Could 1I/'Oumuamua be an Icy Fractal Aggregate?

1I/'Oumuamua is the first interstellar interloper to be detected (Williams 2017). Even though it was the subject of an intense observational campaign, its brief visit left several key questions unanswered. One of them is the number density of free-floating 1I/'Oumuamua-like objects implied from the inferred detection frequency, an aspect that relates to 1I/'Oumuamua's origin. Based on expectations from planetesimal formation models and observations, studies prior to its detection had estimated that the number density of ejected free-floating planetesimals would be so low that the detection of one of these objects crossing the solar system would require the deep surveys of the Large Synoptic Survey Telescope (LSST) era and beyond (Moro-Martín et al. 2009). Therefore, even though the detection of interlopers had been anticipated for decades, the first detection with PanSTARRS came as a surprise. Based on a careful calculation of the PanSTARRS detection volume, Do et al. (2018) estimated the cumulative number density of 1I/'Oumuamua-like objects, assuming a 3.5 yr survey lifetime and that the object is representative of an isotropic background population. In Moro-Martín (2018, 2019), we found that their estimate is orders of magnitude larger than what would be expected from the ejection of planetesimals from circumstellar and circumbinary disks, and from the ejection of exo-Oort cloud objects under the effect of post-main-sequence mass loss and stellar encounters, even when considering the large uncertainties involved in our calculation (like the size distribution of ejected bodies). Other authors have reached a similar conclusion: the inferred number density is significantly higher than what would be expected in the context of a range of plausible origins (Gaidos et al. 2017; Laughlin & Batygin 2017; Trilling et al. 2017; Do et al. 2018; Feng & Jones 2018; Portegies Zwart et al. 2018; Rafikov 2018a; Raymond et al. 2018a, 2018b). This comparison is even less favorable when considering 1I/'Oumuamua's incoming velocity, found to be within 3–10 km s⁻¹ of the velocity of the local standard of rest (Gaidos et al. 2017; Mamajek 2017), as it only favors parent systems with low dispersion velocities. In Moro-Martín (2018, 2019), we argued that this large discrepancy in the number density likely indicates that 1I/'Oumuamua is not representative of an isotropically distributed population, favoring the scenario that it originated from a nearby young system (as suggested by its kinematics; Gaidos et al. 2017).

Another open question is its physical properties (size, shape, rotational state, and albedo). Observations with the Spitzer Space Telescope could not detect its thermal emission, with the 3σ upper limit at 4.5 μm leading to an effective spherical radius of less than [49, 70, 220] m and albedo greater than [0.2, 0.1, 0.01] (Trilling et al. 2018). Other estimates from visible/near-infrared observations lead to an effective radius in the range of 55–130 m (Bannister et al. 2017; Jewitt et al. 2017; Meech et al. 2017; Bolin et al. 2018; Drahus et al. 2018; Fraser et al. 2018), the uncertainties arising from its unknown shape and albedo. Based on its 2–2.5 mag variability (reduced to 1.5–1.9 when correcting for the phase angle of the observations; McNeill et al. 2018), it is estimated that 1I/'Oumuamua has an axis ratio ranging from 3 to 10, most likely in the 6 ± 1:1 range (McNeill et al. 2018). This would make it unusually elongated compared to solar system objects, while other authors suggest it could be unusually oblate (Belton et al. 2018).

