Constraints on the Occurrence of 'Oumuamua-Like Objects

The galactic number density, n_iso, of a given transient interstellar object class can be expressed as,

$$\begin{eqnarray}&&{n}_{\mathrm{iso}}={R}_{\mathrm{env}}{N}_{\mathrm{iso}}{t}_{\mathrm{iso}}\,{V}_{{\rm{g}}}^{-1},\end{eqnarray} \tag{ 1 }$$

where R_env is the formation rate of the origin environment—starless molecular cloud cores for H₂ icebergs and extrasolar systems for most other interpretations—N_iso is the average number of 'Oumuamua-like bodies ejected into the ISM from each birth system, t_iso is the lifetime of the ISOs, and V_g ∼ 10⁶⁷ cm³ is the volume of the galaxy. If t_iso is greater than the Hubble time, then we substitute N_env, the number of ISO-spawning regions that have ever existed in the Milky Way, for R_env t_iso. In this situation, we would have,

$$\begin{eqnarray}&&{n}_{\mathrm{iso}}={N}_{\mathrm{env}}{N}_{\mathrm{iso}}{V}_{{\rm{g}}}^{-1},\end{eqnarray} \tag{ 2 }$$

for long-lasting ISOs.

Among the parameters in Equations (1) and (2), R_env is the best constrained for all birthplaces of interest in the Milky Way. Furthermore, the lifetime t_iso can be reasonably estimated via the material properties of the proposed compositions and knowledge of conditions in the local ISM. In contrast, N_iso remains relatively unknown. Therefore, much of this paper is dedicated to determining and reconciling this value with each hypothesis.

Except for the H₂ ice interpretation, each explanation of "Oumuamua relies upon ISOs that formed in extrasolar systems. Therefore, each of these protoplanetary "disk product" hypotheses demands the production of a similar number of objects from the typical star, adjusted by the lifetime of the characteristic material.

From our fiducial n_iso and V_g, we find that the Milky Way should currently contain of order 3 × 10²⁶ unbound 'Oumuamua-like objects. We assume that the galaxy has generated ISOs from protostellar disks over the last 10 Gyr with an average star formation rate of ∼3 yr⁻¹ (Shu et al. 1987) and find that each system must produce of order N_iso ∼ 10¹⁶ objects. If these bodies have effective spherical radius r_iso and bulk density ρ_iso, which we fiducially take to be 100 m and 1 g cm⁻³, respectively, then we estimate the total mass M_tot that must be ejected per star to be approximately

$$\begin{eqnarray}&&{M}_{\mathrm{tot}}\approx 7{M}_{\oplus }{\left(\displaystyle \frac{{r}_{\mathrm{iso}}}{100\,{\rm{m}}}\right)}^{3}\left(\displaystyle \frac{{\rho }_{\mathrm{iso}}}{1\,{\rm{g}}\,{\mathrm{cm}}^{-3}}\right).\end{eqnarray} \tag{ 3 }$$

This value is generally concordant with models of protoplanetary disk evolution. It is important to note that due to 'Oumuamua's poorly constrained albedo, physical size, and density, this required production could vary by orders of magnitude. Here, the fiducial size which we have adopted corresponds to a mass of order 10¹² g for an individual interstellar object.

In addition to its young inferred age, 'Oumuamua's inbound kinematics were temporally and spatially correlated with the Columba and Carina (COL/CAR) young stellar associations (Mamajek 2017; Gaidos 2018; Hallatt & Wiegert 2020; Hsieh et al. 2021). That is, the ISO was in these regions while they were forming new stars, so it is suggestive that 'Oumuamua may have formed there as well. Therefore, we consider the possibility of detecting a small body analog specifically from COL/CAR in the Pan-STARRS survey. Because these associations are younger than the galactic rotation period, the ISOs from these regions should only fill a volume comparable to that of the stars that comprise these moving groups. For this situation, we can modify Equation (2) by substituting the present volume of the COL/CAR stellar associations, V_local ∼ 10⁶ pc³ (Hsieh et al. 2021), for V_g, and only consider the number density in the Solar neighborhood.

While the number of counted members in stellar associations varies based on the classification methodology, we adopt the value of N_env = 100 stars between COL/CAR as an order of magnitude approximation to the data presented in Table 3 of Hallatt & Wiegert (2020). We assume that each protoplanetary disk ejects the fiducial 7 M_⊕ of primordial debris in the form of 10¹² g interstellar comets, as found in Equation (3). Spreading these objects uniformly over V_local provides a number density of 5 × 10⁻⁴ au⁻³ for ISOs that are conventional solar system analogues. Detecting a planetesimal from COL/CAR with Pan-STARRS would be between a 2–3σ event, according to our calculations in Table 1.

Levine & Laughlin (2021) considered theoretical constraints on forming ISOs composed of solid hydrogen at size regimes ranging from micron-sized dust to centimeter-sized hailstones to the kilometer-scale aggregates that would be required to form 'Oumuamua-like objects. Figure 1 summarizes the examined steps in a hypothetical formation pathway from that study to form H₂ objects. Because of the 3 K temperature requirement for H₂ deposition, Levine & Laughlin (2021) considered the starless cores of giant molecular clouds (GMCs) as formation sites. These frigid temperatures have not been observed in starless cores specifically, although CO(J = 1-0) excitation temperatures of 1 K have been recorded in the outflows in preplanetary nebulae (Sahai et al. 2017). While this observation did not imply that quiescent molecular cloud cores can reach these temperatures, it suggested that adiabatic expansion may cool regions below the temperature of the cosmic microwave background (CMB). Levine & Laughlin (2021) found that H₂ could only freeze onto coagulated dust grains in pockets of adiabatic expansion that are well shielded from electromagnetic radiation.

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Nonetheless, Levine & Laughlin (2021) found that the turbulence characteristic to starless cores may be conducive to forming kilometer-scale H₂ objects that, when weathered, could have properties resembling the size, shape, and composition of 'Oumuamua. If these hydrogen icebergs can grow to sizes such that they attract additional dust via gravitational focusing, they could retain enough ice (Walker 2013) after a journey through the ISM to match 'Oumuamua's nongravitational acceleration during the Solar encounter. Hoang & Loeb (2020) quantified H₂ destruction via drag heating, but this process did not necessarily apply to 'Oumuamua because of its small velocity versus the ambient interstellar matter. Since starless cores are probably magnetically supported (Shu et al. 1987; Kong et al. 2016), it is possible that dust plasma instabilities, such as magnetic resonant drag instabilities (Seligman et al. 2019; Hopkins et al. 2020), also play a role in the formation of these hydrogen icebergs.

The formidable temperature barrier implies that N_iso in Equation (1) may be zero for interstellar H₂ icebergs. If these ISOs do exist, however, the large amount of hydrogen gas in GMCs would suggest that 'Oumuamua-like cloud products could form via an inefficient formation process compared to the requirements for disk products. Nevertheless, the rapid sublimation in the ISM requires that these icebergs would have larger masses upon formation than the objects in other hypotheses. This would increase the implied mass of the galactic population and potentially contradict the limits from the mass budget, despite the larger overall hydrogen reservoir versus that of other substances. 'Oumuamua's correlation with COL/CAR, combined with the sub-100 Myr survival timescale of interstellar solid hydrogen, makes it improbable that an ISO with substantial H₂ passing by Earth would have originated from anywhere other than these associations.

