# Interstellar Objects

Darryl Z. Seligmana and Amaya Moro-Martín bc CONTACT D. Z. Seligman Email:
<EMAIL_ADDRESS>aDepartment of Astronomy and Carl Sagan Institute, Cornell
University, 122 Sciences Drive, Ithaca, NY, 14853, USA; bSpace Telescope
Science Institute, 3700 San Martín Dr., Baltimore, MD 21218; c Department of
Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA

###### Abstract

Since 2017, two macroscopic interstellar objects have been discovered in the
inner Solar System, both of which are distinct in nature. The first
interstellar object, 1I/‘Oumuamua, passed within $\sim 63$ lunar distances of
the Earth, appeared asteroidal lacking detectable levels of gas or dust loss,
yet exhibited a nongravitational acceleration. 1I/‘Oumuamua’s brief visit left
open questions regarding its provenance which has given rise to many
theoretical hypotheses, including an icy comet lacking a dust coma, an
elongated fragment of a planet or planetesimal that was tidally disrupted, and
an ultra-porous fractal aggregate. The second interstellar object, 2I/Borisov,
was distinct from 1I/‘Oumuamua in terms of its bulk physical properties and
displayed a definitive cometary tail. We review the discoveries of these
objects, the subsequent observations and characterizations, and the
theoretical hypotheses regarding their origins. We describe 1I/‘Oumuamua and
2I/Borisov in the context of active asteroids and comets in the Solar System.
The discovery of these two objects implies a galactic-wide population of $\sim
10^{26}$ similar bodies. Forthcoming observatories should detect many more
interstellar planetesimals which may offer new insights into how planetary
formation processes vary throughout the Galaxy.

###### keywords:

Interstellar objects; comets; asteroids; meteoroids; planetary systems:
formation, protoplanetary disks, circumstellar disks; dynamical evolution and
stability; Solar System: formation; Oort cloud; galaxy: local interstellar
matter.

##  1 Comets in the Solar System

###  1.1 Historical Perspective

For hundreds of years prior to the discovery of 1I/‘Oumuamua and 2I/Borisov,
astronomers had predicted that the Galaxy would be filled with icy bodies
ejected from extrasolar planetary systems. Therefore, the existence of small
bodies of extrasolar provenance observed passing through our own Solar System
on hyperbolic trajectories was not inherently surprising. A full detailed
account of the historical perspective on cometary science can be found in [1]
including a discussion of interstellar comets.

As early as 1705, Edmond Halley considered the hypothesis that some comets
arrived from interstellar space [2]. Halley computed the orbits of 24 comets
and demonstrated that none of them had distinctly hyperbolic trajectories —
outlined in the Table captioned The astronomical elements of the motions in a
parabolick orb of all the Comets that have been hitherto duly observ’d. He
therefore concluded that the population of detected comets at the time had all
formed within the Solar System. Immanuel Kant further postulated that comets
formed from diffuse nebular material at large heliocentric distances but were
still gravitationally bound to the Sun [3].

On the other hand, the Italian astronomer Giuseppe (translated in English to
Joseph) Lagrange argued that the high eccentricities and inclinations of
cometary orbits was incompatabile with the nebular hypothesis. Although he
believed that comets formed within the Solar System, he showed that their
orbits could be produced by catastrophic disruption events from impacts with
planets. Lagrange argued that his calculations, in combination with the
nebular hypothesis, explained the entire census of celestial objects within
the Solar System [4].

In 1812, William Herschel obtained detailed observations of two comets, both
of which attained different brightness levels despite similar perihelia
distances. He outlined these findings in two papers published in 1812:
“Observations of a Comet, with Remarks on the Construction of Its Different
Parts” and “Observations of a Second Comet, with Remarks on Its Construction”
[5, 6]. The brightness differences led him to speculate that some comets may
originate beyond the Solar System, and that the variable activity levels could
be attributed to the accumulation of matter in interstellar space:

“Should the idea of age be rejected, we may indeed have recourse to another
supposition, namely, that the present comet, since the time of some former
perihelion passage, may have acquired an additional quantity (if I may so call
it) of unperihelioned matter, by moving in a parabolical direction through the
immensity of space, and passing through extensive strata of nebulosity.”

In 1813 Pierre-Simon de Laplace offered an alternative hypothesis to that of
Lagrange [7]. He argued that the eccentricities and inclinations of comets
could be explained if they originated from interstellar space, echoing the
hypothesis of William Herschel:

“Among the hypotheses that have been proposed on the origin of comets, the
most probable seems to me to be that of Mr. Herschel, which consists in
looking at them as small nebulae formed by the condensation of the nebulous
matter diffused with such profusion in the universe Comets.”

Laplace believed that comets formed via the condensation of nebular material
throughout the Galaxy and subsequently traveled from stellar system to system.
He calculated that 1/5713 comets within a 100000 au sphere around the Sun
would exhibit perihelia $<2$ au with strongly hyperbolic trajectories. He
concluded that the majority of interstellar comets would reach the Earth on
parabolic orbits, consistent with the distribution of cometary orbits observed
at that time. Unfortunately, Laplace neglected to include the proper motion of
the Sun with respect to the galactic motion in his calculations. Herschel had
speculated that the sun moved with respect to other stars in the Milky Way
after observing the motion of several nearby stars decades previously [8].

It was not until 1866 and 1867 that Giovanni Schiaparelli redid the
calculations from Laplace while including the proper Solar motion. He
demonstrated that the trajectories of interstellar comets would almost
entirely be significantly hyperbolic. Therefore, while provocative in nature,
the claim that interstellar comets were regularly seen throughout the Solar
System was largely disregarded.

###  1.2 Long and Short Period Comets

The comets in the Solar System are broadly categorized into two families: the
Long Period Comets (LPCs) and the Short Period Comets (SPCs), the latter of
which are commonly referred to as ecliptic comets or Jupiter Family Comets
(JFCs). The LPCs arrive uniformly across the sky with an isotropic
distribution of inclinations. This was attributed to an isotropic cloud of
comets as the source region of the LPCs, referred to as the Oort cloud [9].
The Oort cloud spans 50000 au and, based on the occurrence of LPCs, it has
been estimated to contain 1011-1012 km-sized Oort cloud objects [10, 11, 12].
The total mass of the Oort cloud is typically quoted as 1 Earth mass (M⊕), but
up to 20 M⊕ is allowable by the current data [13].

