First dust measurements with the Solar Orbiter Radio and

Astronomy & Astrophysics manuscript no. so_dust-2col ©ESO 2021April 21, 2021

First dust measurements with the Solar Orbiter Radio and PlasmaWave instrument

A. Zaslavsky1, I. Mann2, J. Soucek3, A. Czechowski4, D. Pisa3, J. Vaverka5, N. Meyer-Vernet1, M. Maksimovic1,E. Lorfèvre6, K. Issautier1, K. Rackovic Babic1, 7, S. D. Bale8, 9, M. Morooka10, A. Vecchio11, T. Chust12,

Y. Khotyaintsev10, V. Krasnoselskikh13, M. Kretzschmar13, 14, D. Plettemeier15, M. Steller16, Š. Štverák3, 17,P. Trávnícek8, 17, and A. Vaivads10, 18

1 LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, Francee-mail: [email protected]

2 Arctic University of Norway, Tromsø, Norway3 Institute of Atmospheric Physics of the Czech Academy of Sciences, Prague, Czechia4 Space Research Center, Polish Academy of Sciences, Warsaw, Poland5 Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic6 CNES, 18 Avenue Edouard Belin, 31400 Toulouse, France7 Department of astronomy, Faculty of Mathematics, University of Belgrade, Serbia8 Space Sciences Laboratory, University of California, Berkeley, CA, USA9 Physics Department, University of California, Berkeley, CA, USA

10 Swedish Institute of Space Physics, Uppsala, Sweden11 Radboud Radio Lab, Department of Astrophysics, Radboud University, Nijmegen, The Netherlands12 LPP, CNRS, Ecole Polytechnique, Sorbonne Université, Observatoire de Paris, Université Paris-Saclay, Palaiseau, Paris, France13 LPC2E, CNRS, 3A avenue de la Recherche Scientifique, Orléans, France14 Université d’Orléans, Orléans, France15 Technische Universität Dresden, Würzburger Str. 35, D-01187 Dresden, Germany16 Space Research Institute, Austrian Academy of Sciences, Graz, Austria17 Astronomical Institute of the Czech Academy of Sciences, Prague, Czechia18 Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, Royal Institute of Technology,

Stockholm, Sweden

April 21, 2021

ABSTRACT

Context. Impacts of dust grains on spacecraft are known to produce typical impulsive signals in the voltage waveform recorded at theterminals of electric antennas. Such signals are, as could be expected, routinely detected by the Time Domain Sampler (TDS) systemof the Radio and Plasma Waves (RPW) instrument aboard Solar Orbiter.Aims. We investigate the capabilities of RPW in terms of interplanetary dust studies and present the first analysis of dust impactsrecorded by this instrument. Our purpose is to characterize the dust population observed in terms of size, flux and velocity.Methods. We briefly discuss previously developed models of voltage pulses generation after a dust impact onto a spacecraft andpresent the relevant technical parameters for Solar Orbiter RPW as a dust detector. Then we present the statistical analysis of the dustimpacts recorded by RPW/TDS from April 20th, 2020 to February 27th, 2021 between 0.5 AU and 1 AU.Results. The study of the dust impact rate along Solar Orbiter’s orbit shows that the dust population studied presents a radial velocitycomponent directed outward from the Sun, the order of magnitude of which can be roughly estimated as vr,dust ' 50 km.s−1. This isconsistent with the flux of impactors being dominated by β-meteoroids. We estimate the cumulative flux of these grains at 1 AU to beroughly Fβ ' 8× 10−5 m−2s−1, for particles of radius r & 100 nm. The power law index δ of the cumulative mass flux of the impactorsis evaluated by two differents methods (direct observations of voltage pulses and indirect effect on the impact rate dependency on theimpact speed). Both methods give a result δ ' 0.3 − 0.4.Conclusions. Solar Orbiter RPW proves to be a suitable instrument for interplanetary dust studies, and the dust detection algorithmimplemented in the TDS subsystem an efficient tool for fluxes estimation. These first results are promising for the continuation of themission, in particular for the in-situ study of the dust cloud outside the ecliptic plane, which Solar Orbiter will be the first spacecraftto explore.

Key words. Interplanetary dust ; Solar system

1. Introduction

For several decades, radio and plasma wave instruments havedemonstrated their ability to probe dust in different space en-vironments. Voyager’s plasma wave instrument (Gurnett et al.1983) and planetary radio astronomy experiment (Aubier et al.

1983) both observed broadband signals interpreted as producedby dust impacts during the crossing of Saturn’s E ring by Voy-ager 1 and G ring by Voyager 2 – the plasma wave instrument,operated in dipole mode with a roughly symmetrical configu-ration, observing smaller amplitude signals that the radio ex-

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periment, operated in monopole mode. The technique was usedagain along Voyager 2 orbit, with dust measurements at Uranus(Meyer-Vernet et al. 1986; Gurnett et al. 1987) and Neptune(Gurnett et al. 1991; Pedersen et al. 1991). Voyager measure-ments at the outer solar system’s planets were followed by oth-ers in space environments with an expected high dust flux, likecometary trails with e.g. VEGA 2’s plasma wave instrument atcomet Halley (Oberc 1990).

From the years 2000’s or so, radio analyzers aboard missionssuch as Wind (Bougeret et al. 1995), Cassini (Gurnett et al. 2004)or STEREO (Bougeret et al. 2008) recorded a large number ofelectric waveforms characteristic of dust impacts. The improve-ment in the technical performance of these radio detectors com-pared to the previous generation (the higher sampling frequencyof the waveform analyzers in particular) and the large numberof examples available to study has led to a better understand-ing of the mechanisms involved in the voltage pulses generationafter a dust impact. Several recent studies detail this work ofmodelling and comparison to available data, such as works byZaslavsky (2015) on STEREO, Meyer-Vernet et al. (2017) or Yeet al. (2019) on Cassini and Vaverka et al. (2019) on MMS. Thepaper by Mann et al. (2019) provides a complete summary of theworks performed on various spacecraft, a prospect for missionsParker Solar Probe and Solar Orbiter and a review of the voltagepulse mechanism in our present state of understanding. The pa-per by Lhotka et al. (2020) also presents a detailed analysis ofspacecraft charging processes in various plasma environmentsand an application to dust impacts on MMS.

To quickly summarize these models, voltage pulses resultfrom the production of free electric charges by impact ion-ization after a grain of solid matter hits the spacecraft. Thesecharges modify the spacecraft (and, depending on the impact lo-cation, the antennas) potential through two main effects, one be-ing the perturbation of the electric current equilibrium betweenthe spacecraft and the surrounding plasma due to the collectionby the spacecraft of some of these free electric charges, the otherbeing the perturbation of the spacecraft potential by electrostaticinfluence from these free charges that occurs when the impactions/electrons cloud is not neutral on overall (which happensafter some of the charges have been collected or have escapedaway from the spacecraft).

Along the years, and thanks to these refinements in the pulsesmodeling, radio analyzers have thus proven to be able to providerobust estimates of dust fluxes in various mass ranges, vary-ing from the nanometer to the micron. Examples of successfuluse of this technique to derive dust fluxes include the detec-tion of nanometer sized dust with STEREO/WAVES (Meyer-Vernet et al. 2009b) and Cassini/RPWS (Meyer-Vernet et al.2009a), measurements of the interstellar dust flux and direc-tion at 1 AU by STEREO/WAVES (Zaslavsky et al. 2012) andWind/WAVES (Malaspina et al. 2014) or measurements of themicron to ten microns sized dust density in the vicinity of Saturnby Cassini/RPWS (Ye et al. 2014, 2018).

