Whistler wave occurrence and the interaction with strahl electrons during the first encounter of Parker Solar Probe
V.K. Jagarlamudi, T. Dudok de Wit, C. Froment, V. Krasnoselskikh, A. Larosa, L. Bercic, O. Agapitov, J.S. Halekas, M. Kretzschmar, D. Malaspina, M. Moncuquet, S. D. Bale, A. W. Case, J. C. Kasper, K. E. Korreck, D. E. Larson, M. Pulupa, M. L. Stevens, P. Whittlesey
AAstronomy & Astrophysics manuscript no. WhistlersAandA © ESO 2021February 2, 2021
Whistler wave occurrence and the interaction with strahl electronsduring the first encounter of Parker Solar Probe
V.K. Jagarlamudi , , T. Dudok de Wit , C. Froment , V. Krasnoselskikh , A. Larosa , L. Bercic , , O. Agapitov , J.S.Halekas , M. Kretzschmar , D. Malaspina , , M. Moncuquet , S. D. Bale , , , , A. W. Case , J. C. Kasper , , ,K. E. Korreck , D. E. Larson , M. Pulupa , M. L. Stevens , and P. Whittlesey LPC2E / CNRS, 3 Avenue de la Recherche Scientifique, 45071 Orléans Cedex 2, Francee-mail: [email protected] National Institute for Astrophysics-Institute for Space Astrophysics and Planetology, Via del Fosso del Cavaliere 100, I-00133Roma, Italy LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Jules Janssen, 92195Meudon, France Physics and Astronomy Department, University of Florence, Via Giovanni Sansone 1, I-50019 Sesto Fiorentino, Italy Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450, USA Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA Astrophysical and Planetary Sciences Department, University of Colorado, Boulder, CO 80303, USA Physics Department, University of California, Berkeley, CA 94720-7300, USA The Blackett Laboratory, Imperial College London, London, SW7 2AZ, UK School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK Smithsonian Astrophysical Observatory, Cambridge, MA, 02138, USA Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 48109, USA BWX Technologies, Inc., Washington, DC 20002, USAReceived October 30, 2020; Accepted January 12, 2021
ABSTRACT
Aims.
We studied the properties and occurrence of narrowband whistler waves and their interaction with strahl electrons observedbetween 0.17 and 0.26 au during the first encounter of Parker Solar Probe.
Methods.
We used Digital Fields Board (DFB) band-pass filtered (BPF) data from FIELDS to detect the signatures of whistler waves.Additionally parameters derived from the particle distribution functions measured by the Solar Wind Electrons Alphas and Protons(SWEAP) instrument suite were used to investigate the plasma properties, and FIELDS suite measurements were used to investigatethe electromagnetic (EM) fields properties corresponding to the observed whistler signatures.
Results.
We observe that the occurrence of whistler waves is low, nearly ∼ .
5% and less than 0 .
5% in the analyzed peak and averageBPF data, respectively. Whistlers occur highly intermittently and 80% of the whistlers appear continuously for less than 3 s. Thespacecraft frequencies of the analyzed waves are less than 0.2 electron cyclotron frequency ( f ce ). The occurrence rate of whistlerwaves was found to be anticorrelated with the solar wind bulk velocity. The study of the duration of the whistler intervals revealedan anticorrelation between the duration and the solar wind velocity, as well as between the duration and the normalized amplitude ofmagnetic field variations. The pitch-angle widths (PAWs) of the field-aligned electron population referred to as the strahl are broaderby at least 12 degrees during the presence of large amplitude narrowband whistler waves. This observation points toward an EMwave electron interaction, resulting in pitch-angle scattering. PAWs of strahl electrons corresponding to the short duration whistlersare higher compared to the long duration whistlers, indicating short duration whistlers scatter the strahl electrons better than the longduration ones. Parallel cuts through the strahl electron velocity distribution function (VDF) observed during the whistler intervalsappear to depart from the Maxwellian shape typically found in the near-Sun strahl VDFs. The relative decrease in the parallel electrontemperature and the increase in PAW for the electrons in the strahl energy range suggests that the interaction with whistler wavesresults in a transfer of electron momentum from the parallel to the perpendicular direction. Key words.
