<figure><img src="image_1.png" /></figure>

# In Situ Observations of Interplanetary Dust Variability in the Inner Heliosphere

David M. Malaspina<sup>1,2 ID</sup>, Jamey R. Szalay<sup>3 ID</sup>, Petr Pokorný<sup>4,5 ID</sup>, Brent Page<sup>6</sup>, Stuart D. Bale<sup>7,8,9,10 ID</sup>, John W. Bonnell<sup>6 ID</sup>, Thierry Dudok de Wit<sup>11 ID</sup>, Keith Goetz<sup>12</sup>, Katherine Goodrich<sup>6 ID</sup>, Peter R. Harvey<sup>6 ID</sup>, Robert J. MacDowall<sup>13 ID</sup>, and Marc Pulupa<sup>6 ID</sup>

Received 2020 January 14; revised 2020 February 13; accepted 2020 February 13; published 2020 April 3

## Abstract

This work examines the variation of interplanetary dust count rates and directionality during the first three solar encounters made by the *Parker Solar Probe* spacecraft, covering distances between 0.65 au (~140 solar radii, $R_S$) and 0.16 au (~35 $R_S$). Dust detections are made by the FIELDS instrument via plasma clouds, produced by impact ionization of dust grains on spacecraft surfaces and resultant spacecraft potential perturbations. Dust count rates and inferred densities are found to vary by ~50% between the three solar encounters (~5 months per orbit), with most of the variation concentrated below 0.23 au (~50$R_S$). Dust count rates and directionality, as well as the encounter-to-encounter variability in both quantities are found to be consistent with β-meteoroids: dust grains exiting the solar system on hyperbolic trajectories. Interpretation of the dust count rate data and the dust directionality data independently suggest (i) that the β-meteoroid source region is more complex than preliminary models suggest, and (ii) that the primary β-meteoroid source region is approximately located between 10 and 30 solar radii from the Sun. These data offer important clues as to the location and geometry of the β-meteoroid source region, and consequently clues about the collisional and sublimation processing of interplanetary dust grains near the Sun.

*Unified Astronomy Thesaurus concepts: Interplanetary dust (821); Zodiacal cloud (1845); Heliosphere (711)*

*Supporting material: animation*

## 1. Introduction

Interplanetary dust is a term used to describe “finely divided solid matter, with particle sizes in general smaller than meteoroids, moving in, or coming from, interplanetary space.” This is the definition favored by the International Astronomical Union (IAU; Koschny et al. 2019). Following the IAU definition, dust grains range in size from tens of nanometers to approximately 30 µm, and primarily come from larger bodies such as meteoroids, asteroids, comets, and Kuiper Belt objects (Koschny et al. 2019). Forces due to gravity, solar radiation, and electromagnetic interactions with the solar wind plasma define the dynamics of interplanetary dust grains. Grain mass and radius largely determine which forces dominate a grain’s dynamics: for nanometer-sized dust, electromagnetic interactions; for submicron dust, radiation pressure; for few micron and larger, gravity and Poynting–Robertson drag (see Koschny et al. 2019 and references therein).

Larger (>1µm) interplanetary dust grains migrate sunward over $10^4-10^6$ yr via Poynting–Robertson drag (Poppe 2016; or up to billions of years for Kuiper Belt grains >1 mm). As this material, sourced from many locations in the solar system, approaches the Sun, it is expected that dust density increases to the point where the probability of collisions rises significantly (Mann et al. 2004).

Such near-Sun collisional grinding is predicted to produce a population of submicron dust grains that experience a sudden increase in radiation pressure force as they are created. The ratio of radiation pressure force to gravitational force on dust grains is denoted by the parameter $\beta$ (Zook & Berg 1975). If the radiation pressure is sufficient to overcome gravity, these grains are ejected from the near-Sun environment, and from the solar system entirely. These grains are called β-meteoroids, and they have been directly observed by space missions (e.g., Berg & Grün 1973; Zook & Berg 1975; Burns et al. 1979; Wehry & Mann 1999).