The present paper, in the continuation of these works, is de-voted to the study of the dust impact data recorded by the Radioand Plasma Waves instrument, and to the derivation of the inter-planetary dust fluxes along Solar Orbiter’s orbit. This is of par-ticular importance since in-situ measurements of interplanetarydust in the inner heliosphere, which are necessary to constrainand validate dust production models, are not numerous. Notablythere are only few data on the dust collision fragments that formin the inner solar system and then are ejected outward. Flux esti-mates for these dust grains, denoted as β-meteoroids, were madebased on Helios observations (Zook & Berg 1975) and based on

Ulysses observations (Wehry & Mann 1999). The dust collisionevolution inside 1AU were studied with model calculations hav-ing only few observational constrains (Mann et al. 2004).

Recently the Parker Solar Probe (PSP) operates the FIELDSinstrument (Bale et al. 2016) which provides observations of dustimpacts. The PSP dust observations have been presented in anumber of recent works (Page et al. 2020; Szalay et al. 2020;Malaspina et al. 2020). These observations provide a number ofinteresting results on dust fluxes in the close vicinity of the Sun.Interesting in the context of this paper are the works on the sec-ond orbit of PSP with dust measurements between ca. 0.16 and0.6 AU. Szalay et al. (2020) showed that the observations duringthe second solar encounter could be explained with particles thatform as collision fragments near the Sun and then are ejected bythe radiation pressure force. Mann & Czechowski (2021) showedthat the same fluxes could be explained with a model that com-bines collisional production of dust particles and their dynamicsinfluenced by gravity, radiation pressure and Lorentz force; thelatter was found to have only a small effect on the particles thatwere observed with PSP during the second orbit.

In this paper we shall first present and discuss, in section 2,the waveform data recorded by the instrument and the specifici-ties of Solar Orbiter as a dust detector. Then in section 3 wefocus on the statistical study of the time repartition and of thevoltage amplitudes of the hits recorded. Finally, in a last section,we build on this statistical study to determine the flux of the dustpopulation observed, and compare our results to the one obtainedby other missions and to theoretical predictions.

2. Dust measurements with RPW

The RPW instrument aboard Solar Orbiter, a complete descrip-tion of which is given by Maksimovic, M. et al. (2020), is de-signed to measure and analyze the electric field fluctuations fromnear-DC to 16 MHz and magnetic fluctuations from several Hzto 0.5 MHz. In this article we are mainly interested by the elec-tric waveforms provided by the time domain sampler (TDS) sub-system of RPW. TDS provides digitized snapshots of the voltagemeasured between the terminals of two of the spacecraft elec-tric antennas (dipole mode) or between one the spacecraft elec-tric antennas and the spacecraft ground (monopole mode). Thewaveforms used in this article were sampled at a rate of 262.1kHz, after being processed by an analog high-pass filter with acutoff around 100 Hz.

Figure 1 shows examples of impulsive signals recorded byTDS that we interpret as due to dust impacts. The examplesshown here were selected from the so-called triggered snapshotswhich were flagged by the on-board detection algorithm as dustprobable impacts. See section 3.1 for the description of the algo-rithm.

The left column shows events recorded in SE1 mode (forwhich TDS samples three monopoles V1, V2 and V3) whereasthe right column shows events recorded in XLD1 mode (twochannels measure dipole voltages V1-V3 and V2-V1, and thethird channel is linked to the monopole V2). Each channel (CH1,CH2, and CH3) represents voltage difference measured betweenindividual antennas (V1, V2, and V3) for dipoles or between oneantenna and the spacecraft body (SC) for monopoles. It shouldbe noted that presented data are not corrected for transfer func-tion (the existence of “overshoots” in these data is probably ar-tificial). Examples shown on the lower panels of left column arevery typical of signals detected at the terminal of a monopoleantenna by electron collection, similar to the one detected bySTEREO/WAVES for instance.


A. Zaslavsky et al.: First dust measurements with the Solar Orbiter Radio and Plasma Wave instrument

Fig. 1. Six examples of TDS snapshots showing impulsive signals interpreted as due to dust impacts onto the spacecraft. Signals recorded on thethree different channels are represented in different colors. The left column shows signals recorded in monopole mode (SE1 mode) whereas theright column shows signals recorded in dipole on the two first channels and monopole on the third one (XLD1 mode).

2.1. Voltage pulses and their link to mass and velocity ofimpacting dust grains

Before discussing these pictures, let us remind the mechanismthrough which voltage pulses are thought to be produced. First,a dust grain impacts the spacecraft body and expels from it somematerial, part of which is ionized. The amount of free electriccharge Q > 0 in the (overall neutral) cloud of expelled materialis a function of the mass m of the impacting grain and of therelative velocity v of the impactor with respect to the target. The

measurement of Q after an impact in a dedicated collector, to-gether with an independent measurement of v in order to deducethe mass m of the impactor, is the general operating principle ofdust impact ionisation detectors (Auer 2001). Experiments showthat the function Q(m, v) follows the general scaling

Q(m, v) ' Amvα (1)

where m is expressed in kg and v in km.s−1. Since the parametersA and α quite strongly depends on the impacted material (Col-lette et al. 2014), it is of course preferable for the charge yield of



the collector material as a function of m and v to be measured onground. In the absence, for the moment, of such measurementsfor Solar Orbiter’s surface material, we will have to use approx-imate values for A and α. Dietzel et al. (1973) or McBride &McDonnell (1999)) suggest the use of A ∼ 1 and α ∼ 3.5, whichis a rather high charge yield – we shall discuss this point whenevaluating the size of the impactors in the last section of thisarticle.

In the absence of a dedicated and well calibrated collector,but in the presence of electric antennas operated in monopolemode, one can still quite reliably deduce the amount of chargeQ released during an impact, thanks to the different dynamicsof the electrons and the heavier positive charges in the expelledcloud of ionized matter. The dynamics of the light electronsquickly decouple from the one of the heavier positively chargedmatter (Pantellini et al. 2012). The electrons are quickly col-lected by (or repelled away from) the spacecraft, letting positivecharges unscreened in the vicinity of the spacecraft. For a posi-tively charged spacecraft, it can be shown that the combinationof the effect of quick electron collection and ions getting repelledaway from the spacecraft will produce a maximal change in thespacecraft ground potential equal, to a good approximation, toδϕsc ' −Q/Csc (here Csc is the spacecraft’s body capacitance).

In monopole mode the signal recorded is V(t) =Γ (ϕant(t) − ϕsc(t)), where ϕant is the monopole antenna poten-tial and Γ a transfer function accounting for the (mostly capac-itive) coupling between the antenna and the spacecraft body:Γ = Cant/(Cant + Cstray) (in this formula Cant is the antenna’s ca-pacitance and Cstray accounts for the capacitive coupling throughthe preamplifier, the mechanical base of antenna and variouswires). If one assumes that ϕant is roughly constant during theprocess, then the charge Q produced by impact ionisation isquite simply linked to the peak of the voltage pulse measuredin monopole mode by

Q(m, v) 'CscVpeak

Γ. (2)

The use of formulas (1) and (2) therefore makes it possible tolink the properties of the impacting grain to those of the mea-sured voltage signal.

We can see, in the light of these explanations, whymonopole measurements are favourable to dust detection. Themain changes induced by the impact occurs in the spacecraftground potential, while antennas potentials stay roughly con-stant. Dipole measurements, which measure the variation ofan antenna’s potential relative to another antenna, are thereforequite insensitive to this process. Still, signals are quite frequentlyobserved in dipole mode, as can be seen on the right panels ofFig.1.