Meanwhile, the tendency for the SPCs — with orbital periods $<200$ yrs — to
lie within the ecliptic plane with low typical inclinations implies that these
objects come from a different source region than the Oort cloud [14, 15, 16,
17, 18]. It was therefore hypothesized that there existed a reservoir of icy
objects past Neptune that sourced the SPCs. A small fraction of these trans-
Neptunian objects would be gravitationally perturbed onto trajectories
interior to the orbit of Neptune. Subsequent dynamical interactions with the
giant planets would transfer some of these objects into the inner Solar
System[19, 20, 21, 22, 23, 24, 25, 26, 27]. This trans-Neptunian population
was verified in 1993 with the discovery of the first Kuiper belt object (KBO)
(other than Pluto) [28]. Thousands of trans-Neptunian objects have since been
identified and characterized [29, 30, 31, 32, 33]. It is now widely accepted
that the JFCs are transported into the inner Solar System via the Centaur
region between the giant planets [34, 35, 36, 37, 38, 39, 40, 41].

###  1.3 Ejection of Interstellar Comets by the Solar System

The existence of the Kuiper belt and Oort cloud has led to the realization
that the Solar System underwent a period of planetary migration. The migration
of the giant planets specifically would have scattered a large amount of
debris to large heliocentric distances, thereby populating the Kuiper belt and
Oort cloud. There are varying hypotheses regarding the details of the
planetary migration in the early Solar System. For a recent review of
different formation models we refer the reader to [42].

Some authors have claimed that the Solar System underwent a transient period
of violent dynamical instability in a model which is colloquially referred to
as the “Nice model” [43, 44]. Numerical experiments of this instability have
demonstrated that it would have generated $\sim 30M_{\oplus}$ of material in
interstellar comets. More general giant planet driven migration could also
eject a similar amount of material [45, 46].

The majority of this material would be ejected in the form of interstellar
comets. However, a fraction that has been estimated to be between 1-10$\%$
remained in the Solar System due to the effect of galactic tides and stellar
flybys. These objects, now protected from further interactions with the giant
planets and from gravitational ejection, remain bound with eccentricity e $<1$
[45, 47, 12, 48]. These processes likely generated the present day Kuiper belt
and Oort cloud.

Figure 1: The measured nongravitational accelerations of Short-Period Comets
(teal) and Long-Period Comets (purple). The three panels show the radial
(left), transverse (middle) and out-of-plane (right) components of measured
accelerations. Nongravitational accelerations are taken from the JPL Small
Body Database.

###  1.4 Cometary Outgassing

Comets within the Solar System are generally detected via their distinct and
explosive coma — the gas surrounding the nucelus — along with dusty cometary
tails. These coma form when solar radiation received at the surface of the
comet produces an outflow of gas and dust. The energy from the solar
irradiation first powers the phase transition of the surface or subsurface ice
into gas in a process called sublimation. Next, the radiation energy is
converted into kinetic energy which heats the gas to the thermal speed to
power the outflowing jet. Dust particles and debris that are either residing
on the surface of the comet or trapped within the ice typically travel along
with the gas in the outflow. This entire process produces a cometary outflow
and the dusty tail that, in some cases, is detectable from Earth. Solar
photons are then reflected off of the surface of these dust grains, which
gives rise to the beautiful cometary tails. The wavelengths of light that are
reflected depends on the size of the dust grains. For example, optical photons
are reflected by $\sim$ micron-sized dust grains. This dust production can
make the comet orders of magnitude brighter.

This mass loss produces a recoil effect on cometary nuclei [49, 50]. The force
of the outflowing material can produce a nongravitational acceleration of the
nucleus, typically written as $\vec{\alpha}_{ng}$. A formalism to describe the
nongravitational accelerations of comets was introduced by [51] as,

$\vec{\alpha}_{\rm
ng}=\bigg{(}\underbrace{A_{1}\hat{\mathbf{r}}}_{\textrm{Radial}}+\underbrace{A_{2}\hat{\mathbf{t}}}_{\textrm{Transverse}}+\underbrace{A_{3}\hat{\mathbf{n}}}_{\textrm{Out-
of-plane}}\bigg{)}\,\underbrace{g(r_{H})}_{\textrm{Radial dependance}}\,.$ (1)

In Equation 1, $\hat{\mathbf{r}}$, $\hat{\mathbf{t}}$, $\hat{\mathbf{n}}$ are
the radial, transverse, and out-of-plane directions with respect to the orbit
of the comet. The $g(r_{H})$ function, or Marsden function, is a function that
parametrizes the dependence on the heliocentric distance $r_{H}$. The
magnitudes of the three components of the acceleration are $A_{1}$, $A_{2}$,
and $A_{3}$, normalized to a heliocentric distance of $r_{H}=1$ au.

This recoil acceleration is related to the amount of mass lost in the outflow,
written as $dM/dt$ with speed $V_{s}$. If the outflow is perfectly collimated
in one direction — typically thought to be normal to the surface — the outflow
imparts momentum in one direction. If the outflow is completely isotropic then
the change of momentum perfectly cancels. We parametrize the degree of
collimation in the outflow with the parameter $k_{R}$, where $k_{R}$ = 1 and
$k_{R}$ =0 correspond to the collimated and isotropic cases, respectively.
Realistically, cometary outflows are somewhere between these two extremes and
$0<k_{R}<1$. Assuming that the comet has a spherical nucleus with radius
$r_{n}$ and bulk density $\rho_{\textrm{bulk}}$, the mass loss can be written
as,

$\frac{dM}{dt}=\,\bigg{(}\,\underbrace{4\pi
r_{n}^{3}\rho_{\textrm{bulk}}\bigg{/}3}_{\textrm{ Mass of
Nucleus}}\,\bigg{)}\,\bigg{(}\,\underbrace{|\vec{\alpha}_{ng}|\bigg{/}k_{R}V_{s}}_{\textrm{
Rate}}\,\bigg{)}\,.$ (2)

The velocity of the outgassing species is related to the thermal speed. For
example, H2O ice interior to 2 au has a sublimation temperature $T\sim$ 200 K
which corresponds to a velocity $V_{s}\sim$ 500 m s-1. This effect has been
measured on a subset of comets in the Solar System. In Figure 1, we show
measured nongravitational accelerations of Short and Long Period Comets.

###  1.5 Composition of Comets

Cometary tails are typically observed in optical wavelengths via the
reflection of solar photons off of micron-sized dust particles in the
outflows. However, emission and absorption of photons through the gas coma can
also be measured spectroscopically, providing a direct probe of the volatile
content of the coma. Therefore, the composition of the sublimating gas itself
in the coma has been directly measured in many cases. This volatile
composition can be related to the bulk composition of the comet, with the
caveat that it only represents the species active at the time of the
observation. Subsurface or inactive surface ices of other species may be
present in the nucleus but not the coma, thereby evading detection at any
given point during an apparition.