Levine & Laughlin (2021) estimated the efficiency of building H₂ ice objects in the overall GMC complexes to compare with the star formation efficiency, and Hsieh et al. (2021) discussed forming objects of 'Oumuamua's present size in COL/CAR. Here, we discuss creating the required kilometer-scale progenitors in the failed cores. We assume, perhaps conservatively, that there were a similar number of star-forming and starless cores (Vázquez-Semadeni et al. 2005), the latter of which could produce H₂ rich ISOs. Taking the characteristic lifetime of 'Oumuamua-like objects to be longer than the age of these associations, we then set N_env = 100 and apply Equation (2).

To match the inferred ISO number density with the kilometer-scale progenitors from Levine & Laughlin (2021), each starless core must generate of order 10¹⁹ ISOs. Because rapid H₂ sublimation demands that these cosmic icebergs must be created with mass of order 10¹⁵ g to resemble 'Oumuamua when they reach the Solar System, this productivity would result in each core forming 4 M_⊙ of H₂ ice. This value is too high to reasonably be formed in small pockets of adiabatic expansion, although the 95% confidence interval's lower bound would only require that 0.1 M_⊙ of H₂ ice objects are born in each core.

The H₂ interpretation predicts the presence of both actively outgassing ISOs and their remnants. Because H₂ ice would be required to drive the nongravitational acceleration, 'Oumuamua would necessarily be a member of the former population in this hypothesis. Moreover, the objects rich in H₂ would necessarily be younger and found closer to their birthplaces, since sublimation removes the volatile, exotic ice on timescales faster than the galactic rotation period. In contrast, the long-lived remnant population could spread uniformly in the galaxy. The composition of the remnants would depend both on their origin environment and on the interstellar conditions though which they pass. Without their original H₂ ice endowment, however, their compositions would most likely be dominated by a combination of refractory and icy material acquired in the molecular cloud of origin.

If 'Oumuamua were an exotic H₂ iceberg, the fact that it would have still contained significant H₂ implies that the local concentration of active objects is higher than the average galactic number density of their inactive descendants. Furthermore, the stringent thermodynamic requirement for hydrogen deposition and increasing CMB temperature with redshift means that H₂ ISOs would be recent phenomena in galactic history (White 1996). For example, Levine & Laughlin (2021) found that H₂ deposition would be infeasible at reasonable starless core pressure for redshift z ≳ 0.1. We assume that the remnants without H₂ survive indefinitely in the ISM. Although they could experience breakup during stellar encounters, as seen in Solar System comets, the rate of close encounters for any given ISO is exceedingly low. Thus, the ratio of active to inactive cloud product ISOs would constrain the lookback time at which H₂ ice became possible in the Milky Way.

Assuming the same productivity, N_iso, per starless core for as long as H₂ deposition has been feasible, we compare the number density of 'Oumuamua-like objects from COL/CAR to that of their remnants to find,

$$\begin{eqnarray}&&f\left(\displaystyle \frac{{N}_{\mathrm{env}}}{{V}_{\mathrm{local}}}\right)=\left(\displaystyle \frac{{R}_{\mathrm{core}}{t}_{\mathrm{look}}}{{V}_{\mathrm{gal}}}\right).\end{eqnarray} \tag{ 4 }$$

Here, f is the ratio between these two number densities and N_env = 100 is the assumed number of starless cores for COL/CAR. Additionally, ${R}_{\mathrm{core}}{t}_{\mathrm{look}}$ is the rate of starless core formation multiplied by the lookback time at which H₂ iceberg formation became feasible, giving the number of systems that would have created 'Oumuamua-like objects over Galactic history. We have eliminated N_iso, implicitly assuming that it would be the same between COL/CAR and any other starless cores that form hydrogen ISOs. If the rate of failed cores is similar to star-producing ones, then the Milky Way can generate an overall ISO number density equal to the local one from COL/CAR (f = 1) in t_look ∼ 10 Myr.

This rapid formation of a Galactic population is shorter than the age of the COL/CAR associations. If the H₂ hypothesis is correct, then it would be statistically unlikely to observe an active iceberg instead of a remnant from the broader Galaxy. While this tension could be resolved if the failed cores in these specific moving groups became unusually cold, this degree of fine-tuning is not supportive of the H₂ hypothesis. Explanations requiring that the Solar System inhabit a special region are generally disfavored, and the hydrogen ice interpretation would demand this conclusion to be compatible with the inferred ISO population.

Desch & Jackson (2021) estimate that our Solar System ejected N_iso ∼ 2 × 10¹⁴ nitrogen ice collisional fragments in their Table 1, and then generalize this calculation to estimate the population of fragments in the Milky Way. We compactly reexpress this calculation as

$$\begin{eqnarray}&&{N}_{\mathrm{iso}}=\displaystyle \frac{{M}_{\mathrm{kb}}{f}_{\mathrm{big}}{f}_{{\rm{N}}}{f}_{{{\rm{N}}}_{2}}{f}_{\mathrm{surf}}{f}_{\mathrm{stick}}{f}_{\mathrm{coll}}{f}_{\mathrm{ej}}{f}_{\mathrm{ss}}}{{M}_{\mathrm{iso}}},\end{eqnarray} \tag{ 5 }$$

where the terms are defined as follows:

• 1.  
  M_kb: the mass of a typical extrasolar Kuiper Belt region.
• 2.  
  f_big: the mass fraction of the Kuiper Belt residing in objects large enough to purify nitrogen via hydrothermal chemistry.
• 3.  
  f_N: the mass fraction of nitrogen in these large KBO analogues.
• 4.  
  ${f}_{{{\rm{N}}}_{2}}$: the mass fraction of nitrogen on these objects converted to N₂.
• 5.  
  f_surf: the mass fraction of molecular nitrogen that outgasses and freezes in a surface ice layer.
• 6.  
  f_stick: the mass fraction of this surface N₂ ice layer that does not sublimate before the dynamical instability.
• 7.  
  f_coll: the mass fraction of the remaining surface nitrogen ice that is excavated from the KBOs via collisions.
• 8.  
  f_ej: the fraction of collisional shards from impacts that are ejected from the Solar System.
• 9.  
  f_ss: the stellar mass-weighted fraction of extrasolar systems that satisfy the conditions to form nitrogen fragments in this manner.
• 10.  
  M_iso: the mass of the N₂ collisional fragments upon ejection.

In their study, Desch & Jackson (2021) assumed that a Kuiper Belt of mass M_kb ∼ 35 M_⊕ would contain approximately 6 M_⊕ of material in objects large enough to support thick layers of surface N₂ ice (f_big ∼ 0.2). Given a mass fraction of nitrogen f_N ∼ 0.05, the perfect efficiency of geochemical processes in transporting pure N₂ to the surface (${f}_{{{\rm{N}}}_{2}}={f}_{\mathrm{surf}}=1$), and the expectation that these KBO analogues would retain all of this surface ice (f_stick = 1), then about 0.3 M_⊕ of N₂ ice would be exposed before impacts are capable of ejecting N₂ fragments.

During the ensuing and required dynamical instability of the giant planets, Desch & Jackson (2021) proposed that 0.043 M_⊕ of N₂ collisional fragments are generated and ejected into interplanetary space (f_coll ∼ 0.15). Of this mass, the study proposes that 0.008 M_⊕ survives to be ejected into interstellar space (f_ej ∼ 0.19) as shards with mass M_iso ∼ 2 × 10¹¹ g. In addition, Desch & Jackson (2021) suggested that only GKM stars can produce these fragments, so f_ss ∼ 0.5. Therefore, the resulting number of ISOs would be of order N_iso ∼ 1 × 10¹⁴ per exoplanetary system for galaxy-wide production. Because N₂ icebergs survive longer than the rotation period of the Milky Way, the spatial distribution of these ISOs should be nearly isotropic.