For a signal to be observed in dipole mode, it must produce asignal quite stronger on a particular antenna than on the two oth-ers. An example of such a signal recorded on monopole modecan be seen on the top left panel of Fig.1, with a peak ampli-tude on monopole V3 much larger than on V1 and V2. An in-terpretation for these signals is that the impact location may beclose to a particular antenna, the potential of which would inturn undergo a much stronger variation under electrostatic influ-ence from the positively charged cloud than the other monopoles(Meyer-Vernet et al. 2014). The derivation of the charge Q fromdipole measurements is therefore more complicated, since theamplitude of the voltage pulse not only depends on Q but alsoon the position of the impact with respect to the monopoles. Anorder of magnitude of such a signal is Vpeak ∼ ΓQ/(4πε0Lant)(assuming only one arm of the dipole sees the whole unscreened

charge Q), so that the charge in the cloud can be linked to thepeak voltage in dipole mode by

Q(m, v) ∼4πε0LantVpeak,dipole

Γ, (3)

where Lant is the length of an antenna. Importantly, it should benoted that, unlike the signal observed in monopole mode (for theat least two monopoles showing similar peak voltages), which isquite accurately linked to the released charge Q by eq.(2), eq.(3)only provides a rough order of magnitude, since the voltage pro-duced will in fact be very dependent on the location of the im-pact. An impact occurring at equidistance from two arms of thedipole for instance, would produce a very small signal in dipolemode, even for an important release of charge, whereas an im-pact cloud expanding in the close vicinity of a particular dipolearm could produce a signal quite stronger than the estimationabove.

On the right column of figure 1 (XLD1 mode) are shown afew examples of events where the signal is mainly registered bya single antenna - hence not mainly produced by the variationof the spacecraft potential, but rather by electrostatic influenceon a particular antenna. The impact must be close to antennaV2 on cases shown on top and bottom right panels (that showidentical pulses in channels CH2 and CH3) and to antenna V1in the middle right panel (inverted pulses in channels CH1 andCH2).

2.2. Parameters for Solar Orbiter as a dust detector

Now that we have detailed the main principles through which weinterpret voltage pulses after a dust impact, we describe in thispart their application to the specific case of Solar Orbiter.

Solar Orbiter orbits the Sun along a series of roughly ellip-tical orbits, with a minimum perihelion of 0.28 AU and a max-imum inclination with respect to the ecliptic above 30◦. A de-scription of the mission and its science objectives can be foundin Müller, D. et al. (2020).

RPW’s electric sensors are three stacer monopoles of lengthL = 6.5 m and radius a = 0.015 m, mounted on 1 m rigid boomsto separate them from the spacecraft body, electrically biased inorder to reduce variations of their potential with respect to theplasma at low frequencies (Maksimovic, M. et al. 2020). Theyare in the same plane and make angles of roughly 120◦ witheach other. The disposition of the antennas with respect to thespacecraft body is shown on Fig.2. Let us note, in relation withthe previous discussion on the generation of electric pulses aftera dust impact, that the three monopoles are mounted on oppositesides of the spacecraft quite far away from each other (similarlyto the case of spacecraft like WIND, MMS or Parker Solar Probe,but unlike the cases of Voyager, Cassini or STEREO), which im-plies that the effect of electrostatic influence can be very differ-ent from an antenna to the others, and explains why signals arefrequently observed in dipole mode.

The capacitance associated to each monopole base has beenmeasured on ground. Numbers found are Cb = 76.3 ± 4 pF forthe monopole V1, Cb = 78.9 ± 3 pF for V2 and Cb = 76.2 ± 2.7pF for V3. The stray capacitance is to a good approximation thesum of this base capacitance and of the preamplifier capacitanceCamp, which, when both preamplifiers are ON, is Camp = 29 pF.Since the base capacitances are equal within measurement un-certainties, we shall use for the three monopoles the same valueof the stray capacitance, Cstray ' 77 + 29 ' 108 pF.

Assuming the monopoles are in vacuum and considering thespacecraft as an infinite ground plane, one finds the capacitance



Fig. 2. Geometrical configuration of RPW’s electric sensors (labelledANT1, 2 and 3), heat shield and deployed solar panels with respect tothe spacecraft body.

of a monopole Cant = 2πε0L/(ln L/a − 1) ' 71 pF. The pres-ence of solar wind’s plasma, however, at the frequencies we areinterested in (smaller than the local plasma frequency), decreasethe capacitance to values Cant ∼ 2πε0L/(ln LD/a) where LD isthe local Debye length (Meyer-Vernet & Perche 1989). With theDebye length varying in a range ∼ 3 − 10 m along the space-craft’s orbit, one obtains Cant ∼ 55 − 70 pF (the capacitance in-creasing when going closer to the Sun). Using these values, theattenuation factor can be evaluated as Γ = Cant/(Cant + Cstray) '0.34 − 0.39.

The isopotential surface of the spacecraft’s body has beenevaluated from the Solar Orbiter numerical model. This valuecan be estimated from 25.11 m2, taking into account only thesurface of the 5 satellite walls plus the heat shield, up to 31.43m2 when we consider the envelope including the overall space-craft.. The solar panels (6 panels of 2.1 m × 1.2 m) are, at leasttheir backside, isopotential to the spacecraft body. The additionalsurface is then S panels = 15.12 m2 (taking only one side into ac-count). Therefore we can evaluate the area of the interface be-tween the plasma and the isopotential parts of the spacecraft tobe S sc ' S body + S panels ' 43.4 ± 3.2 m2. The capacitance of aconductor of such a complex shape is difficult to estimate. Anorder of magnitude estimation is given by the vacuum capaci-tance of the sphere of equivalent surface Csc ∼ ε0

√4πS sc ∼ 210

pF. This number is an underestimation that does not take into ac-count sheath effects at the surface of the satellite between othereffects, and we shall, in this paper use a value Csc = 250 pFwhen this number is needed. A more appropriate determinationof Csc could be made using a numerical model for Solar Orbiterand its interaction with the surrounding plasma, a work that willbe undertaken in the future.

The surface S sc discussed above would approximately cor-respond to the dust collecting area if the dust population ve-locity distribution was isotropic in the frame of the spacecraft.As we will see in the following, it is probably not the case for

the majority of the dust observed by Solar Orbiter, the velocityof which is mostly directed toward the heat shield. Thereforethe dust collecting area to consider is strongly reduced com-pared S sc, and is rather of the order of the heat shield’s surfaceS col ' 2.5 m × 3.1 m ' 8 m2.

Finally let us briefly discuss the relaxation time of pertur-bations of Solar Orbiter’s floating potential. Linear theory givesτsc ' CscTph/Ie, where Ie = eneveS sc is the electron current ontothe spacecraft isopotential surface (e is the electron charge, nethe local electron density and ve =

√kTe/(2πme), with Te the

local electron temperature and me the electron mass). Tph ∼ 3 Vis the temperature of the photoelectrons ejected from the space-craft body expressed in electric potential unit. The assumptionunderlying this formula is that photoelectron current from thespacecraft is dominating over solar wind’s electron current, thespacecraft potential being as a consequence positive (assump-tion justified pretty much all along Solar Orbiter’s trajectory,putting apart short periods in the shadow of Venus). Assumingtypical variation of electron parameters in the solar wind (seee.g. Issautier et al. (1998)) one obtains for the relaxation timeτsc ∼ 40 µs at 1 AU and ∼ 10 µs at 0.5 AU. These numbershave their importance in that the estimation of the peak ampli-tude of the pulses observed in monopole mode Vpeak ∼ −Q/Cscis strictly valid only in the case were the rise time of the pulseτrise (controlled by the positive charges dynamics in the vicin-ity of the spacecraft) isn’t large compared to the relaxation timeτsc of spacecraft electric potential perturbations. In the oppositecase where τsc is small compared to τrise the amplitude of thesignal is reduced by a factor of the order of τsc/τrise � 1 (Za-slavsky 2015). This effect will not be taken into account in thisarticle. A more precise study of the waveforms – which requiresa very careful calibration work – will be the subject of forth-coming studies, and will among other things make it possible toquantify this effect.