In the 1970s the *Helios* spacecraft provided measurements of interplanetary dust grains between ~0.3 and ~1 au from the Sun (Leinert et al. 1978, 1981; Gruen et al. 1980), returning a total of 235 dust impact observations between 1974 and 1980 (Altobelli et al. 2006). The *Helios* measurements provided information on the sunward radial profile of interplanetary dust number density, estimated to be proportional to $\approx 1/r$ for gains on near-circular orbits (Mann et al. 2004), where $r$ is radial distance to the Sun. These measurements are important to constrain our understanding of processing of dust in the near-Sun environment (Mann et al. 2004).

With the *Parker Solar Probe* mission, it is now possible to probe the dust environment even closer to the Sun, reaching down

<footnote n="1"><sup>1</sup> Astrophysical and Planetary Sciences Department, University of Colorado, Boulder, CO, USA; David.Malaspina@colorado.edu</footnote>

<footnote n="2"><sup>2</sup> Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO, USA</footnote>

<footnote n="3"><sup>3</sup> Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA</footnote>

<footnote n="4"><sup>4</sup> NASA Goddard Spaceflight Center, Greenbelt, MD, USA</footnote>

<footnote n="5"><sup>5</sup> The Catholic University of America, Department of Physics, Washington, DC, USA</footnote>

<footnote n="6"><sup>6</sup> Space Sciences Laboratory, University of California, Berkeley, CA, USA</footnote>

<footnote n="7"><sup>7</sup> Physics Department, University of California, Berkeley, CA 94720-7300, USA</footnote>

<footnote n="8"><sup>8</sup> Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450, USA</footnote>

<footnote n="9"><sup>9</sup> The Blackett Laboratory, Imperial College London, London SW7 2AZ, UK</footnote>

<footnote n="10"><sup>10</sup> School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK</footnote>

<footnote n="11"><sup>11</sup> LPC2E, CNRS, and University of Orléans, Orléans, France</footnote>

<footnote n="12"><sup>12</sup> School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA</footnote>

<footnote n="13"><sup>13</sup> NASA Goddard Space Flight Center, Greenbelt, MD, USA</footnote>
to 0.046 au (9.8 solar radii, $R_S$) by 2024. These new observations can help place new constraints on our understanding of dust collisional grinding and sublimation, and possibly on the chemical composition, of near-Sun dust grains. While the *Parker Solar Probe* does not carry a dedicated dust detector instrument, the FIELDS instrument (Bale et al. 2016) is capable of detecting dust impacts on the spacecraft surface. These hypervelocity impacts create plasma clouds that generate perturbations in the spacecraft floating potential that are detectable by FIELDS electric field instruments. Detection of dust grain impacts by electric field instruments has been demonstrated on a wide variety of spacecraft (e.g., Gurnett et al. 1983, 1986; Laakso et al. 1989; Tsurutani et al. 2003; Meyer-Vernet et al. 2009; Zaslavsky et al. 2012; Malaspina et al. 2014; Andersson et al. 2015; Kellogg et al. 2016). While FIELDS-based dust detections are unable to determine dust mass, composition, or precise directionality from each impact, the effective collecting area is essentially the entire spacecraft surface. As a result, FIELDS detects dust at a much higher rate than the *Helios* dust detectors, registering more impacts in a given 24 hr than *Helios* did over 6 yr (Altobelli et al. 2006).

Two recent works presented the first examination of near-Sun dust via FIELDS observations (Page et al. 2020; Szalay et al. 2020). By examining dust count rates from solar encounter 2 (~0.16 au, 35 $R_S$ perihelion) and through comparison with models of near-Sun dust dynamics, Szalay et al. (2020) concluded that FIELDS observations are dominated by β-meteoroid detections.

In this work, FIELDS dust observations from *Parker Solar Probe*'s first three solar encounters are compared. Each of these three orbits of the Sun have nearly identical perihelion distances ($35 R_S$). The similarities and differences between the dust observations on these three solar encounters provides new insight into near-Sun dust dynamics and provides further evidence that FIELDS detects primarily β-meteoroids.

## 2. Data Sets

This study makes use of data from the *Parker Solar Probe* FIELDS instrument (Bale et al. 2016). FIELDS has five voltage sensors that are capable of detecting voltage perturbations due to dust impacts. Four of these are 2 m whip antennas in the plane of, and extending away from, the *Parker Solar Probe* heat shield ($V_1, V_2, V_3, V_4$). The fifth is a ~21 cm antenna located near the end of the magnetometer boom ($V_5$). This study uses data from two FIELDS receivers: the Time Domain Sampler (TDS; Bale et al. 2016) and the Digital Fields Board (DFB; Malaspina et al. 2016).