The most recent puzzle regarding 1I/'Oumuamua is the 3σ detection of a non-gravitational acceleration observed in its outbound orbit, showing a dependency of ${\rm{\Delta }}a\propto {\left(\tfrac{r}{\mathrm{au}}\right)}^{n}$, with the best fit for n = −2, which has been interpreted as evidence of outgassing (Micheli et al. 2018). Because no gas or dust has been observed in 1I/'Oumuamua (Jewitt et al. 2017; Meech et al. 2017), Micheli et al. (2018) attributed the lack of activity to the presence of a thin insulating mantle. The newly released Spitzer results by Trilling et al. (2018), however, imply strict upper limits to the CO and CO₂ outgassing that result in overall outgassing levels that are significantly lower than previously allowed by other observations. Specifically, the Spitzer CO 3σ upper limit is four orders of magnitude lower than that invoked by Micheli et al. (2018) to account for the observed non-gravitational acceleration, challenging the outgassing scenario. Trilling et al. (2018) have suggested the existence of outgassing from a different gas species (unconstrained by Spitzer) and have put forward the proposal that it might be H₂O. However, under this scenario, even when adopting outgassing levels of CO and CO₂ at the 3σ upper limit, if one assumes that these species have a similar relative abundance with respect to H₂O as found in comets, the inferred level of H₂O outgassing would only be 1% of that required. This implies that for this scenario to work, the object would have to be devolatized of CO and CO₂ prior to Spitzer observations (Trilling et al. 2018). Another challenge is the expectation that the implied outgassing torques would have spun up the object in a timescale of few days, leading to its breakup (Rafikov 2018b). However, a recent study by D. Seligman et al. (2019, in preparation) of the rotational dynamics of 1I/'Oumuamua found that its observed stable rotation period could be consistent with the reported nongravitational acceleration if caused by outgassing from a jet launched from the substellar point of maximal solar irradiation.

Given the challenges to the outgassing scenario, Bialy & Loeb (2018) have suggested that the non-gravitational acceleration could be due to radiation pressure, $P={C}_{R}\tfrac{L\odot }{4\pi {r}^{2}c}$ (where C_R is of order unity and depends on the objects composition and geometry, and r is the distance to the Sun), that would produce an acceleration of $a=\tfrac{{PA}}{m}=\left(\tfrac{L\odot }{4\pi {r}^{2}c}\right)\left(\tfrac{A}{m}\right){C}_{R}$ $=\,4.6\,\times {10}^{-5}{\left(\tfrac{r}{\mathrm{au}}\right)}^{-2}{\left(\tfrac{m/A}{{\rm{g}}{\mathrm{cm}}^{-2}}\right)}^{-1}{C}_{R}\,\mathrm{cm}\,{{\rm{s}}}^{-2}$ (where A and m are the area and mass of the object, respectively). This acceleration has the same radial dependency as that found by Micheli et al. (2018) as the best fit for 1I/'Oumuamua's excess acceleration, ${\rm{\Delta }}a\,={a}_{0}{\left(\tfrac{r}{\mathrm{au}}\right)}^{n}$, with n = −2, and a₀ = (4.92 ± 0.16) × 10⁻⁴ cm s⁻². By equating the two expressions for the excess acceleration, Bialy & Loeb (2018) found that for radiation pressure to be responsible for the observed non-gravitational acceleration, the required area-to-mass ratio of 1I/'Oumuamua would have to be

$$\begin{eqnarray}&&\displaystyle \frac{A}{m}=\displaystyle \frac{1}{(9.3\pm 0.3)\times {10}^{-2}\,{C}_{R}}\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}.\end{eqnarray} \tag{ 1 }$$

They argued that for this condition to be fulfilled, the required physical properties would have to be that of a sheet 0.3–0.9 mm in width, suggesting that 1I/'Oumuamua represents a new class of thin interstellar material of an unknown natural or artificial origin (such as a lightsail). As an alternative to this planar-sheet scenario, and given the strict Spitzer upper limits to outgassing, in this Letter we assess whether a naturally produced mass fractal structure with a high area-to-mass ratio could contribute to a radiation-pressure-driven 1I/'Oumuamua.

Fractal structures exhibit self-similar and scale-invariant properties at all levels of magnification. They are found in many forms in nature and their formation processes involve an element of stochasticity (like particle collisions in a solution) in a turbulent circumstellar cloud, or in a protoplanetary disk (environments characterized by low local particle concentrations and large diffusion lengths). Interplanetary dust particles exhibit a fractal structure, and laboratory studies of analogs of their cores (unaffected by atmospheric entry or flash heating from solar flares) indicate that these aggregates are mass fractal with a mass fractal dimension of N_f = 1.75 (Katyal et al. 2014).