Waves – Scattering – Plasmas – Magnetic fields – Sun: heliosphere
1. Introduction
Whistler waves are right-handed polarized electromagneticmodes observed between the lower hybrid frequency ( f LH ) andelectron cyclotron frequency ( f ce ) in the plasma frame. Therange between f LH and f ce is usually referred to as the whistlerrange since whistler waves are the dominant electromagneticmodes observed in this range. In the solar wind, whistlers aredominantly observed in the range between f LH and 0 . f ce (Zhang et al. 1998; Lacombe et al. 2014; Tong et al. 2019a; Jagarlamudiet al. 2020).Whistler wave modes through their interaction with electronsare thought to be one of the prime contributors in the regula-tion of fundamental processes in the solar wind (Vocks & Mann2003; Pagel et al. 2007; Kajdiˇc et al. 2016; Tang et al. 2020).Wave particle interactions, such as those between whistler wavesand electrons, might play a significant role in explaining many Article number, page 1 of 10 a r X i v : . [ phy s i c s . s p ace - ph ] J a n & A proofs: manuscript no. WhistlersAandA physical process such as the heating, acceleration, and scatter-ing of the particles in the solar wind. The electron velocity dis-tribution can be mainly divided into three parts: a low energyisotropic distribution called the core, a high energy isotropic partcalled the halo, and the heliospheric magnetic field aligned highenergy component called the strahl (Feldman et al. 1978; Pilippet al. 1987b,a). While collisions were shown to isotropise thedense low energy electron population referred to as the electroncore, they are not su ffi cient to regulate the more tenuous higherenergy electron populations such as the halo and strahl (Ogilvie& Scudder 1978; Pilipp et al. 1987b). Wave particle interactionshave a crucial role in explaining the phenomena happening in thehigh energy ranges.Due to their small mass, electrons reach high thermal veloc-ities in the hot solar corona. The fastest electrons such as strahlcan escape the solar corona almost undisturbed, carrying the ma-jority of the heat flux stored in the solar wind. The rate of radialdecrease in electron heat flux from the Sun suggests the existenceof the scattering mechanism during solar wind expansion (Scimeet al. 1994; Hammond et al. 1996; Štverák et al. 2015). There-fore, understanding the evolution of strahl electrons and the wavemodes interacting with them gives us valuable insight into theglobal solar wind thermodynamics and energy transport. Obser-vations have shown that the strahl pitch-angle width (PAW) in-creases as we move further from the Sun (Hammond et al. 1996;Graham et al. 2017; Berˇciˇc et al. 2019). It is also seen that therelative density of the electron halo increases, while the relativedensity of the strahl decreases as we move away from the Sun(Maksimovic et al. 2005; Štverák et al. 2009). Whistler waveswith their interaction with strahl electrons could be able to ex-plain the observed evolution of electron velocity distributions(Vocks 2012; Kajdiˇc et al. 2016; Boldyrev & Horaites 2019;Tang et al. 2020).There are quite a few studies on the whistler waves in thefree solar wind at 1 au. One of the early studies to show the clearpresence of whistler waves in the free solar wind was done byZhang et al. (1998). In their study, the authors used the high-resolution electric and magnetic field wave form data on boardthe Geotail spacecraft. They observed that whistler waves havefrequencies between 0 . f ce and 0 . f ce , and the wave vectors weredominantly aligned to the magnetic field direction and propagat-ing in the anti-sunward direction. Whistler wave packets wereobserved for short durations (less than 1 s).Lacombe et al. (2014), using the magnetic spectral matrixroutine measurements of the Cluster / STAFF instrument, stud-ied the long duration whistlers (5-10 min). They have studied20 events, which were observed in the slow wind with a fre-quency range between 0 . f ce and 0 . f ce . The observed waveswere quasi-parallel and narrowband. Tong et al. (2019a) car-ried out a large statistical study of whistler waves using 3 yr ofmagnetic field spectral data from the ARTEMIS (Acceleration,Reconnection, Turbulence, and Electrodynamics of the Moon’sInteraction with the Sun) spacecraft. They show that the occur-rence of whistler waves was dependent on the electron tempera-ture anisotropy, and the amplitude of whistler waves were typi-cally small, below 0.02 of the background magnetic field.A statistical study on whistler waves in the solar wind in theinner heliosphere (0.3 to 1 au) was performed by Jagarlamudiet al. (2020), who used the search coil spectral data to identifythe signatures of whistler waves. Their observed whistler waveshave frequencies between 0 . f ce and 0 . f ce . They show di ff er-ent properties of whistler waves and find that the slower the bulkvelocity of the solar wind, the higher the occurrence of whistlers. They show that the occurrence probability of whistler waves islower as we move closer to the Sun and suggest that whistler oc-currence and variations in the halo and core anisotropy as wellas the heat flux values were related.Cattell et al. (2020) studied the large amplitude whistlerwaves in the solar wind at frequencies of 0.2–0.4 f ce using theSTEREO electric and magnetic field waveforms. These waveswere often observed in association with the stream interaction re-gions. Their studies show that the large amplitude and obliquelypropagating, less coherent whistlers were able to resonantly in-teract with electrons over a broad energy range.A recent study by Agapitov et al. (2020), using the ParkerSolar Probe’s (PSP’s) magnetic and electric waveform data, hasshown the presence of whistler waves when magnetic field dipswere observed around switchback boundaries. The observedwaves were quasi-parallel to dominantly oblique, wave normalangles were close to the resonance cone. The observed whistlerwave packets have frequencies below 0 . f ce .In this study, we focus on the whistler waves observed inthe solar wind in the inner heliosphere between 0 .
17 and 0 . f LH and 0 . f ce always corresponded to a narrowband whistler wave. For ourstudy we assume that any local enhancement of spectral powerobserved in the frequency range between f LH and 0 . f ce is awhistler wave signature (Zhang et al. 1998; Lacombe et al. 2014;Jagarlamudi et al. 2020). The advantage of using band-pass datais that we have high resolution continuous measurements, whichallows us to analyze wave parameters statistically. However, thedrawback is that we only have a single component of data avail-able and we do not have the polarization information, whichhas been compensated for by using the polarization informationfrom the analysis of low time resolution cross-spectral data mea-sured by the search coil magnetometer. Waveform data are usefulto show the presence of whistlers in PSP’s data. However, onlylow frequency whistlers can be seen in the continuous waveform(with the sampling rate of 293 s − and less), that is to say we canuse waveforms for special cases, such as when there are drops inthe magnetic field (Agapitov et al. 2020).This article is structured as follows. In Section 2 we showthe data and the methodology followed to identify the whistlers.In Section 3 we present the basic properties of whistler waves,as well as their occurrence and generation conditions. In Section4, using the strahl distributions, strahl PAW of electrons and thestrahl parallel temperatures, we investigate the interaction be-tween whistlers and strahl electrons. In Section 5 we present theconclusions for our study.