The TDS has a bandpass from a few kHz to 1 MHz. It produces burst waveform captures (~15 ms in duration for the first three solar encounters) as well as summary statistics, including the TDSmax, which reports the largest (signed) value recorded by the TDS during a fixed time interval. During the first three solar encounters, the TDSmax cadence was once every 55.92 s beyond 55 $R_S$ and once every 6.99 s sunward of 55 $R_S$. TDSmax samples six channels at any given time. During the first three solar encounters, the most common setting had four of these configured to sample data from FIELDS voltage sensors: $V_{34}$, $V_2$, $V_{12}$, and $V_5$. Differential voltage measurements are indicated by double subscripts, as $V_{12} = V_1 - V_2$.

The DFB has a bandpass from DC to 75 kHz. Among other data products, it produces continuous time-series data on up to 12 channels. During the first three solar encounters, these data included the differential voltage channels $V_{12}$ and $V_{34}$. These

channels were sampled at ~293 Samples/s at all times sunward of 55 $R_S$ on solar encounters 2 and 3, and they were sampled at an increasing rate (~73, then ~146, then ~293 Samples/s) with decreasing solar distance on solar encounter 1. Single-ended potential measurements ($V_1, V_2, V_3, V_4$) were also recorded, at ~2.3 Samples/s during solar encounter 1, and ~293 Samples/s during solar encounters 2 and 3. These data were not recorded outside of 55 $R_S$.

Dust impacts on the *Parker Solar Probe* spacecraft were identified using both the TDSmax and DFB continuous waveform data sets.

## 3. Analysis: Dust Impact Rate and Density

First, the variation in dust impact rate (impacts/s) between the first three solar encounters is explored. Because the TDSmax data product was configured in a nearly identical mode for all three encounters, the TDSmax data set is used to compare dust impact rates for the first three solar encounters.

Following Page et al. (2020), TDSmax values with absolute value amplitudes >50 mV are considered to be due to dust impacts. Figure 1 supports this interpretation.

Figure 1(a) shows 1 hr of TDSmax data recorded on 2019 April 4. TDSmax reports not only the magnitude of the largest signal observed in a given interval, but also the sign of this signal (+ or - relative to zero volts). Therefore TDSmax peak amplitudes may be positive or negative. To show dust impact amplitudes over a large dynamic range in amplitude, we present a Y-axis in units of $log_{10}(mV)$, but with a + or - sign to indicate whether the detected peak amplitude was positive or negative.

Red circles in Figure 1(a) indicate TDSmax peak detections for which TDS burst data captures were made. Figures 1(b) and (c) show burst data time series for the two peak detections indicated by the red circles in Figure 1(a) adjacent to the red letters “b” and “c.” In both instances, the time-series waveform shapes are consistent with the shape of dust impact signals observed by other spacecraft (e.g., (Gurnett et al. 1983; Zaslavsky et al. 2012; Malaspina et al. 2016; Ye et al. 2018).

All available TDS waveforms during this interval (red circles) show waveforms consistent with dust impacts whose maximum amplitude matches that reported by the TDSmax data product. All have amplitudes with absolute values >50 mV. Similar results are found for any randomly selected interval during solar encounters 1 and 2, when the TDS waveform capture was configured to trigger on large amplitude signals only. Based on this analysis, and the waiting time analysis shown by Page et al. (2020), we have high confidence that the vast majority of TDSmax values with absolute value amplitudes >50 mV are due to signals consistent with dust impacts.

Each instance of TDSmax data exceeding 50 mV from channel $V_{34}$ is considered to be a dust impact. The total number of impacts detected in each 12 hr window is determined, and divided by the number of seconds during that window when valid dust observations could be made. No valid dust observations could be made during times when the FIELDS instrument was off or engaged in a calibration bias sweep, nor during times when the spacecraft thrusters were fired. Figure 2 shows the resulting dust impact rate for the first three solar encounters, as a function of days from closest approach. The black, blue, and red curves correspond to encounters 1, 2, and 3, respectively. For this figure, dust impact rates are calculated
<figure><img src="image_2.png" /><figcaption>Figure 1. (a) TDSmax peak detector amplitudes over 1 hr on 2019 March 31. Red circles indicate events for which time-series data were available. (b), (c) Time-series waveforms of dust impact events corresponding to the events marked b and c in red in panel (a).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2. Dust impact counts per unit time as a function of days from perihelion, for the first three solar encounters.</figcaption></figure>

at 24 hr intervals. Closest approach was a similar distance from the Sun (~35.6R<sub>S</sub>) for these encounters. The near-perihelion dust impact rate varies by ~50% from encounters 1 to 2 and 3. Encounters 2 and 3 show significantly more asymmetry about close approach than encounter 1. All encounters show similar count rates outside of ±10 days from encounter.

