Solar Energetic Particle Track Accumulation in Edgeworth-Kuiper Belt Dust Grains

Interplanetary dust grains (IDPs) originate from a wide variety of sources in the solar system, including asteroids, comets, and Edgeworth-Kuiper Belt (EKB) objects (e.g., see review by Koschny et al., 2019). After their birth, these grains are subject to several forces, including gravity, solar radiation pressure, Poynting-Robertson and solar-wind drag, and electromagnetism (e.g., Burns et al., 1979; Gustafson, 1994), which in turn allows IDPs to migrate long distances from their birthplace (e.g., Grün et al., 1985; Jackson & Zook, 1992; Liou et al., 1995; Landgraf et al., 2002; Moro-Martín & Malhotra, 2003). Thus, the influx of interplanetary dust grains to any object in space is dependent both on the location of such object and the time-integrated dynamics of IDPs originating from various sources. At Earth, for example, multiple lines of evidence suggest that the IDP influx is primarily composed of dust originating from Jupiter-family comets (JFCs) (e.g., Nesvorný et al., 2010; Carrillo-Sánchez et al., 2016) with smaller contributions from Oort Cloud comets (Nesvorný et al., 2011), Halley-type comets (Pokorný et al., 2014), and the main asteroid belt (e.g., Durda & Dermott, 1997; Nesvorný et al., 2010). In contrast, the IDP influx in the outer solar system is believed to transition from JFC-dominated near Jupiter to EKB-dominated near Neptune (e.g., Kuchner & Stark, 2010; Vitense et al., 2012; Poppe, 2016; Poppe et al., 2019; Piquette et al., 2019; Bernardoni et al., 2022). Additionally, dynamical simulations have also suggested the possibility that IDPs from the EKB could potentially migrate all the way to 1 au and comprise a component of the zodiacal cloud at Earth (e.g., Liou et al., 1996; Moro-Martín & Malhotra, 2003); however, supporting evidence for an influx of EKB grains to Earth has, until recently, remained lacking.

As interplanetary dust grains migrate through the solar system, they are subjected to charged-particle irradiation over a wide range of species and energies. Among these various populations, high-$Z$ ($Z\geq 26$) ions with energies of $\sim$1 MeV/nuc leave visible damage tracks within meteoritic minerals due to local melting and subsequent amorphization (e.g., Fleischer et al., 1975; Szenes et al., 2010). These track-inducing particles, comprised mainly of iron (Fe, $Z=26$) with minor contributions from even heavier elements (e.g., Ni, Zn, etc.), primarily originate from solar flares near the Sun’s surface or from coronal mass ejections that propagate through the heliosphere and are part of a broader population of ‘solar energetic particles’ (SEPs) (e.g., Reames, 2013, 2019). The convolution of the track-inducing SEP distribution throughout the heliosphere and the time history of IDP trajectories governs the rate at which IDPs accumulate damage tracks. Additionally, energetic particle irradiation of interplanetary dust grains by both SEPs and galactic cosmic rays (GCRs) can also stimulate the formation of cosmogenic radionuclides (e.g., ¹⁰Be, ²⁶Al, ⁵³Mn, ⁶⁰Fe), observations of which have recently been used to infer an outer solar system origin for several terrestrial micrometeorites (e.g., Feige et al., 2024). While highly complementary to the analysis of SEP-induced track densities studied here, we note that the production of cosmogenic nuclides within IDPs is not the focus of the current study and is left to future work.

