Narrowband oblique whistler-mode waves: Comparing properties observed by Parker Solar Probe at <0.2 AU and STEREO at 1 AU
C. Cattell, B. Short, A. Breneman, J. Halekas, P. Whittesley, J. Kasper, Mike Stevens, Tony Case, M. Moncuquet, S. Bale, J. Bonnell, T. Dudok de Wit, K. Goetz, P. Harvey, R. MacDowall, D. Malaspina, M. Pulupa, K. Goodrich
AAstronomy & Astrophysics manuscript no. narrowband c (cid:13)
ESO 2020September 29, 2020
Narrowband oblique whistler-mode waves: Comparing propertiesobserved by Parker Solar Probe at <0.3 AU and STEREO at 1 AU
C. Cattell , B. Short , A. Breneman , J. Halekas , P. Whittesley , D. Larson , J. Kasper , M. Stevens , T. Case , M.Moncuquet , S. Bale , , J. Bonnell , T. Dudok de Wit , K. Goetz , P. Harvey , J. MacDowell , D. Malaspina , M.Maksimovic , M. Pulupa , and K. Goodrich School of Physics and Astronomy, University of Minnesota, 116 Church St. SE Minneapolise-mail: [email protected] Department of Physics and Astronomy,University of Iowa, Iowa City, IA 52242, USA Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450, USA Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109, USA Smithsonian Astrophysical Observatory, Cambridge, MA 02138 USA LPC2E, CNRS and University of Orléans, Orléans, France Solar System Exploration Division, NASA / Goddard Space Flight Center, Greenbelt, MD, 20771 Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, 92195Meudon,France Department of Physics, University of California, Berkeley, Berkeley, CA 94709 USASeptember 29, 2020
ABSTRACT
Aims.
Large amplitude narrowband obliquely propagating whistler-mode waves at frequencies of ∼ f ce (electron cyclotron fre-quency) are commonly observed at 1 AU, and are most consistent with the whistler heat flux fan instability. We want to determinewhether similar whistler-mode waves occur inside 0.3 AU, and how their properties compare to those at 1 AU. Methods.
We utilize the waveform capture data from the Parker Solar Probe Fields instrument to develop a data base of narrowbandwhistler waves. The SWEAP instrument, in conjunction with the quasi-thermal noise measurement from Fields, provides the electronheat flux, beta, and other electron parameters.
Results.
Parker Solar Probe observations inside ∼ / Bernstein waves at higher frequencies. This is likely due to the more variable solar windobserved closer to the Sun. The whistlers usually occur within regions when the magnetic field is more variable and often with smallincreases in the solar wind speed. The near-sun whistler-mode waves are also narrowband and large amplitude, and associated withbeta greater than 1. Wave angles are sometimes highly oblique (near the resonance cone), but angles have been determined for only asmall fraction of the events. The association with heat flux and beta is generally consistent with the whistler fan instability althoughthere are intervals where the heat flux is significantly lower than the instability limit. Strong scattering of strahl energy electrons isseen in association with the waves, providing evidence that the waves regulate the electron heat flux.
Key words.
Physical data and process:Instabilities, plasmas, waves,(Sun:) solar wind,Sun: heliosphere
1. Introduction
Determining which wave modes control the evolution of solarwind electrons has long been of interest, from the early studiesof their properties, characterizing three populations – core, haloand strahl (Feldman et al. 1975). Observations indicated that thepitch angle width of strahl was much broader at 1 AU than wouldbe expected due to the conservation of the magnetic moment.In addition to collisional scattering, various wave modes wereexamined to see if they could provide the required scattering.Early theoretical work was hampered by the lower time resolu-tion measurements of wave spectra obtained by spacecraft in thesolar wind. The development of waveform capture instrumentsprovided high time resolution full waveform data. Studies utiliz-ing STEREO waveform data near 1 AU revealed the presence oflarge amplitude, narrowband whistler-mode waves with frequen-cies of ∼ f ce . The waves propagate at highly oblique anglesto the solar wind magnetic field with significant parallel electric fields enabling strong interaction with solar wind electrons with-out requiring the counter-propagation needed with parallel prop-agating waves. These waves are frequently observed, most oftenin association with stream interaction regions (SIRs), but alsowithin coronal mass ejections (CMEs) (Breneman et al. 2010;Cattell et al. 2020a) and wave groups can be observed to last forintervals of days.Inside ∼ ∼ f ce ) maybe more common (Malaspina et al. 2020), particularly in regionsof quiet radial magnetic field. These waves include both elec-tron Bernstein and electrostatic whistler-mode waves. The occur-rence frequency decreases with distance from the Sun, consis-tent with their absence in the STEREO waveform data at 1 AU.Lower frequency sunward propagating whistler-mode waves arealso observed by Parker Solar Probe (Agapitov et al. 2020), pri-marily in association with decreases in the magnetic field or the Article number, page 1 of 8 a r X i v : . [ phy s i c s . s p ace - ph ] S e p & A proofs: manuscript no. narrowband rapid change in magnetic field