Both Szalay et al. (2020) and Page et al. (2020) determined that the count rate of dust detections on solar encounter 2 is consistent with the interpretation that FIELDS detections are primarily due to β-meteoroids. The results shown here extend that conclusion to all three encounters. Detections dominated by dust grains on near-circular orbits are expected to show (i) nearly symmetric count rates about perihelion, and (ii) a

drop in count rates near perihelion (see Szalay et al. 2020, Figure 7). Neither of these features are observed on any of the three solar encounters examined here. The 50% orbit-to-orbit variability shown in Figure 2 is inconsistent with a near-circular zodiacal dust population.

Assuming that the detected dust is primarily β-meteoroids, theoretical profiles as a function of position along the Parker Solar Probe orbit can be determined for (i) the net impact velocity on the spacecraft (determined by the spacecraft velocity and β-meteoroid velocity) and (ii) an estimate for the spacecraft surface area exposed to the β-meteoroid flow. These profiles (shown for encounter 2 parameters in Figures 3(a) and (b)) assume a uniform β of 0.7 (best fit from the analysis in Szalay et al. 2020), a thin-ring source of β-meteoroids located at 5R<sub>S</sub> (Szalay et al. 2020), and grains on prograde orbits. While consideration of grains on retrograde orbits may modify these area and velocity profiles, we assume here that the vast majority of the observed grains are prograde. This assumption is reasonable because (i) the number density of retrograde grains is expected to be significantly lower than prograde grains due to their higher probability of colliding with material in the zodiacal cloud (e.g., Steel & Elford 1986), and (ii) both observations (e.g., Reynolds et al. 2004) and modeling (e.g., Nesvorný et al. 2010, 2011b, 2011a) constrain the percentage of zodiacal material on retrograde orbits to <10%. From the count rate (R<sub>dust</sub>), collecting area (A), and impact velocity (v<sub>imp</sub>), one can determine the density of dust as:

$$n_{\text{dust}} = \frac{R_{\text{dust}}}{A v_{\text{imp}}}. \qquad (1)$$

Using these assumptions, Figure 3(c) shows the dust density along the Parker Solar Probe orbit for the first three solar encounters. Because the three orbits are similar, the 50% variation persists. The symmetry of dust density about perihelion is different for each encounter, with encounters 1 and 2 showing higher dust density just after perihelion and encounter 3 showing a ~12% dip near perihelion. All encounters show similar behavior and symmetry beyond ~10 days from perihelion.
<figure><img src="image_4.png" /><figcaption>**Figure 3.** (a) Spacecraft impact-sensitive area estimate as a function of days from perihelion, assuming β-meteoroids. (b) Estimated impact velocity, in the spacecraft frame, as a function of days from perihelion, assuming β-meteoroids. (c) Dust density based on count rate data in Figure 2 and the estimates in (a) and (b).</figcaption></figure>

Szalay et al. (2020) empirically fit the dust density as a function of radial distance for encounter 2 using Equation (2) (assuming $0.6 < \beta < 0.8$).

$$n_{\text{dust}}(r) = 0.5 \left( \frac{r}{1 \text{ au}} \right)^{-2} \qquad (2)$$

Figures 4(a) and (b) show the data from all three encounters with this fit overlaid as a green dashed line. Figure 4(a) shows the inbound leg of each orbit and Figure 4(b) shows the outbound leg of each orbit. Error bars show Poisson $\sqrt{N}$ counting statistics errors. Figures 4(c) and (d) show the same data, but with the fit in Equation (2) subtracted. What is now evident is that all three encounters deviate from the fit in Equation (2). The number of dust detections drops relative to the fit close to the Sun, beginning at a different distance each encounter, but generally between $40R_s$ and $50R_s$. Further, the encounter-to-encounter deviation from the fit becomes increasingly large sunward of $80R_s$.