At Earth, interplanetary dust grains that have entered the terrestrial atmosphere can be collected in the stratosphere for inspection and analysis in ground-based laboratories. Bradley et al. (1984) reported the first discovery of SEP-induced tracks in stratospherically collected IDPs and subsequent studies have used SEP track densities to establish the exposure ages of IDPs and by extension, constrain their parent populations (e.g., Sandford, 1986; Flynn, 1989; Thiel et al., 1991). Building on this idea, Flynn (1994) and Flynn (1996) suggested that one could identify EKB grains that managed to transit to 1 au based on an unusually high amount of space exposure in the form of SEP-induced tracks. Recently, Keller & Flynn (2022) have reported the possible discovery of such EKB grains in the stratospheric IDP collection, based on a combination of unusually high SEP-induced track densities within some IDPs, $\sim$0.4–5$\times 10^{11}$ tracks cm^-2, and a revised calibration for the SEP track-production rate at 1 au based on lunar samples returned from the Apollo missions (Keller et al., 2021). By employing an analytical model of interplanetary dust grain dynamics under the influence of only Poynting-Robertson drag (i.e., without planetary perturbations), Keller & Flynn (2022) noted that grains released from the EKB region ($\sim$40-50 au) tended to accumulate between 0.4–4.0$\times 10^{10}$ tracks cm^-2, somewhat lower than their observed distribution. Keller & Flynn (2022) further suggested that, based on the dynamical results of Liou et al. (1996), trapping within MMRs outside the orbit of Neptune could yield the additional fraction of accumulated track densities needed to achieve a more satisfactory comparison with the observed high-track-density SEPs; however, an explicit dynamical calculation of this potential effect was not performed.

Here, we build upon and extend the work of Keller & Flynn (2022) by using a dynamical dust grain model that includes all major perturbing forces to investigate the dynamics and track accumulation of interplanetary dust grains originating from the Edgeworth-Kuiper Belt. In particular, we explicitly assess the role that planetary perturbations, including trapping within MMRs, play in the overall accumulation of SEP-induced tracks within IDPs. Section 2 describes the modeling approach used in the study, including both the interplanetary dust dynamics model and the distribution of track-inducing SEPs. Section 3 presents the results of our simulations while Section 4 provides a discussion of our findings in the context of explaining high-track-density IDPs at 1 au. Finally, we conclude in Section 5.

In order to model the dynamics and SEP-induced track accumulation within interplanetary dust grains, we combine the results from the IDP dynamical model previously described in Poppe (2016) and Poppe et al. (2019) and an analytical description for the rate of SEP track accumulation as a function of heliocentric distance. Below, we describe both model components in detail.

The simulations presented above have further quantified both the accessibility of EKB grains to 1 au and the degree of SEP-induced track accumulation such grains gain during their interplanetary transit. In general agreement with previous simulation studies (e.g., Liou et al., 1996; Moro-Martín & Malhotra, 2003), we find that EKB grains can transit to 1 au in non-negligible fractions, ranging from $\sim$30% for 2 $\mu$m grains to $\sim$1-3% for grains $\simeq$100 $\mu$m when neglecting collisions (although see below for further discussion on this point). One question that naturally arises from this finding is the degree to which these EKB grains contribute to the overall mass flux of interplanetary dust to Earth in comparison to that from other sources such as comets (e.g., Jupiter-family, Halley-type, etc.) and asteroids. If we assume a standard crushing law for the distribution of masses generated in the EKB, and apply both the overall EKB dust mass production rate of $\sim$2$\times 10^{7}$ g s^-1 reported in Poppe et al. (2019) and the relative fraction of grains capable of reaching 1 au as presented in Figure 1 here, we estimate a mass accretion rate at Earth of several $\times 10^{3}$ tons yr^-1. In comparison, estimates of the total IDP flux to Earth vary from $\sim$$5\times 10^{4}$ tons yr^-1 from the LDEF experiment (Love & Brownlee, 1993), $\sim$$10^{5}$ tons yr^-1 from comparison of a dynamical model to thermal infrared emission (Nesvorný et al., 2010), to $1.5\times 10^{4}$ tons yr^-1 as inferred from terrestrial lidar measurements of ablated meteoric material (Carrillo-Sánchez et al., 2016). Thus, we estimate that EKB grains could represent somewhere between 1% and a few tens of percent to the total mass flux at Earth; however, we generally favor the lower end of this range because, as discussed earlier, this work does not account for grain-grain collisions, which will tend to remove mass from the EKB dust distribution. More quantitative modeling and analyses of the EKB mass flux contribution to Earth and other inner solar system bodies is clearly warranted in future work.