orientation called ‘switchbacks’or jets (Bale et al. 2019; Kasper et al. 2019).The properties of the electron distributions have been char-acterized inside ∼ .2 AU by Parker Solar Probe (Halekas et al.2020a,b), between ∼ .3AU and ∼ .75 AU by Helios, at 1 AU byWind and Cluster, and outside 1 AU by Ulysses (Maksimovicet al. 2005; Štverák et al. 2009; Wilson III et al. 2019). Al-though the radial dependence of the changes in the propertiesof core, halo and strahl are consistent between these studies, thespecific mechanisms that provide the scattering and energizationhave not been definitely identified. To understand the role theobserved narrow-band whistler-mode waves play in modifyingthe electron distributions and regulating heat flux, it is impor-tant to determine how their occurrence and properties depend ondistance from the Sun.In this report, we describe comparisons of narrowbandwhistler-mode waves observed in the waveform data obtainedby Parker Solar Probe from Encounters 1 through 4, and bySTEREO. Section 2 presents the data sets and methodology. Ex-ample waveforms and statistical results on the waves are dis-cussed in Section 3. Conclusions and possible consequences forsolar wind evolution are presented in Section 4.
2. Data sets and methodology
We utilize the Level 2 waveform capture data obtained duringthe first four solar encounters by the Parker Solar Probe FieldsSuite (Bale et al. 2016). The details of the waveform capture in-strument are described by Malaspina et al. (2016). During thefirst encounter, three components of the magnetic field using thesearch coil instrument were obtained, enabling determination ofthe wave vector direction. Subsequent encounters obtained twocomponents. Although three components of the electric field(potential di ff erence across probes) are transmitted, we utilizeprimarily the two components in the plane perpendicular to thespacecraft-Sun line obtained by the longer antennas. A boomlength of 3.5 m is used to covert potential di ff erences to electricfields; a smaller e ff ective boom length would increase electricfield amplitudes. The waveform data utilized in this study wereobtained for 3.5 s intervals at 150 ksamples / s. As implementedon STEREO, the highest quality (usually defined by amplitudeof the electric field) captures are stored and transmitted. In addi-tion, intervals of interest in the summary data were selected bythe Fields team for transmission of waveform data to the ground.Note that in the first three encounters dust impacts often trig-gered the quality flag. For later encounters, software modifica-tions reduced the number of dust triggers. The wave amplitudesobtained from the first three encounters are therefore, on aver-age, smaller than those from the fourth. We also utilize one elec-tric field and one magnetic field channel in the DC coupled spec-tral data, which is obtained at a rate of 1 spectra /
64 Cy, where1 Cy = ∼
10 Hz to 4.8 kHz(Malaspina et al. 2016). The spectra are ∼
30 s averages. We havealso examined one electric field and one magnetic field channelin the DC coupled bandpass filter (BPF) data which is obtainedat a higher cadence of 1 spectrum /
3. Waveform examples and statistics
Figure 1 presents an overview of 31 hour interval from 12 UTon November 2, 2018 to 19 UT on November 3, 2018 that in-cluded 9 waveform captures with narrowband whistlers, as wellas higher frequency electrostatic waves. The top two panels,which plot the DC-coupled BPF electric field spectrum and theDC-coupled BBF magnetic field from 12 to 4000 Hz clearlyshows the distinction between the higher frequency electrostaticwhistlers / Bernstein waves discussed by Bale et al. (2019) andMalaspina et al. (2020) and the narrowband whistlers that arethe focus of this letter. Examples of the higher frequency elec-trostatic waves are at ∼ ∼
03 and 05 UT on November 3, as wellas for shorter intervals on both days. Examples of the narrow-band electromagnetic whistlers can been seen in both spectra at ∼ ∼
09 and 11 UTand ∼ ∼ ∼
13 to ∼
15 on November 3. Note that some changesin the pitch angle distributions are associated with changes in themagnetic field orientation. A detailed discussion of the scatter-ing and specifics of the resonant mechanisms are presented inCattell et al. (2020b). The fourth panel plots the radial compo-nent of the proton plasma velocity in blue (with 300 km / s sub-tracted to make changes clearer) and the radial component ofthe magnetic field in red. The third panel plots magnetic field inRTN coordinates. As described in Malaspina et al. (2020), thehigh frequency electrostatic waves occur primarily in quiet ra-dial magnetic field. The narrowband whistlers occur primarilywithin regions with more variable magnetic field and slightly in-creased flow, and, at times, within or on the edges of structurescalled ‘magnetic switchbacks’ or ‘jets’ (Bale et al. 2019; Kasperet al. 2019).One component of the electric field waveforms for seven ofthe waveform captures containing narrowband whistlers is plot-ted in the right hand set of panels; Article number, page 2 of 8. Cattell et al.: Narrowband oblique whistler-mode waves inconvertible yaxis units
314 eV204 eV102103 f ( H z ) f ( H z ) -50050050100150 PA PA × × × B ( n T )
234 56 78
Fig. 1.