3. Statistical analysis of dust impacts

3.1. Impact rate and estimation of the impactors radialvelocity

In this section we present the results of the analysis of the im-pacts voltage pulses recorded along Solar Orbiter’s orbit fromApril 20th, 2020 to February 27th, 2021. For this purpose, weshall mainly use the data provided by the on-board analysis ofTDS samples through an algorithm that flags a snapshot as be-ing produced by a dust impact if it contains a signal impulsiveenough. This dust detection algorithm has been working withconstant settings from April 20th 2020, hence the date at whichwe start our analysis.

The detection algorithm described in detail in (Soucek &other authors 2021) works as follows: the instrument takes onewaveform snapshot of 16384 samples every second. Each snap-shot exceeding a minimum amplitude threshold is processed bythe TDS on-board software to calculate the maximum and me-dian amplitude and calculate the Fourier spectrum from the snap-shot. From this spectrum the software determines the frequencycorresponding to the largest spectral peak and the FWHM (fullwidth at half maximum) bandwidth of this peak. The algorithmthan classifies the observed snapshots based on comparing theratio R between the maximum and median absolute value in thesnapshot and the spectral bandwidth to predefined thresholds.Specifically, snapshots with large R and large spectral bandwidthare identified as dust impacts. This way, the algorithm allows toidentify even relatively small amplitude dust spikes.



The outcome of this detection is then used to select the “best”wave and dust snapshots to be transmitted to the ground and alsoto build statistical data products. The key data product used hereis the number of detected dust impacts in a 16 second intervalwhich is transmitted in short statistical data packet every 16 sec-onds. Due to the fact that the detection algorithm only examinesone snapshot of 62 ms every second, the reported dust countsare much lower than the actual number of dust impacts, but thenumber of detected dust impacts can be considered directly pro-portional to the actual number of dust impacts.

Since some impulsive signals may be erroneously taken fordust (e.g. solitary waves, (Vaverka et al. 2018) and various space-craft generated effects), the dataset has been cleaned by remov-ing all periods of fast sampling at 524 kHz, all measurementsinfluenced by active sweeps performed by the BIAS subsystemof RPW and several days (in particular during commissioning)where TDS was configured to non-standard operation modes.We also removed the Venus flyby interval on December 27th,2020 when TDS detected numerous solitary waves and countedthem as dust impacts.

We considered this TDS dust data product on a timescale of1h, and computed the impact rate for each hour by dividing thenumber of snapshots flagged as dust by the total number of snap-shots recorded during this hour multiplied by the duration of onesnapshot (∆t = 62 ms): impact rate R = Nimpact/(Nsnapshots∆t).

Fig.3 shows the evolution of the impact rates with time. Theupper panel shows the raw (i.e. not corrected for the duty cycle)cumulative impact number, showing that the total number of im-pact detected by the algorithm during the period of our study is2758. One can also notice several small data gaps correspondingto periods during which the instrument is switched off.

The middle panel shows the impact rate as a function of time,showing an increase of the flux with decreasing distance to theSun, a general behaviour in agreement with remote and in-situmeasurements from Helios (Leinert et al. 1981) or Parker SolarProbe (Szalay et al. 2020; Page et al. 2020).

Fig.4 illustrates the evolution of the impact rate with distancefrom the Sun. On the left panel of this figure, the impact ratesmeasured when the spacecraft is going toward the Sun (space-craft radial velocity vr,sc < 0) are separated from the ones mea-sured when the spacecraft is going outward (vr,sc > 0). It canbe seen that the impact rate is in average slightly larger whenvr,sc < 0 than when vr,sc > 0. This is consistent with the dustpopulation measured having a mean velocity directed outwardfrom the Sun.

One can use this difference in the impact rates to obtain afirst estimation of the radial velocity vr,dust of the dust population:assuming that the velocity and fluxes are function of the distanceto the Sun only (neglecting all time variability) and neglecting –for an order of magnitude estimation – the effect of tangentialvelocities, it can easily be shown that

vr,dust ∼Rin + Rout

Rin − Rout

∣∣∣vr,sc

∣∣∣ (4)

where vr,sc is the radial velocity of the spacecraft, Rin the impactrate when the spacecraft is going toward the Sun and Rout whengoing outward. The middle panel of Fig.4 shows the result of ap-plying formula (4) with the impact rates Rin and Rout shown onthe left panel. The error bars are very large but the mean valueobtained is reasonably constant with radial distance. The rightpanel shows a histogram of the values of vr,dust obtained, with apeak value at vr,dust = 30 km.s−1 and an averaged value around50 km.s−1. The large errorbars, the variations of the measuredfluxes and the use of a simple model let us only hope for an

order of magnitude estimation of course, but this value is con-sistent with expectations for small particles on hyperbolic orbits,and to results from numerical simulations of particles dynamicsdiscussed in the last section of this paper.

Fig. 5 shows the distribution of the number of impactsrecorded during time intervals of 6 hours, for three different val-ues of the impact rate. The three intervals on which these num-ber of occurrence distributions have been computed are high-lighted in yellow on Fig.3. They correspond to distances to theSun ∼ 0.7 AU (left panel, mean impact rate ∼ 140 day−1), ∼ 1AU (middle panel, mean impact rate ∼ 50 day−1) and ∼ 0.5 AU(right panel, mean impact rate ∼ 350 day−1). The comparisonwith Poisson distribution, over-plotted in red, shows a very goodagreement consistent with the data being due to independentevents at roughly constant rates, as expected for interplanetarydust impacts.

3.2. Peak voltages distribution and power-law index of theimpactor’s cumulative mass flux

In order to further characterize the population of dust grains im-pacting Solar Orbiter, we look at the distribution of voltagesmeasured in monopole mode. To this purpose we look at thesnapshots dataset, which does not include all of the dust impactsdetected by the onboard algorithm on which the results of theprevious section are based. We shall assume that the subset oftriggered snapshots is a random sample from the ensemble of allthe recorded dust impact signals, and therefore that both sharethe same statistical properties – or since this can’t be exactlytrue, we shall assume that selection bias are small and do notimpact importantly the voltage amplitude statistics.

Measurements in monopole mode, as discussed in section2, are required in order to properly (as unambiguously as pos-sible) link the peak amplitude of the pulse to the charge gen-erated by impact ionisation. Unfortunately they are, concerningmonopoles V1 and V3, only active during a small fraction of themission time, i.e. mainly during two periods, from May 30th toJune 8th (185 dust snapshots telemetered) and from July 27thto August 13th (103 dust snapshots). Things are different formonopole V2, which is quite routinely operated with 934 dustsnapshots telemetered from April 1st to November 1st of 2020.Hence the particular focus on monopole V2 in the following.

Fig.6 shows the normalized distributions of peak voltage as-sociated to dust impacts for different monopoles, and differenttime periods. We can see that the peak voltage distribution hasa power-law behaviour. The left panel shows distributions com-puted on the whole period Apr. 1st - Nov. 31st, with differentcolors corresponding to peak voltages at the terminals of differ-ent monopoles. One can see that voltage distributions are simi-lar on all monopoles - which is to be expected since in averageall monopole should react in the same manner to dust impacts.The results of least-square fitting these histograms with powerlaws is presented in table 1, where it can be seen that power-lawexponents are, within uncertainties, equal from a monopole toanother, around −4/3.