2. Methods and data for the whistler waves analysis
For the purposes of this paper, whistler analysis was performedusing the data from the FIELDS (Bale et al. 2016) and SWEAP(Kasper et al. 2016) instruments on board PSP during the first en-counter with the Sun (October 31 – November 11, 2018). For thedetection of the signatures of narrowband whistlers, we used theDC BPF measurements obtained from the Digital Fields Board(DFB) for FIELDS on board PSP (Malaspina et al. 2016). DFB
Article number, page 2 of 10agarlamudi et al.: Whistler wave occurrence and the interaction with strahl electrons F r e q u e n c y ( H z ) f LH f ce l o g ( P e a k B P F ( n T )) F r e q u e n c y ( H z ) f LH f ce l o g ( M e a n B P F ( n T )) Fig. 1: Example of the peak and average band-pass filtered (BPF)data used for the analysis of whistler waves.Fig. 2: Example of the spectra showing signatures of whistlerwaves in the average BPF data as a function of f / f ce on Novem-ber 5, 2018. The black vertical lines correspond to f LH / f ce and0.5, respectively.gives the peak absolute and the average absolute values in eachband-pass time series sample of ∼ .
87 s, covering the frequencyrange of 0.5 Hz to 9 kHz. The DC BPF data are organized in 15frequency bins; for each, we have the mean amplitude of themagnetic field and the peak amplitude. BPF data are availablefor only one component of the magnetic field. Here, we have theBu component of the SCM (Jannet et al. 2020). However, themain advantage compared to the three component cross-spectraldata ( ∼
28 s) is that BPF data are of a higher time resolution( ∼ .
87 s) and importantly both the peak and average data areavailable.In Figure 1 we show an example of peak and average BPFdata using a 3 minute interval when the BPF spectra showed alocal enhancement of power. The data output of average BPFdata is zero when the signal is very low in the correspondingfrequency channels.For the detection of the whistler signatures, we used a similarmethod as those used in the studies of Jagarlamudi et al. (2020)and Tong et al. (2019a), where a local enhancement of spectralpower in the whistler range was inferred to indicate the presence of a narrowband whistler wave. First, we squared the peak andaverage BPF data and divided the squared values by the corre-sponding frequency bin width, which gives us an equivalent ofthe power spectral density (PSD) values. Using the PSD values,we identified the presence of one single local maximum in thewhistler range which clearly stands out with respect to the PSDof the background turbulence (Alexandrova et al. 2012, 2020).Mathematically speaking, the indicator for whistler wave influ-enced PSD spectra is, as we go toward higher frequencies at acertain frequency, dPS Dd f will be positive and then it naturally be-comes negative again. However, we would like to mention thatthe suggested method could only be used with higher confidencefor the average spectra. The reason is that the observations todate have shown the presence of whistlers in waveform data tothe presence of local enhancement of spectral power in the aver-age spectral data only.An example of average PSD spectra which contain whistlersis shown in Figure 2, where spectra with distinctive local en-hancement in the whistler range were selected. After selectingthe spectra with whistler signatures, we studied the plasma prop-erties corresponding to those whistler signatures. We mainly fo-cused on the strahl electron properties.The advantage of BPF data is that thanks to their time res-olution of ∼ .
87 s, they gives us a much better statistics andinformation on the duration of the whistlers compared to thelow resolution cross-spectral data ( ∼
28 s). However, the cross-spectral data give us the approximate information on the abso-lute ellipticity. The study of cross-spectral data from PSP’s firstperihelion by Froment et al. (2020) has shown that all the cross-spectra, which have shown the local enhancement of power inthe whistler range, have higher ellipticity ( ∼ ∼ .
22 s (Case et al. 2020). The electron velocity distributionfunctions were measured by Solar Probe Analyzer (SPAN) elec-tron sensors on the ram (ahead) and anti-ram (behind) faces ofthe spacecraft (Whittlesey et al. 2020) and the data available forthe first perihelion was of ∼
28 s cadence.We used the 4 Hz magnetic field data and interpolated theseto the resolution of available BPF data. For proton and electronparameters, we considered the closest available value to the BPFinterval with the whistler signature. The magnetic field data andthe proton moments are taken from PSP Science Gateway.The electron density, core temperatures, and heat flux aretaken from the work of Halekas et al. (2020a) and Halekas et al.(2020b), where a bi-Maxwellian distribution is assumed to fit thecore parameters. The strahl pitch-angle widths (PAWs), the cutsthrough the strahl electron VDFs, and the strahl parallel tem-peratures ( T s (cid:107) ) are taken from the work of Berˇciˇc et al. (2020).PAWs represent the full-width-at-half-maximum of a Gaussianfit to pitch-angle distribution functions at every instrument en-ergy bin. The maximal values of these fits by definition appearat a pitch-angle of 0 deg and thus form the parallel cut throughthe strahl VDF. In using this technique to study the properties ofthe strahl along the magnetic field, we account for the portionof the strahl VDF which is sometimes blocked by the spacecraft Article number, page 3 of 10 & A proofs: manuscript no. WhistlersAandA heat shield (see Berˇciˇc et al. (2020) for more details about theanalysis). We note that T s (cid:107) is a Maxwellian temperature of thestrahl along the magnetic field direction.For our analysis, we also use the low-frequency receiver(LFR) data from the Radio Frequency Spectrometer on boardPSP (Pulupa et al. 2017). Using the ∼ f pe and 1.1 f pe .