Considering a lifetime for N₂ icebergs of t_iso ∼ 2 Gyr, the optimistic upper bound on 'Oumuamua's age from Jackson & Desch (2021), with our assumed values for the star formation rate R_env and V_g, we find n_iso ∼ 2 × 10⁻⁴ au⁻³. This value is within a factor of a few of the one provided in Table 1 of Desch & Jackson (2021) specifically for nitrogen ice fragments. Nonetheless, Desch & Jackson (2021) claim that the Galactic reservoir of nitrogen shards corroborates the 2σ lower bound from Portegies Zwart et al. (2018). However, the number density applied for this comparison, of order 10⁻³ au⁻³, corresponds to the total population of shards and not just those of nitrogen ice. Considering only this subset revises n_iso down by a factor of 10 and places the observation of one such body by Pan-STARRS around the lower bound of the 3σ confidence interval. Thus, even with the assumed widespread geochemical differentiation of extrasolar KBOs and ubiquity of dynamical instabilities, 'Oumuamua's appearance would still be quite unexpected.

Given the unsatisfactorily low n_iso if 'Oumuamua-like N₂ fragments are formed via the mechanism proposed in Desch & Jackson (2021), we consider the extreme case for the maximum theoretical production from exo-KBOs. We set each fraction, f, in Equation (5) to unity except for f_N, which we leave as 0.05, in line with expectations from cosmic abundances (Draine 2011). From this estimate, we find N_iso ∼ 5 × 10¹⁶ and n_iso ∼ 0.1 au⁻³. Essentially, reconciling the n_iso estimate from Do et al. (2018) requires that all extrasolar Kuiper Belts convert the entirety of their cosmic abundance of nitrogen into 'Oumuamua-sized ISOs. Immediately, the widespread N₂ ice on present-day Pluto and Triton rules out this scenario for our Solar System.

In addition, we determine the fraction of nitrogen in the minimum mass Solar nebula (MMSN) that must be converted to N₂ icebergs to satisfy the inferred n_iso. Siraj & Loeb (2021) also examined constraints based on the MMSN, but investigated the mass budget required to build the KBO progenitors to N₂ fragments. Here, we consider the more ambitious upper bound of converting all available nitrogen to 'Oumuamua-like shards.

In both classic (Weidenschilling 1977) and more recent MMSN (Desch 2007) models, the protoplanetary disk mass is never above 0.1 M_⊙. Assuming that the entire cosmic abundance of nitrogen in this upper limit is converted to icebergs, we find the resulting number density would be of order 1 au⁻³. For this exercise to reflect the true occurrence of 'Oumuamua-like objects, it would require condensation and purification of N₂ far inside its ice line through unknown processes. If 'Oumuamua is representative of the most likely value for the galactic population of these N₂ icebergs, then approximately 10% of all nitrogen in protoplanetary disks must be incorporated in these ISOs.

The 'Oumuamua-like ISO formation pathway from Desch & Jackson (2021) requires impacts on bodies with purified surface N₂ ice: analogues of KBOs at least the size of Gonggong (∼600 km). Impact cratering is thoroughly described by Melosh (1989), including relationships between ejecta and projectile dimensions. While studies of the bulk properties of N₂ ice are limited, they are sufficient to acquire order-of-magnitude estimates of the impactor, crater, and ejecta characteristics.

Lightly shocked surface material is ejected in a process known as spallation (Melosh 1984). The interference between the compressional shock wave delivered by the impact and the tensional rarefaction wave that reflects off the free surface reduces the maximum pressure experienced by the material. However, the surface layer is accelerated upward by the pressure gradient from both waves, which enables some material to reach the escape velocity. Spall layers are the source of the large ejecta blocks, and the remainder of the ejecta is produced by the excavation flow of highly shocked material. Desch & Jackson (2021) attribute ejected material to the excavation flow; however, excavation velocities are at most between 1/3 and 1/5 of the peak particle velocity (Melosh 1989), which itself is upper-bounded by half the impact velocity, U/2. Therefore, it might be responsible for some secondary cratering effects, but is unlikely to be responsible for fragments that reach the escape velocity of the Pluto or Gonggong analogues. Implicit in the analysis of Desch & Jackson (2021) is that the entirety of the crater is ejected; however, one should restrict the analysis to the spall layer, which separates at the depth where the tensional pressure of the rarefaction wave equals the target's tensile strength σ_t . Per Melosh (1984), peak particle velocity v_p a distance r from the impact site may be calculated as,

$$\begin{eqnarray}&&{v}_{p}={C}_{V}\displaystyle \frac{U}{2}{\left(\displaystyle \frac{a}{r}\right)}^{1.87},\end{eqnarray} \tag{ 6 }$$

where the projectile radius and velocity are denoted as a and U, respectively, the exponent 1.87 is found empirically (Perret & Bass 1975), and the coupling constant C_V approximately accounts for differences between projectile and target density. The pressure from the shock near the surface is approximately P ≃ ρ_t c_L v_P , for target density and sound speed, ρ_t and c_L . Evaluating the pressures induced by the shock and rarefaction waves and performing a Taylor expansion to first order in depth z gives the depth of spall layer z_s as (Melosh 1984)

$$\begin{eqnarray}&&{z}_{s}\simeq \left(\displaystyle \frac{{\sigma }_{t}}{P(r)}\right)\left(\displaystyle \frac{\beta {c}_{L}{ \mathcal T }}{2d}\right)\left(\displaystyle \frac{r}{1-1.87\beta {c}_{L}{ \mathcal T }/r}\right),\end{eqnarray} \tag{ 7 }$$

Here, d is the equivalent depth of the explosion, ${ \mathcal T }=a/U$, and β is a factor of order unity related to the decay time of the stress pulse ($d/{c}_{L}=\beta { \mathcal T }$). Different projectile and target materials are incorporated as $d\simeq 2a\sqrt{{\rho }_{p}/{\rho }_{t}}$. Substituting in the ejection speed v_e ≈ 2v_p d/r (Melosh 1984), and making a further approximation ${ \mathcal T }{c}_{L}\ll \sqrt{{r}^{2}-{d}^{2}}$, one arrives at,

$$\begin{eqnarray}&&{z}_{s}\simeq \left(\displaystyle \frac{{\sigma }_{t}}{{\rho }_{t}{c}_{L}}\right)\left(\displaystyle \frac{d}{{v}_{e}}\right).\end{eqnarray} \tag{ 8 }$$

This depth is an upper limit to the thickness of spall layers. Flaws or other structural properties of the target may cause shallower layers to fragment. For ejection velocities exceeding ∼0.5 km s⁻¹, material within and below the spall layer experiences further fragmentation (Grady & Kipp 1980, 1987; Melosh 1989), a trend reproduced in numerical simulations (Melosh et al. 1992). The mean size of Grady–Kipp fragments, l_GK, may be estimated (Melosh 1989) through,

$$\begin{eqnarray}&&{l}_{\mathrm{GK}}=\left(\displaystyle \frac{{\sigma }_{t}}{{\rho }_{t}{v}_{e}^{2/3}\,{U}^{4/3}}\right)d.\end{eqnarray} \tag{ 9 }$$

Comparisons carried out by Artemieva & Ivanov (2004) and McEwen et al. (2005) showed that this approximation agrees (within a factor of ∼2) with more sophisticated models when predicting the largest size of ejecta fragments.