Implications of these observations for the β-meteoroid interpretation and model are discussed in Section 5.

## 4. Analysis: Dust Directionality

The directionality of dust impacts on the Parker Solar Probe spacecraft is explored in addition to the impact rate. To explore directionality, we use time-series data from the five single-ended voltage probes as recorded by the DFB continuously at ~293 Sample/s throughout encounters 2 and 3, when the spacecraft is sunward of $55 R_s$. Figure 5 shows these data from a one hour interval on 2019 March 31 (encounter 2). The abrupt spikes indicated by red arrows correspond to dust impacts. The zoomed portion of the figure (right column) shows the time-series signal of a single dust impact in these data. The time between data samples (~3.4 ms) is comparable to the duration of many dust impact voltage pulses (see Figure

1 from Page et al. 2020), therefore the detection efficiency for this data product is not as high as for peak-detection data products such as the TDSmax or the DFB bandpass filter banks (Malaspina et al. 2016).

The DFB DC-coupled voltage probe measurements are natively sampled at 150 kHz, then subjected to both analog and digital filtering to produce the ~293 Sample/s data. Dust impacts are identified in these data, independently for each monopole antenna channel ($V_1, V_2, V_3, V_4$), using the following procedure: (i) the data are subdivided into 294-sample windows (~1 s.), (ii) the derivative of the signal within each window is computed, (iii) any derivative values greater than four times the standard deviation of all derivative values within the window are isolated, (iv) the window is considered to contain a dust impact if the largest and smallest derivative values satisfying condition (iii) are located within four samples of one another (indicating a sharp pulse), (v) the impact event amplitude is defined as the signed (+ or -) signal amplitude corresponding to the maximum absolute value amplitude associated with each large-derivative pair. A maximum of one impact identification per ~1 s window is allowed. In the few cases where more than one is present, the one with the highest amplitude is chosen. This procedure is repeated across all ~293 Sample/s data, with 50% window overlap and all duplicate detections removed. Only when impact events are identified independently in two or more monopole antenna signals are they considered part of the impact data set. Impact events where the largest and second largest amplitude signals are on opposite sides of the heat shield (e.g., $V_1$ largest, $V_2$ next largest) are excluded from further consideration (22% of the 12,682 impact events identified during encounter 2, and 20% of the 18,878 events identified during encounter 3), as it is not currently understood how to accurately interpret these impacts' directionality.

Impact events detected by this method were compared to TDS and DFB time domain burst captures (similar to Figures 1(b), (c)) on several randomly chosen days to verify that the sharp spikes identified in the ~293 Sample/s data correspond to waveform shapes consistent with dust impacts.

Once dust impact events are identified on all voltage probes, the approximate location of the impact on the spacecraft can be determined in the plane of the heat shield using the assumption that the voltage sensor closest to the impact location observes the largest impact signal amplitude. This assumption was used in the analysis of dust impact data on the Wind spacecraft to determine the direction of the interstellar dust flow through the solar system (Malaspina et al. 2014; Wood et al. 2015).

The specific algorithm used on Parker Solar Probe data is as follows. First, a given dust impact event must be identified on no fewer than two of the four $V_1 - V_4$ voltage sensors for consideration. Second, the most probable impact location, in the plane of the heat shield, is described as a wedge with a 90° open-angle centered on the pointing direction of the antenna with the highest impact signal (absolute amplitude over background). The ratio of the impact signal amplitude on the antenna with the second highest impact signal ($V_{2nd}$) to that on the antenna with the highest impact signal ($V_{1st}$) is then used to "tilt" the center of the probable impact wedge toward the
<figure><img src="image_5.png" /><figcaption>**Figure 4.** (a) Dust density as a function of distance from the Sun, the inbound part of the orbit. (b) Dust density as a function of distance from the Sun, outbound part of the orbit. The first three encounters are shown with black, blue, and red, respectively. Green curves show the best-fit line for a *β*-meteoroid source much closer to the Sun than the spacecraft Szalay et al. (2020). (c), (d) Same data as (a), (b), but with the best-fit curve subtracted.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 5.** (a)–(e) Time-series voltages measured by the five FIELDS voltage sensors at ~293 Samples/s. Red arrows indicate identified dust impacts (see the text for details). (f)–(j) Magnified view of rightmost dust impact from (a), as observed by all five voltage sensors.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Figure 6.** (a) Schematic of the Parker Solar Probe, showing spacecraft coordinates x and y. Spacecraft coordinate +z points toward the Sun. The orientations of and angles between the four FIELDS antennas in the plane of the heat shield are shown. (b) Polar plot of the normalized histogram of dust impact location, in the spacecraft coordinate system x-y plane. The four colored lines indicate the four antennas in the plane of the heat shield. The black wedge illustrates the contribution to the histogram of a single impact. (c) The same histogram as in (b), but not plotted as a polar plot.</figcaption></figure>