The middle panel of Fig.6 compares the peak amplituderecorded on monopole V2 at different distances from the Sun.The limited number of impacts on which such a comparison canbe made imply quite important uncertainties on the values of thedistribution. The two last lines of table 1 show the results of lin-ear fitting for these distributions, showing a slope a bit steeper atthe perihelion than at the aphelion. This difference being withinthe uncertainties, it is hard to conclude on this result; one shouldwait for more statistics to see if this trend is confirmed.



Fig. 3. Upper panel: raw cumulative dust count as a function of time since April, 1st, 2020. By raw, it is meant that it is the integer number ofimpact provided by the detection algorithm, uncorrected for the instrument’s duty cycle. Middle panel: Impact rate as a function of time sinceApril, 1st, 2020. Each point correspond to a 2 days time interval. The error bars are computed from

√N/∆t, where ∆t is the time covered by

TDS measurements on the 2 days considered, and N the number of impacts during these 2 days. The yellow areas correspond to time periods onwhich the number of occurrence distributions of Fig.5 have been computed. The green areas correspond to times periods on which the amplitudedistributions shown on the right panel of Fig.6 have been computed. Lower panel: Distance from the spacecraft to the Sun in astronomical units,as a function of time since April, 1st, 2020.

Table 1. Power law indices of the peak voltage distributions. The uncertainties show 95% confidence interval on the linear regression coefficient.

Monopole Time interval Number of events Power-law indexV1 (SE1 mode) Apr. 1st – Nov. 31st 328 −1.34 ± 0.14V2 (SE1 mode) Apr. 1st – Nov. 31st 328 −1.34 ± 0.14

V2 (XLD1 mode) Apr. 1st – Nov. 31st 934 −1.37 ± 0.10V3 (SE1 mode) Apr. 1st – Nov. 31st 328 −1.36 ± 0.11V2 (SE1 mode) May 30th – Jun. 8th (Perihelion) 185 −1.37 ± 0.19

V2 (XLD1 mode) Sep. 17th – Nov. 2nd (Aphelion) 161 −1.20 ± 0.17V2 (SE1 and XLD1 modes) Apr. 1st – Nov. 31st 1262 −1.34 ± 0.07

The right panel of Fig.6 shows the distributions of all im-pacts recorded on monopole V2 on the whole time of our volt-age amplitude analysis, i.e. from Apr. 1st to Nov. 31st, 2020,and the corresponding power-law least-square fit, with index−1.34 ± 0.07.

From these observations it seems reasonable to approximatethe rate of observation of signals having peak voltages betweenVpeak and Vpeak + dVpeak by dR = g(Vpeak)dVpeak, with

g(Vpeak) = g(V0)(

Vpeak

V0

)−a

(5)



Fig. 4. Left panel: impact rate as a function of radial distance. The black points show fluxes recorded when the spacecraft is moving toward theSun, the red points when moving outward from the Sun. Each point is computed by averaging the impact rate data on 50 distance intervals linearlyspaced between 0.5 and 1 AU. Error bars show one standard deviation error on the computation of the mean. Middle panel : radial component ofthe dust velocity Vr,dust computed from eq.(4). Error bars are computed by propagating errors on the impact rates shown on the left panel. Rightpanel : histogram of the obtained values of Vr,dust.

Fig. 5. Distribution of number of impacts per time intervals of 6 hours, for three different periods of time corresponding to different mean impactrates. The red curve shows the Poisson distribution calculated from the mean impact rate observed in each of these periods of time. Errorbars onthe histograms values are

√Nbin, with Nbin the number of counts in the histogram bin.

where a ' 1.34 and V0 an arbitrary voltage in the range wherethe power-law behaviour applies.

An interesting result, of course, would consist in the deriva-tion from these data of an information on the mass distributionof the impacting dust particles. We have seen in section 2.1 thatthe released charge Q, and hence the peak voltage Vpeak is linkedto the mass, but also to the velocity of the impacting particle,and we do not have an independent measurement of the latterfor each of the impacts. Therefore one can only make inferenceson the mass distribution by assuming the existence of a rela-tionship v(m) between the mass of the particle and its velocitywith respect to the spacecraft. If such a relationship exists, thenthe function Vpeak(m, v) becomes a function of m only and – un-der the assumption that two different values of m cannot pro-duce a peak voltage of the same amplitude, i.e. that the functionVpeak(m) is bijective on the observed mass interval – the massdistribution of the impactors f (m) can be directly linked to themeasured distribution g(Vpeak) by

f (m) = g(Vpeak)

∣∣∣∣∣∣dVpeak

dm

∣∣∣∣∣∣ . (6)

For a first order estimation, one could assume that the impactvelocity is independent of the mass on the given mass range.Then, according eqs.(1) and (2),

Vpeak 'Γ

CscAmvα (7)

is a linear function of m, and the mass distribution trivially hasthe same power-law shape than the distribution of voltage peaks.The cumulative mass flux of particles of mass larger than m ontothe spacecraft (defined as F(m) =

∫ +∞

m f (m′)dm′) would then begiven by

F(m) = F(m0)(

mm0

)−δ(8)

where δ = a − 1 ' 0.34 and F(m0) is the cumulative flux ofparticles of mass larger than m0 (that may depend on the distanceto the Sun).

Let us note that this estimation of the power-law index δ ofthe cumulative mass flux in the observed mass range must likelybe an underestimation, since if the velocity is an increasing func-tion of m (which is probably the case in the observed mass range,



Fig. 6. Normalized density (i.e. number of dust detected per unit voltage interval) of voltage peaks in monopole mode. The left panel shows thedistribution of the voltage peaks on all monopoles from Apr. 1st to Nov. 30th, 2020. Different colors accounts for different monopoles: V1 (blue),V2/SE1 (red), V3 (green), V2/XLD1 (black). The middle panel shows the distribution of peak amplitudes on monopole V2 during two differentperiods (highlighted in green on fig.3). Red points correspond to the high impact rate period close to the perihelion (May 13th – Jun 8th), blackpoints to the low impact rate period around the aphelion (Sep 17th – Nov 3nd). The right panel shows the result of the least square fitting of allthe data recorded on monopole V2 from Apr. 1st to Nov. 30th, 2020. The slope of the red curve is −1.34 ± 0.07. On all these figures, errorbars arecomputed from

√Nbin/(∆VbinNtot), where Nbin is the number of counts in the bin, ∆Vbin the bin width in mV and Ntot the total number of events

from which the histogram is computed.

see next section), f (m) will decrease with a steeper slope thang(Vpeak). This can easily be seen from eq.(6), taking for instanceVpeak ∝ m1+ε with ε > 0. One would then obtain for f (m) apower law index a + (a − 1)ε which is always larger than a (ifa > 1 which is the case here). Therefore, even without any pre-cise knowledge of the function v(m), but under the assumptionthat this is an increasing function of m in the observed mass in-terval, it is possible to derive from these observations of peakvoltages a lower bound for the power law index of the cumula-tive mass flux δ & 0.34.

To conclude this part let us note that a more detailed deriva-tion of the mass distribution of the particles could be obtainedfrom these measurements by computing the function v(m) fromnumerical simulations, with proper assumptions on initial con-ditions and dust β parameter. Since this function may dependon the distance from the Sun (which may explain the possiblechange of the power law index of the voltage distributions fromperihelion to aphelion), this study may also require some time toaccumulate more statistics and be able to construct not too noisydistributions of voltages at different distances from the Sun. Sucha work is beyond the scope of this first results paper, but it offersan interesting perspective for a future study.

