Collisional Evolution of the Inner Zodiacal Cloud

The PSP Fields Experiment (FIELDS; Bale et al. 2016) detects dust impacts on the spacecraft surface. Dust grains traveling at high relative velocities (>1 km s⁻¹) to the spacecraft vaporize and ionize upon impact, creating a transient plasma cloud detected by the FIELDS electric field antennas as a high-amplitude (tens to thousands of mV), impulsive (tens of μs) voltage spike. Since dust is a fundamental part of the ambient near-Sun environment, and because FIELDS is sensitive to the voltage perturbations induced by dust impacts, FIELDS unavoidably measures dust. Since the entire spacecraft surface area acts as part of the "detector," antenna-based dust detection has the advantage of high count rates. PSP is bombarded by thousands of such impacts each orbit, creating a statistically robust data set of dust detections (e.g., Malaspina et al. 2020; Page et al. 2020; Szalay et al. 2020a).

FIELDS has four 2 m whip antennas in the plane of PSP's heat shield (V1, V2, V3, V4) and a fifth, 21 cm antenna situated along the magnetometer boom (V5). FIELDS dust counts are most readily determined in peak detection data from the Time Domain Sampler (TDS) receiver. The TDS records signals from each antenna in a bandpass from a few kHz to 1 MHz. It produces a data product called TDSmax, which reports the largest (signed) amplitude value on each configured channel recorded by the TDS over a short time interval. The TDSmax data product also records the number of zero-crossings associated within ∼13 ms surrounding the time of the largest-amplitude signal. This information is used to distinguish dust impact voltage spikes (few zero-crossings) from plasma waves (many zero-crossings).

Voltage spikes produced by impulsive dust impact voltage signals are clearly distinguished from plasma-wave-induced signals in TDSmax data by amplitude >50 mV and <5 zero-crossings (Page et al. 2020). Since PSP's first solar encounter in 2018, TDSmax data for the V2 monopole channel have been continuously produced whenever FIELDS is powered on, producing a vast database of dust impacts. In this work, we analyze impacts registered by FIELDS above 50 mV identified in the V2 TDSmax data set. In addition to count rates, FIELDS can determine basic directionality information for each dust impact by comparing voltage spike signal strength across its multiple antennas (Malaspina et al. 2020). The time domain waveform shapes of these voltage spikes, determined via high-resolution waveform captures, are consistent with previous observations of dust impact voltage spikes (Mann et al. 2019; Bale et al. 2020).

Changes in solar wind plasma density and temperature cause the spacecraft floating potential to vary and could affect dust impact observations. Because the amplitude of measured dust voltage spikes is partially determined by the amount of impact-liberated charge recollected on spacecraft surfaces, variations in the spacecraft floating potential will produce some variation in the minimum detectable dust impact voltage spike amplitude, and therefore variation in the dust count rate. However, the spacecraft floating potential has varied weakly over orbits 1–6, with most excursions less than 5 V in magnitude (Bale et al. 2020). Therefore, we do not expect the impact count rate to vary significantly over any given orbit owing to spacecraft charging effects when a fixed amplitude threshold is used.

The identified dust impact rates have been consistent with a "memory-less" process, such that the probability of receiving an impact is independent of the probability of when the next impact will occur (Poissonian). While there may be additional non-Poissonian sources of similar waveforms (Mozer et al. 2020), the finding that PSP's identified dust impact rates are highly consistent with a Poisson process, along with their waveform similarity to known dust impact signals, reinforces that the vast majority of observed abrupt voltage spikes are due to dust impacts (Page et al. 2020).

Figure 1(a) shows the impact rates observed by the FIELDS instrument on PSP for each orbit in high resolution for a voltage threshold of 50 mV. Errors are given for $\sqrt{N}$ counting statistics, where N is the total number of impacts in each measurement. To discern the dust populations responsible for these impact rates, we seek to understand the large-scale, broad features in the data. Hence, we apply a 1-day time binning to the data, shown in Figure 1(b); this work focuses on these time-binned data. Figures 2(a) and (b) show the rates as a function of the distance from the center of the Sun. Figure 2(c) shows color-coded trajectories according to the impact rates, where orbits 1–3 and orbits 4–5 have been averaged together, and orbit 6 is shown individually. The innermost distance visited by Helios and its dedicated dust detector of 0.3 au is marked in Figure 2(c), where the majority of the impact rate substructure observed by PSP is inside this distance.