antenna with the second highest signal as:

$$ \theta_{\text{shift}} = \theta^* \left( \frac{V_{2\text{nd}}}{V_{1\text{st}}} \right). \qquad (3) $$

Here, $\theta^*$ is the half-angle between each probe pair (e.g., $\theta^* = 95^\circ/2$ between $V_1$ and $V_4$). With this formulation, approximately equal amplitude on $V_{2\text{nd}}$ and $V_{1\text{st}}$ results in a wedge centered approximately between the antennas that recorded $V_{2\text{nd}}$ and $V_{1\text{st}}$. Figure 5(b) shows an example case. Here, the largest amplitude signal was on $V_4$, the second largest on $V_1$, and $\theta_{\text{shift}} \approx 30^\circ$ toward $V_4$. Figure 6(a) shows a schematic of the FIELDS antenna configuration in the plane of the heat shield. The $+x$ and $+y$ directions are in spacecraft coordinates. The $+x$ direction is approximately the ram direction of the spacecraft at perihelion and the $+y$ direction points within a few degrees of ecliptic south.

Once the wedge center angle is determined, a value of 1 is added to a histogram of pseudo-counts versus angle for $\pm 45^\circ$ about the wedge center angle, as in Figure 6(c). Here $0^\circ$ is along $+x$, $+90^\circ$ is between $V_4$ and $V_2$, and so on in a counterclockwise sense. After many dust impacts, the shape of this histogram indicates the surface in the plane of the heat shield where the bulk of dust impacts are striking the spacecraft.

Figure 7(d) shows such a histogram, using 24 hr of dust impacts detected via the DFB continuous waveform data, centered on 2019 April 6. The histogram has been normalized to its peak value and plotted as a polar plot (as in Figure 6(b)). The four antennas in the plane of the heat shield are indicated using the same colors as Figure 6. In this case, near perihelion, the histogram peaks strongly along $+x$, the approximate ram direction of the spacecraft. Figure 7(c) shows the mean position of the Parker Solar Probe along its orbit in the eclipticJ2000 coordinate system XY plane, for the 24 hr of dust detections included in the histogram. By plotting similar histograms centered on times 12 hr apart, movies were created showing time variation in the dust impact direction as a function of the Parker Solar Probe orbit location (see the animated version of Figure 7). This type of analysis is possible for encounter 2 and encounter 3 data, but not encounter 1 data, as the voltage sensor sample rate for encounter 1 (~2.3 samples/s) was too slow for consistent dust impact detection.

Figure 7 shows several still frames from these movies which illustrate the basic characteristics of the dust directionality

observations. The left column shows data from encounter 2, the right column encounter 3. The top row shows times near the inbound part of the orbit, the middle row shows times near perihelion, and the bottom row shows times near the outbound part of the orbit. When the spacecraft is inbound, dust impacts are distributed more isotropically in the heat shield plane. Near perihelion, the most probable impact location focuses to the $+x$ direction. When the spacecraft is outbound, the most probable impact location begins to again spread away from the $+x$ direction, but does not reach as symmetric of a profile as on the inbound leg. Encounters 2 and 3 show qualitatively similar variation in directionality.

To quantify the directionality of the dust impacts, we examine the fraction of counts in the directionality histograms that are localized to the ram direction.