4. Estimation of the β-meteoroids flux andcomparison to models and results from othermissions

We now compare the observed impact rates to a dust flux modelthat bases on a number of assumptions. The existence of dustin the inner solar system can be inferred from the brightness ofthe Zodiacal light and the F-corona which show that dust in theapproximate 1 to 100 micrometer size range forms a cloud withoverall cylindrical symmetry about an axis through the center ofthe Sun, perpendicular to the ecliptic (cf. Mann et al. (2014)).The size distribution at 1 AU is estimated from a number ofdifferent in-situ observations and described in the interplane-tary dust flux model (Gruen et al. 1985). The majority of dustgrains form by fragmentation from comets, asteroids and their

fragment grains. The larger grains are in bound orbit about thesun; as a result of the Poynting – Robertson effect they lose or-bital energy and angular momentum and fall into the Sun aftertime scales of the order of 105 years. However, the majority ofthe Zodiacal dust is within shorter time fragmented by collisionwith other dust grains, the smaller fragments leave the inner so-lar system and collision production from larger grains is neededto replenish the dust cloud (Mann et al. 2004). The dust withsizes smaller than roughly a micrometer experiences a larger ra-diation pressure force which is directed outward. If the radiationpressure to gravity ratio, often denoted as β is sufficiently high,the dust can be ejected outward. Those grains in hyperbolic or-bits are often denoted as β-meteoroids those in in bound orbitsas α-meteoroids (Zook & Berg 1975). Assuming that the largerdust grain that is fragmented moves in a circular orbit, its frag-ment attains a hyperbolic orbit if the radiation pressure to gravityratio β exceeds 0.5. Based on light scattering models for differ-ent assumed dust compositions (Wilck & Mann 1996), this is thecase for dust with sizes less than few 100 nm.

4.1. Mass of the impactors

The mass of the impactors can be estimated from the voltage ob-served, using eq.(7) and spacecraft parameters from section 2.2.For this one needs an estimation of the velocity of the impactorsand of the charge yield of the impacted material. For the particlesvelocity, we could have used the order of magnitude obtainedfrom the observations of impact rates in direction forward andbackward with respect to the Sun. But, as pointed out in section3.1 this is only a rough estimation, associated to large uncertain-ties. Therefore we chose to rely in this section on estimationsof dust particles velocities from numerical simulations of dustdynamics in the interplanetary medium. The simulation we usetakes into account gravitational and radiation pressure forces, butnot the electromagnetic force (that should not be dominant forparticles of sizes & 40 nm). Initial conditions and values of βare chosen consistently with observations of dust from asteroidalorigin.



Fig. 7. Left panel : relative velocity with respect to Solar Orbiter as a function of particle mass. The solid line shows the average along thespacecraft trajectory, the upper dahsed line shows the impact velocity at the perihelion and the lower dashed line the impact velocity at theaphelion. Right panel : expected peak voltage as a function of the mass of the impactor, calculated using values of impact velocities shown onthe left panel. The solid line shows the peak voltage for the averaged velocity (solid line from left panel) and dashed lines for the perihelion andapehlion impact velocities. The black curves assume a high charge yield with parameters A = 0.7 and α = 3.5 and the red curves a lower chargeyield with parameters A = 2.5× 10−3 and α = 4.5. The points show the values of the velocity/peak voltage obtained from 4 numerical simulations,corresponding to size ranges 40 − 75 nm, 75 − 100 nm, 100 − 140 nm and 140 − 200 nm. The points are placed at the middle of the mass intervalfor each of the 4 simulated size ranges. The horizontal green line shows the detection threshold ∼ 5 mV.

The charge yield of the impacted material is another un-known of our study, which of course plays an important rolein determining the mass of the impactors. Fig.7 shows the im-pact velocities from the numerical simulations and the expectedpeak voltage for two examples of charge yield. The dark areaon the right panel shows the region of expected voltage peaks asa function of the mass of the impactor for parameters A = 0.7and α = 3.5 from McBride & McDonnell (1999). The red areais obtained for parameters A = 2.5 × 10−3 and α = 4.5, a quitelower charge yield, corresponding to materials like germanium-coated Kapton, or solar cells and MLI (multi-layer thermal in-sulation) from STEREO’s spacecraft, the charge yield of whichwere measured on ground and can be found in table 1 of Colletteet al. (2014).

Fig. 7 shows that particles in the size range 40 − 75 nm, re-gardless of the charge yield parameters used, are too small andnot fast enough to produce measurable signals. Grains with sizes75 − 100 nm should produce (for the larger of them) signalsabove the detection threshold in the high charge yield case, butnot in the low charge yield one; grains with sizes & 100 nmfinally, should produce measurable signals regardless of the pre-cise charge yield. An estimation of the mass of the smallest par-ticles detected (we consider a threshold voltage of 5 mV) fromthis figure gives m ' 7.4 × 10−18 kg (high charge yield) andm ' 1.2 × 10−17 kg (low charge yield), corresponding to sizes(assuming, as in the whole of this paper, a mass density ρ = 2.5g.cm−3 and grains of spherical shapes for size-mass conversions)r ' 89 nm and r ' 103 nm respectively – one can quite confi-dently affirm that the smallest grains detected have sizes around100 nm.

The curves for different charge yields diverge when massesare increased, and for signals of amplitude e.g. 30 mV, one havesizes r ' 107 nm (high yield) and r ' 150 nm (low yield),a larger mismatch of course, showing the necessity of groundmeasurement if one wants to reach a better mass calibration onthe whole voltage interval. That being said, the power-law de-crease of the peak voltages distribution shown in the previous

section implies that the fluxes are dominated by impact fromsmall grains, so that the determination of the mass of impactorsproducing high amplitudes peaks is less critical for our study.

This discussion of particles masses is based on the measure-ment of the voltage pulses in monopole mode, which, as wasdiscussed previously, are the most reliable when it comes to es-timating the charge released by impact ionisation, and thereforethe dust particles masses. However, the dust detection algorithmfrom which fluxes are computed works on a TDS channel thatis operated in dipole mode most of the time – when the instru-ment is on XLD1 mode. The discussion above, and the curvepresented on Fig.7 stays mainly relevant to this case as long asthe signal produced is proportional to the charge released Q. Ac-cording to the estimation given by eq.(3) this should be the casefor dipole measurements when considering a large enough num-ber of hits. Assuming Vdipole = ΓQ/4πε0Lant, the smallest massmeasured in dipole would be a factor 4πε0Lant/Csc ∼ 3 larger(and therefore the sizes a factor ∼ 1.4 larger). But the precisefactor is complicated to evaluate, and could be closer to 1 in av-erage since observations of waveforms shows that differences inpeak voltage from a monopole to another is often of the order ofmagnitude of the peak voltage itself. This provides a clear moti-vation for for developing a quantitative theoretical modeling ofthe generation of signals generation in dipole mode, at least on astatistical basis.