We consider the plausible sizes of fragments originating from a KBO impact, given the bulk properties of solid N₂. The maximum compressive stress of N₂ ice before fracture is about 9 MPa at 5 K, correpsonding to brittle failure mode (Yamashita et al. 2010). At larger temperatures, the ice switches to a ductile failure mode, and can only withstand compression of ≲1 MPa. The transition occurs at temperatures ∼30–40 K, depending on the strain rate. We adopt σ_t ∼ 1.4 MPa as the tensile strength of N₂ ice, as measured at 40 K (Pederson et al. 1998). The minimum ejection speed required by the N₂ hypothesis for 'Oumuamua is the escape velocity of Pluto, v_e ≥ 1.2 km s⁻¹. Escape of spall material necessitates an impact of at least twice the escape velocity U ≥ 2.4 km s⁻¹, if the projectile and target are composed of identical materials. At Pluto's distance from the Sun, projectiles should mainly be KBOs with densities ranging between 1 and 3 g cm⁻³ for high ice and rock fraction, respectively (Brown 2012). The mean encounter speed of a KBO with Pluto is 2.46 km s⁻¹ (Dell'Oro et al. 2013), which amounts to an impact speed of 2.73 km s⁻¹. This speed is only marginally above the threshold needed to eject spall material; many impacts will not eject any at all.

Desch & Jackson (2021) argued that, in the early Solar System, small KBOs were dynamically excited to speeds of ∼3.5 km s⁻¹ relative to large KBOs. For the following analysis, we adopt a nominal impact speed of U = 3.7 km s⁻¹ for excited KBOs where Pluto's escape velocity has been added in quadrature. We note that the analytic model (Melosh 1984) suggests that this assumption of more violent impacts than in today's Kuiper Belt is required to possibly eject material that could be a progenitor of 'Oumuamua. Additionally, we take the density of N₂ ice as ρ_t ≈ 1 g cm⁻³ (Trowbridge et al. 2016) and the longitudinal sound speed c_L ≈ 1.8 km s⁻¹ (Yamashita et al. 2010).

A spall layer 100 m thick ejected from Pluto requires d ≈ 150 km, using Equation (8). Assuming an unlikely projectile consisting of only rock, its diameter must be at least ∼90 km. As discussed above, the spall thickness is an upper bound of the typical size of high-speed ejecta, owing to the elastic energy within the spall plate and subsequent Grady–Kipp fragmentation (Equation (9)). The majority of spalled mass will be in the form of these smaller fragments. Even a rocky projectile still must be ∼250 km wide in order for 100 m ice chucks to survive finer fragmentation. In the case of a pure ice projectile, the diameter must be ∼450 km.

Statistics for KBOs with diameters exceeding 100 km are given by Bierhaus & Dones (2015). They showed that an impact on Pluto by such an object is unlikely over the past 4 Gyr and that the largest expected impactor is about 60 km. Singer et al. (2019) interpreted craters imaged by New Horizons using Schmidt–Housen–Holsapple scaling relations (Holsapple 1993; Housen & Holsapple 2011). With the exception of Sputnik Basin (which may have formed by impact of a 150–275 km diameter projectile, likely more than 4 Gyr ago), the remaining largest craters were formed by projectiles with diameters not exceeding ∼50 km.

We consider whether large-scale (>50 km) impacts could be responsible for the N₂ ice population postulated by Jackson & Desch (2021). One may estimate the ratio of ejected spall mass, m_ej to projectile mass, m_i , (Melosh 1984, 1985; Armstrong et al. 2002), using,

$$\begin{eqnarray}&&\displaystyle \frac{{m}_{\mathrm{ej}}}{{m}_{i}}=\displaystyle \frac{0.75{P}_{\max }}{{\rho }_{t}{c}_{L}U}\left({\left(\displaystyle \frac{U}{2{v}_{e}}\right)}^{5/3}-1\right),\end{eqnarray} \tag{ 10 }$$

where ${P}_{\max }\approx \beta {\sigma }_{t}$ is the maximum compressive pressure experienced by the ejecta (β ∼ 4). For the nominal values reported above, and assuming an impact speed of 3.7 km s⁻¹, we find m_ej/m_i ≈ 7 × 10⁻⁴. For example, an exceptionally large icy impactor of size 200 km and density 1 g cm⁻³ would produce about 3 × 10¹⁵ kg of spall, or 10⁷ fragments with mean radius 40 m (mass ∼2.4 × 10⁸ kg) determined from Equation (9). Desch & Jackson (2021) acknowledged that Pluto experienced of order unity (up to about 4) impacts of this scale; hence, there should be approximately a few 10⁷ spall fragments the size of 'Oumuamua ejected from Pluto—an estimate five orders of magnitude lower than the number that Desch & Jackson (2021) suggested are ejected into interstellar space. This striking difference arises mainly from three cratering-related processes:

• 1.  
  N₂ ice is relatively weak, and is easily fragmented into <10 m chunks during impacts exceeding 2–3 km s⁻¹.
• 2.  
  At least ≳2.4 km s⁻¹ impacts are needed to eject any lightly shocked material, which in turn reduces the maximum size of ejected fragment.
• 3.  
  Only a fraction of a percent of the impactor mass is ejected from the KBO analog.

These considerations significantly revise down the fragment production estimates of Desch & Jackson (2021), which relied on the assumption that the entirety of the crater is ejected via excavation flow, and that 50 m fragments are the most commonly produced size.

In order to validate the estimates in the previous subsection, we simulate a KBO impact on Pluto with the iSALE-2D (Dellen) hydrodynamical code (Collins 2014). The numerical setup is depicted in Figure 2. The code is based on the SALE algorithm (Amsden et al. 1980), and incorporates a number of sophisticated material models (Wünnemann et al. 2006; Melosh et al. 1992; Ivanov et al. 1997; Collins et al. 2004, 2011). Our simulation employs a Tillotson equation of state (EoS) for N₂. Specific heat and bulk modulus are obtained from Trowbridge et al. (2016) and Yamashita et al. (2010), respectively. We use an initial density of 0.995 g cm⁻³. The remaining EoS parameters are manually varied to fit to the Hugoniot profile used by Trowbridge et al. (2015). While the internal energies of complete (E_CV ) and incipient (E_IV ) vaporization are not provided in the literature, we take E_CV as one third of of the Tillotson E₀ parameter, and E_IV as one fourth of E_CV , which are roughly the same ratios as in the case of water ice (Melosh 1989). Our choices of E_IV and E_CV for N₂ are roughly an order of magnitude lower than those of water, reflecting N₂'s significantly higher volatility. Under the Tillotson EoS, iSALE-2D computes pressure from density and internal energy (P = P(ρ, E)) in three distinct regimes, each obeying a different functional form: compressed (E < E_IV ), transition (E_CV > E > E_IV ), and expanded (E > E_CV ). Similar to Trowbridge et al. (2015), we adopt a Lundborg strength model for N₂, using methane as a proxy for Simon melting parameters and shear strength (Haynes 1971). An H₂O ice layer in the target is modeled with the ice Tilloston EoS included with iSALE-2D. For H₂O, we use the strength and damage models of Johnson et al. (2016), with the same parameter values.

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It is emphasized that the simulations presented here are an approximation of real impact cratering processes. The simulations neglect potentially important parameters such as impact angle, the porosity of N₂ ice, the actual ice shell thickness, and the possibility of a subsurface ocean. Nevertheless, they still offer important insight into the pressures and temperatures experienced at the impact site, and the displacement of the target mass. We validated our simulation by first considering a 2 km s⁻¹ projectile and the same target layering as Trowbridge et al. (2015). We recover several qualitative aspects of their craters, including a central uplift when N₂ is added, steeper walls and deeper center compared to H₂O only, and the buildup of material at and beyond the crater rim.