Despite demonstrating that EKB grains are dynamically capable of transiting to 1 au, our quantitative assessment of track accumulation in EKB grains does not achieve full agreement with the observed track density distributions in stratospheric dust populations reported by Keller & Flynn (2022). Indeed, a primary finding from our simulations is that the inclusion of planetary perturbations tends to reduce the accumulated track density in IDPs compared to calculations with only Poynting-Robertson drag. Our simulations do show that trapping within planetary MMRs, in particular outside Neptune’s orbit, does significantly increase the time grains spend at distances $>$30 au; however, track accumulation rates are relatively low at such distances (i.e., assuming an $r^{-1.7}$ scaling, fluxes at 42.5 au are 0.2% that at 1 au). Subsequently, our simulations also show that planetary perturbations significantly reduce the amount of time that IDPs originating from the EKB spend transiting through the outer and inner solar systems compared to PR drag, where SEP track accumulation rates are higher. In total, our dynamically integrated IDPs accumulated a factor of $\sim$2 less SEP tracks compared to the analytical, PR-drag only computation. Briefly, we note that use of the SEP flux obtained in Poppe et al. (2023), which is a factor of $\sim$25$\times$ higher than that determined in Keller et al. (2021), would yield model-predicted track density distributions in EKB grains greater than that observed in Keller & Flynn (2022); however, we again note that the nature of the discrepancy in the Fe-group SEP flux at 1 au is not presently understood. Thus, in light of our finding of fewer tracks in EKB grains at 1 au with the use of the Keller et al. (2021) track-inducing SEP flux, we consider below several additional ideas to explore in order to bring about a better understanding of the origin(s) of high track density IDPs collected at 1 au.

First, the results of our simulations have demonstrated a critical need for a better understanding of high-$Z$ SEP dynamics throughout the heliosphere. Due to a lack of such understanding, previous work has relied on observations and modeling of the behavior of the peak proton SEP flux as a function of heliocentric radial distance (e.g., He et al., 2017; He & Wan, 2019); however, it is possible, if not likely, that the average $Z>26$ SEP flux maintains a different radial scaling. Indeed, full-particle integration of both proton and Fe SEPs through Parker-spiral interplanetary magnetic fields has demonstrated varying degrees of electromagnetic drift as a function of the SEP charge-to-mass ratio (Marsh et al., 2013). A full understanding of high-$Z$ SEP dynamics would also account for variations in solar cycle including the effects of focusing versus defocusing interplanetary magnetic fields, the degree of scattering due to interplanetary turbulence, and the distribution of SEP source locations. Such simulations could be tested against our findings that a relatively shallower high-$Z$ SEP profile with exponential slope, $\alpha$$\sim$$1.0$ (i.e., see Figure 6), allows for a consistent data-model comparison for accumulated SEP tracks in EKB grains.

While high-$Z$ SEPs have been assumed here as the sole source of tracks observed within IDPs, one may consider other sources of high-energy particles that may contribute to track formation. Keller & Flynn (2022) considered the possibility that galactic cosmic rays (GCRs) could contribute to track formation, yet concluded this was unlikely as GCRs must penetrate on the order of meters in depth before depositing their energy and inducing track formation, a far greater depth than IDP radii considered here. Despite this, it is theoretically possible that GCR irradiation of EKB parent bodies with sizes meters and larger could provide an initial set of GCR-induced tracks before an individual EKB dust grain was generated (e.g., via mutual EKB parent body collisions) and released into interplanetary space. Stochastic increases in the GCR flux in the EKB could also occur during periods where the heliosphere passed through dense and/or cold interstellar clouds (e.g., Müller et al., 2006, 2008; Opher et al., 2024) or was subjected to supernovae ejecta (Fields et al., 2008; Miller & Fields, 2022). Either type of event could expose both the EKB parent bodies and the interplanetary dust populations in the outer solar system to increased fluxes of energetic particles; however, the present uncertainty in the timing, duration, and energetic particle intensity of such events currently prevents us from quantitatively assessing their potential contribution to track formation within EKB IDPs.

