π |k · VSW| ∼ 6 Hz.Note that this estimate ofk, usingf ∼ fobs into the dispersionrelation (f is the plasma frame frequency), exceeds the exactsolution fork by one up to ten percent. An exact solution fork(fobs, fce, θkB0 , fpe) is found by solving the cubic equationresulting from the dispersion relation together with the Dopplershift equation. Values of the refractive index based on this solu-tion are similar to the range given above. Relative to the plasmaframe frequencies, the range of Doppler shift is [-4,-7]Hz or[3.9,6.2]Hz, corresponding tok = ±u0. These ranges are notsymmetrical because the amplitude ofkdiffers slightly on eitherside of the dispersion relation relative tofobs.

We have considered the dispersion relation for a whistlerwave that is right-hand polarized in the plasma frame. In orderto observe a right-handed wave that was also right-handed in theplasma frame, eitherk is parallel toB0, or k is anti-parallel toB0 with the additional condition that the wave speed, assumedto be the phase speed, satisfies|vφcos(θkVSW

)| < |VSW|. Allthe TDSS wave events during the in-situ type III have observa-tionally deduced wavevectors that respect this condition.

For the TDSS events under discussion, an electric field sig-nal is also avalaible from the WIND WAVESx-antenna. Butbecause this channel is DC coupled, it records mostly a quiteregular spacecraft interference pattern,Ex0 . Nevertheless, forone TDSS event, the one at 14:42:39 UT, a significant quasi-sinusoidal variation aboveEx0 at the signal frequency is found.The detection of an electric wave component for that eventseems to have been favoured byEx0 being close to the zero of theinstrument (where the sensitivity relative to the superimposed

Fig. 3. The first panel of this figure is a 3D perspective of a portionof the magnetic waveform of one of the quasi-monochromatic TDSSevents (at 14:42:39 UT), in the minimum variance frame. Just one thirdof the waveform is shown to ease vizualisation. Its projection onto thepolarization plane (u1,u2) is represented in dashes. Field variations inthe direction of minimum field variance (u0) are clearly small. Thefour other panels decompose this sample into succesive time intervals,of sample length slightly less than one cycle period, so as to make thewave polarization evident: the wave is here left hand polarized withrespect tou0.

signal is the highest), a strong magnetic signal, and by hav-ing thex-antenna direction close to the polarization plane ((x-antenna,u0)∼ 70◦). The peak value of the observed electric fieldon thex-antenna leads to an estimate of the electric field ampli-tude of the wave, sinceE rotates in the polarization plane. With|E| = 1.8 10−4 ± 0.5 10−4 Vm−1 and|B| ∼ 0.54 ± 0.03 nT,n‖ = c|B|/|E| = 900 ± 300 (this simple expression of the re-fraction index is only valid for parallel propagation). This valueis about 2 times larger than the refraction index calculated above,based on the frequencies in the observation frame. Its lower limitcould match the highern‖ that is associated to a whistler waveof lower frequency in the rest frame (fork · v > 0, f = 21 Hz,n = 507, for k · v < 0, f = 35 Hz, n = 419).

One could consider the effect of the Lorentz transforma-tion on the considered events. As a first approximation,Bis unchanged in such transformation. For the electric field,E = E + B ∧ VSW, it appears that for the highly obliqueθkVSW

observed, the electric components in the polarisationplane would not be very affected, but some electric field alongk would result. We do not feel that a single spacecraft observa-tion allows a precise enough determination ofk for a worthwhileinvestigation on this.

4. Discussion

For these observations, the IMF was found not connected tothe bow-shock, eliminating the possibility of energetic particlesstreaming from the foreshock being responsible for excitingthe low frequency e/m waves. One has therefore to considerthe hypothesis that the presence of the whistler waves is one

708 O. Moullard et al.: Whistler waves observed at a solar type III radio-source

aspect of the type III event: is it a result of an interaction withsome electron beam (either the type III electron beam or a subproduct of it) or a product of a type III wave-wave process? Aminimal hypothesis would be to consider the large scale densitystructure observed, that possibly helps the type III emissionmechanism, as the cause for the presence of the whistlers (onenotes that whistler waves activity has been reported during ionflux enhancements in the foreshock, Anderson et al. 1981).

On the one hand, whistlers are good candidate to participat-ing into the wave-wave type III interaction as they are at lowfrequency, but they seem a poor candidate as far ask is con-cerned. The whistler wavenumber is parallel (or antiparallel) tothe IMF, and as such offers littleE‖ to interact with a Langmuirelectrostatic field. Participation is possible, though, if the TDSFevents are to be interpreted as obliquely propagating z-modes.

Otherwise, for direct particle-wave interaction to occur, theexciter electrons should be much slower than the fast type III as-sociated electron beam, because of the whistler waves phase ve-locity (vϕ = c/n‖ � c/3). Such electrons could arise from non-linearly created tails in the distribution function (from the energyconversion of another wave with a small phase speed). Anotherhypothesis for the production mechanism of the whistlers wouldbe an electron heat flux instability, appearing due to a shift inthe electron core distribution, in reaction to the electron beam.The possibility of having fast ions in provenance of the samesource as the electron beam might also be plausible.

Evaluation of possible mechanisms involved in the presentevent obviously requires examination of the particle data and theuse of kinetic theory, cold plasma linear theory being adequateonly for identifying the waves as whistlers.

Acknowledgements.We thank Keith Goetz, Paul Kellogg (PrincipalInvestigator of TDS) and Steve Monson (University of Minnesota), aswell as Jean-Louis Bougeret (PI of WAVES, Observatoire de Meudon)for their permission to use the WIND WAVES data and its Windlibdatabase. We also thank the WIND 3DP team (University of California,Berkeley) for letting us show the presented KP electron flux, and ChrisOwen (at Queen Mary and Westfield) for providing the WIND MFI3 second resolution magnetic field data. We also thank the referee forprecise and enriching comments. One of the authors, O. Moullard,acknowledges a research studentship funded by QMW.

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