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There are multiple features of note across each of these six orbits in Figure 2. All orbits exhibit a peak on the inbound, pre-perihelion portion of the orbital arc. Outbound, post-perihelion, orbits 4 and 5, and to a lesser extent orbit 6, show a clear second peak in their impact rate profiles, while the remaining have an extended "shoulder" that generally decreases monotonically from the pre-perihelion peak. The location of the first peak occurs at similar longitudes/true anomalies across the six orbits. We seek to explain these various features and compare the observed impact rates to a dust model described in the next section.

There have been two distinct dust populations observed by in situ detection methods that are directly related to our zodiacal cloud. The bulk of the material in the zodiacal cloud is composed of meteoroids on bound, elliptic orbits slowly spiraling into the Sun under the influence of Poynting–Robertson drag (e.g., Grün et al. 1985). Grains with these orbital characteristics have been termed α-meteoroids (Grun & Zook 1980). These grains collide and fragment into smaller grains, which can experience sufficient force from radiation pressure to be gravitationally unbound from the Sun. Once unbound, grains move along hyperbolic orbits, with trajectories that are governed by β, the ratio of solar radiation and gravitational forces (e.g., Zook & Berg 1975; Burns et al. 1979). Hence, these grains are termed β-meteoroids. We incorporate both α-meteoroids and β-meteoroids into a two-component model to compare with PSP impact rates. While there may also be a minor contribution of interstellar grains (e.g., Grün et al. 1993; Sterken et al. 2012; Strub et al. 2019), we do not model this population, as their fluxes are expected to be particularly small given their exclusion from the inner solar system due to radiation pressure.

Dust impacts into a target (PSP) generate an impact charge according to the relation

$$\begin{eqnarray}&&{Q}_{\mathrm{imp}}={{Cm}}_{\mathrm{imp}}^{a}{v}_{\mathrm{imp}}^{b},\end{eqnarray} \tag{ 1 }$$

where m_imp is the impactor mass, v_imp is the impactor speed, and C, a, and b are empirically determined constants based on the impactor and target properties (Auer 2001). These parameters can vary for different surfaces, and the constant C has been experimentally determined to span a large range (Collette et al. 2014). We will perform our fits, described in the next sections, on ${\tilde{Q}}_{\mathrm{imp}}\equiv {Q}_{\mathrm{imp}}/C$ to remove any dependence on this coefficient. Without a specific calibration for the various surfaces and target materials on PSP, we assume typical values of a = 1 and b = 3.5 (Auer 2001) for the calculations and analysis below, where m_imp is in kg and v_imp in km s⁻¹. Any detection method based on the amount of impact charge generated, in this case via the capacitively coupled transient voltage changes measured by FIELDS, will have a critical value of impact charge below which an impact creates too little charge to detect, Q_c . For any given impact speed, Q_c sets the minimum detectable radius via

$$\begin{eqnarray}&&{s}_{\min }={\left(\displaystyle \frac{3{Q}_{c}}{2\pi \rho {v}_{\mathrm{imp}}^{b}}\right)}^{1/3}={C}_{a}{v}_{\mathrm{imp}}^{-b/3},\end{eqnarray} \tag{ 2 }$$

where ρ is the bulk mass density of the impactors and ${C}_{a}={\left(3{Q}_{c}/2\pi \rho \right)}^{1/3}$. We have left b = 3.5 as a parameter to show the dependence on this exponent in subsequent equations. To roughly estimate the expected impact charge threshold, we assume that PSP is spherical with a capacitance of C_PSP = 200 pF. The voltage amplitude generated by a dust impact is given by Q_imp = C_PSPΔV/Γ_q , where ΔV is the potential change and Γ_q is the efficiency factor, typically ∼0.2 (Collette et al. 2015, 2016). With a detection threshold of ΔV_c = 50 mV and Γ_q = 0.2, the threshold impact charge is estimated to be Q_c ≈ 0.3 × 10⁹ electrons.

We use the following functional form for the number density n_α of bound α-meteoroids on elliptic orbits,

$$\begin{eqnarray}&&{n}_{\alpha }(r,a)={n}_{0\alpha }{f}_{\alpha }(r){r}^{-1.3}{\left(\frac{s}{{s}_{0}}\right)}^{-3\alpha },\end{eqnarray} \tag{ 3 }$$

where n_0α is the cumulative number density at 1 au for grains with radii greater than the reference grain size s₀ = 1 μm, approximating the size distribution using a single power-law, and r is the heliocentric distance in au. Mass indices varying from 0.4 to 1.3 were observed over a large mass range at 1 au (Grün et al. 1985), and modeling efforts suggest that the size distribution is expected to differ from this inside 1 au (Ishimoto & Mann 1998). To reduce model parameters, we assume a single power-law dependence with α = 0.9, consistent with the size index for ∼100 μm grains at 1 au (Grün et al. 1985; Pokorný & Brown 2016) and with the collisionally produced size distributions assumed for the meteoroid stream analysis discussed in this work (Appendix A). f_α (r) is given by the following empirical relation (Stenborg et al. 2020) determined via fits to the Wide-field Imager for Parker Solar Probe (WISPR) remote sensing data (Vourlidas et al. 2016):