For a mass fractal composed of self-similar structures, the number of primary particles, N, scales as $N={\left(\tfrac{D}{{D}_{0}}\right)}^{{N}_{f}}$, where D₀ is the primary particle size (assuming a single-size distribution), D is the aggregate size, and N_f is the mass fractal dimension, an index that characterizes its space-filling capacity, i.e., the packing efficiency of the aggregate. N_f is in the range from 1 to 3, with N_f ∼ 3 corresponding to compact, dense structures and N_f ∼ 1 corresponding to "stringy" ones. The mass of the fractal, m, scales with the number of primary particles, $m\propto N\propto {\left(\tfrac{D}{{D}_{0}}\right)}^{{N}_{f}}$, while its volume, V, is V ∝ D³. The resulting bulk density, ρ, scales as $\rho =\left(\tfrac{m}{V}\right)\propto {D}^{{N}_{f}-3}$, i.e., it decreases as the aggregate size increases.

Following Bowers et al. (2017), who studied mass fractals in the context of marine flocs and their interaction with light, the area-to-mass ratio of a mass fractal is given by $\tfrac{A}{m}$, where the area is A = D² (i.e., not assuming that these irregular fractal structures have spherical symmetry), and the mass is $m=N{\rho }_{0}{D}_{0}^{3}={\left(\tfrac{D}{{D}_{0}}\right)}^{{N}_{f}}{\rho }_{0}{D}_{0}^{3}$, where ρ₀ is the primary particle bulk density, leading to

$$\begin{eqnarray}&&\displaystyle \frac{A}{m}=\displaystyle \frac{{D}^{2}}{{\left(\tfrac{D}{{D}_{0}}\right)}^{{N}_{f}}{\rho }_{0}{D}_{0}^{3}}={\left(\displaystyle \frac{{D}_{0}}{D}\right)}^{{N}_{f}-2}\displaystyle \frac{1}{{\rho }_{0}{D}_{0}}.\end{eqnarray} \tag{ 2 }$$

The area-to-mass ratio decreases as N_f increases because, as the structure becomes more compact, the primary particles hide behind each other. Within the limit of compact structures, N_f = 3, the area-to-mass ratio becomes $\tfrac{A}{m}=\tfrac{1}{{\rho }_{0}D}$, as expected for an object with uniform bulk density. For N_f = 2, the area-to-mass ratio, $\tfrac{A}{m}=\tfrac{1}{{\rho }_{0}{D}_{0}}$, becomes independent of the size D, as it can be seen in Figure 1. Equation (2) is not valid in the N_f = 1 limit because, as Bowers et al. (2017) pointed out, for these tenuous and stringy mass fractals A ∝ D (instead of A = D², assumed in the derivation of Equation (2)), which would lead to $\tfrac{A}{m}\propto \tfrac{1}{{\rho }_{0}{D}_{0}^{2}}$.

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The bulk density of a mass fractal is given by

$$\begin{eqnarray}&&\rho =\displaystyle \frac{m}{V}=\displaystyle \frac{{\left(\tfrac{D}{{D}_{0}}\right)}^{{N}_{f}}{\rho }_{0}{D}_{0}^{3}}{{D}^{3}}={\left(\displaystyle \frac{D}{{D}_{0}}\right)}^{{N}_{f}-3}{\rho }_{0},\end{eqnarray} \tag{ 3 }$$

and following Richardson et al. (2002), its porosity would be

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{Porosity} & = & 1-\displaystyle \frac{\mathrm{sum}\,\mathrm{of}\,\mathrm{primary}\,\mathrm{particle}\,\mathrm{volumes}}{\ \mathrm{bulk}\,\mathrm{volume}}\\ & = & 1-\displaystyle \frac{{{NV}}_{0}}{V}=1-\displaystyle \frac{{\left(\tfrac{D}{{D}_{0}}\right)}^{{N}_{f}}{D}_{0}^{3}}{{D}^{3}}=1-{\left(\displaystyle \frac{D}{{D}_{0}}\right)}^{{N}_{f}-3}.\end{array}\end{eqnarray} \tag{ 4 }$$