3. Whistler wave occurrence and their properties
We have detected 2492 and 17313 spectra with the whistler sig-natures in the 1142095 average / peak samples of BPF data. Weobserved that whistlers occur intermittently. The spectra whichshowed the whistler signatures represent less than 0 .
5% of theaverage BPF data and around ∼ .
5% of the peak BPF data. Thereason for the relatively higher number of whistlers observed inthe peak BPF data compared to the average BPF data is under-standable, since if the whistlers have a low amplitude or a veryshort lifetime, they are not visible in the average spectra, but theycan only be observed in the peak data. However, if the whistlersare of a large amplitude or long duration, they would appear inaverage BPF data and in peak BPF data.From both the average and peak spectra showing the whistlerwaves signatures, we observe that the occurrence of whistlerwaves is low ( < f ce , which is similar to previous observations in the solarwind (Tong et al. 2019a; Jagarlamudi et al. 2020). Meanwhile,from Figure 3 (b), we can observe that peak BPF data show asignificant fraction of whistlers in the low normalized frequency( < .
05) range.In Figure 4 (a) and (b), we show a histogram of the log ofnormalized peak amplitudes and the ratio of peak and averageamplitudes corresponding to the whistlers. The method followedto estimate the approximate amplitude of the fluctuations that areassociated with whistler waves is as follows: The spectral valueof the identified local maximum is multiplied with its respectivefrequency of the wave and the square root of this value is inter-preted as the amplitude of the fluctuation. We note that δ B p rep-resents the peak amplitude calculated using the peak BPF dataand δ B m represents the average amplitude calculated using theaverage BPF data. (a) f / f ce (b) f / f ce Fig. 3: Histogram of normalized frequencies of the whistlerwaves in the average and peak BPF data. We show the nor-malized frequency of whistlers observed in average BPF datain panel (a) and the normalized frequency of whistlers observedin the peak BPF data in panel (b).In Figure 4 (a), the blue histogram corresponds to inter-vals when whistlers are observed both in the peak and averageBPF data, whereas the gray histogram corresponds to intervalswhen the whistlers are only observed in the peak BPF data, butnot in the average. We observe a clear separation between thetwo distributions. Normalized peak amplitudes of the whistlers,which are only observed in the peak band-pass data, are smaller(gray) than the ones which are observed in both peak and aver-age BPF data (blue). We observe that most of the whistlers areof a low amplitude, and these whistlers are not observed in theaverage BPF data. We cannot deduce whether the low-amplitudewhistlers are short-lived or not. However, we can observe thatthere is a considerable overlap between the gray and blue his-tograms, which suggests that there are whistlers which might beof a large enough amplitude to be visible in average BPF data,but they are very short-lived. Therefore, they are not visible inthe average BPF data. We can also understand that most of thelow normalized frequency whistlers observed in Figure 3 (b) areof a low amplitude and that is the reason they are not visible inthe average BPF data.In Figure 4 (b), we show the ratio of peak and average ampli-tude of the whistlers when whistlers are observed simultaneouslyin the average and peak BPF data. This relation is importantin understanding the variability of the envelope of the whistler
Article number, page 4 of 10agarlamudi et al.: Whistler wave occurrence and the interaction with strahl electrons wave. From the plot, we observe that their ratios are concen-trated between 3 to 7. This shows that when the whistler signa-tures are observed in both average and peak data, the ratios arenearly constant and there is no high variability. This leads us toconclude that there might not be high variability in the whistlerenvelopes in our study when the whistlers are observed in bothpeak and average BPF data.In Figure 5 we show a histogram of whistlers as a functionof the duration of their observation. The minimum whistler du-ration is dependent on the resolution of BPF data; therefore, theminimum duration of the whistler is ∼ .