$$\begin{eqnarray}{f}_{\alpha }(r)=\left\{\begin{array}{rl}0 & \,\ \mathrm{if}\ \,r\lt {r}_{0},\\ \displaystyle \frac{r-{r}_{0}}{{r}_{1}-{r}_{0}} & \,\ \mathrm{if}\ {r}_{0}\leqslant r\leqslant {r}_{1},\\ 1 & \,\ \mathrm{if}\,r\gt {r}_{1}.\end{array}\right.\end{eqnarray} \tag{ 4 }$$

Equation (3) matches the Helios remote observations outside r > r₁ (Leinert et al. 1978b) and provides an estimated representation for how the density would trend inside r₁ toward the dust-free zone (e.g., Leinert et al. 1978a; Stenborg et al. 2020) approximated here to occur at r₀ = 5R_⊙. We use a value of r₁ = 19R_⊙ as empirically determined by comparison with WISPR data (Stenborg et al. 2020), which is inside the perihelion distance for orbits 1–6 discussed in this work. All grains are assumed to be on perfectly circular orbits with orbital speeds of ${v}_{\mathrm{orb}}=\sqrt{\mu /r}$, where μ = 1.327 × 10²⁰ m³ s⁻² is the Sun's gravitational parameter. At any given location along PSP's orbit, the observed zodiacal impact flux is

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\alpha }(r)={n}_{0\alpha }{f}_{\alpha }(r){\left({s}_{0}/{C}_{a}\right)}^{3\alpha }{v}_{\mathrm{imp}}^{1+\alpha b}{r}^{-1.3}.\end{eqnarray} \tag{ 5 }$$

The impact speed between α-meteoroids and PSP is given by (e.g., Szalay et al. 2020a)

$$\begin{eqnarray}&&{v}_{\mathrm{imp}}^{2}=\mu \left(\displaystyle \frac{3}{r}-\displaystyle \frac{1}{a}-2\sqrt{\displaystyle \frac{a(1-{e}^{2})}{{r}^{3}}}\right),\end{eqnarray} \tag{ 6 }$$

where a and e are PSP's semimajor axis and eccentricity, respectively, and PSP and all grains are assumed to have inclination i = 0. For bound grains on circular orbits, we assume they have the density and β characteristics of nominal old cometary grains (Wilck & Mann 1996), such that grains with radii above 0.5 μm have β < 0.5 and are bound.

Initial analyses assumed all β-meteoroids were produced at a single location and had the same β value (Malaspina et al. 2020; Page et al. 2020; Szalay et al. 2020a). Here, we utilize a forward model to track β-meteoroid trajectories from a dispersed source region with a distribution of masses and β values. We model the dynamics of β-meteoroids under the attractive solar gravitational force and repulsive solar radiation force: F = μ(1 − β)/r². Grains collisionally produced at perihelion of their parent body's orbit will be unbound from the Sun's gravity for β ≥ 0.5(1 − e), where e is the eccentricity of the parent body (Grün et al. 1985). For example, β-meteoroids produced from a parent grain on a perfectly circular orbit are unbound for β ≥ 0.5. The value of β is dependent on the grain composition, albedo, porosity, and size. We assume collisional products are similar to canonical "young" cometary grains (Wilck & Mann 1996) to determine the relation between mass and β. Assuming collisions in the nominal zodiacal cloud occur between grains on perfectly circular orbits, collisional products with radii less than 1.2 μm are unbound and become β-meteoroids.

We estimate PSP impact rates using the following numerical scheme. In a uniform grid of 100 bins in radial position from 0 to 1 au, we release β-meteoroids and track their location and speed as they travel away from the Sun. The simulation is performed in 1D, assuming PSP and all grain trajectories are in the same plane. From their radial speed, we accumulate residence times for grains released at all initial positions. We assume the mass distribution follows a power law with differential slope α = 0.9 (Appendix A) and follow grain trajectories within 50 logarithmically spaced mass bins corresponding to a radius range of 50 nm to 1.2 μm. We normalize residence times from grain trajectories according to the size and collisional mass production distribution to account for which initial starting locations and masses contribute to the density at any location.