We proceeded to simulate a KBO impact on Pluto involving a 3.7 km s⁻¹ projectile, as discussed in the previous section, and maintained the 3 km deep N₂ ice layer modeled by Trowbridge et al. (2015). After 200 seconds, the modified crater exhibited a more complex floor morphology, which was depressed at the center. The steep walls were slightly terraced, and the buildup at the crater rim formed a scarp (left side of Figure 2). The peak shock pressures, as recorded by a dense set of Lagrangian tracer particles extending 5 km deep and 10 km wide, agree within a factor of ∼2 of those predicted by the wave-interference model presented in Melosh (1984). The latter is shown as contours on the right side of Figure 2.

To further investigate the fate of high-speed ejecta, we filtered tracer particles to those which reached a height of at least 50 m while simultaneously having a positive vertical velocity component. Their phase space coordinates were transferred to massless test particles in a rebound N-body simulation (Rein et al. 2019), centered on a massive body with the physical characteristics of Pluto. Horizontal velocities were reoriented at random (without modifying their magnitudes) to simulate ballistic trajectories in three dimensions. It is important to note that this step has no effect on the distance that particles travel from the impact site. Figure 3 depicts some example trajectories for a subset of test particles. In total, about 0.12% of the ∼8000 particles from the excavated crater in iSALE-2D had sufficiently high velocity to escape, whereas the rest collided with Pluto.

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As an order-of-magnitude estimate of the corresponding mass, we note that approximately half of these tracer particles were classified as high-speed ejecta. The ratio of the mass excavated to the mass of the projectile was ∼100, yielding approximately 0.06 of the impactor's mass that escaped. This fraction is roughly 85× larger than that predicted strictly from the wave-interference model, which might possibly be attributed to inaccuracies in the model beyond ejection speeds of 1 km s⁻¹ (Melosh 1984), the adopted material properties in the iSALE-2D simulation (e.g., the impactor and target surface comprise different materials), or the ejection of some material from beneath the spall layer (Melosh 1985). Nevertheless, the coupled hydrodynamical and dynamical simulations confirm that only a minuscule portion of the excavated volume attains the velocity required to escape the KBO. This effect results in a downward revision of f_ej in Equation (5) and a corresponding decrease in N_iso in our Equation (1).

Oblique impacts could be responsible for an enhancement of mass ejected from the KBO. Simulated 10 km s⁻¹ asteroid impacts on Mars indicate that up to ∼100× more high-speed ejecta in oblique impacts than in vertical ones (Artemieva & Ivanov 2004); however, this applies only to the narrow range in impact angle near 30°, with more typical enhancements of order 10–30×. At 35 km s⁻¹, oblique comet impacts generate an enhancement only up to ∼12×. These factors do not provide sufficient revision to f_ej to be compatible with the N₂ hypothesis.

Seligman & Laughlin (2020) calculate 'Oumuamua's mass evolution and sublimation rate demanded by the observed nongravitational acceleration throughout the object's trajectory for a number of candidate ices. For this order-of-magnitude analysis, however, we follow Equation (4) from Jackson & Desch (2021) to compute the magnitude of the nongravitational force, F_ng, from outgassing of volatiles as

$$\begin{eqnarray}&&| {F}_{\mathrm{ng}}| =| {M}_{\mathrm{iso}}{a}_{\mathrm{ng}}| \approx \displaystyle \frac{1}{3}\left(\displaystyle \frac{{{dM}}_{\mathrm{iso}}}{{dt}}\right){v}_{\mathrm{jet}},\end{eqnarray} \tag{ 11 }$$

where M_iso is the ISO mass, a_ng is the magnitude of the nongravitational acceleration, and the jet velocity is

$$\begin{eqnarray}&&{v}_{\mathrm{jet}}\approx \tau \,\sqrt{\displaystyle \frac{8{{kT}}_{{\rm{s}}}}{\pi \mu {m}_{{\rm{H}}}}},\end{eqnarray} \tag{ 12 }$$

where T_s is the surface temperature of the ISO, μ is the molar mass of the outgassing particle, m_H = 1 amu, and τ is related to an average of the outflow velocites and the Mach number of the jet. We use τ ≈ 0.45, as suggested by Crifo (1987) and adopted in Section 2.3 of Jackson & Desch (2021). For an outgassing species x with production rate Q(x), we can write (dM_iso/dt) = Q(x)μ m_H.

For the magnitude of the nongravitational acceleration, we assume the model from Micheli et al. (2018), where 'Oumuamua's non-Keplerian trajectory depends on the inverse square of the heliocentric distance r_h:

$$\begin{eqnarray}&&{a}_{\mathrm{ng}}={A}_{1}{\left(\displaystyle \frac{1\,\mathrm{au}}{{r}_{{\rm{h}}}}\right)}^{2}.\end{eqnarray} \tag{ 13 }$$

Here, A₁ = 4.9 × 10⁻⁴ cm s⁻² is the radial nongravitational acceleration at r_h = 1 au, per the formalism of Marsden et al. (1973). From these equations, the production rate Q(x) can be expressed as,

$$\begin{eqnarray}&&Q(x)\approx \displaystyle \frac{3{A}_{1}{M}_{\mathrm{iso}}}{\mu {m}_{{\rm{H}}}{v}_{\mathrm{jet}}}{\left(\displaystyle \frac{1\,\mathrm{au}}{{r}_{{\rm{h}}}}\right)}^{2}.\end{eqnarray} \tag{ 14 }$$

In addition, the number density, n(x), of species x in the coma of an actively outgassing object can be calculated from Equation (1) in Ootsubo et al. (2012) as

$$\begin{eqnarray}&&n(x)\approx \displaystyle \frac{Q(x)}{4\pi {v}_{\mathrm{ex}}{r}_{\mathrm{nuc}}^{2}}\exp \left(\displaystyle \frac{-{r}_{\mathrm{nuc}}}{{v}_{\mathrm{ex}}{\tau }_{x}}\right),\end{eqnarray} \tag{ 15 }$$

where v_ex is the expansion velocity, r_nuc is the nucleocentric distance, and τ_x is the photodissociation timescale of the species. For this analysis, we approximate that v_ex ∼ 10 v_jet. Observations of CO and other volatile species in the comet Hale-Bopp's outflow demonstrated that v_ex ∼ 1000 m s⁻¹ once the gas is warmed by solar radiation (for example, see Figure 2 in Biver et al. 1997), which will satisfy this relation within a factor of order unity for either H₂ or N₂. Substituting Equation (14) into Equation (15), the number density may be expressed as,

$$\begin{eqnarray}&&n(x)\approx \displaystyle \frac{3{A}_{1}{M}_{\mathrm{iso}}}{320{\tau }^{2}{{kT}}_{{\rm{s}}}{r}_{\mathrm{nuc}}^{2}}{\left(\displaystyle \frac{1\,\mathrm{au}}{{r}_{{\rm{h}}}}\right)}^{2}\exp \left(\displaystyle \frac{-{r}_{\mathrm{nuc}}}{10\,{v}_{\mathrm{jet}}{\tau }_{x}}\right).\end{eqnarray} \tag{ 16 }$$

Equation (15) assumes a spherically symmetric outflow, although it should still hold for lines of sight behind the nucleus. We will apply this simple coma model to the candidate exotic ices—H₂ and N₂—in order to predict the number density of outgassing volatiles that may be found in future observations.