Figure 8(a) shows the ratio of the number of counts in the ram direction ($0^\circ < \theta < 45^\circ$ or $315^\circ < \theta < 360^\circ$) to the number of counts in the anti-ram direction ($135^\circ < \theta < 225^\circ$). Encounters 2 and 3 are shown in blue and red, respectively. Both encounters show a ratio near 1 on the inbound part of the orbit, indicating a balanced ram/anti-ram ratio. They both increase to higher values near perihelion, indicating relatively more ram impacts, and both peak after perihelion. Then both encounters show a return to a more balanced ram/anti-ram ratio, with localized excursions toward higher ram counts.

Figure 8(b) shows ram/anti-ram impact ratios predicted using the analytic dust model from Szalay et al. (2020) for two populations: (i) dust on circular orbits, shown with the black dashed line, and (ii) $\beta$-meteoroids in the solid colored curves. In each case, detailed geometry of the Parker Solar Probe spacecraft surface area is used (Page et al. 2020) to quantify the relative area of the spacecraft body and heat shield exposed to the $\beta$-meteoroid flow at each time. For this simplified model, we assume only grains on prograde orbits. The reasoning behind this assumption is stated in Section 3. The contribution of grains on retrograde orbits can be included in later refinements of the model-derived curves.

Impactors with circular orbits are predicted to reach values of ram/anti-ram ratio much greater than 5 at perihelion because, in this model, these grains are entirely ram impacting at perihelion due to the high relative velocity of the spacecraft with respect to dust populations. The ram/anti-ram ratio for circular orbiting impactors is expected to be nearly symmetric about perihelion. The predictions for $\beta$-meteoroids assume a
## Encounter 2

<figure><img src="image_8.png" /><figcaption>**Figure 7.** (a), (c), (e) Location of the *Parker Solar Probe* (red) in the eclipticJ2000 x-y plane (Sun in orange) at three times during the second encounter. (b), (d), (f) Polar plots of dust impact location histograms for the times corresponding to the locations in (a), (c), (e), (g), (i), (k) Same as (a), (c), (e) but for the third solar encounter. (h, j, l) Polar plots of dust impact location histograms for the times corresponding to the locations in (g), (i), (k). The mean radial distance from the Sun for each time window is indicated in (a), (c), (e), (g), (i), (k). An animation of the time variation in the dust impact direction as a function of the *Parker Solar Probe* orbit location is available. The animated version is the same as the static figure with the location of the *Parker Solar Probe* on the left and the polar plots of dust impact on the right. The animation includes encounter 2 from 2019 March 3 to April 10 and encounter 3 from 2019 August 27 to September 7, both in 12 hr steps.</figcaption></figure>

(An animation of this figure is available.)

## Encounter 3

<figure><img src="image_9.png" /></figure>

thin-ring source with various radial positions (indicated by line color). As the β-meteoroid source region is moved further from the Sun, the ram/anti-ram ratio approaches the observed ratios. The asymmetry of the β-meteoroid curves about perihelion is qualitatively consistent with the data.

## 5. Discussion

Based on the data shown in Section 3, it is evident that the thin-ring source β-meteoroid model used in Szalay et al. (2020) is not fully consistent with dust detections closer than ~45*R<sub>S</sub>* from the Sun. The *r*<sup>-2</sup> behavior of Equation (2) is a consequence of particle conservation combined with the assumptions that a thin-ring source for β-meteoroids is located sunward of 35*R<sub>S</sub>* and that the β-meteoroids complete their acceleration due to radiation pressure by the time they reach 35*R<sub>S</sub>*. The thin-ring model may produce an over-estimate if (i) β-meteoroids are not fully accelerated to their near-asymptotic

velocity by the time they encounter the *Parker Solar Probe*, (ii) the β-meteoroid production region is spread over a range of radial distances between 5 *R<sub>S</sub>* and 40 *R<sub>S</sub>*; (iii) the material colliding to produce β-meteoroids has a variable *β* (in time or space), or (iv) some combination of these. Explanation (i) by itself, with a 5 *R<sub>S</sub>* thin-ring source, is unlikely because it does not explain the observed encounter-to-encounter variation in dust counts. Detailed modeling of β-meteoroid production exploring such a parameter space could help distinguish between these possibilities.