To approximate the functional form of collisional mass production, we follow previous conventions (Zook & Berg 1975; Steel & Elford 1986), by assuming that the collision rate per unit distance is proportional to ${n}_{\alpha }{\left(r\right)}^{2}v(r)\sigma (r)$, where n_α is the spatial zodiacal density given in Equation (3), v is the average impact speed, and σ is the cross-sectional area. The average impact speed is assumed to follow the Keplerian trend proportional to r^−0.5. Taking into account the threshold energy to catastrophically destroy grains (Appendix A, Equation (A4)), we approximate the cross-sectional area to be proportional to r^−α+2/3. Therefore, we represent the differential collisional mass production as

$$\begin{eqnarray}&&{M}^{+}(r){dV}\propto {n}_{\alpha }{\left(r\right)}^{2}v(r)\sigma (r)4\pi {r}^{2}{dr}\propto {f}_{z}^{2}{r}^{-1.33},\end{eqnarray} \tag{ 7 }$$

where the integral over ∫M⁺(r)dV = ${M}_{\mathrm{tot}}^{+}$ is a fit parameter. The density of β-meteoroids detectable by PSP is then ${n}_{\beta }(r,a)\propto {n}_{\beta }(r){s}_{\min }^{-3\alpha }\propto {n}_{\beta }{v}^{\alpha b}$. The incident impact flux of β-meteoroids observed by PSP is

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\beta }={n}_{\beta }(r,a)v(r)\propto {n}_{\beta }{v}_{\mathrm{imp}}^{1+\alpha b}.\end{eqnarray} \tag{ 8 }$$

For any combination of the three fit parameters (n_0α , ${\tilde{Q}}_{c}$, and ${M}_{\mathrm{tot}}^{+}$), the model can produce synthetic impact rates to the PSP spacecraft. The fits are performed using a χ² minimization (Markwardt 2009) between synthetic forward-modeled impact rates and the rates observed by PSP. We individually fit each orbit, with fit values given in Table 1.

Table 1. Two-component Fit Values for Individual Orbits and All Orbits Together

Orbit	n0α	${\tilde{Q}}_{c}$	${M}_{\mathrm{tot}}^{+}$	Φβ (1 au)
	(km −3)	(109 e−)	(kg s−1)	(10−4 m−2 s−1)
1	0.3	1.4	60	0.4
2	0.1	1.0	110	0.6
3	0.3	1.8	100	0.6
4	0.6	3.4	85	0.5
5	0.6	3.4	110	0.6
6	0.7	6.6	100	0.8
1–6	0.5	3.4	100	0.6

Note. Columns (2)–(4) give the model fits directly from the two-component model, while the last column (Φ_β ) gives the expected flux of β-meteoroids at 1 au.

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Figures 3 and 4 show the results of the model fits, where each orbit arc is shown separately in Figure 3 along with model curves for all orbits up to and including 24 to illustrate the expected profiles to be encountered in future orbits. In Figure 4, the top subpanels show the expected impact speeds. The second subpanels show the minimum detectable size threshold corresponding to the fitted ${\tilde{Q}}_{c}\equiv {Q}_{c}/C$. These values of charge threshold, given in Table 1, are similar to our back of the envelope estimate of Q_c ≈ 0.3 × 10⁹ e⁻ for C = 0.04–0.2, which is well within the range of expected values for relevant spacecraft surface materials (Collette et al. 2014). The third subpanels show the PSP data along with model rates for α-meteoroids, β-meteoroids, and combined total impact rate. The last subpanels show the difference between the data and modeled rates.

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As perihelion is reduced, each successive orbital group shows an increasing prominence in α-meteoroids versus β-meteoroids. For orbits 1–3, the large majority of the impact rate profile can be reproduced with β-meteoroids, notably for orbit 2, where almost no α-meteoroids are found to contribute to the impact rates. For orbits 4 and 5, which have a lower perihelion distance, the post-perihelion portion has a region that is dominated by α-meteoroids. Finally, for orbit 6, both the pre-perihelion and post-perihelion arcs are dominated by α-meteoroids near close approach.

Our model is able to reproduce the overall structure of the PSP measured impact rates for each orbit with three notable exceptions. The first is outside ∼0.7 au, where the model predicts larger counts than observed by PSP. This feature is likely due to the nonstandard orientation of the spacecraft due to communications and momentum management attitude changes via yaw maneuvers at the outermost portions of the orbit. For example, the lower counts in Orbit 2's inbound arc before and after ∼0.75 au exhibit a step-like change. This change exactly coincides with when PSP's attitude transitioned from a nonstandard orientation with the heat shield off-pointed from the solar direction to one in which PSP's heat shield was directly pointed to the solar direction. We use an effective collecting area assuming that the PSP +X vector is always aligned with the ram direction and that the +Y vector is aligned with PSP's orbital plane normal vector, which is often not the case outside ∼0.7 au (see Malaspina et al. 2016 for spacecraft coordinate definitions). Outside ∼0.7 au, PSP is often oriented with rotations about multiple axes compared to its nominal solar pointed ram configuration. Estimating the effective area more precisely for these configurations would require time-dependent 3D modeling of the spacecraft geometry and could be investigated in future studies.