For a hydrogen-propelled 'Oumuamua at 1 au, we find v_jet ∼ 113 m s⁻¹ and use T_s = 6 K (Seligman & Laughlin 2020). With a photodissociation rate of ${\tau }_{{{\rm{H}}}_{2}}\sim 9\times {10}^{6}\,{\rm{s}}$ for a quiet Sun at this r_h (Huebner et al. 1992), the e-folding length for molecules to be destroyed is of order 10⁷ km. Thus, we can approximate the exponential term in Equation (16) to be unity for relatively small r_nuc. From these values, we can estimate the number density profile as

$$\begin{eqnarray}&&n\left({{\rm{H}}}_{2}\right)=1\times {10}^{5}\,{\mathrm{cm}}^{-3}\left(\displaystyle \frac{{M}_{\mathrm{iso}}}{5\times {10}^{10}\,{\rm{g}}}\right){\left(\displaystyle \frac{{10}^{8}\,\mathrm{cm}}{{r}_{\mathrm{nuc}}}\right)}^{2},\end{eqnarray} \tag{ 17 }$$

where we have based the fiducial mass on the estimate of Seligman & Laughlin (2020) for the case where ISO density ρ ∼ 0.5 g cm⁻³. We note that a pure hydrogen ice ISO would not reconcile the observed nongravitational acceleration, as the surface coverage fraction required for an oblate ellipsoid scales as $0.06({\rho }_{\mathrm{iso}}/{\rho }_{{{\rm{H}}}_{2}})$ (Seligman & Laughlin 2020). Objects denser than H₂ ice, as would be expected for heavily weathered bodies, would require higher hydrogen surface coverage.

Although hydrogen ice outgassing would be undetectable at infrared and optical wavelengths, H₂ can dissociate via ultraviolet photons. For example, any of the following pathways may occur (Feldman et al. 2004):

• 1.  
  H₂ + h ν → H + H (844.7 Å),
• 2.  
  H₂ + h ν → H ₂ ⁺ + e⁻ (803.67 Å),
• 3.  
  H₂ + h ν → H + H⁺ + e⁻ (695.8 Å).

For the above processes, we give the wavelength of the minimum possible energy photon in parentheses.

Emission from excited H₂ states has already been detected in Solar System small bodies by the Far Ultraviolet Spectroscopic Explorer (FUSE), a NASA spacecraft which launched in 1999 and was operational for almost a decade, and had wavelength coverage from 905Å to 1187Å. Specifically, Feldman et al. (2002) attributed three lines (1071.6Å, 1118.6Å, and 1166.8Å) from the comet C/2001 A2 (LINEAR) to fluorescence from solar Lyman-β photons. While these lines were attributed to H₂O ice, a similar signature could appear from hydrogen iceberg ISOs.

While simply confirming the presence of H₂ ice in 'Oumuamua-like objects would be a remarkable result, detailed studies of these ISOs could constrain their D/H ratios. Because these objects would necessarily form in dark, cold, optically thick regions in GMCs, cloud products should incorporate matter that is otherwise difficult to detect. There may be nontrivial fractionation in the ISM (Kong et al. 2016), but D/H ratios in actively outgassing H₂ ice objects could illuminate the chemical conditions in the starless cores from which they were born.

In the absence of a mechanism to purify the H₂ ice, these hypothetical ISOs would collect and retain volatiles less tenuous than H₂ along with refractory substances. Nevertheless, neither micron-sized dust nor volatiles endemic to molecular clouds such as CO were found to emanate from 'Oumuamua. This nondetection is still somewhat curious, even for the H₂ hypothesis, and it would imply that the ISO's outgassing was dominated by the exotic ice.

Similar to our calculation for hydrogen ice, we can determine the observational signature of a nitrogen coma at 1 au. With T_s = 25 K (Seligman & Laughlin 2020), we find jet velocity 61 m s⁻¹. This v_jet is slightly lower than what was published by Jackson & Desch (2021), although the python code provided with the manuscript returns this 61 m s⁻¹. We use ${\tau }_{{{\rm{N}}}_{2}}\sim 7\times {10}^{5}\,{\rm{s}}$ for a quiet Sun (Huebner et al. 1992), which gives an e-folding distance for photodissociation of ${v}_{\mathrm{ex}}{\tau }_{{{\rm{N}}}_{2}}\sim 4\times {10}^{5}\,\mathrm{km}$. Thus, we again set the exponential term in Equation (16) to unity and estimate the number density profile as

$$\begin{eqnarray}&&n\left({{\rm{N}}}_{2}\right)=7\times {10}^{3}\,{\mathrm{cm}}^{-3}\left(\displaystyle \frac{{M}_{\mathrm{iso}}}{{10}^{10}\,{\rm{g}}}\right){\left(\displaystyle \frac{{10}^{8}\,\mathrm{cm}}{{r}_{\mathrm{nuc}}}\right)}^{2},\end{eqnarray} \tag{ 18 }$$

for small nucleocentric distance ${r}_{\mathrm{nuc}}\ll {v}_{\mathrm{jet}}{\tau }_{{{\rm{N}}}_{2}}$.

Implicit in this fiducial size is the predicted albedo of 0.65 from Jackson & Desch (2021), and the study considers Pluto's overall albedo to represent a good match for 'Oumuamua. However, 'Oumuamua-sized nitrogen fragments would lose around 90% of their mass during the Solar encounter (Jackson & Desch 2021); this sublimation should uncover fresh ice with a potentially higher albedo. Instead of considering the weathered terrain covering most of Pluto and Triton as the best comparison, the relatively young, nearly pure N₂ terrain of Sputnik Planitia might be more in line with expectations for a nitrogen iceberg. Unlike the predicted albedo of 0.65 from Desch & Jackson (2021) and the reddish observed color of 'Oumuamua (Meech et al. 2017), however, Sputnik Planitia has an albedo of nearly unity and a bluish color (Olkin et al. 2017). Thus, a nitrogen fragment should match the color of Pluto in interstellar space but not necessarily after its strongest outgassing activity surrounding perihelion.

As with H₂, we expect N₂ outgassing to be detectable at ultraviolet wavelengths (Jackson & Desch 2021). Common photodissociation reactions for N₂ include (Huebner et al. 1992; and references therein):

• 1.  
  N₂ + h ν → N + N (1270.4 Å),
• 2.  
  N₂ + h ν → N ₂ ⁺ + e⁻ (796 Å),
• 3.  
  N₂ + h ν → N+ N ⁺ + e⁻ (510.4 Å).

In Solar System comets, attempts by the FUSE spacecraft to identify molecular nitrogen outgassing resulted in nondetections (Bockelée-Morvan et al. 2004). Because N₂ is one of the least spectroscopically active nitrogen-bearing species (Cochran et al. 2000), searches for this constituent have focused on the weak ${{\rm{N}}}_{2}^{+}$ (0, 0) band at 3914 Å. Furthermore, space-based observatories seem better suited to search for N₂ in comets (Feldman et al. 2004), given the plethora of molecular nitrogen in the Earth's atmosphere. Nonetheless, this feature was unambiguously identified from ground-based telescopes in the comet C/2016 R2 (Opitom et al. 2019a; Mousis et al. 2021). Moreover, the object's unusual composition led Desch & Jackson 2021 to suggest that it may be a collisional fragment from our own solar system. While not an interstellar object, the formation pathway would be consistent with that the N₂ hypothesis for 'Oumuamua.

Unlike 'Oumuamua, however, a bright visible coma and strong CO emission were also detected from C/2016 R2. Thus, these objects could not be directly analogous, since 'Oumuamua would require nearly pure N₂ to match the observational constraints. If 'Oumuamua-like ISOs do have N₂ as a dominant constituent, the aforementioned 3914 Å feature could be discoverable in future interlopers.

Solar radiation pressure was originally discussed and dismissed as important for 'Oumuamua (Micheli et al. 2018) because the magnitude of nongravitational acceleration would require a bulk density orders of magnitude lower than any other known small body. Nonetheless, Bialy & Loeb (2018) revisited this hypothesis and found that 'Oumuamua could be propelled by this phenomenon if its bulk density were ρ ∼ 10⁻⁵ g cm⁻³ or if it were very thin. Moro-Martín (2019a) examined the feasibility of building the ultraporous diffusion-limited aggregates from grains in protoplanetary disks, and Luu et al. (2020) proposed that a similar physical process may occur in the tails of fragmented comets. The former formation mechanism has no preference for 'Oumuamua's geometry, while the latter would result in less favored, but still-allowed prolate geometry.