87 s. For this studywe use the whistlers observed in the average BPF data, as thisprovides the only approximate representation of how long thewhistlers are continuously observed. Most of the whistlers in av-erage BPF data are of a comparatively large amplitude and oc-cur for a time that is long enough to be observed in average BPFspectra. We observe that 80% of the time, whistlers occur contin-uously for less than 3 s and the probability of observing whistlerscontinuously for a long duration ( >
30 s) is low. This shows thatmost of the whistlers occur intermittently, and the probabilitythat whistlers occur for a long duration is low. There is an ex-ponential decrease in the duration of the time whistlers are con-tinuously observed. However, even when the whistlers appearcontinuously in the BPF data, it does not necessarily mean that alarge whistler wave packet is present for such a long period. Webelieve that it could be a continuous occurrence of short durationwhistler wave packets for a long time.We have presented some of the basic features of the observedwhistler signatures. Now we explain how we studied the prop-erties of whistlers as a function of di ff erent physical parameters.First, we directly related the presence of whistlers to their ob-served conditions. Second, we related the plasma conditions tothe duration of a consecutive whistler appearance. The first onegives information on the conditions when the whistlers are ob-served, while the second one gives important information on thedi ff erences in the conditions when whistlers are observed for ashort duration compared to when they are observed continuouslyfor a long duration. For these studies, we used the whistlers ob-served in the average BPF data, the reason is that they representthe whole interval size unlike the whistlers that are only observedin the peak BPF.In Figure 6 we show the percentage of whistlers as a func-tion of solar wind bulk velocity, that is to say the number ofwhistlers in the velocity bin to the number of spectra availablein the corresponding velocity bin, which takes the occurrencerate of di ff erent solar wind speeds into account. We observe thatthe lower the velocity of the wind, the higher the presence ofwhistler waves. A similar behavior is shown in the study of Ja-garlamudi et al. (2020), where the authors show the anticorrela-tion between the occurrence of whistler waves and the solar windvelocity. The authors explain the reason why for slower windspeeds, the conditions were better for the generation of whistlersthrough whistler temperature anisotropy instability (WTA) andwhistler heat flux instability (WHFI).We also looked into the relation between magnetic field gra-dients (such as drops, jumps and discontinuities) and the occur-rence of whistlers. We used the ratio | B −(cid:104) B (cid:105)(cid:104) B (cid:105) | as an indicator forthe magnetic field gradients, and we observe that nearly ∼ | B −(cid:104) B (cid:105)(cid:104) B (cid:105) | ) are less than 30%, that is to say most of thewhistlers appear when there are not any large absolute magneticfield gradients. This guided us in concluding that large magneticfield gradients are not necessary for the occurrence of whistlers. (a) log( B p / B ) (b)Fig. 4: Histogram of peak and average amplitudes. In panel (a),we show the log of normalized amplitudes of whistlers observedin the peak; blue corresponds to the data where whistlers are ob-served in both peak and average BPF, and gray corresponds towhen the whistlers are observed only in the peak BPF spectra. Inpanel (b), we show the ratio of the peak and the average ampli-tude of spectra with whistler signatures. Duration (s) Fig. 5: Histogram of the duration of whistler wave’s continuousobservations in the average BPF data.
Article number, page 5 of 10 & A proofs: manuscript no. WhistlersAandA
250 300 350 400 450 500 550 600 650 V SW ( km / s ) % o f w h i s t l e r s Fig. 6: Occurrence rate of whistler waves as a function of thesolar wind bulk speed ( V sw ). For each velocity bin, we show thefraction of BPF data that have the signature of whistler waves.
10 20 30 40 50
Duration (s) B / B (a)
10 20 30 40 50
Duration (s) V s w ( k m / s ) (b)
10 20 30 40 50
Duration (s) N p ( c m ) (c)
10 20 30 40 50
Duration (s) | ( BB ) / B | (d) Fig. 7: Di ff erent properties of whistlers as a function of the du-ration of their observations; blue and red correspond to the meanand median values, respectively. In panel (a), we show the nor-malized amplitude of whistler waves; in panel (b), the bulk ve-locity of the solar wind is shown; in panel (c), the density ofthe solar wind is shown; and, in panel (d), the magnetic fieldvariations ( | B −(cid:104) B (cid:105)(cid:104) B (cid:105) | ) are shown. Error bars show the standard error( σ √ n ).We also studied the relation between the occurrence ofwhistlers and the structures with sudden changes in the radialmagnetic field orientation, called switchbacks (Bale et al. 2019;Kasper et al. 2019; Dudok de Wit et al. 2020). For this, we usedthe switchbacks identified in the work of Larosa et al. (2020).We observed that only ∼
15% of the switchbacks showed thepresence of whistler waves close to their boundaries or insidethe structure. c | q e / q | Vasko et al 2019 (WFI), s / c = 2Vasko et al 2019 (WFI), s / c = 0.5 Fig. 8: Normalized heat flux of the whistlers observed in theaverage BPF data. We show the normalized heat flux ( q e (cid:107) / q )as a function of electron core parallel beta ( β e (cid:107) c ), the dashedlines correspond to the thresholds of whistler fan instability for ∆ s / ∆ c = . ∆ s / ∆ c =
2, given by Vasko et al. (2019).In Figure 7 we show the mean (blue) and median (red) of dif-ferent plasma parameters when the whistlers are observed, as afunction of their duration. We observe that the normalized ampli-tudes of the whistler waves which occur continuously are slightlyhigher compared to the whistlers of short duration. The veloc-ity of the solar wind corresponding to the whistlers is relativelylower for the cases when the whistlers are observed continu-ously for a long duration. The density is higher for long durationwhistlers. We also observe that normalized magnetic field vari-ations ( | B −(cid:104) B (cid:105)(cid:104) B (cid:105) | ) are lower when the whistler waves are observedfor a long duration. Similarly, we have also studied the varia-tions in the radial magnetic field as a function of the duration ofthe whistlers (not shown here). We observed that radial magneticfield variations were lower when the whistlers were observed fora long duration. This indicates that the probability of long du-ration whistlers is lower when there are switchbacks. Long du-ration whistlers occur when the conditions are quiet. Now, inthe following subsection, we look into the possible generationmechanism for the observed whistlers. Studies by Lacombe et al. (2014), Stansby et al. (2016), Tonget al. (2019a,b) and Jagarlamudi et al. (2020) show that whistlerheat flux instability is at work when whistlers are observed. Forour case, in which we studied the whistlers which are observedcloser to the Sun, we do not have an accurate estimate for thewhistler heat flux instability threshold in the literature yet. Thelevel of threshold is sensitive to variations in the densities ofelectron core and halo populations, and also their temperatures(Gary et al. 1994), which vary with radial distance. Therefore,we could not verify whether the whistler heat flux instability isat work or not. However, using the work of Vasko et al. (2019),where the instability thresholds were estimated by consideringthe electron core-strahl velocity distribution functions typical forthe solar wind closer to the Sun (0.3- 0.4 au), we could verifythe probability of whistler fan instability (for oblique whistlers)working. For our study, we used the normalized heat flux valuesfrom the work of Halekas et al. (2020b). In Figure 8 we present