While the comparison between data and modeling for the ram/anti-ram ratios presented in Figure 8 is qualitatively favorable, quantitative differences exist. These differences may be attributed to the simplifications involved in using a thin-ring β-meteoroid model, or possibility to the assumptions underlying the directionality determination. Improved dust modeling, combined with data from future *Parker Solar Probe* orbits, will allow more precise model-data comparisons.
<figure><img src="image_10.png" /><figcaption>**Figure 8.** (a) Observed ratio of ram-side impact detections to anti-ram-side impact detections as a function of days from perihelion on encounter 2 and 3. (b) Modeled ratio of ram-side impact detections to anti-ram-side impact detections as a function of days from perihelion for the *Parker Solar Probe* orbit relevant to encounters 1–3. The dashed black line shows model results for impactors with circular orbits, the solid colored lines show model results for a thin-ring source of β-meteoroids at various solar radial distances.</figcaption></figure>

## 6. Conclusions

This work examines heliospheric dust impact directionality and variability between 0.16 au (~35 $R_S$) and 0.65 au (~140 $R_S$) using *Parker Solar Probe* FIELDS data recorded during the first three solar encounters. Dust detection count rates, inferred dust density, and inferred dust directionality are all found to be consistent with the prior interpretation (Szalay et al. 2020) that *Parker Solar Probe* FIELDS dust detections are dominated by β-meteoroids.

Dust detection count rates and inferred dust density varied by as much as 50% from orbit to orbit. Nearly all of this variability is confined to regions sunward of 0.23 au (~50$R_S$), which we speculate could be related to the stochastic nature of β-meteoroid production (created by discrete collision events). Prior observations of β-meteoroid variability were constrained to decades long timescales by the instrumentation in use (Wehry et al. 2004). In the near-Sun region, observed dust detections decreased relative to expectations for a thin-ring β-meteoroid source region much closer to the Sun than *Parker Solar Probe* encounter 1–3 perihelion distances.

Impact directionality in the plane of the *Parker Solar Probe* heat shield was examined using FIELDS monopole antenna measurements. A transition was observed from mostly isotropic impacts on the inbound part of the orbit near 0.23 au (~50$R_S$), to a strong ram-side focus near perihelion, to a moderately ram-side focus on the outbound part of the orbit near 0.23 au (~50$R_S$). The ratio of ram to anti-ram impacts over the orbit

is in good qualitative agreement with modeled impacts of β-meteoroids, but quantitative differences remain.

The data presented here indicate a β-meteoroid source region further from the Sun than the $5R_S$ thin-ring source first approximation given by Szalay et al. (2020). Based on the ratio curves in Figure 8, a β-meteoroid source region closer to $20R_S$ or $30R_S$ is more consistent with the data. A β-meteoroid source region at these distances would also be consistent with recent optical measurements of the F-corona indicating a decrease in density of larger dust (β-meteoroid parent bodies) near $17R_S$ (Howard et al. 2019).

These data offer important clues as to the location and geometry of the β-meteoroid source region, and consequently, clues about the collisional and sublimation processing of interplanetary dust grains near the Sun. More detailed modeling combined with data closer to the Sun from subsequent orbits of *Parker Solar Probe* will doubtless bring further insights.

The authors thank the *Parker Solar Probe* team, especially the FIELDS team for their support. The FIELDS experiment on the *Parker Solar Probe* spacecraft was designed and developed under NASA contract NNN06AA01C. Dr. Pokorný's work was supported by a NASA Internal Scientist Funding Model award. S.D.B. acknowledges the support of the Leverhulme Trust Visiting Professorship program. All data used in this work are available on the FIELDS data archive: http://fields.ssl.berkeley.edu/data/.

Facility: *Parker Solar Probe* (FIELDS).

Software: SPEDAS (Angelopoulos et al. 2019).

## ORCID iDs

David M. Malaspina https://orcid.org/0000-0003-1191-1558

Jamey R. Szalay https://orcid.org/0000-0003-2685-9801

Petr Pokorný https://orcid.org/0000-0002-5667-9337

Stuart D. Bale https://orcid.org/0000-0002-1989-3596

John W. Bonnell https://orcid.org/0000-0002-0675-7907

Thierry Dudok de Wit https://orcid.org/0000-0002-4401-0943

Katherine Goodrich https://orcid.org/0000-0002-4288-5084

Peter R. Harvey https://orcid.org/0000-0002-6938-0166

Robert J. MacDowall https://orcid.org/0000-0003-3112-4201

Marc Pulupa https://orcid.org/0000-0002-1573-7457

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