Interval during Encounter 1 with narrow band whistler-mode waves and higher frequency electrostatic waves. Left panels: DC-coupledBPF electric field spectrum from 12 to 4000 Hz; DC-coupled BBF magnetic field from 12 to 4000 Hz; magnetic field in RTN coordinates, Rcomponent of magnetic field in red with radial component of ion flow -300 km / s in blue. Pitch angle spectra for electrons with center energy of314 and 204 eV. Units for the wave spectra are volts and nT, and for the electron data are eV / cm s. Right panels: Spacecraft x component of theelectric field (in mV / m) snapshots from seven di ff erent waveform captures during this interval at approximate times indicated by arrows with bluearrows indicating more tatn one snaphot. Note that the time durations vary. See text for details. quently contains more than one wave packet. Examination of themagnetic field hodograms (not shown) indicates that the wavesare right-hand polarized, as expected for whistler-mode waves.The total number of waveform captures containing narrow-band whistlers versus radial distance is plotted in Figure 2, colorcoded by encounter number. Note that instrument modes and so-lar wind conditions varied between encounters, as did the on-board program for triggering waveform captures. For the set ofevents identified in Encounter 1, when three components of thesearch coil data were obtained, the wave vector direction with re-spect to the background magnetic field and the solar wind veloc-ity was determined using minimum variance analysis. The wavevector angle with respect to the magnetic field is plotted in Fig-ure 3 for these events. Although the average angle is very similarto that at 1 AU (Cattell et al. 2020a), the distribution is broaderand extends to lower angles. Most of the observed waves areobliquely propagating near the resonance cone. Note that therewas a very small number of Encounter 1 events compared to theSTEREO database for wave angle determination.Statistics of the properties for the waves identified in thefirst 4 encounters are shown in Figures 4 and 5. The number ofevents is not normalized by total number of waveform capturesobtained. Figure 4 plots the spacecraft frame frequencies at peakpower, color coded by encounter, and the magnitude of the back-ground solar wind magnetic field for each event. The top panelsplot the number of events versus wave frequency, f, and the num-ber of events versus frequency normalized by electron cyclotronfrequency (f / f ce ), and the background magnetic field. The bottompanels plot f, f / f ce and the magnitude of the solar wind magneticfield versus radial distance from the Sun. There is not a clear ra-dial dependence of the wave frequency in the spacecraft frame.The normalized frequency, f / f ce , has a tendency to increase withdistance from the Sun, consistent with the higher average f / f ce of ∼ / f ce may provide information on the instability mech-anism and associated changes in heat flux and beta with radialdistance. In contrast to the case at 1 AU, where Breneman et al.(2010) showed that Doppler shifts were insignificant, there are Figure 2. Number of narrowband whistler wave captures color coded by encounter number Figure 3. Wave vectors for narrowband whistler wave captures for Encounter 1.
Figure 4. Spacecraft frame frequencies for narrowband whistler wave captures color coded by encounter. Left: Number of events versus frequency and frequency normalized by electron cyclotron frequency; right: Event frequency and frequency normalized by electron cyclotron frequency versus radial distance from the Sun.
Fig. 2.