The second feature not predicted by the model is the magnitude of the pre-perihelion peak impact rates. A pre-perihelion peak in impact rate is expected for β-meteoroid impactors due to the enhanced impact speed on the inbound orbit arc (Szalay et al. 2020a). Since the impact rate from α-meteoroids is symmetric about perihelion, this leads to modeled rates that always peak before perihelion. While the model predicts such a feature and is able to reasonably reproduce the location of this peak, it is not able to fully reproduce the large impact rates observed by PSP. Specifically, orbits 2, 4, and 5 exhibit pre-perihelion enhancements over the model fits of approximately 10, 20, and 35 hr⁻¹ respectively.

The final aspect for which the model deviates from the data is in the post-perihelion rates within ∼5 days from perihelion. Across all six orbits discussed here, the model is deficient in reproducing larger impact rates in this region. During orbits 1–3, this enhancement manifests itself as an extended "shoulder" on the impact rate profile, which still monotonically decreases from the expected pre-perihelion peak. During orbits 4–5, and to a lesser extent in orbit 6, this enhancement forms a second peak in the total observed impact rates, with the data–model difference also clearly showing this unexpected feature. The difference between data and model rates for the post-perihelion enhancement maximizes during orbits 4–5. No such feature is predicted by the two-component model, and we present possible explanations for this post-perihelion enhancement in Section 4.

The model also allows for a comparison with the fitted impact threshold across the orbits. Figure 5 shows the impact speed and size ranges for the two dust populations in this model. Gray contours show isoimpact-charge features, where any impact on a specific contour is expected to generate the same impact charge and therefore the same impact voltage spike magnitude. The fitted ${\tilde{Q}}_{c}$ values are shown in black, and the modeled α-meteoroid and β-meteoroid populations are marked with the two boxes. The shaded portions of each box show the range of detectable impactors for each population according to the model fits. As shown here, for the similar values of ${\tilde{Q}}_{c}$, PSP is expected to be able to detect a large portion of available impactor populations. It also shows that even with the difference in both speed and mass of the two populations, the impact charge relation suggests both populations are able to be detected each orbit contemporaneously.

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Given the model fits to the zodiacal dust cloud, we can provide estimates on the total collisional production rate of grains in the inner solar system. Volumetric mass-loss rates are initially calculated in the model assuming β-meteoroid fluxes are uniformly distributed throughout all inclinations, as the model is inherently one-dimensional. The conversion from observed flux back to M⁺ assumes a full-sky averaged flux as an input. In reality, the zodiacal cloud has an inclination distribution that consists primarily of low-inclination orbits (e.g., Nesvorný et al. 2010). Since PSP observed the flux near the ecliptic plane, which is larger than the latitudinally averaged flux, we must apply a correction factor. Using a latitudinal dependence (Leinert et al. 1978b) proportional to $f(\lambda )=1-\sin | \lambda |$, we scale the model mass production values by 〈f(λ)〉 = 0.36. Table 1 shows the results of the fitted total mass production rates for fits of each orbit separately, and combined across all of the first six orbits in the last row.

The model predicts that the majority of collisions producing β-meteoroids that stream throughout the solar system occur within 10–20 solar radii (Figure 6(a)). Inside of ∼10 solar radii, the modeled β-meteoroid density monotonically decreases toward the Sun (Figure 6(b)), indicating a precipitous drop in collisional production near the Sun and suggestive that the size distribution of zodiacal material changes as a function of radial distance (Ishimoto & Mann 1998). The location of peak production is consistent with a collisional source mechanism eroding the zodiacal cloud, as opposed to sublimation driven erosion where grains are expected to sublimate inside ∼10 solar radii (Mann et al. 2004). Across all orbits, we find a zodiacal collisional production rate of at least ${M}_{\mathrm{tot}}^{+}$ = 100 kg s⁻¹ is consistent with the fluxes of β-meteoroids observed by PSP. We have assumed that all collisional products are distributed into β-meteoroids; hence, this number is likely an underestimate, which may explain why it is approximately 5–10 times lower than previous collisional estimates (Grün et al. 1985).