2.1. Application to 1I/'Oumuamua

We now compare the area-to-mass ratio calculated above using Equation (2), shown as the inclined lines in the top panel of Figure 1, to the value that would be required to support 1I/'Oumuamua's radiation pressure scenario (Equation (1)), shown as the horizontal black solid line. For a given set of parameters (D₀, ρ₀, and D, defining each of the inclined lines), the required area-to-mass ratio is achieved at the mass fractal dimension given by the intersection of the corresponding inclined line and the horizontal black solid line. The circles in the middle and bottom panels of Figure 1 show the bulk density and porosity of the corresponding aggregates. As the figure shows, for D = 98 m, 140 m, and 440 m, these bulk densities are ρ ∼ 9 · 10⁻⁶ g cm⁻³, 7 · 10⁻⁶ g cm⁻³, and 2 · 10⁻⁶ g cm⁻³, respectively, all of which imply a porosity ∼1. If we were to assume that only 10% (1%) of the non-gravitational acceleration is due radiation pressure, the comparison would be made to 10% (1%) of the $\tfrac{A}{m}$ value in Equation (1), shown as the horizontal dotted (dashed), black line in the top panel of Figure 1. The stars in the middle and bottom panels show the bulk density and porosity of the aggregates that would fulfill the above 1% condition. As the figure shows, for D = 98 m, 140 m, and 440 m, these bulk densities are ρ ∼ 9 · 10⁻⁴ g cm⁻³, 7 · 10⁻⁴ g cm⁻³, and 2 · 10⁻⁴ g cm⁻³, respectively, all of which also imply a porosity ∼1, specifically 0.9997, 0.9998, and 0.99993, respectively.

3.1. A Formation Scenario

3.2. Open Questions

1I/'Oumuamua is a known interstellar interloper exhibiting a non-gravitational acceleration in its outbound orbit that cannot be accounted for by outgassing, given its lack of cometary activity and the strict upper limits to outgassing revealed by Spitzer observations (unless the relative abundances of the common volatiles are very different from those found in comets). It has therefore been suggested that, rather than outgassing, the non-gravitational acceleration could be due to radiation pressure (Bialy & Loeb 2018). The required area-to-mass ratio would correspond to the physical properties of a thin sheet 0.3–0.9 mm in width that would have been produced by an unknown natural or artificial processes. As an alternative to this planar-sheet scenario, we assess whether a naturally produced, mass fractal structure with a high area-to-mass ratio could account for or contribute significantly to the observed non-gravitational acceleration observed for 1I/'Omuamua. We find that the required type of aggregate would have to be extraordinarily porous, with a density of ∼10⁻⁵ g cm⁻³. Such porous aggregates can naturally arise from the collisional grow of icy dust particles beyond the snowline of a protoplanetary disk, and we propose that 1I/'Oumuamua might be one of those ejected icy aggregates. There are many open questions that need to be addressed in order to assess the viability of this scenario, including how the aggregate would be affected by ram pressure from the gas (encountered in its parent system and during travel), by tidal disruption during ejection, and by collisions with interstellar grains and rotational spin-up during travel. This hypothesis is worth investigating because if 1I/'Oumuamua were to have such an origin, its discovery could open a new observational window on to study the of the building blocks of planets around other stars (generally limited to the two extremes of size distribution, the dust and the planets), and this can set unprecedented constraints on planet formation models.

A. M.-M. thanks the anonymous referee for very helpful suggestions that have significantly improved the manuscript. After this paper was in its final form, we learned about the work of Sekanina (2019) that proposes 1I/'Oumuamua is the porous debris resulting from the disintegration before perihelion of an interstellar comet.