Number of narrowband whistler wave captures color coded byencounter number. The number is not normalized by total number ofwaveform captures obtained. sometimes significant Doppler shifts in the waves observed byPSP. For the Encounter 1 events, for which the shifts could bedetermined, the shifts increased the average f / f ce only slightlyto ∼ ff erence. Whistler events usually occurred in regions withreduced magnetic field magnitudes. The wave amplitudes, deter-mined from the peak amplitude seen in any component in eachevent, are plotted in Figure 5, color coded by encounter. The toppanels show the number of whistler captures versus amplitude ofthe wave electric field, amplitude of the wave magnetic field andof the wave magnetic field normalized by background magneticfield ( δ B w / B ) where δ B w is the magnitude of the wave magneticfield. The bottom panels show the radial dependence of these Article number, page 3 of 8 & A proofs: manuscript no. narrowband
Figure 2. Number of narrowband whistler wave captures color coded by encounter number Figure 3. Wave vectors for narrowband whistler wave captures for Encounter 1.
Figure 4. Spacecraft frame frequencies for narrowband whistler wave captures color coded by encounter. Left: Number of events versus frequency and frequency normalized by electron cyclotron frequency; right: Event frequency and frequency normalized by electron cyclotron frequency versus radial distance from the Sun.
Fig. 3.
Wave vector angle with respect to background magnetic field fornarrowband whistler wave captures for Encounter 1. amplitudes. There is a clear decrease in wave amplitudes withradial distance from the Sun, although the decrease in( δ B w / B )is not as strong. Although PSP sees a decrease in the electricfield amplitudes with radial distance, the average amplitude atradial distances around 0.3 AU is only slightly larger than thoseobserved at 1 AU by STEREO. As noted in Section 2, the ampli-tudes for the first three encounter are on average lower than forencounter 4, because many waveform captures were triggeredby dust until the algorithm was modified. For this reason, manyof the intervals with whistlers occurred in dust-triggered eventsrather than ones triggered by wave amplitude. Data from addi-tional encounters will be required to determine if the observedamplitude di ff erences between PSP and STEREO are due to dif-ferences in the waveform capture selection criteria or to physicsassociated with wave growth and saturation. Note that STEREOdid not have a search coil magnetometer so wave magnetic fieldswere not directly measured.The association of the whistler events with electron param-eters is shown in Figure 6. For most waveform captures, theelectron parameters were determined within a few seconds ofthe capture, with median times of ∼ ∼ < ff erences from the results for all in-tervals during the encounters 1 and 2 presented by Moncuquetet al. (2020). Their results show that the core electron temper-ature decreases with radial distance, and the suprathermal tem-perature was almost constant. For intervals with the waves, wesee a slight increase in the core temperature, possibly indicatingheating of core electrons by the waves, and a slight decrease inthe suprathermal temperature. Note that our statistics are smalland the observed variability at a given radial distance is as largeas the average change with radial distance.Possible instability mechanisms are examined in Figures 7.The left panel of Figure 7 shows temperature anisotropy versusparallel electron beta. The upper red line is the whistler tem-perature anisotropy threshold, T e ⊥ T e (cid:107) = + / β e (cid:107) and the lower red line is an arbitrary firehose instability (both from Lacombeet al. (2014), based on Gary et al. (1999)). The middle panelplots the normalized electron heat flux versus parallel beta, withthe linear instability threshold for the heat flux fan instability(Vasko et al. 2019, for the parameters of 0.5 and 1 in their Ta-ble 1). The most striking feature is that the waves occur whenbeta >
1. Halekas et al. (2020a) showed that during encounters1 and 2 inside 0.24 AU, beta was usually <
1. This associationof narrowband whistler waves with beta > ∼
10 to 20eV; thus this mechanism would require beams with energies of ∼
40 to 80 eV. This is an order of magnitude lower than would berequired for the mechanism to operate at 1 AU. To date, we havenot yet been able to identify beam features at the appropriateenergies in either event list.To better assess the occurrence probability of these waveswe utilized one electric field channel in the DC coupled spectraldata, at 30 s resolution. We examined by eye the spectral data foreach hour during the first encounter interval shown in the BPFdata in Figure 1, which covers 31 hours on November 2 and 3.This yields only a very rough estimate of occurrence rate. Theindividual waveform captures (duration 3.5 s) usually containseveral individual wave packets. An example of a 3.5 s wave-form capture was shown above in Figure 1, packet ∼ ∼ /
64 Cy) to the BPF data (1 sample / Article number, page 4 of 8. Cattell et al.: Narrowband oblique whistler-mode waves
Fig. 4.