An additional source not considered by Keller & Flynn (2022) that are within the appropriate energy range for generating track formation are anomalous cosmic rays (ACRs). ACRs are a population of approximately 0.5$-$50 MeV/nuc energetic ions that likely originate from the acceleration of interstellar and interplanetary pickup ions at the distant heliospheric termination shock (or somewhere beyond) that stream inwards into the heliosphere proper (e.g., Klecker et al., 1998; Jokipii & Giacalone, 1998; Giacalone et al., 2022). The seed populations of ACRs come from three primary sources: (i) inflowing interstellar neutrals (e.g., Fisk et al., 1974), (ii) an ‘inner’ source of neutrals originating from solar wind interactions with interplanetary dust (e.g., Gloeckler & Geiss, 1998; Schwadron et al., 2000; Quinn et al., 2018), and (iii) an ‘outer’ source of neutrals from solar wind interactions with Edgeworth-Kuiper Belt dust grains (e.g., Schwadron et al., 2002; Schwadron & Gloeckler, 2007). ACRs are comprised of a broad composition reflecting both the interstellar neutral gas and solar wind sources from which they arise (e.g., Reames, 1999; Cummings & Stone, 2007). ACRs up to Ar ($Z=18$) have been reported at 1 au (Reames, 1999) while analysis of Voyager observations have reported ACR detections up to Fe ($Z=26$) (Stone & Cummings, 1997). Despite these Voyager observations, however, little remains known about the full intensity and distribution of Fe ACRs in the outer heliosphere. A population of Fe ACRs could contribute additional track formation to interplanetary grains, in particular those grains that originate from the EKB outwards, as ACR fluxes increase as one approaches the Termination Shock (located near $\sim$70-150 au; McComas et al., 2019). Further measurements and/or modeling of Fe (and heavier) ACRs in the outer solar system are clearly needed to better understand the potential contribution of Fe ACRs on IDP track accumulation rates.

We have neglected grain-grain collisions in our analysis here, however, they are likely to play some role in the distribution of track densities for grains that transit to 1 au. First, grain-grain collisions may decrease the fraction of EKB grains that successfully transit to 1 au, although previous simulations that implemented collisional-grooming algorithms (e.g., Poppe, 2016) still demonstrate a non-zero flux of EKB IDPs to 1 au. While not explicitly calculated in Poppe (2016), estimates of the EKB mass flux to 1 au in the fully collisional case are on the order of $\sim$1% the total mass to Earth (e.g., Nesvorný et al., 2010; Carrillo-Sánchez et al., 2016). The relatively low value of this estimate is primarily dictated by the collisional destruction of larger dust grains that possess the majority of the IDP mass flux. Grain-grain collisions may also affect the total accumulation of SEP tracks in IDPs, albeit in two competing directions. First, grain-grain collisions can effectively limit the lifetimes of grains entrained in MMRs, at least for grains with radii larger than $\sim$5 $\mu$m (i.e., see Figure 10, Koschny et al., 2019). Thus, the “enhancement” in SEP track densities that grains $>$5 $\mu$m may theoretically receive while trapped in MMRs could be severely limited as such grains are collisionally ground down on faster timescales. In contrast, however, grain-grain collisions may instead offer a path for an accumulation of SEP tracks starting in very large (e.g., $\sim$1 mm) grains that are then successively ground down in a cascade of smaller grains, each of which accumulates tracks during its own lifetime before disruption. A more quantitative assessment of these processes requires a combination of a collisional-grooming algorithm for interplanetary dust grains and a Monte Carlo-type method for simulating SEP track accumulation in individual grains as they are collisionally broken up.

If the primary populations of the Edgeworth-Kuiper Belt are not the source of high-track-density IDPs, one could consider alternative sources. Keller & Flynn (2022) briefly considered Oort Cloud cometary (OCC) grains as a possible source, yet dismissed it as unlikely due to expectations that OCC grains cross Earth’s orbit at relatively high speeds and thus, are likely to suffer thermal annealing effects during atmospheric entry. Indeed, dynamical simulations of OCC grains at 1 au tend to support this hypothesis (e.g., Nesvorný et al., 2011; Pokorný et al., 2018) and barring any new simulations that demonstrated a dynamical pathway for OCC grains to arrive at 1 au on relatively low-eccentricity, low-inclination orbits, we would agree with the conclusion that OCC grains are a less likely source high-track-density grains than the EKB. To be clear, we do note that neither Keller & Flynn (2022) nor our work here has actually calculated the predicted SEP track densities within OCC grains that reach 1 au. Such an exercise may be worthwhile to at least establish to first order if OCC grains can accumulate the observed number of tracks. If they do, this may provide motivation to revisit more critically the assumption that high velocity OCC grains will not maintain a full record of their tracks as they enter Earth’s atmosphere and decelerate.