Article number, page 6 of 10agarlamudi et al.: Whistler wave occurrence and the interaction with strahl electrons the normalized heat flux as a function of electron core parallelbeta ( β (cid:107) c ).From Figure 8 we infer that the whistler fan instability (foroblique whistlers) is probably at work, as the whistler intervalsare around those thresholds (Vasko et al. 2019). However, faninstability is only pronounced for oblique whistlers and we donot have information on the angle of propagation. Therefore, itis important to know the angle of the whistler wave propagationwith the mean magnetic field to properly identify for which casesthe fan instability is at work. This will be one of the importantgoals for the future study.Recent study by Jagarlamudi et al. (2020) have suggestedthat whistler core and halo anisotropy instabilities might be atwork when the whistlers are observed. For our study, only coreelectron anisotropy values are available and they are of a lowresolution; therefore, we are not able to identify whether thewhistler anisotropy instabilities are the source of our observedwhistlers.While analyzing the electron parameters, such as the den-sity and temperature measurements obtained from the QTNtechnique (Moncuquet et al. 2020), to study the conditions ofwhistler generation, we observed that for most of the times whenthe whistlers were observed, no halo or core temperatures wereavailable corresponding to the whistler interval. This frequentlyobserved behavior led us to probe the LFR data used for theelectron parameter estimation in the QTN technique. Interest-ingly, we observed that the LFR spectra showed the presenceof a large spectral enhancement around the electron plasma fre-quency whenever there was a whistler wave during that time pe-riod. We identify these enhancements in LFR spectra as Lang-muir waves, as all the jumps are centered around an electronplasma frequency (0.9 to 1.1 f pe ). The simultaneous presence ofwhistlers and Langmuir waves is similar to what has been re-ported in the study of Kennel et al. (1980) using the data fromISEE-3.We identified that 85% of the time, intervals correspondingto whistlers in the average BPF showed the presence of Lang-muir waves. A glimpse of this behavior can be seen in Figure 9,where the Langmuir waves normalized frequency and their PSDalong with the whistlers normalized frequency and their PSD isshown in blue and red. From this plot, we can infer that there is aclear correlation between the occurrence of whistlers (red dots)and Langmuir waves (blue dots) during this interval. These si-multaneous observations of whistlers and Langmuir waves giveus a clue that there might be a common generation source forboth the whistlers and Langmuir waves; therefore, we have tobroaden our ideas as to potential whistler generation sources. Anadvanced study will be performed in the future using the wave-form and high resolution particle data to accurately identify thesource of the whistlers closer to the Sun.
4. Whistlers and strahl electrons
In Figure 10 we show the mean strahl pitch-angle width (PAW)of electrons when the whistlers are observed both in the aver-age BPF data (red) and when the whistlers are not observed atall (black). We observe that the strahl PAWs are significantlylarger in all the strahl energy ranges when the whistlers are ob-served. These observations point toward an interaction betweenwhistler waves and the strahl electrons, which results in the ob-served broadening of the strahl electron population. The recentstudy by Agapitov et al. (2020) identified the presence of sun-ward whistlers along the switchback boundaries which couldinteract with the anti-sunward strahl electrons and scatter the B ( n T ) f / f p e P S D ( V / H z ) f / f c e Nov 2018 P S D ( n T / H z ) Fig. 9: Example of simultaneous observation of whistlers andLangmuir waves in the PSP data. Panel 1 shows the absolutemagnetic field, panel 2 shows the normalized frequency of Lang-muir waves with electron plasma frequency, panel 3 shows thespectral density of the observed Langmuir waves, panel 4 showsthe normalized frequency of whistler waves with the electroncyclotron frequency and panel 5 shows the spectral density ofwhistler waves.strahl. However, in our study, we do not have any informationon the direction of whistler wave propagation.In Figure 11 we show the di ff erence in the strahl PAW be-tween the intervals with whistlers observed in the average BPFand the intervals with no whistlers. We observe that the PAWis at least 12 degrees broader for sampled energies above 200eV. The di ff erence between PAW is the largest for the energiesbetween 500 and 700 eV. A similar behavior was observed inthe study of Kajdiˇc et al. (2016) at 1 au. An energy-dependentincrease in strahl PAW is expected for the resonant interactionwith narrowband whistler waves (Behar et al. 2020).In Figure 12 we show the mean strahl PAW of electrons cor-responding to the whistlers by separating them on the basis of theduration of their consecutive observation. Type 1 correspondsto the family of whistlers which are observed for less than ∼ ∼
20 s. Interestingly, we observe thatshort duration whistlers show broader PAW than the long dura-tion whistlers. This distinction can be clearly seen in the energyrange of 200-600 eV. This is an interesting result as we wouldexpect the long duration whistlers to scatter the strahl broaderthan the short duration one. Instead, we observe in our study thatshorter duration whistlers scatter the strahl more than the oneswhich are observed for a long duration.
Article number, page 7 of 10 & A proofs: manuscript no. WhistlersAandA
200 300 400 500 600 700 800 900
Energy (eV) P A W ( ° ) WhistlersNo Whistlers
Fig. 10: Mean strahl PAW of electrons as a function of electronenergy of whistler intervals observed in average BPF data (red)and of non-whistler intervals (black). Error bars show the stan-dard error ( σ √ n ).