Spacecraft frame frequencies for narrowband whistler wave captures color coded by encounter. Top: Number of events versus frequency,frequency normalized by electron cyclotron frequency and magnitude of the background magnetic field. Bottom: Whistler event frequency, fre-quency normalized by electron cyclotron frequency and background magnetic field versus radial distance from the Sun.
Fig. 5.
Whistler peak amplitudes color coded by encounter. Left panels: Number of whistler captures versus amplitude of electric field, magneticfield and magnetic field normalized by background magnetic field. Right panels: Event amplitude of electric field, magnetic field and magneticfield normalized by background magnetic field versus radial distance from the Sun.
4. Discussion and conclusions
We have compared statistics of the properties of the narrow-band whistler-mode waves observed in waveform capture data from Parker Solar Probe during the first four encounters inside ∼ Article number, page 5 of 8 & A proofs: manuscript no. narrowband
Fig. 6.
Whistler dependence on core density, core and suprathermal temperature (from the QTN measurement).Top panels plot the number ofevents versus core electron density, core and suprathermal temperature. Bottom panels plot the same quantities versus radial distance from theSun.
Fig. 7.
Comparison to possible instability mechanisms. From left to right:Temperature anisotropy versus parallel electron beta, upper red line isthe whistler temperature anisotropy threshold, = + / and the lower red line is an arbitrary firehose instability (both from Lacombe et al.2014, based on Gary et al., 1999).Normalized electron heat flux vs parallel beta with the linear instability threshold from equation 5 (Vasko et al.,2019) for the parameters of .5 and 1 in their Table 1. Comparison to possible instability mechanisms. Electron Alfven energy. rowband and large amplitude. The association with heat fluxand beta is generally consistent with the whistler fan instabil-ity although there are intervals where the heat flux is signif-icantly lower than the instability limit. In both data sets thewhistlers are observed only for beta >
1, and the average temper-ature anisotropy was ∼ .9. The PSP electron data show significantscattering at strahl energies, as documented in detail by Cattellet al. (2020b). This is consistent with a study of electron heatflux (Halekas et al. 2020b) for Encounters 1 through 5, whichshowed that the heat flux and beta were constrained by the faninstability threshold, providing evidence that these waves regu-late the electron heat flux.At 1 AU, two distinct populations of whistler-mode waveswith frequencies of f / f ce of ∼ ∼ f lh and 0.5 f ce , identified in search coil magnetic field at distances of 0.3 to0.9 AU. The observed spectral peaks were identified as whistler- Article number, page 6 of 8. Cattell et al.: Narrowband oblique whistler-mode waves mode based on similarities to Lacombe et al. (2014), but po-larization, wave vectors and Doppler shifts could not be deter-mined. The waves were observed almost exclusively in the slowsolar wind ( <
400 km / s).Figure 8 plots histograms of the number of whistler eventsversus solar wind speed in the Cattell et al. (2020a) STEREOdatabase (left) and the number of PSP events color coded by en-counter (right) versus solar wind speed. The center panel plotsthe PSP events versus solar wind speed and radial distance. Thehighly oblique whistlers observed at 1 AU by STEREO are pre-dominantly seen with solar wind speeds of ∼
400 km / s, but arealso observed with speeds up to ∼
700 km / s. PSP events are asso-ciated with lower solar wind speeds ( ∼
300 km / s). The bi-modaldistribution is likely due to radial distance e ff ects, di ff erencesin conditions during each encounter, and to the small numberof events, as indicated by the center panel which plots the PSPevents versus solar wind speed and radial distance. Encounter4 events were all obtained inside ∼
50 solar radii and solar windspeeds were ∼
200 km / s, whereas events during Encounters 2 and3 were primarily outside ∼
50 solar radii with solar wind speedsof ∼