The mechanical stability of these dust aggregates subjected to tidal torques around perihelion was demonstrated by Flekkøy et al. (2019). Furthermore, Seligman et al. (2021) demonstrated that the spin-state and thus, the lightcurve, of objects driven by solar radiation pressure is stable. Moreover, the creation of extremely porous aggregates would not deplete the mass reservoir of rocky and icy material in extrasolar systems. With N_iso ∼ 10¹⁶ and applying Equation (3) from Section 2, populating the galaxy with these objects requires roughly 7 × 10⁻⁵ M_⊕ for the fiducial size r_iso ∼ 100 m. This result introduces no tension with the mass budget of protoplanetary disks.

While this compatibility holds if objects are directly assembled from micron-sized dust grains, the proposed mechanism of Luu et al. (2020) requires a decameter-sized comet fragment to host the growing aggregate. Therefore, the theoretical upper bound on number density for these objects would be driven by the mass reservoir of the intermediary 10 m boulders. With boulders of density 0.6 g cm⁻³, then each protoplanetary disk must devote 4 × 10⁻³ M_⊕ of material to this formation pathway as determined from Equation (3). We have fiducially assumed that each boulder forms one ISO. Therefore, even this more mass-intensive channel could still easily satisfy the inferred ISO reservoir.

Despite the reconciliation with the required mass reservoir, there is no proposed or apparent destructive mechanism for these dust aggregates in the ISM. This implies that there should be no preference for kinematically young objects like 'Oumuamua. If the formation of these aggregates is widespread throughout the galaxy, then 'Oumuamua's LSR velocity would be anomalously low. Interestingly, the dust aggregate hypothesis does allow for a single protostellar disk in COL/CAR to populate the local region with n_iso ∼ 0.1 au⁻³ by ejecting of order 1M_⊕ of porous bodies. Thus, 'Oumuamua's kinematic age would suggest an origin from an abnormal protoplanetary disk in COL/CAR as opposed to an undiscovered, yet common astrophysical process. This interpretation would corroborate the conclusion from Moro-Martín (2018, 2019b) that 'Oumuamua could not be a member of an isotropic background population if it originated from an extrasolar system. This scenario's mass budget requires the direct assembly from Moro-Martín (2019a) as opposed to the fragment-mediated pathway from Luu et al.(2020).

If the grains in ultraporous dust aggregates consist mostly of cometary volatiles as presented by Moro-Martín (2019a) and Luu et al. (2020), then the ISOs would be subject to destruction during the Solar encounter. Taking water ice as an example, we find that all of the object's mass could be lost within 1 hour at 1 au. As 'Oumuamua received more than 10¹² erg cm⁻² of Solar flux while it was inside 2 au (Seligman & Laughlin 2020), the ISO would require substantial refractory substances to retain its structural integrity. This complete dessication, however, could increase the porosity and decrease the density, making propulsion by solar radiation pressure more effective.

Seligman et al. (2021) showed that carbon monoxide (CO) outgassing could reconcile the energetics of the nongravitational acceleration with outgassing. While this solar system volatile could place the ISO within known realms of small bodies, the Spitzer nondetection places strict limits on cometary activity from this substance during the observational window. Because the images were collected only during a 33 hour time frame, (Seligman et al. 2021) suggested that 'Oumuamua could have experienced sporadic jets and been in a low-activity state during the attempted Spitzer observation.

An explanation of 'Oumuamua as a solar system analog would be a priori compelling, as these comparatively benign objects were expected as interstellar interlopers before Pan-STARRS. If this ISO were a comet-like body, however, its inbound kinematics versus the LSR would imply an unexpectedly low age. Furthermore, 'Oumuamua's extreme aspect ratio would still make it an anomaly even if its bulk composition is not exotic. Population-level statistics will help constrain small body formation processes in extrasolar systems and determine whether this interpretation is viable.

Initially, it was speculated that 'Oumuamua may have been a Solar System object that was scattered onto a hyperbolic trajectory. However, Schneider (2017) found that this was unlikely due to the ISO's inbound direction from the galactic apex. Moreover, its orbital energy was too large to be the result from a single scattering event with any of the known or hypothetical giant planets (Wright 2017). While de la Fuente Marcos et al. (2018) hypothesized that 'Oumuamua may have been a perturbed Oort cloud object, all of these interpretations involving an origin in our own solar system would necessitate 'Oumuamua's physical attributes to be an extreme outlier among the population of known solar system small bodies of similar size.

Bialy & Loeb (2018) suggested that 'Oumuamua could be artificial, since no natural explanation has been perfectly satisfactory. Due to the uncertainty in the prevalence of such bodies, we cannot propose reasonable estimates for any parameters in Equation (1). Nevertheless, the theoretical stability of any ellipsoidal object's spin state under radiation pressure, including a lightsail, was demonstrated by Seligman et al. (2021).

One could posit that if 'Oumuamua were artificial, then attempts to detect radio signals from the object would have been successful. However, observations with the Robert C. Byrd Green Bank Telescope (Enriquez et al. 2018), the Murchison Widefield Array (Tingay et al. 2018) and the Allen Telescope Array (Harp et al. 2019) resulted in nondetections.

To explain the elongated geometry, Hansen & Zuckerman (2017), Rafikov (2018), and Katz (2018) offered hypotheses that 'Oumuamua's birthplace was a post-main-sequence star system. As an alternative, Jackson et al. (2018) and Ćuk, (2018) both proposed that 'Oumuamua was a rocky body ejected from a circumbinary system. However, the later discovery of 'Oumuamua's nonballistic trajectory has largely ruled out these interpretations.

While nongravitational effects have been detected in active asteroids (Hui & Jewitt 2017), the magnitudes of the resulting accelerations are significantly smaller for these objects than for 'Oumuamua. Although the magnitude of 'Oumuamua's nongravitational acceleration is among the highest when compared to those of solar system small bodies, its physical size is also among the smallest of the population for which this effect has been measured. Thus, this relatively high value for 'Oumuamua should be expected if its composition were similar to these previously observed objects. Members of the Manx (Meech et al. 2016) and Damacloid (Jewitt 2005) groups, although they are unusual objects for their locations in the solar system, could not be analogues for 'Oumuamua. Their low activity levels preclude them from attaining the non-Keplerian trajectory demanded for generic 'Oumuamua-like objects with typical cometary volatiles, and no exotic ices have been found.

Raymond et al. (2018) proposed that 'Oumuamua could be a fragment from a tidally destroyed small body, and Zhang & Lin (2020) demonstrated that this process would generally create a prolate geometry. Because typical cometary volatiles would fuel the nongravitational acceleration, this formation mechanism requires the progenitors to be abundant in CO or other energetically efficient propellants. However, the population constraints as described in Section 2 for any extrasolar system product would demand that a substantial fraction of the ejecta be converted to these tidally disrupted ISOs.

While the nature of 'Oumuamua remains unresolved, C/2019 Q4 (later renamed 2I/Borisov) was identified ³ in 2019 and immediately determined to be a cometary body. This second ISO—with inbound velocity v_∞ = 32.3 km s⁻¹ and eccentricity e = 3.35 ⁴ —was discovered before perihelion, allowing for detailed studies of its composition and evolution during its Solar encounter.