Despite these complications, the volatile content of a large set of comets has
been measured. The majority of comets consist primarily of H2O ice [52, 53,
54, 55, 56]. The next two most abundant volatiles in comets are CO2 and CO
[56]. Other carbon and nitrogen species can be abundant as well including CH4,
C2H2, C2H6, CH3OH, NH3 and HCN (see Figure 2 in [57]). In Figure 2, we show
typical compositions of carbon enriched and carbon depleted Solar System
comets.

Figure 2: The typical compositions of carbon enriched and depleted Solar
System comets. This is a generalized version of an analogous figure in [58],
and adapted from [59]. The carbon depleted comet is representative of many of
the Solar System comets for which production rate measurements of CO2, CO and
H2O exist (see Table 1 in [59]). The carbon enriched comet is C/2006 W3
Christensen [60].

The composition of a comet can be linked to its formation location within the
protoplanetary disk that initially formed from the Solar nebulae. The
temperature of the ambient gas in the disk decreases with increasing distance
from the Sun. Therefore, certain volatile species only freeze onto dust grains
exterior to a characteristic temperature front, or snowline. For example, it
is believed that in the protosolar disk, H2O and CO were frozen exterior to
the current day orbits of Jupiter and Neptune, respectively. An overview of
cometary composition measurements, including measured production rates of CO,
CO2 and H2O, was provided by [61]. Based on the lack of hypervolatiles
detected in the coma of most comets, they argued that the majority of comets
formed in the giant planet region, where these hypervolatiles would not exist
as ices to be incorporated into comets. The Akari spacecraft provided a
homogeneous survey of CO2, CO and H2O production rates in Solar System comets
[60]. This provides a further line of evidence that the Kuiper belt and Oort
cloud objects formed at closer heliocentric distances and were subsequently
scattered outwards. However, it is important to note that this simplified
picture does not incorporate the, potentially significant, post-formation
processing that also removes volatiles and hypervolatiles from comets.

##  2 1I/‘Oumuamua

###  2.1 Discovery

The first interstellar object was discovered by Robert Weryk on 2017 October
19 from Haleakalā on Maui, Hawaii [62]. It was identified during the course of
typical operations of the Pan-STARRs project [63], a NASA funded all-sky
survey optimized for detecting small Solar System bodies. The survey uses two
1.8-meter telescopes and associated gigapixel detectors on the summit of
Haleakalā. It is sensitive to a limiting magnitude of V = 22 and produces
nightly images that have $\sim 6000\,{\rm deg}^{2}$ resolution.

The object was initially flagged as a potentially hazardous near-Earth object
(NEO) — a population of small bodies from the asteroid belt that have been
gravitationally perturbed onto Earth crossing trajectories. After only a few
days of intensive and globally coordinated follow-up observations, the orbit
of the object was confirmed to be hyperbolic with an eccentricity $e=1.198$.
The possibility that it was a Solar System object that had been
gravitationally perturbed onto an unbound trajectory was quickly ruled out
[64, 65]. The hyperbolic trajectory therefore confirmed that the object could
not have originated from within our Solar System and definitively formed
elsewhere. It was discovered when it was $\sim$ 63 lunar distances from the
Earth, after it had reached its closest approach to the Sun on 2017 September
9 and as it was rapidly departing the Solar System. The object had a closest
approach distance to the Sun of $q\sim 0.255$ au and inclination
$i=122.8^{\circ}$.

There was explosive interest in the object after it was announced to be
interstellar, both from the scientific community and from the general public.
Due to its close proximity to the Earth and its resulting rapid sky motion,
the object was only observable for $\sim 4$ weeks with ground based
telescopes. There was a global scramble to observe the rapidly moving object
and director discretionary time was awarded to observe it on many major
telescopes. The last successful ground based observation of the object was on
2017 November 21. In the following subsection, we review all of the
measurements obtained of the rapidly fading object. For recent reviews, see
[66] and [67].

###  2.2 Observations

Figure 3:  An image of 1I/‘Oumuamua taken with the 2.5 m Nordic Optical
Telescope on 2017 October 26. The object displays no distinct cometary tail.
In the figure, $r_{H}$ corresponds to the heliocentric distance of the object
when the image was taken. This figure has been reproduced from [68].

Immediately following the announcement of the discovery of the object, [69]
obtained the first optical spectrum reflected from its surface on 2017 October
25 with the Palomar 5-meter Hale telescope. The spectrum spanned from 520 to
950 nm and was entirely featureless with a reddened slope. Further imaging and
spectroscopic observations were taken of 1I/‘Oumuamua the following night with
the same telescope that indicated a consistently reddened surface color [70].

In a paper often credited with the discovery of 1I/‘Oumuamua, [71] reported
time resolved photometric observations of the object from the nights of 2017
October 25, 26 and 27. These observations included 3.5 hr on the Very Large
Telescope (VLT) 8-meter telescope, 3.5 hr on Gemini south, 3 hr on the Keck
10-meter telescope, 9 hr on the United Kingdom Infrared Telescope (UKIRT), and
8 hr on the Canada–France–Hawaii telescope (CFHT). Deep stacks of the images
showed no evidence of cometary activity or dust tail.

In [68], observations were reported on the nights of 2017 October 25, 26, 29
and 30 with the 2.5-meter diameter Nordic Optical Telescope (NOT) and 4.5 hr
on the WIYN telescope, located at Kitt Peak National Observatory in Arizona.
They measured the optical colors of the nucleus to be B-V $=0.70\pm 0.06$, V-R
$=0.45\pm 0.05$ and found a lack of micron-sized dust particles. Figure 3
shows an image of 1I/‘Oumuamua taken with the NOT telescope, clearly lacking a
dust tail and apparent coma.