350 km / s. The di ff erences in wave association with solarwind speed between PSP events inside .3 AU and the STEREOevents at 1 AU may just be due to the evolution of the solar wind.The Jagarlamudi et al. (2020) observations which cover the dis-tances between .3 AU and .9 AU, however, were associated withslow flow. Wave vector angles have been determined for only asmall fraction of the PSP events; therefore, it is not yet possi-ble to determine if there is a relationship between wave obliq-uity and solar wind speed at these radial distances. The parallelpropagating waves and the oblique waves may represent two dif-ferent modes, or di ff erent sources of free energy. However, thedistinction may also be due di ff erences in instrumentation. Fu-ture studies utilizing the Parker Solar Probe data set may resolvethe relationship between the parallel and highly oblique waves.There are two main di ff erences between the characteristicsof the whistlers identified in waveform captures inside 0.2 AUand the waves at 1 AU: (1) the association with larger scalesolar wind properties and structure; and (2) the occurrence ofa broader band less coherent mode at 1 AU that has not yetbeen identified in PSP waveform data. In addition, inside 0.2 AUthe narrowband electromagnetic whistlers are interspersed withlower amplitude electrostatic whistler-mode waves and Bern-stein waves at frequencies of ∼ f ce to > f ce (Malaspina et al.2020; Bale et al. 2019), which have not been observed at 1 AUin the STEREO waveform data.At 1 AU, the narrowband oblique whistlers are most oftenassociated with SIRs, often filling the downstream region of in-creased solar wind speed, and often variable magnetic field andlower electron parallel beta. The waves are also seen withinCMEs (Cattell et al. 2020a). As shown in Figure 1, inside ∼ ∼ .3 AU.Both the wave magnetic field amplitudes normalized to thebackground magnetic field and the electric field amplitudes ob-served by PSP decrease with radial distance from the Sun, how- ever, the average electric field amplitudes observed by STEREOat 1 AU are comparable to those seen by PSP near .3 AU. Thismay be due to the di ff erent selection criteria for burst data forthe two spacecraft or to di ff erences in the physics. For exam-ple, the waves may, on average, be more oblique at 1 AU or thewave growth and saturation mechanisms may be di ff erent due todi ff erences in the solar wind.Initial results on whistler-mode waves observed by ParkerSolar Probe identified in the magnetic field data during the firstencounter were presented by Agapitov et al. (2020), utilizing the ∼
300 samples / s waveform data. The observed waves had largeamplitudes ( ∼ ∼ f ce , and variable wave angles. We interpret thesewaves as being the lower frequency component of the wavesdescribed herein, although there are di ff erences including av-erage f / f ce that warrant additional studies for other encounters.This will require developing a method to accurately determinewave vector direction when only two components of the searchcoil data are available, utilizing an approach similar to that usedon STEREO based on the three components of the electric fieldwaveform and the cold plasma dispersion relation (Cattell et al.2008).In conclusion, we have shown that narrowband whistlermode waves observed in the PSP waveform capture data in-side ∼ .3 AU have many characteristics similar to those seenby STEREO at 1 AU. In both regions the waves are consistentwith the whistler heat flux fan instability and occur when beta isgreater than 1. The waves at 1 AU have slightly higher averagef / f ce and are on average more oblique, but both of these di ff er-ences may be due to the small number of PSP events for whichwe have determined wave angle and Doppler shifts. When thereare wave events, the radial dependence of the core and suprather-mal temperatures is di ff erent from that seen for the full electrondata set (Halekas et al. 2020a), possibly indicating that the wavesheat core electrons. At PSP, the waves are often associated withvariable magnetic field and slightly enhanced solar wind flow,sometimes with ‘switchbacks,’ whereas at 1 AU, the waves aremost often seen in the downstream region of SIRs, also regionsof enhanced flow. Inside ∼ .3 AU, the regions containing wavepackets tend to last for intervals of hours, whereas at 1 AU, theycan last for days. It is very likely these di ff erences are due tothe fact that the solar wind is much more variable on short timescales at PSP compared to at 1 AU.The waves are associatedwith scattering of strahl energy electrons. A very rough estimateof the wave occurrence at PSP suggests that the waves are oftenthe dominant wave mode at frequencies below ∼ Acknowledgements.
We acknowledge the NASA Parker Solar Probe Mission,and the FIELDS team led by S. D. Bale, and the SWEAP team led by J. Kasperfor use of data. The FIELDS experiment on the Parker Solar Probe spacecraft wasdesigned and developed under NASA contract NNN06AA01C. Work at Univer-sity of Minnesota and at University of Iowa was supported under the same con-tract.
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Article number, page 7 of 8 & A proofs: manuscript no. narrowband
Fig. 8.
The relationship of whistler occurrence to solar wind speed on PSP and STEREO. From left to right: the number of events versus solarwind speed on STEREO from the Cattell et al. (2020a) database, PSP whistler events versus solar wind velocity and radial distance, and numberof PSP whistler events versus solar wind speed.
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