200 300 400 500 600 700 800 900
Energy (eV) P A W ( ° ) Fig. 11: Di ff erence in the mean strahl PAW of electrons ofwhistlers observed in average BPF data and of non-whistler in-tervals as a function of electron energy.In Figure 13 (a), we show the normalized amplitude ofwhistlers as a function of strahl PAW for electrons of energy486 eV. We observe that there is no correlation ( ∼ .
06) betweenthe normalized amplitude of whistlers and strahl PAW. From thetrends of normalized amplitudes of whistlers as a function of du-ration (see Figure 7 (a)) and no correlation between the normal-ized amplitude of whistlers and strahl PAW, we can conclude thatamplitudes of the waves may not be a reason for the observeddi ff erences between the strahl PAW of short duration (Type 1)and long duration (Type 2) whistlers shown in Figure 12.In Figure 13 (b), we show the normalized magnetic field vari-ations ( | B −(cid:104) B (cid:105)(cid:104) B (cid:105) | ) as a function of strahl PAW for electrons of en-ergy 486 eV. A positive correlation ( ∼ .
54) between these twoparameters was found. We also found a similar correlation be-tween the normalized magnetic field variations and the PAW ofstrahl electrons for other strahl energies (200 to 700 eV). Inter-estingly, short duration whistlers have relatively higher normal-
200 300 400 500 600 700 800 900
Energy (eV) P A W ( ° ) Type 1Type 2No Whistlers
Fig. 12: Mean PAW of whistlers separated on the basis of theirduration of observation and mean PAW of non-whistlers as afunction of electron energy. Type 1 corresponds to the familyof whistlers observed consecutively for less than ∼ ∼
20 s, and the black curve corresponds to thenon-whistler intervals. Error bars show the standard error ( σ √ n ).ized magnetic field variations than the long duration ones (seeFigure 7 (d)). These observations suggest that strahl PAW ofelectrons corresponding to the whistlers that are generated closerto the larger normalized magnetic field variations are broader andthat the short duration whistlers are generated close to the largernormalized magnetic field variations, which can be connectedto the result in Figure 12. Therefore, magnetic field variabilitymight be one of the factors for the higher strahl PAW observedfor the short duration whistlers compared to the long durationones as observed in Figure 12.The recent study by Agapitov et al. (2020) have shown thepresence of oblique whistler waves closer to the Sun, and stud-ies such as Artemyev et al. (2014), Artemyev et al. (2016),Roberg-Clark et al. (2018), Vasko et al. (2019), Verscharen et al.(2019) and Cattell et al. (2020) have suggested that obliquewhistlers scatter the strahl electrons better than the parallel ones.Therefore, our observations may suggest that whistlers gener-ated around the relatively higher magnetic field variations mightbe comparatively more oblique than the ones which are gener-ated around relatively low magnetic field variations.In Figure 14 we show the parallel cut through the strahl elec-tron VDF, that is to say the portion of the strahl velocity distri-bution function aligned with the magnetic field. We observe thatfor the non-whistler intervals, the distribution curves can be wellrepresented by a Maxwellian VDF which forms a straight linein parameter space (Halekas et al. 2020a; Berˇciˇc et al. 2020).On the other hand, for the whistler intervals, the distribution iscurved compared to the non-whistler cases, corresponding to aKappa distribution function better ( see Figure 11 in Berˇciˇc et al.(2020) for a comparison between Maxwellian and Kappa fits tothe strahl parallel VDF). The distribution of strahl electrons wasobserved to evolve with radial distance; in the near-Sun regions,the strahl was found to be close to a Maxwellian VDF, whilefurther from the Sun it is better represented with a Kappa VDF.Kappa values were found to decrease with radial distance, whichmeans that the relative density of high-energy tails increases as Article number, page 8 of 10agarlamudi et al.: Whistler wave occurrence and the interaction with strahl electrons (a)
20 30 40 50 60 70 80 90
PAW (°) ( B / B ) (b)
20 30 40 50 60 70 80 90
PAW (°) | ( BB ) / B | Fig. 13: 2d histogram of the normalized amplitudes of whistlerwaves in panel (a) and magnetic field variations correspondingto whistler waves in panel (b) as a function of the strahl PAW of486 eV electrons. The black line and the dashed line correspondto the mean and median of the whistler wave’s normalized am-plitudes and the magnetic field variations corresponding to thewhistlers, respectively.we move away from the Sun. A second suprathermal electroncomponent, the halo, was found to be more important for largerdistances from the Sun. The electron halo as well was found to bewell represented by a Kappa distribution function (Maksimovicet al. 2005; Štverák et al. 2009). Our observational results revealthat whistler waves can a ff ect the shape of the strahl VDF, andthey could be one of the prominent mechanisms responsible forthe radial evolution of strahl VDF.In Figure 15 we show the mean strahl parallel electron tem-peratures ( T (cid:107) s ) corresponding to the whistlers observed in theaverage BPF data and intervals with no whistlers. We find thatmean T (cid:107) s values are lower for whistler intervals compared totheir counterparts of non-whistlers with the same proton bulkvelocity. There is more than a 10% decrease in the strahl temper-atures corresponding to whistlers when compared to their coun-terparts corresponding to intervals with no whistlers. As shownby Berˇciˇc et al. (2020), an anticorrelation between T (cid:107) s and thesolar wind velocity can be seen for non-whistler cases. How-ever, this anticorrelation between the T (cid:107) s and solar wind velocityis not observed for the whistler intervals because these whistlersmainly appear in the slow solar wind.During the presence of whistler waves, T (cid:107) s appears to besmaller than at other times. This observation together with the in-crease in strahl PAW shown in Figure 10, leads to the conclusionthat during the wave-particle interaction, the parallel strahl elec-tron momentum is converted to perpendicular momentum (Veltri
200 300 400 500 600 700
Energy (eV) f s / f No whistlerswhistlers
Fig. 14: Mean of the parallel cuts through the strahl VDFs ( f s )normalized to the VDFs value at 200 eV ( f ). The black curvecorresponds to the non-whistler intervals, while the red curvecorresponds the whistler intervals.