Spectroscopic observations of 1I/‘Oumuamua were reported in [72], with data
from the 4.2-meter William Herschel Telescope (WHT) on La Palma on 2017
October 25 and the X-shooter spectrograph located at the European Southern
Observatory 8.2 m Very Large Telescope (VLT) on 2017 October 27. The resulting
spectrum covered 0.3–2.5 $\mu$m, and was also featureless and reddened.
Photometric observations (8.06 hr) were reported by [73] obtained with the
Gemini North 8.1-meter telescope on 2017 October 27 and 28 with extremely high
temporal cadence, resulting in 431 r’-band images. Additional spectroscopic
observations were described by [74] obtained with the Gemini telescope (2 hr)
and the 4.2 m William Herschel Telescope (WHT) (2 hr), on 2017 October 29 and
30, respectively. One those same dates, [75] obtained observations (4 hr)
using the Apache Point Observatory (APO) ARCTIC camera on the 3.5-meter
telescope (2017 October 29) and [76] obtained photometric data (2.8 hr) with
the Lowell Observatory 4.3-meter Discovery Channel Telescope (DDT) (2017
October 30).

The NASA/ESA Hubble Space Telescope (HST) alloted 9 orbits of time to monitor
1I/‘Oumuamua. These data were taken with the UVIS channel from the Wide-Field
Camera 3 (WFC3) using the F350LP filter. These observations occurred during
2017 November, December and 2018 January over all 9 orbits. Photometric
brightness variations were reported during 2017 November 21 and 22, and the
remaining observations provided astrometric measurements as well [77]. They
also presented data in the same paper with the CFHT MegaCam imager from 2017
November 22 and 23 and the Magellan-Baade 6.5-meter telescope at Las Campanas
Observatory from 2017 November 21, 22 and 23. They compiled a composite light
curve over a 29.3 day period spanning about 0.13 au of the trajectory
containing a total of 818 photometric observations of the object reported by
[71, 75, 74, 73, 78, 68, 76, 77].

Table 1: Summary of all measured upper limits on production rates of various volatile species and dust from 1I/‘Oumuamua. Note that the measurement indicated with ∗ had a typographical error which was later fixed.  Species | Physical Property | Value | Distance | Reference
---|---|---|---|---
CN | Q(CN)[molec s-1 ] | $<2\times 10^{22}$ | 1.4 au | [70]
C2 | Q(C2)[molec s-1 ] | $<4\times 10^{22}$ | 1.4 au | [70]
C3 | Q(C3)[molec s-1 ] | $<2\times 10^{21}$ | 1.4 au | [70]
OH | Q(OH)[molec s-1 ] | $<1.7\times 10^{27}$ | 1.8 au | [79]
CO2 | Q(CO2)[molec s-1 ] | $<9\times 10^{22}$ | 2.0 au | [80]
CO∗ | Q(CO)[molec s-1 ] | $<9\times 10^{21}$ | 2.0 au | [80]
CO | Q(CO) [molec s-1 ] | $<9\times 10^{23}$ | 2.0 au | [81]
Dust | Q(Dust)[kg s-1 ] | $<1.7\times 10^{-3}$ | 1.4 au | [71]
Dust | Q(Dust)[kg s-1 ] | $<2\times 10^{-4}$ | 1.4 au | [68]
Dust | Q(Dust)[kg s-1 ] | $<10$ | 1.4 au | [70]

In addition to these detections of 1I/‘Oumuamua, several attempts to observe
the object resulted in non-detections. Some of these provided critical upper
limits on the production rates of dust and certain volatile species. [70]
attempted to observe 1I/‘Oumuamua with the Canadian Meteor Orbit Radar, and
the non-detection provided upper limits on the production of CN, C2 and C3
(Table 1). An upper limit on the production rate of OH via the OH 18-cm line
(Table 1) were reported by [79] based on 4 hr of observations with the Green
Bank Telescope on 2017 November 12.

The Spitzer Space Telescope observed 1I/‘Oumuamua for 32.6 hr on 2017 November
21 and 22. These observations were taken with the 4.5 $\mu$m band in the IRAC
channel 2, which would have detected fluoresence of carbon-based molecules
such as CO or CO2. However, these observations resulted in a non-detection
which provided an upper limit on the production of CO and CO2 of the object
[80] (Table 1). Note that the production of CO contained a typographical error
and was later corrected by [81].

A precovery of 1I/‘Oumuamau prior to perihelion from 2017 September was
attempted by [82]. Their search for the object in extant data from Solar
TErrestrial RElations Observatory (STEREO) and the Solar and Heliospheric
Observatory (SOHO) resulted in nondetections.

Several teams attempted to detect radio signal from 1I/‘Oumuamua, all of which
were unsuccessful. Data were obtained with the Robert C. Byrd Green Bank
Telescope beginning on 2017 December 13 [83], the Murchison Widefield Array
(MWA) on 2017 November 28 [84] and the Allen Telescope Array from 2017
November 23 through December 5 [85]. All of these upper limits on production
rates are summarized in Table 1.

###  2.3 Nucleus Properties

####  2.3.1 Size

The size of asteroids can be related to their absolute magnitude [86] with the
following relationship,

$2\bigg{(}\,\frac{r_{\rm
n}}{1\textrm{km}}\,\bigg{)}=\,\bigg{(}\,\frac{1329}{\sqrt{p}}\,\bigg{)}\,10^{-0.2\,H}\,.$
(3)

In Equation 3, $H$ is the absolute magnitude inferred from the brightness and
geometry of the orbit (H = 22.4 for 1I/‘Oumuamua), $p$ is the geometric albedo
and $r_{\rm n}$ is the radius in kilometers of the assumed to be spherical
nucleus. For the case of asymmetrical shaped objects, $r_{\rm n}$ is estimated
as the effective radius. This is approximated as the circular cross-section of
an ellipse with aspect ratio $a:b$, and therefore $r_{\rm n}=(ab)^{1/2}$. The
albedo is a measure of the fraction of light reflected off of the surface
versus absorbed. The albedo of nitrogen ice seen on the surface of Pluto can
be as high as $p=0.8-0.9$, while H2O ice on the surface of Charon has a more
moderate albedo $p\sim 0.25$ [87]. However, the albedos of carbonaceous
surfaces of asteroids are much smaller with $p\sim$ 0.04.

The surface composition of 1I/‘Oumuamua is unconstrained and therefore the
exact size of the object is not known. Literature estimates of the size varied
from 55 m [68], 70$\pm$3 m [71], 80 m [73] to 114 m [76]. Assuming an albedo
$p=0.1$, [66] estimated an effective radius of 80 m. This value is consistent
with the nuclear radius calculated with Equation 3 using an absolute magnitude
of $H=22.4$.

####  2.3.2 Colors

The surface colors of small bodies can be measured spectroscopically. These
colors do not give definitive information of the surface compositions but can
be used to identify surface features. For example, asteroids in the inner
Solar System have reddish colors that are due to iron produced by particle
bombardment.