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If submicron-sized grains are responsible for the abundance of pickup ions near the Sun (Schwadron et al. 2000), we expect pickup ion production would be enhanced near the peak β-meteoroid density location around 10–20 solar radii. Previous estimates found a lower limit for the dust geometric cross section of Γ_σ ≥ 1.3 × 10⁻¹⁷ cm⁻¹ is needed to produce inner source pickup ions (Schwadron et al. 2000), almost two decades larger than the value used previously (Holzer 1977; Fahr et al. 1981; Gruntman 1996), Γ_σ = 2 × 10⁻¹⁹ cm⁻¹. A geometric cross section for inner source pickup ions of Γ_σ ≥ 1.3 × 10⁻¹⁷ cm⁻¹ is four decades larger than the β-meteoroid geometric cross section found here based on collisional production in the zodiacal cloud; this discrepancy raises the question about whether dust from zodiacal can explain the inner source.

The distribution of inner source pickup ions indicates that the grain population producing the inner source peaks at ∼10 R_⊙, which is within the region of maximum β-meteoroid collisional production between 10 and 20 R_⊙ found here. While not modeled here, collisional fragmentation can also produce grains with radii ≲50 nm. This population of nanograins, which are highly susceptible to electromagnetic forces, can become trapped in the innermost regions of the solar system inside ∼30 R_⊙ (Czechowski & Mann 2010). Impacts from nanograins in the range of 30–40 nm have been estimated to have impact speeds in the range of 20–45 km s⁻¹ during PSP's first three orbits (Mann & Czechowski 2021). Such impacts would produce an impact charge of approximately 10⁵–10⁶ electrons, orders of magnitude lower than the estimated detection threshold of ${\tilde{Q}}_{c}\sim {10}^{9}$ electrons even accounting for a few orders of magnitude variation in C (Collette et al. 2014). Hence, this population of nanograins is not expected to be directly detectable in the FIELDS impact data.

Dust grains can serve as the neutralizing agent for solar wind ions that penetrate these grains, and could potentially explain the large fluxes of inner source pickup ions observed (Schwadron et al. 2000). Wimmer-Schweingruber & Bochsler (2003) suggest that the size of such dust particles is less than or comparable to the penetration range of solar wind ions in dust material, <100 nm. Thus, the collisional production of zodiacal grains discussed here also suggests the generation of extremely small dust particles that may explain the origin of inner source pickup observed in the inner heliosphere (Schwadron et al. 2000). We have ruled out larger β-meteoroids for the inner source of pickup ions, given their low geometric cross section due in part to their relatively short lifetimes in the inner solar system. If dust is responsible for generating the inner source, then it must be from nanograins with radii below ∼50 nm. While this nanograin population is likely not detectable directly with FIELDS measurements, PSP may be able to observe pickup ions in the inner solar system directly with PSP's SWEAP instrument (Kasper et al. 2016). These pickup ions can also seed energetic particles accelerated via shocks in the inner solar system that could be detected by the IS⊙IS instrument (McComas et al. 2016, 2019). Hence, the innermost PSP orbits may yield critical information on the inner source of pickup ions across its in situ instrument suites.

The estimated densities necessary to account for the post-perihelion enhancement are similar to densities of meteoroid streams inferred by Helios in situ dust measurements of 10–100 km⁻³ (Krüger et al. 2020). Applying a similar analysis, we utilize the Interplanetary Meteoroid Environment for eXploration (IMEX) model (e.g., Soja et al. 2019) to estimate the number flux PSP encounters near transits with cometary orbits. This model tracks the trajectories of grains with radii greater than 100 μm that are released from cometary activity to build up a density distribution along the comet's orbit. It accounts for gravitational and solar radiation forces acting on dust grains, as well as the collisional lifetimes. Grains with radii smaller than 100 μm are also likely to exist in a more extended cross-sectional area; however, they dynamically decouple from their parent comets' orbits much more rapidly for smaller sizes.

We performed a comprehensive search across all known comets in the inner solar system to determine which orbits have the closest approach points near the region of peak impact rate enhancement in PSP's orbits 4–5. From this search, we identified three cometary candidates: 342P/SOHO, 323P/SOHO, and 96P/Machholz (Table 2). We also investigate the Geminids meteoroid stream, whose parent body is likely asteroid (3200) Phaethon. Figure 7 shows these four orbits along with the PSP orbits and region of enhanced post-perihelion impact rates for orbits 4–5. Dots mark the location on each orbit closest to the orbit 4–5 enhancement. As shown in this figure, the stream parent bodies identified have close transits with PSP's orbit, with 342P transiting the nearest to the region of interest. For the cometary candidates, only one had sufficient brightness data to constrain the stream number densities: 96P. For this stream, we find its impact rates would peak a few days before the observed enhancement with an upper limit of ∼10⁻³ hr⁻¹, making it an unlikely explanation for the post-perihelion enhancement.