4.2. Flux of β-meteoroids, comparison to predictions andmeasurements from other spacecraft

Fig.8 presents the impact rates averaged over 2 days, already pre-sented on Fig.3 of this article, together with impact rates com-puted for three models of the beta-meteoroid flux. The green lineis the most simple model, with the impact rate given by

R = F1AUS col

( r1 AU

)−2 vimpact

vβ(9)



where S col = 8 m2 is the collection area (taken equal to the heatshield surface, cf. section 2.2), vimpact =

∣∣∣∣∣∣vβ − vsc

∣∣∣∣∣∣ is the relativespeed between the spacecraft and the β-meteoroids, the velocityof which is taken radial and constant vβ = 50 km.s−1. Fβ,1AU isthe flux of particles in the detection range, which is to a good ap-proximation equal to the cumulative flux of particles larger than∼ 100 nm. The 1/r2 scaling of the β-meteoroids flux is a con-sequence of mass conservation (and of their production rate byfragmentation of larger particles being negligible at the distancesfrom the Sun at which the spacecraft orbits). A fit of the datawith eq.(9) gives a value of the cumulative flux F1AU ' 8 × 10−5

m−2s−1.This simple model provides, as can be seen on the figure, a

fairly good agreement with the data, although it seems to sys-tematically underestimate the high impact rate values around theperihelion. A reason for that can be seen from the left panel ofFig.7: the mass of an impactor producing a given peak voltagewill be smaller at the perihelion than at the aphelion (because thespacecraft’s velocity with in the Sun’s frame is larger at the per-ihelion that at the aphelion). Since smaller particles have higherfluxes, an increase in the rate of measurable signals is expectedclose to the Sun as compared to the previous simple model.

This effect of decrease of the dust particles mass measuredwhen approaching the Sun can be quantified by assuming a cu-mulative mass flux varying in power law with an exponent δ, aswritten in previous section’s eq.(8). The impact rate is then foundto be

R = F1AUS col

( r1 AU

)−2 vimpact

vβ

(vimpact

vimpact(1 AU)

)αδ(10)

where F1AU is (as previously) the cumulative flux of parti-cles above the detection threshold at 1 AU, and the factor(vimpact/vimpact(1 AU))αδ accounts for the variation of the massof the detected impactors with the impact velocity.

One can fit eq.(10) to the data in order to obtain the productαδ. The resulting curve is shown in red on Fig.8. It shows a bet-ter agreement with data than the previous model, and fits quitewell the high impact rates observed at the perihelion. The valueobtained is αδ = 1.3, which, considering values of α = 3.5−4.5,provides an estimation of the power-law index of the cumulativemass distribution of the impactors δ = 0.29 − 0.37. This value –obtained from a dataset including no voltage measurements butonly impact counts per unit time – is similar to the one derivedin the previous section by fitting peak voltage distributions, indi-cating that the estimation of δ in RPW’s detection range seemsquite robust. Let us note finally that, assuming the measurementof δ from voltage distributions to be reliable enough, one coulduse this estimation of αδ to independently estimate the power-law index α of the charge yield for Solar Orbiter material. Wewould then obtain α ' 1.3/0.34 ' 3.9.

The black curve on Fig.8, finally, shows the prediction of im-pacts onto the spacecraft from a model of production of smalldust grains by collisional fragmentation. This model assumesthat the parent bodies move in Keplerian orbits within the cir-cumsolar dust disk. Their mass distribution is a modified versionof the interplanetary dust flux model (Gruen et al. 1985). Thesize distribution of the collision fragments are described basedon models by Tielens et al. (1994) and Jones et al. (1996). It de-scribes the fragmentation and partial vaporization of a target andprojectile composed of a certain dust material. The vaporizedand fragmented mass of the target are proportional to the pro-jectile mass and to the velocity – and material-dependent coeffi-cients. The mass distribution of fragments is of the form m−0.76,

with the largest fragment mass specified as some (collision-velocity dependent) fraction of the target mass. A brief descrip-tion of the collision model is given in Mann & Czechowski(2005). The derivation of dust fluxes is described in Mann &Czechowski (2021). They are obtained from the dust trajecto-ries under the influence of gravity and radiation pressure (sincethe Lorentz force does not have a strong influence for the con-sidered dust sizes). The same trajectories were used to produceFig.7 of this article. The black curve shows the prediction fromthis model of the number of particles comprised between 100 nmand 200 nm impacting a surface S col = 8 m2 per day. The curveobtained from the model considers a constant minimal size ofdetected dust at 100 nm all along the trajectory. It does not in-clude the effect of variation of minimal mass detected discussedpreviously. It fits, without varying any free parameter, well thehigh impact rates at perihelion but quite overestimates the lowfluxes period - a result that would tend to indicate that the sizeof the particles detected is closer to 100 nm at the perihelion andprobably a bit larger at aphelion.

Some effects that can play a role on the derivation of the par-ticle flux from the observed impact rates have not been takeninto account in this first study. They include a better model forthe collection surface and its possible variation with distance tothe Sun (the direction of dust’s velocity in the spacecraft framevarying along the trajectory), although given the mostly cubicshape of the spacecraft this effect is not expected to be very im-portant. A possible difference in charge yield for an impact onthe heat shield surface and one of the other 5 spacecraft wallscould also have some importance.

The result that we obtained for the β-meteoroid flux issimilar (although slightly higher) than the one derived usingSTEREO/WAVES by Zaslavsky et al. (2012), of Fβ ' 1−6×10−5

m−2s−1 at 1 AU. Similar also to the measurement with SolarProbe Plus FIELD instrument Fβ ' 3− 7× 10−5 m−2s−1 interpo-lated at 1 AU (Szalay et al. 2020). Similar, finally, to theoreticalexpectations, as shown in this paper.

To conclude, let us note that, if the presented data can bewell described with a flux of β-meteoroids, it lacks, in compar-ison with observations from STEREO (Zaslavsky et al. 2012;Belheouane et al. 2012) or Wind (Malaspina et al. 2014) an ob-served flux of interstellar dust. The latter studies indeed showed anoticeable component of the impact rate modulated along the so-lar apex direction, that is not observed with Solar Orbiter RPW.This lack of an apparent interstellar dust component in the data ispuzzling. It could be explained by a deflection of the interstellardust grains in the solar magnetic field, and the consequent deple-tion of their flux inside 1 AU – which is expected for grains ofsmall size (Mann 2010). This is a point which deserves furtherstudies.

5. Conclusions

1. The analysis of the first data from Solar Orbiter Radio andPlasma Wave instrument shows this instrument to be a quitereliable dust detector for dust grains in the size range & 100nm. Fluxes of particles derived are consistent with previousobservations in this size range and with theoretical predictionfrom models of dust production by collisional fragmentation.

2. The analysis of the difference in impact rates when the space-craft’s velocity vector is directed in the sunward or anti-sunward direction is shown to be able to provide a directmeasurement of the order of magnitude of dust grains radialvelocities vr,dust ∼ 50 km.s−1 consistent with theoretical pre-dictions in the observed size range.



Fig. 8. Dust impact rate onto the spacecraft - the dots show the same data as the one presented on fig.3. The green curve shows the expected impactrate for beta meteoroids having a constant outward velocity vβ = 50 km/s, and a flux density F1AU = 8×10−5 m−2s−1 at 1 AU. The red curve showsthe flux from eq.(10) with F1AU = 8 × 10−5 m−2s−1 and αδ = 1.3. The black curve shows the prediction from numerical simulation based on amodel of production of dust by collisional fragmentation. The collecting area is assumed to be equal to the heat shield’s surface, S col = 8 m2.

3. The analysis of voltage distribution in monopole mode, andthe analysis of the impact rates taking into account a varia-tion of the mass of the smallest grains detected as a functionof the impact velocity provide two independent methods forestimating the power law index δ of the cumulative mass fluxof particles in our detection range. These two methods con-sistently provide a result δ ' 1/3.