Most objects in the Solar System have slightly reddened reflectance spectra,
with the exception of cold classical KBOs and some Centaurs. The inclination
distribution of the classical KBOs is known to be bimodal. Objects with low
inclinations $i<5^{\circ}$ are referred to as the cold classical KBOs, while
objects with larger inclinations are hot classical KBOs [88, 89]. The cold
classical KBOs likely formed in situ and therefore have little or no residency
time in the inner Solar System [42]. These cold classical KBOs and some
inactive Centaurs have surface reflectance spectra consistent with “ultra-red”
material [90, 91, 92]. It is believed that the ultra-red material is caused by
carbon compounds that are unstable and depleted in the warmer inner Solar
System, and produced via space weathering from cosmic rays and interstellar
medium (ISM) plasma [68].

Therefore, a natural hypothesis is that the surface colors of interstellar
objects that are exposed to harsh galactic environments should resemble the
surfaces of cold classical KBOs. Somewhat surprisingly, published measurements
of the color of 1I/‘Oumuamua are more broadly consistent with the material in
the inner Solar System and the object lacked ultra-red material.

####  2.3.3 Shape

For the majority of Solar System objects, photometric light curves provide the
only information available regarding the shape of the object. Sometimes the
shape models inferred from light curves can be verified and/or updated with
radar measurements. Notable examples include the “dog-bone” shaped asteroid
(216) Kleopatra [93] and 1998 KY26 [94]. In special cases, in-situ space based
measurements reveal detailed geometry and terrain features. Therefore, much
effort has gone into interpreting the shape of an object from photometric
light curves alone.

The composite light curve of 1I/‘Oumuamua displays several salient features
[77, 66]. The first is that the brightness varied by a factor of about $\sim
12$ — note that the y-axis in most published depictions of the lightcurve
figure is in the scale of visual magnitudes, which is a logarithmic scale. At
the time of the detection of 1I/‘Oumuamua, no object in the Solar System had
displayed such extreme amplitude brightness variations. It is worth noting
that since the discovery of 1I/‘Oumuamua, the NEO 2016 AK193 exhibited
brightness variations of $\sim 2.5-3$ magnitudes during its discovery
apparition and in subsequent followup observations [95]. Measurements of 2021
NY1 and 2022 AB were reported by [96] indicating aspect ratios of $\geq 3.6$
and $\geq 1.6$ respectively.

The effects of both the orbital configuration and the geometry of an object
can lead to amplitude variations, which can be difficult to disentangle. The
phase angle, or the angle between the object sun and observer, can increase
the amplitude of the light curve variations. Lightcurve variations are
intrinsically driven by two features: an (i) elongated shape of the body
and/or a (ii) nonuniform reflectance (or abledo) across the surface of the
object. In the case of 1I/‘Oumuamua, the aspect ratio implied by the
lightcurve is $6:1$ when correcting for the phase of the object throughout its
trajectory. However, literature estimated of the aspect ratio varied from
$5:3:1$ [74], $6:1$ by [68, 97] to $10:1$ [71]. It was unclear whether the
elongation corresponded to a prolate or oblate ellipsodal geometry at the time
of the discovery. A rigorous and exhaustive fit to the light curve using $\sim
1$ GPU-year of computational time was performed by [98] demonstrating that the
oblate or “thin-disk” geometry with a $6:1$ aspect ratio was favored with a
$91\%$ likelihood. In retrospect, this geometry is intuitive because only an
oblate geometry would produce deep minima during each circulation. The extreme
shape was suggested to be the result of continuous bombardment and abrasion by
interstellar dust particles [99, 100, 101], a violent collision [102], a tidal
disruption of a larger object that came too close to a giant planet [103] or
its parent star [104] before it was ejected to interstellar space, or a
fractal aggregate structure [105]. It should be noted that a geometry of an
ultra-thin minor axis was shown to produce a low ($\sim$1%) probability of
generating the observed large amplitude [106].

To recreate these types of variations from only albedo features, the object
would need to have one hemisphere darkened with respect to the other. Space
weathering and processing in the ISM would have been approximately isotropic.
Therefore, this interpretation has been more or less disregarded. However,
alternative reflection models such as Lambertian or specular reflection and
single scattering diffusive and backscatter could plausibly reproduce the
observed brightness variations with a less extreme aspect ratio [107].

The second salient feature is that there is an approximately constant
periodicity of $\sim 8$ hr. If the object was elongated and rotating then each
cycle would correspond to complete circulations as the objected reflected
sunlight from the maximum and minimum cross-sectional areas. While the
amplitude variations maintain constant periodicity, each individual cycle
exhibits significant asymmetries. This was highlighted in [73], who showed
phase-folded photometric data obtained with Gemini North telescope on 2017
October 27 and 28. The folded data show $\sim$10% differences at each
circulation. This was interpreted as the object existing in an excited or
tumbling rotational state [78, 73, 77]

###  2.4 Nongravitational Acceleration

Despite the lack of visible dust coma or detected outgassing species, [108]
reported a 30-$\sigma$ significant detection of nongravitational acceleration
in 1I/‘Oumuamua’s trajectory. This acceleration was based on astrometric
fitting over a 2.5 month arc of the orbit.

The only significant component of the nongravitational acceleration of
1I/‘Oumuamua was the radial component A1, where $A_{1}\sim 2.5\times
10^{-4}\,{\rm cm\,s^{-2}}$ at $r\sim 1.4\,~{}{\rm au}$ to a 30-$\sigma$
significance. The best fitting $g(r_{H})$ functions for the nongravitational
acceleration were those that depended inversely on the distance with exponents
ranging from $r_{H}^{-1}$ to $r_{H}^{-2}$. It is important to note that the
exponent could not be constrained any better than being somewhere in the -1 to
-2 range. The magnitudes of the best fitting nongravitational acceleration
components in the transverse and normal directions were consistent with zero.
In [108] it was concluded that the most likely cause of the nongravitational
acceleration was outgassing. While some asteroids exhibit nongravitational
accelerations caused by the Yarkovsky effect and radiation pressure (see
subsections2.6.1 and 2.6.2), the magnitude of the acceleration was too large
to be explained by these effects. The nongravitational acceleration combined
with the lack of visible coma led to a wide array of hypotheses regarding the
provenance of the object which we review in the following subsection.