Apart from OCC grains, one could also consider the possibility of the existence of a source of dust grains more distant than the main Edgeworth-Kuiper Belt on low-eccentricity, low-inclination orbits. While the ‘outer’ EKB dust grain population that we have considered here does not accumulate sufficient tracks (i.e., see the orange distribution in Figure 3), these outer grains are launched on relatively high eccentricity orbits that tend to bring their perihelia close to Neptune (between $\sim$30-40 au). These close encounters with Neptune tend to scatter the grains prematurely and thus, limit the degree of tracks they can accumulate. If, however, there was a low-eccentricity component to the outer EKB, such grains may remain dynamically decoupled from Neptune for much longer periods of time, allowing them to accumulate a greater number of tracks as they slowly drift inwards under the influence of P-R drag. For example, using the analytic approach to calculating track densities, a 25 $\mu$m radius, 2.0 g cm^-3 grain would accumulate $\sim$6$\times 10^{10}$ tracks cm^-2 (near the median observed by Keller & Flynn (2022)) if it originated at 100 au on a zero-eccentricity orbit. Curiously, we do note that the New Horizons Student Dust Counter, which is currently transiting through the EKB near $\sim$60 au, has recently reported higher than expected dust fluxes compared to earlier model predictions (Doner et al., 2024). While a full understanding of this model-data discrepancy is an active area of research, one hypothesis suggested by Doner et al. (2024) is the presence of a more distant population of the EKB as an additional, and previously unaccounted for, source of IDPs (see also Fraser et al., 2023). Continued exploration of the Edgeworth-Kuiper Belt and its ultimate extent will help to further test this intriguing hypothesis.

A study of SEP-induced track accumulation in interplanetary dust grains originating from the Edgeworth-Kuiper Belt has shown that such grains do not accumulate sufficient tracks in comparison to high-track-density grains reported in the stratospheric dust collection at 1 au (Keller & Flynn, 2022). In fact, dynamically integrated trajectories for EKB IDPs tend to accumulate a factor of approximately two less track density compared to analytical integrations with only Poynting-Robertson drag. Thus, with our current understanding of outer solar system dust dynamics as well as the magnitude and radial distribution of the flux of high-$Z$ SEPs throughout the heliosphere, the origin of such high-track-density grains remains an open problem. Despite this, research into several key areas could further improve and/or change our understanding. In particular, a better understanding of the dynamics of high-$Z$ ($Z>26$) SEPs throughout the heliosphere and the resulting average flux experienced by interplanetary dust grains is of key importance. Simulations of these SEP dynamics are well within reach using current computational methods (e.g., Marsh et al., 2013; Dalla et al., 2017a, b). Additionally, the presence of Fe and heavier anomalous cosmic rays in the outer heliosphere (e.g., Stone & Cummings, 1997) may be an additional source of tracks within IDPs. Further research into the flux and distribution of these ACR populations is thus warranted. One could also consider exploring how variations in the assumed IDP particle properties (e.g., material density, optical scattering properties) that control perturbing forces such as Poynting-Robertson and/or solar wind drag affect the overall track accumulation. Finally, a full reconciliation between lunar-derived SEP-induced track rates (Keller et al., 2021) and in-situ Fe-group SEP flux measurements (Poppe et al., 2023) is also required to fully understand SEP track accumulation in interplanetary dust grains.

The authors acknowledge support from NASA’s New Frontiers Data Analysis Program, grant #80NSSC18K1557. The authors also thank the reviewers for helpful comments that improved the manuscript.