Unlike 'Oumuamua, Borisov displayed a brilliant visible coma. Optical images with the Hubble Space Telescope provided evidence for a nucleus size of 200–500 m (Jewitt & Luu 2019). While H₂O sublimation drove activity starting at 6 au (Fitzsimmons et al. 2019; Jewitt & Luu 2019; Ye et al. 2020), carbon-bearing and nitrogen-bearing species were also detected in the outflow throughout the ISO's trajectory (Opitom et al. 2019b; Kareta et al. 2020; Lin et al. 2020; Bannister et al. 2020). Notably, the coma was rich in CO compared to typical comets in the solar system (Bodewits et al. 2020; Cordiner et al. 2020). Dust in the cometary tail was found to have a color of $g^{\prime} -r^{\prime} =0.63\pm 0.03$ (Bolin et al. 2020; Jewitt & Luu 2019; Guzik et al. 2020), and there was a paucity of micron-size dust. Instead, most grains were larger than 100 μm (Kim et al. 2020).

In contrast with 'Oumuamua, Borisov was far brighter than the apparent magnitude limit for surveys such as Pan-STARRS. Thus, its observation does not as tightly constrain the galactic population of its class. Because pathways of traditional small body formation are better known (Chiang & Youdin 2010; Morbidelli & Raymond 2016) compared to those of 'Oumuamua-like ISOs, the population of Borisov-like objects may be best derived from theoretical estimates until VRO determines tighter observational constraints.

Gravitational focusing can increase the occurrence of stellar encounters for young ISOs such as 'Oumuamua over those such as Borisov. We quantify the impact parameter b_iso per Raymond et al. (2018) as

$$\begin{eqnarray}&&{b}_{\mathrm{iso}}^{2}={q}^{2}\left(1+\displaystyle \frac{{v}_{\mathrm{esc}}^{2}}{{v}_{\infty }^{2}}\right),\end{eqnarray} \tag{ 19 }$$

where v_∞ is the inbound ISO velocity relative to the Solar System and v_esc is the escape velocity from the Sun at perihelion distance q.

Although the nature and velocity distribution of 'Oumuamua-like objects is unknown, we take this first-detected member as representative. Thus, we use v_∞ = 26 km s⁻¹ and q = 0.25 au to find b ≈ 11q for these young ISOs. As a comparison, Borisov had impact parameter b ≈ 2q. Due to the Sun's velocity versus the LSR drawn from the dispersion of Population I stars, it is improbable for a given ISO to match the Sun's galactic velocity. Nonetheless, gravitational focusing can enhance the observation rate of kinematically young objects by a factor of a few. In the future, the typical impact parameter for ISOs will be determined by telescopes such as VRO.

Because Borisov-like small bodies originate in extrasolar systems, some proposed formation scenarios for 'Oumuamua-like objects would then require that the protoplanetary disk's mass reservoir be split between building these two types of ISO. In our previous analysis on the theoretical number density of disk product hypotheses, we have assumed that 'Oumuamua-like objects can harbor the entire available mass. Given Borisov's size and impact parameter, the mass density of these bodies is far lower than what's inferred for 'Oumuamua-like objects. Therefore, it seems as though more of the ejecta should be small objects without visible coma. While the lack of identifications of other Borisov-like objects is interesting, it does not create tension with constraints on 'Oumuamua-like objects. In reality, both 'Oumuamua and Borisov are members of a size distribution of ISOs (Bolin et al. 2020), and future surveys may discover a diverse population.

The forthcoming VRO/LSST will provide narrower constraints on the prevalence of interstellar objects. Provided that the discoveries of 'Oumuamua and Borisov were indicative of galactic reservoirs, then VRO should provide population-level statistics by detecting objects up to three magnitudes dimmer than Pan-STARRS (Trilling et al. 2017). Furthermore, it will identify ISOs early enough in their trajectories through the Solar System to permit extensive follow-up observations. Within the next decade, the timely detection of an ISO may lead to an in situ mission such as the ESA's Comet Interceptor (Snodgrass & Jones 2019), or the NASA concept study BRIDGE (Moore et al. 2021). Visiting one 'Oumuamua-like object would provide unparalleled detail on material that originated outside of our Solar System (Seligman & Laughlin 2018).

Table 2 outlines the predicted number of 'Oumuamua-like objects to be identified by VRO, N_VRO, as a consequence of the various interpretations. In addition, we discuss the number objects N_young with age less than 1 Gyr. For each interpretation, we assume that the ISOs have number density equal to the minimum of our fiducial n_iso as inferred from Pan-STARRS and the theoretical upper limit from their formation pathway. Simply from the occurrence rate of similar ISOs in the future, VRO could differentiate between the proposed interpretations for the first interstellar visitor.

If 'Oumuamua was a protoplanetary disk product, then future surveys will be critical to determining the prevalence of these objects which we would consider anomalous in our Solar System. By placing 'Oumuamua in the context of other ISOs, we can place our Solar System in the context of exoplanetary systems. The mass reservoir of protoplanetary disks can satisfy the inferred n_iso, so N_VRO should be similar to the prediction from the VRO/LSST team (Ivezić et al. 2019).

While hydrogen icebergs face perhaps insurmountable temperature barriers to formation, starless cores could provide a sufficiently large mass reservoir to supply the local Solar neighborhood with the inferred population of ISOs. Because of the transient nature of these objects, any future H₂ icebergs should mirror "Oumuamua's low LSR velocity. If this hypothesis is correct, it would suggest that any other objects with H₂ activity would most likely arrive from COL/CAR in order to reconcile constraints on the galactic population of their remnants. In contrast, the theoretical bounds on the reservoir of N₂ icebergs dictate that observing them should be rare. Notwithstanding the issues surrounding the cratering process's ability to excavate N₂ ice from exo-Plutos, the widespread formation of these collisional shards would still not predict the detection of one by Pan-STARRS. Even with a decade-long survey by VRO, it would be unlikely to detect another nitrogen iceberg. However, Desch & Jackson (2021) suggest that the population of H₂O shards could be nearly an order of magnitude higher than those composed of N₂. If these collisional byproducts do exist, then VRO may detect a water ice fragment.

VRO/LSST is also expected to expand the population of identified Solar System small bodies by at least tenfold (Ivezić et al. 2019). Because Desch & Jackson (2021) predicted that 0.1% of long-period comets gravitationally bound to the Sun could be collisional fragments from our Kuiper Belt, a naïve extrapolation suggests that VRO/LSST should identify at least several of these objects. While the aforementioned nitrogen-rich C/2016 R2 was mentioned as a candidate for this class of object by Desch & Jackson (2021), its spectrum was starkly different from that of 'Oumuamua (Mousis et al. 2021). If 'Oumuamua-like objects are N₂ icebergs, then the expanding small body catalog may begin to include more direct analogues originating in our solar system.

If 'Oumuamua was a dust aggregate, then the small mass budget required for a widespread galactic process would suggest that VRO will find similar objects—albeit with a wide inbound velocity distribution. Because Pan-STARRS would have seen one such object, there would be no a priori reason that observing an ultraporous object would be a fluke. Thus, N_VRO should be similar to previous predictions based on the identification of 'Oumuamua. In the scenario where these ISOs originated in one atypical protoplanetary disk from COL/CAR, then N_VRO ∼ N_young.

'Oumuamua-like ISOs may represent samples of frigid interstellar environments, extrasolar systems with divergent evolutionary tracks, planetary systems at different stages in their life cycle, or analogues of regions of our Solar System that are difficult to access. Although the window to gather data from 'Oumuamua has passed, deeper surveys such as VRO/LSST will permit detailed follow-up of future interlopers. Regardless of the final verdict on their composition, these interstellar objects will provide insight about previously unconsidered astrophysical processes.