###  2.5 The Provenance of 1I/‘Oumuamua

####  2.5.1 Radiation Pressure-Driven Fractal Aggregate or Membrane

The two main causes of nongravitational accelerations seen on asteroids are
the Yarkovsky effect [109] and solar radiation pressure [110]. The Yarkovsky
effect results from anisotropic reradiation of thermal photons and typically
manifests in the transverse $\hat{\mathbf{t}}$ direction. Solar radiation
pressure is only detected in the radial $\hat{\mathbf{r}}$ direction and is
weaker than outgassing effects but stronger than Yarkovsky effects for typical
size and compositions of asteroids. Therefore it has only been measured on a
handful of small asteroids [111, 112, 113, 114, 115, 116, 117]. For a more
detailed discussion, we refer the reader to Subsections 2.6.1 and 2.6.2.

Radiation pressure is therefore a natural explanation for the source of the
acceleration of 1I/‘Oumuamua, which was only significant in the radial
direction. However, this was originally considered and dismissed by [108]
because it would imply an extremely low bulk density or minor axis thickness.
Given the lack of detectable dust coma, the hypothesis of radiation pressure
induced acceleration was reconsidered by several authors. The theories that
were published invoking radiation pressure can be categorized by those
invoking (i) a naturally produced, ultra-low density aggregate [105, 118, 119]
or (ii) a membrane-like structure of a very thin material (less than a mm
thick) of an unknown natural or artificial origin, similar to a lightsail
[120].

Regarding the former, a fractal aggregate with a density of $\sim 10^{-5}$ g
cm-3 (about 100 times less than air) could provide the surface-to-mass ratio
required to account for the observed acceleration of 1I/‘Oumuamua [105, 118].
A fractal structure could also help explain its unusual shape. However, the
lowest density solid known (10 times less dense than air) is graphene aerogel
and is synthetically produced. Therefore, it is unclear how such an ultra-
porous structure could be naturally produced.

Fractal aggregates are found in many forms of nature and are thought to arise
naturally because their formation processes involve an element of
stochasticity. In a protostellar disk, the relative motions of neighboring
dust particles are small and therefore collisions are gentle. These conditions
may be amenable to diffusion-limited aggregation [121]. Numerical simulations
investigating planetesimal growth via dust collisions in a protoplanetary disk
show that beyond icelines, if the tiny dust particles are covered with ice and
are about 0.1 $\mu$m in size, the aggregates that form will have increasingly
smaller densities as they grow [122, 123]. This occurs because in the early
phases when the particles are small and strongly coupled to the gas, the
relative velocities of the colliding aggregates is low. Therefore, the
collisions are not energetic enough to restructure the aggregates. This leads
to a rapid increase of porosity as the aggregate grows. As the aggregates
become larger, collisional compression occurs. However, this compression is
inefficient and the porosity of the growing aggregate continues to increase.
This increase occurs because most of the colliding energy is spent compressing
the new voids that are created when two aggregates collide and stick to each
other, rather than compressing the voids that were already present in the
colliding aggregates (see review by [124]). What these studies show is that at
$\sim$ 100 meters, about the size of 1I’/Oumuamua, the planetesimals can
obtain ultra-low densities that are comparable to what would be required for
1I/‘Oumuamua to be “pushed” by radiation pressure [123]. It was therefore
suggested that 1I/‘Oumuamua could be one of these intermediate products of the
planet formation process [105].

If this were its origin, it would be extraordinarily exciting because very
little is known about these intermediate/early products of planet formation.
Studying these objects could help set unprecedented constraints on planet
formation models. In particular, the intermediate stage of planet formation,
in which cm-sized particles grow into km-sized planetesimals, is not well
understood because that process should theoretically be very inefficient.
Several mechanisms have been proposed to help overcome this “meter-sized
barrier” and one of them is the presence of very high porosity planetesimals.
The high porosity could favor the growth process because the larger cross
section [122] would allow a longer lifetime against the effect of radial drift
in the inner regions of the protoplanetary disk. This would both facilitate
growth [123] and make the colliding aggregates less susceptible to
fragmentation and bouncing.

There are other origins that have been been proposed for an ultra-low density
1I/‘Oumuamua. Coma aggregates collected from 67P/Churyumov-Gerasimenko with
the ESA Rosetta mission had low densities $<$1 kg m-3 [125] and fractal
structure [126]. It was therefore hypothesized that 1I/‘Oumuamua was a similar
but larger-scale fractal aggregate formed in the coma of an active comet, that
then escaped [119]. Another suggestion is that it was an ultra-porous
desicated fragment that resulted from the disintegration of an “ordinary” and
larger interstellar comet as it passed near perihelion [118].

Regarding the survival of such an ultra-porous structure to the hazards of
interstellar travel, somewhat counter-intuitively, [127] demonstrated that it
could be stable to tidal disruption. Furthermore, they argued that the
interaction of such an ultra-low density aggregate with the solar radiation
could explain the changes observed in the rotational period of 1I/‘Oumuamua.
It remains to be studied if this fractal structure could survive the ejection
from its parent system and the passage near the Sun.

####  2.5.2 Tidally-Disrupted Planetesimal or Planet Fragment

The extreme aspect ratio of 1I/‘Oumuamua remains somewhat of a mystery. In
another line of reasoning, several authors considered that its extreme shape
was primordial and caused by tidal forces. Tidal forces can have significant
effects on small bodies like comets and asteroids. These manifest as body
deformation in the mildest cases and catastrophic disruption in the most
extreme cases. A noteable example is the tidal disruption of the comet
Shoemaker-Levy 9 when it passed close to Jupiter [128, 129, 130, 131]. Chains
of craters on the surfaces of Callisto and Ganymede may have been caused by
catastrophic disruption of objects that subsequently impacted these surfaces
[132]. Double craters that are seen on Solar System bodies [133, 134, 135,
136, 137] may have been caused by objects that underwent satellite formation
from tidal disruption [138].

If 1I/‘Oumuamua was ejected from its host system following a close encounter
with a giant planet or its host star, it is possible that it too was subject
to tidal forces that produced an elongated fragment. The dynamical simulations
in [103, 139, 140] show that $\sim$1% of planetesimals pass within the tidal
disruption radius of a gas giant on their pathway to ejection. If 1I/‘Oumuamua
was ejected from its host system following such a close encounter with a giant
planet, it is possible that it too was subject to tidal forces, producing an
elongated fragment [103, 139, 140]. Furthermore, these studies argued that
these fragments might have a characteristic size of $\sim$ 100 m, similar to
1I/‘Oumuamua’s size, as opposed to a wider size distribution. Alternately,
[104] proposed that 1I/’Oumuamua is a fragment that resulted from the tidal
disruption of a planet, or a small body, that came too close to its parent
star and that was later ejected to interstellar space. Based on detailed
numerical simulations for a range of impact parameter and material properties,
they suggested this process could produce a prolate object with the observed
aspect ratio.