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Estimating the peak rates for 342P and 323P requires comprehensive knowledge of the absolute brightness of these comets not available at the time of this analysis. Of these two candidates, 323P/SOHO does not exhibit activity like a normal comet (Battams & Knight 2017); its activity is similar to 322P/SOHO, which exhibits activity more similar to an asteroid than a comet (Knight et al. 2016). Thus, dust production from 323P is likely minimal, and a substantial debris trail is unlikely. While we cannot directly estimate these meteoroid stream densities, with knowledge of the impact speeds from each stream, we can estimate the required densities necessary to produce the orbit 4–5 enhancement, n_lim given in Table 2. These density limits are at the position of PSP. Given that PSP flies within a few solar radii of 342P and 323P, these density limits are applicable to the core of the stream. Note that n_lim is the limiting density needed to produce the observed impact rates; it does not signify that any of these meteoroid streams actually have these densities, as that would require an exact determination of the source of the PSP impact rate enhancement.

Phaethon, the parent body of the Geminids meteoroid stream, does not continually replenish this stream in sufficient quantities via the relatively low activity level of active asteroid Phaethon (e.g., Jewitt & Li 2010; Jewitt et al. 2013), nor is meteoroid bombardment of Phaethon sufficient to source the stream (Szalay et al. 2019). However, unlike the other meteoroid streams discussed here, we have direct observations of its flux. At 1 au, the number flux of Geminids with radii ≥100 μm is 4 × 10⁻¹¹ m⁻² s⁻¹, which corresponds to a number density of 1.2 × 10⁻⁶ km⁻³ for their heliocentric speed of 33 km s⁻¹ (Blaauw 2017). Its closest encounter with the PSP trajectory is at ∼0.14 au, where the Geminids have a heliocentric speed of ∼109 km s⁻¹. Scaling the density as r^−1.5 (Appendix A) at 0.14 au gives an expected density of 2 ×10⁻⁵ km⁻³. With a relative impact speed between PSP and the Geminids of 62 km s⁻¹, an effective area of 6 m², and assuming PSP flew directly through the core of this meteoroid stream, PSP could expect impact rates of 3 × 10⁻⁵ hr⁻¹ for grains with radii ≥100 μm, well below the rates necessary to explain the impact rate feature. The cumulative mass index of the Geminids was found to be α_g = 0.68. Even if we assume a power-law size distribution holds to radii as small as 1 μm, the expected impact rate from grains ≥1 μm would be 0.4 hr⁻¹, still significantly lower than the ∼40 hr⁻¹ observed in the enhancement. PSP also does not transit directly through the core of the stream; its close approach point during the enhancement period is approximately 0.06 au from the core of the stream. Therefore, we do not attribute the enhancement to direct Geminids observations; however, we explore another alternative related to the Geminids in the next section.

As an alternative to a direct meteoroid stream encounter, the post-perihelion enhancement could be due to β-meteoroids produced by collisions between meteoroid streams and the nominal zodiacal dust distribution. The timing and location of the post-perihelion enhancement coincide with PSP's intersection of β-meteoroid trajectories produced by collisions between the Geminids meteoroid stream and the nominal zodiacal cloud (Figure 8), which we term a "β-stream." From previous estimates of the Geminids collisional lifetime and total stream mass, the stream loses ∼6–40 kg s⁻¹ from collisions and would register impact rates on PSP in the range of ∼0.1–30 hr⁻¹ during the post-perihelion enhancement period for orbits 4–5 (Appendix A). The enhanced impact rate features post-perihelion above the modeled rates are therefore qualitatively consistent with Geminids β-stream fluxes. Figure 8 shows the possible detection geometry for a Geminids β-stream. The blue contours show the approximate density profile of larger meteoroids in the Geminids stream, integrated from >14,000 orbits of visual meteors (Jenniskens et al. 2018). The gray fan-like shape shows the example path taken by β-meteoroids for β = 0.7 produced in the region in the Geminids (gray tube) that would account for 95% of potentially detectable fluxes during PSP's orbits 4–5.

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A β-stream detection could also explain why PSP observed a post-perihelion enhancement for each orbit, as the β-stream would be expected to be dispersed and could intersect multiple orbits. However, to reach PSP from the core of the Geminids stream, the collisional process must generate fragments with transverse spread ∼10°–20° out of plane above their original trajectories (Figure 11). If the enhancement is due to the Geminids β-stream, it suggests the Geminids stream could be more spatially extended than inferred from the core of larger grains that cause visual meteors at Earth (Appendix B).