4. These first results are on overall very promising. Still, nu-merous works remain to be done, in particular a modelingof the signal generation mechanism in monopole mode thatwould including the effect of variation of the floating poten-tial relaxation time with the local plasma parameters, but alsomodels of signal generation in dipole mode. Such works, to-gether with a more precise modeling of grain’s velocity andadditional statistics could make it possible to derive more in-formation on the dust cumulative mass flux from the peakvoltage distributions.

5. Solar Orbiter will reach perihelion close to 0.3 AU in spring2022. The impact rate should be ∼ 3 times (without takingthe mass detection threshold effect) larger at this point thanat the perihelion studied in this article. Solar Orbiter’s or-bit will also reach increasingly higher latitudes in the yearsto come, and will provide the first in-situ exploration of thedust cloud out of the ecliptic. These perspectives are verypromising, and these first results show that RPW will havethe capabilities to provide scientific return from these oppor-tunities.

Acknowledgements. IM has been supported by the Research Council of Norway(grant no. 262941). JV was supported by the Czech Science Foundation underthe project 20–13616Y. MM and YK are supported by the Swedish NationalSpace Agency grant 20/136. AZ, IM and JV acknowledge discussions during theISSI team on dust impacts at the International Space Science Institute in Bern,Switzerland.

ReferencesAubier, M. G., Meyer-Vernet, N., & Pedersen, B. M. 1983, Geophysical Re-

search Letters, 10, 5

Auer, S. 2001, Instrumentation, ed. E. Grün, B. Å. S. Gustafson, S. Dermott, &H. Fechtig (Berlin, Heidelberg: Springer Berlin Heidelberg), 385–444

Bale, S. D., Goetz, K., Harvey, P. R., et al. 2016, Space Sci. Rev., 204, 49Belheouane, S., Zaslavsky, A., Meyer-Vernet, N., et al. 2012, Solar Physics, 281,

501Bougeret, J.-L., Goetz, K., Kaiser, M. L., et al. 2008, Space Science Review, 136,

487Bougeret, J. L., Kaiser, M. L., Kellogg, P. J., et al. 1995, Space Science Reviews,

71, 231Collette, A., Grün, E., Malaspina, D., & Sternovsky, Z. 2014, Journal of Geo-

physical Research: Space Physics, 119, 6019Dietzel, H., Eichhorn, G., Fechtig, H., et al. 1973, Journal of Physics E: Scientific

Instruments, 6, 209Gruen, E., Zook, H. A., Fechtig, H., & Giese, R. H. 1985, Icarus, 62, 244Gurnett, D. A., Grün, E., Gallagher, D., Kurth, W. S., & Scarf, F. L. 1983, Icarus,

53, 236Gurnett, D. A., Kurth, W. S., Granroth, L. J., & Poynter, S. C. A. R. L. 1991,

Journal of Geophysical Research, 96, 19,177Gurnett, D. A., Kurth, W. S., Kirchner, D. L., et al. 2004, Space Science Reviews,

114, 395Gurnett, D. A., Kurth, W. S., Scarf, F. L., et al. 1987, Journal of Geophysical

Research: Space Physics, 92, 14959Issautier, K., Meyer-Vernet, N., Moncuquet, M., & Hoang, S. 1998, Journal of

Geophysical Research, 103, 1969Jones, A. P., Tielens, A. G. G. M., & Hollenbach, D. J. 1996, ApJ, 469, 740Leinert, C., Richter, I., Pitz, E., & Planck, B. 1981, Astronomy and Astrophysics,

103, 177Lhotka, C., Rubab, N., Roberts, O. W., et al. 2020, Physics of Plasmas, 27,

103704Maksimovic, M., Bale, S. D., Chust, T., et al. 2020, A&A, 642, A12Malaspina, D. M., Horanyi, M., Zaslavsky, A., et al. 2014, Geophysical Research

Letters, 41, 266Malaspina, D. M., Szalay, J. R., Pokorný, P., et al. 2020, The Astrophysical Jour-

nal, 892, 115Mann, I. 2010, Annual Review of Astronomy and Astrophysics, 48, 173Mann, I. & Czechowski, A. 2005, ApJ, 621, L73Mann, I. & Czechowski, A. 2021, Astronomy and AstrophysicsMann, I., Kimura, H., Biesecker, D. A., et al. 2004, Space Science Reviews, 110,

269Mann, I., Meyer-Vernet, N., & Czechowski, A. 2014, Physics Reports, 536, 1,

dust in the Planetary System: Dust Interactions in Space Plasmas of the SolarSystem

Mann, I., Nouzák, L., Vaverka, J., et al. 2019, Annales Geophysicae, 37, 1121McBride, N. & McDonnell, J. A. M. 1999, Planetary and Space Science, 47,

1005Meyer-Vernet, N., Aubier, M. G., & Pedersen, B. M. 1986, Geophysical Re-

search Letters, 13, 617



Meyer-Vernet, N., Lecacheux, A., Kaiser, M. L., & Gurnett, D. A. 2009a, Geo-physical Review Letters, 36, L03103

Meyer-Vernet, N., Maksimovic, M., Czechowski, A., et al. 2009b, Solar Physics,256, 463

Meyer-Vernet, N., Moncuquet, M., Issautier, K., & Lecacheux, A. 2014, Geo-physical Research Letters, 41, 2716

Meyer-Vernet, N., Moncuquet, M., Issautier, K., & Schippers, P. 2017, Journalof Geophysical Research: Space Physics, 122, 8

Meyer-Vernet, N. & Perche, C. 1989, Journal of Geophysical Research, 94, 2405Müller, D., St. Cyr, O. C., Zouganelis, I., et al. 2020, A&A, 642, A1Oberc, P. 1990, Icarus, 86, 314Page, B., Bale, S. D., Bonnell, J. W., et al. 2020, The Astrophysical Journal

Supplement Series, 246, 51Pantellini, F., Landi, S., Zaslavsky, A., & Meyer-Vernet, N. 2012, Plasma Physics

and Controlled Fusion, 54Pedersen, B. M., Meyer-Vernet, N., Aubier, M. G., & Zarka, P. 1991, Journal of

Geophysical Research: Space Physics, 96, 19187Soucek, J. & other authors. 2021, A&A, this issueSzalay, J. R., Pokorný, P., Bale, S. D., et al. 2020, The Astrophysical Journal

Supplement Series, 246, 27Tielens, A. G. G. M., McKee, C. F., Seab, C. G., & Hollenbach, D. J. 1994, ApJ,

431, 321Vaverka, J., Nakamura, T., Kero, J., et al. 2018, Journal of Geophysical Research:

Space Physics, 123, 6119Vaverka, J., Pavlu, J., Nouzák, L., et al. 2019, Journal of Geophysical Research:

Space Physics, 124, 8179Wehry, A. & Mann, I. 1999, A&A, 341, 296Wilck, M. & Mann, I. 1996, Planetary and Space Science, 44, 493Ye, S.-Y., Gurnett, D. A., Kurth, W. S., et al. 2014, Journal of Geophysical Re-

search: Space Physics, 119, 6294Ye, S.-Y., Kurth, W. S., Hospodarsky, G. B., et al. 2018, Geophysical Research

Letters, 45, 10,101Ye, S.-Y., Vaverka, J., Nouzak, L., et al. 2019, Geophysical Research Letters, 46,

10941Zaslavsky, A. 2015, Journal of Geophysical Research: Space Physics, 120, 855Zaslavsky, A., Meyer-Vernet, N., Mann, I., et al. 2012, Journal of Geophysical

Research, 117, A05102Zook, H. A. & Berg, O. E. 1975, Planetary and Space Science, 23, 183


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First dust measurements with the Solar Orbiter Radio and