However, [98] demonstrated that the oblate shape was by far the most likely
geometry of the object, which casts into doubt both tidal fragment hypothesis
as the source of the extreme geometry. Moreover, [141] demonstrated that the
lightcurve of 1I/‘Oumuamua was consistent with no tidal deformation during its
observed passage through the inner Solar System.

####  2.5.3 Sublimating Icy Comet

In [108], it was argued that the most natural explanation for the
nongravitational acceleration was cometary outgassing. However, [142] compared
1I/‘Oumuamua to comets for which the rotational periods of the nuclei had been
measured and argued that the magnitude of the nongravitaitonal acceleration
should have caused a measurable change in the nuclear spin period. Using an
outgassing model, [143] argued that a rapidly mobilizing outflow that tracked
the point of maximal solar irradiance would not result in significant spin-up
of the object. However, this model is highly idealized and in reality cometary
nuclei do experience secular spin-up that can lead to disintegration [144,
145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156]. In [127], it was
reported that in the high-cadence data of 2017 October, 1I/‘Oumuamua
experienced a slight spin-down in its rotational period that could be
attributed to the YORP effect on a fractal body with low ultra-low density.

A further issue with the outgassing hypothesis is that 1I/‘Oumuamua did not
receieve sufficient energy in the form of solar irradiation to power typical
outgassing of H2O or CO2 (see subsections 1.4 and 1.5) [157]. The sublimation
rate per unit surface area can be calculated as an equilibrium solution (as
described in Section 4.1 of [66]) to the equation

$\bigg{(}\,\underbrace{\frac{(1-p)\,L_{\odot}}{4\pi r_{H}^{2}}}_{\textrm{Solar
energy}}\,\bigg{)}\,k_{R}=\,\underbrace{\varepsilon\sigma
T_{S}^{4}}_{\textrm{Re-
radiated}}+\underbrace{Hf_{s}(T_{S})}_{\textrm{Sublimation}}+\underbrace{C(T_{S})}_{\textrm{Interior}}\,.$
(4)

In Equation 4, $p$ is the albedo, $r_{H}$ the heliocentric distance,
$L_{\odot}$ is the Solar luminosity, $\varepsilon$ is the surface thermal
emissivity, $\sigma$ is the Stefan-Boltzmann constant, $T_{S}$ (K) is the
temperature at the surface, $H$ is the latent heat of sublimation, $f_{s}(T)$
is the sublimation rate and $k_{R}$ is the degree of collimation of the
outflow described in Equation 2. The LHS of Equation 4 is the total energy
received from solar radiation, and the RHS indicates the total energy required
to produce the outflow. On the RHS, $\varepsilon\sigma T_{S}^{4}$ is the
energy reradiated from the surface of the comet, $Hf_{s}(T_{S})$ is the energy
deposited in the form of the latent heat of sublimation to convert the ice
into a gas, and $C(T_{S})$ represents heat conduction into the interior. The
last term is negligible in most cases.

Equation 2 can be solved using both the nongravitational acceleration
magnitude and fiducial size of 1I/‘Oumuamua. This produces a required
sublimation rate of $\dot{M}=$ 24 kg s-1 needed to provide the acceleration
[66]. From Equation 4, H2O and CO2 are insufficient to provide this
sublimation for 1I/‘Oumuamua due to the relatively high latent of these
species. Since H2O and CO2 are the most common volatiles seen in Solar System
comets (subsection 1.5), if 1I/‘Oumuamua was outgassing it is unlike most icy
objects we have seen in the Solar System. [158] demonstrated that when
considering these bulk energetics, only hypervolatiles such as molecular
hydrogen H2, molecular nitrogen N2, CO or more exotic species such as Xenon,
Neon, Krypton or Argon could have been feasible accelerants. The noble gases,
however, exhibit relatively low cosmic abundance and are therefore a priori
not likely to be bulk constituents of 1I/‘Oumuamua.

The subsurface layers of 1I/‘Oumuamua are required to reach sufficient
temperatures for the outgassing volatiles to sublimate in order to power the
acceleration. In [68], it was first estimated that the thermal skin depth of
1I/‘Oumuamua was $\sim 0.5$ m via an order of magnitude calculation to argue
that the internal temperature could remain at $\sim 10$ K throughout the
trajectory. In [72] a more detailed numerical thermal model was presented that
demonstrated that H2O was stable to depths of $\gtrsim$30 cm (see Figure 4 in
[72]). The thermal modelling of the interior requires numerical solutions to
the heat conduction equation,

$\frac{dT}{dt}=\frac{\kappa}{\rho_{Bulk}c_{P}}\frac{1}{z}\frac{\partial}{\partial
z}\,\bigg{(}\,z\frac{\partial T}{\partial z}\,\bigg{)}\,.$ (5)

In Equation 5, $T$ is the temperature, $\kappa$ is the thermal conductivity,
$c_{P}$ is the specific heat capacity, and $z$ is the depth. The thermal
properties of 1I/‘Oumuamua are entirely unconstrained, but typical cometary
properties are $\rho_{Bulk}=0.5$ g cm-3 [159], $c_{P}=2000$ J kg-1 and
$\kappa=10^{-2}-10^{-1}$ W K-1 m-1 [160]. We show the results of this thermal
modelling for 1I/‘Oumuamua in Figure 4, with the sublimation temperatures of
H2O, CO2 and CO in the top panels. The remaining volatile species have been
investigated further but, because of theoretical and/or observational
arguments, none are thought to be the prime constituent of 1I/‘Oumuamua.

In [158], the hypothesis that 1I/‘Oumuamua was composed of solid H2 was
explored. H2 has a sublimation temperature of $\sim$6 K and this scenario
suggested that 1I/‘Oumuamua originated in a failed prestellar core of a giant
molecular [161]. The continuous ablation of H2 from the surface via cosmic ray
exposure and solar photons would naturally produce the elongated shape. Other
authors argued that the cosmic radiation would have destroyed a macroscopic H2
body before it reached the Solar System [162, 163], although [164] showed that
km-scale progenitors could survive for timescales $\leq 100$ Myr. However, any
theory must account for not only the existance of 1I/‘Oumuamua, but also for
the progenitor galactic population of similar-sized objects. This population
is inferred to exist based on 1I/‘Oumuamua’s detection frequency, and is
estimated to contain $\sim 10^{26}$ objects (see discussion in subsection
4.1). The primary caveat with the solid H2 scenario is that the frigid
temperature requirements for the prestellar cores would be extremely
challenging to achieve ubiquitously throughout star forming regions to account
for the progenitor population of interstellar objects.