250 300 350 400 450 500 550 600 650 V sw ( km / s ) T s ( e V ) WhistlersNo Whistlers
Fig. 15: Mean strahl parallel temperatures ( T (cid:107) s ) as a function ofsolar wind bulk velocity, for whistlers observed in average BPFdata (red) and for non-whistler intervals (black). Error bars showthe standard error ( σ √ n ).& Zimbardo 1993). Further analysis of waves and electron VDFsare required to determine whether or not the total electron energyis conserved during this mechanism.
5. Conclusions
Our analysis of PSP DFB BPF data from the first perihelion hasshown the presence of bursts of quasi-monochromatic electro-magnetic waves. These bursts are observed between 20 and 700Hz. Despite only one component of the magnetic field data beingavailable and even though the absence of accurate polarizationmeasurements prevents us from accurately characterizing thesewaves, based on the knowledge from di ff erent studies at 1 au andthe information from the cross-spectral data analysis, the burstsobserved in the PSP’s DFB BPF data in the solar wind are in-terpreted as most likely due to the whistler waves. The statistical Article number, page 9 of 10 & A proofs: manuscript no. WhistlersAandA study of these wave properties and their relation to the strahlelectrons o ff er a unique opportunity in understanding the signifi-cance of the whistlers in strahl electron scattering. These results,in turn, help in gaining the insight into the solar wind energytransport, as strahl electrons carry the majority of the heat flux.Our study has shown that whistlers occur highly intermit-tently and the spacecraft central frequencies of the waves arebetween f LH and 0 . f ce . The occurrence probability of whistlerswhich are observed in the magnetic field is low ( < .
5% in aver-age BPF data and around 1 .
5% of the time in peak BPF data. Theoccurrence of whistlers is highly dependent on the bulk velocityof the solar wind. We observe that the lower the velocity of thesolar wind, the higher the occurrence of whistlers. A lower oc-currence of whistlers suggests that even though whistlers mightplay a role in regulating the heat flux, they might not be ableto completely explain the regulation of the heat flux in the solarwind.Around 80% of the whistlers are observed for less than 3 scontinuously. The occurrence of long duration whistlers ( >
30 s)is very low. We show that the velocity of the whistlers is lowerfor the cases when the whistlers are observed continuously fora long duration. We also show that conditions are found to bequieter, that is to say magnetic field variations such as jumps,drops, and discontinuities are low when the whistler waves areobserved continuously for a long duration.In our study we observe the simultaneous occurrence ofwhistler and Langmuir waves, which confirms the idea that theremight be a common source or a mechanism for the generation ofthese waves. An in-depth analysis on the reason for the simulta-neous presence of whistlers and Langmuir waves should be donein the future to find the common source for both the waves.The strahl PAW of electrons in the strahl energy ranges arebroader when the whistlers are observed, which suggests thatwhistlers are interacting with the strahl electrons and scatter-ing the strahl. Our observations also show that short durationwhistlers scatter the strahl electrons better than the whistlerswhich are observed for a longer duration. The strahl paralleltemperatures are observed to be lower for the intervals corre-sponding to the whistler waves than to the non-whistler intervals,which suggests that while whistlers are resonantly interactingwith the strahl electrons and scattering them, they transfer themomentum from the parallel direction, leading to the decreasein strahl parallel temperatures for whistler intervals.Whistler waves were found to have an e ff ect on the shape ofthe parallel cut through strahl electron VDF. We therefore sug-gest that whistlers have an important role in the radial evolutionof the strahl VDF and the formation of the Kappa-like halo ob-served farther from the Sun. Acknowledgements.
Authors thanks M. Liu for helpful discussion. TheFIELDS experiment was developed and is operated under NASA contractNNN06AA01C. AL, VK, TD, CF, VKJ and CR acknowledge financial sup-port of CNES in the frame of Parker Solar Probe grant. O.A. was supportedby NASA grants 80NNSC19K0848, 80NSSC20K0697, 80NSSC20K0218. SDBacknowledges the support of the Leverhulme Trust Visiting Professorship pro-gramme. Parker Solar Probe was designed, built, and is now operated by theJohns Hopkins Applied Physics Laboratory as part of NASA’s Living with a Star(LWS) program (contract NNN06AA01C). Support from the LWS managementand technical team has played a critical role in the success of the Parker So-lar Probe mission. The data used in this study are available at the NASA SpacePhysics Data Facility (SPDF), https://spdf.gsfc.nasa.gov . Figures wereproduced using Matplotlib v3.1.3 (Hunter 2007; Caswell et al. 2020)
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