There are many additional meteoroid streams that could produce β-streams detectable by PSP, listed in Table 4 in Appendix C. The Geminid β-stream is preliminarily a favorable candidate, and initial analyses on the directionality inferred by FIELDS observations also support this source mechanism (Pusack et al. 2021). A comprehensive comparison between multiple meteoroid stream origins along with directionality and amplitude analysis would be crucial in determining the source of the post-perihelion enhancement.

After orbit 7, PSP's perihelion is inside r₁ = 19R_⊙ (Table 3), such that the density of bound α-meteoroids on elliptic orbits is no longer expected to increase with a power-law relation. Therefore, inside this critical distance, the PSP impact rates will be more governed by the relative impact speed to dust. Figure 9 shows the expected impactor parameters for the two-component model in the upcoming orbital groupings, along with the peak impact speeds and rates for α-meteoroids and β-meteoroids. Figure 3 also highlights the expected impact rates for subsequent orbits in the four gray curves with the largest impact rates.

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Table 3. Predicted Quantities during Each of PSP's Orbital Groups

Orbit	rph	${v}_{\alpha }^{\max }$	${v}_{\beta }^{\max }$	Rα	Rβ	Rtot	$\tfrac{{E}_{\alpha }}{{E}_{\alpha }(6)}$	$\tfrac{{E}_{\beta }}{{E}_{\beta }(6)}$	$\tfrac{{{EF}}_{\alpha }^{\max }}{{{EF}}_{\alpha }^{\max }(6)}$	$\tfrac{{{EF}}_{\beta }^{\max }}{{{EF}}_{\beta }^{\max }(6)}$
	(au) (R⊙)	(km s−1)	(km s−1)	(hr−1)	(hr−1)	(hr−1)
1–3	0.16 (36)	39	160	6	31	33	0.26	0.62	0.16	0.37
4–5	0.13 (28)	46	163	20	49	59	0.45	0.71	0.36	0.58
6–7	0.095 (20)	57	167	51	83	130	1	1	1	1
8–9	0.074 (16)	66	171	79	110	187	1.7	1.2	2.2	1.5
10–16	0.062 (13)	74	174	88	120	212	2.2	1.3	3.7	1.9
17–21	0.053 (11)	81	176	97	140	228	3.0	1.5	5.3	2.3
22–24	0.046 (9.9)	89	179	110	150	253	3.7	1.6	7.3	2.7

Note. r_ph—perihelion distance; ${v}^{\max }$—peak impact speed; R—peak detectable impact rate; E—total deposited energy throughout the orbit; and ${{EF}}^{\max }$—peak energy flux. Ratios are given with respect to values during orbit 6.

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Dust presents a hazard to the PSP spacecraft, via direct impacts both to instruments and to the spacecraft subsystems. On orbit 2, the IS⊙IS instrument registered a permanent increase of noise in one of its 80 apertures that has been attributed to a dust impact (Hill et al. 2020). The timing and orientation of the affected aperture during the noise event suggested the impact was a β-meteoroid (Szalay et al. 2020a), as it occurred exactly when the flux of β-meteoroids to that aperture was expected to peak and the orientation at that time would have prevented α-meteoroids on perfectly circular orbits from impacting the aperture foil. Initial models suggested a total of 1–10 more impacts of this type could occur between orbits 1 and 6 (Szalay et al. 2020a). Additionally, the WISPR instrument often records images that are dominated by features attributed to impact ejecta spray from the spacecraft due to dust impacts.

Table 3 gives an indication of the expected maximum impact speed and rate for all orbit groups. By orbit 6, the β-meteoroid impactor population has a peak impact speed of 167 km s⁻¹, not far from its overall mission peak of 179 km s⁻¹. Between orbits 6 and 24, the impact rate of β-meteoroids is expected to approximately double. Therefore, the β-meteoroid population is expected to minimally increase in overall impact energy for the remainder of the mission. On the other hand, the α-meteoroid population increases significantly in both impact speed and total impact flux. We estimate the peak and total deposited energy for each orbit. The peak deposited energy flux is determined by multiplying the total peak impact rate (independent of detection threshold) by the average energy per impact. The total deposited energy is the integral of the impact rate multiplied by average energy per impact along the entire orbit. Table 3 lists these quantities as ratios to their values during orbit 6 to give an indication of how much these quantities increase in subsequent orbits. As given in this table, the peak energy flux is expected to be as much as ∼7 times larger during orbits 22–24 compared to orbit 6. Additionally, the possibility exists that PSP could directly encounter meteoroid streams from cometary activity, posing a hazard in addition to those discussed here.