It was subsequently hypothesized that 1I/‘Oumuamua was composed of solid N2
instead, implying that it was a remnant from an impactor event on an exo-Pluto
analogue that generated significant fragments of solid nitrogen [165, 166].
Given that such bodies are large enough to differentiate volatiles, this
theory may also explain the lack of dust coma seen in the object. However,
this would require a very high efficiency of ejection of nitrogen-rich
material from planetary systems if stellar populations were producing such
objects uniformly – exacerbated by the fact that that high velocity impactors
do not generically produce fragments with sufficient kinetic energy to escape
from the host body [167]. However, some of these issues would be alleviated if
only M stars produced 1I/‘Oumuamua like interstellar objects and if the
typical impacts were at indirect impact angles [168]. If this theory proves
correct, then it is possible that the discovery of 1I/‘Oumuamua was an outlier
event, and we can expect few or no similar discoveries in the future [167].

In [81], it was investigated whether CO outgassing could produce the
nongravitational acceleration, despite the nondetection with Spitzer. While
theoretically viable, this explanation requires a highly fine-tuned sporadic
outgassing throughout the trajectory.

Figure 4: Numerical solutions of the radial heat equation (Equation 5) for
1I/‘Oumuamua spanning the inbound and outbound trajectory interior to 4 au. We
adopt a bulk density $\rho_{Bulk}=0.5$ g cm-3, specific heat capacity of
$c_{P}=2000$ J kg-1 K and thermal conductivity $\kappa=10^{-2}$ W K-1 m (left
panels) and $\kappa=10^{-1}$ W K-1 m (right panels). Contours on the left
panels indicate sublimation fronts of CO (28 K), CO2 (86 K) and H2O (144 K)
[169]. Contours on the right panels indicate where H2 outgassing is expected
during the annealing of amorphous H2O ice for temperatures of $\sim$15–140 K.
Adapted from [170].

In [170] it was demonstrated that the crystallization of amorphous water ice
would provide sufficient radiolytically-produced and entrapped H2 to account
for the observed nongravitational acceleration. Energetic processing of an
H2O-rich icy body irradiated by galactic cosmic rays would produce entrapped
H2, a process that has been demonstrated in laboratory experiments [171, 172,
173, 174, 175, 176, 177]. This crystallization would occur in the absence of
sublimation of the overall ice matrix, thereby explaining the lack of dust
coma observed.

This explanation requires the subsurface of 1I/‘Oumuamua to reach sufficient
temperatures to crystallize ice via annealing of the amorphous water matrix.
Moreover, the required temperatures between 15-140 K [178, 172, 175] must be
reached at sufficient depths within the interior to produce sufficient H2 to
power the acceleration, given a laboratory measured $\sim 20-35\%$ yield of
entrapped H2 [172]. More realistic H2/H2O yields of tens of percent are
predicted for the suburface meters of a porous cometary composition exposed to
cosmic rays [179], which can penetrate to depths of tens of meters [180].

Solutions to the thermal depths presented in [170] are shown in Figure 4.
Indeed, the subsurface meters reach sufficient temperatures to crystallize
amorphous ice without producing significant H2O sublimation. This explanation
would therefore partially explain the lack of observed dust (Table 1). Without
the bulk ice matrix sublimating, the release of entrapped H2 within a few
meters of the subsurface would not release dust trapped within the ice matrix.
The lack of surface dust may be due to interactions with ambient gas in the
interstellar medium which preferentially remove small dust grains from the
surface of long-period comets and interstellar comets [181].

###  2.6 1I/‘Oumuamua in the Context of Solar System Asteroids

####  2.6.1 Active Asteroids

Small bodies throughout the Solar System have classically been categorized
based on their volatile-driven activity. Comets were defined as icy objects
that produced dusty comae and presumably spent little or no time in the inner
Solar System. Meanwhile, asteroids lacked volatiles due to their closer
proximity to the Sun which subjects them to prolonged and intense irradiation.
However, recent advances have shown that this simple classification is not
entirely accurate. Specifically, a subset of asteroids appear active and
either have detectable dust activity or nongravitational accelerations
potentially caused by outgassing [182, 183, 184]. Within this context, the
active asteroids are directly relevant to 1I/‘Oumuamua which displayed a
hybrid of cometary and asteroidal properties.

The Main Belt Comets (MBCs) reside in the asteroid belt and display low levels
of cometary activity [185]. The first MBC to be discovered was Comet
133P/(7968) Elst-Pizarro [186, 187, 188, 189]. Several other MBCs have since
been identified, and occurrence rates of $<1/500$ and $\sim 1/300$ have been
inferred from surveys [190, 191, 192, 193].

The cause of dust activity in these active asteroids is not completely clear.
As discussed previously, outgassing induces nongravitational accelerations
[49, 50] which have been detected on some active asteroids with related dust
activity [194]. However, other effects caused from impacts [195] and rotation
[196] can produce dust activity in the absence of outgassing.

Intriguing cases of active asteroids that do not exhibit obvious outgassing
are (3200) Phaethon and (101955) Bennu, the target of the OSIRIS-REx mission.
(3200) Phaethon was first identified to be active because of its association
with the Geminid meteoroid stream [197, 198]. It produces a small dust tail
around perihelia with optically observed micron-sized dust production rates of
$\sim 3$ kg s-1 [199, 200, 201, 202]. However, this level of activity was
incompatible with the flux from the meteoroid stream. Therefore other effects
such as thermally induced stresses [199], sublimation of minerologically bound
sodium [203], rotation [204, 205] and geometry [206, 207] have been used to
explain the activity. (101955) Bennu was identified as active only when
particle ejection events were measured by the OSIRIS-REx spacecraft [208,
209]. The measured mass flux was $\dot{M}_{\rm Dust}\sim 10^{-4}$ g s-1 [210].
However, the source of the activity of (101955) Bennu remains unsolved [211,
212, 213].

Figure 5: The dark comet 1998 KY26 which exhibits no dust coma and a
significant nongravitational acceleration. The image was taken with the VLT
and incorporates $\sim$ 1 hr of temporal coverage in 2020 December. The $\sim
30$ m object is faint and indicated with a red circle. Reproduced from [214].

####  2.6.2 Dark Comets (Inactive Asteroids Experiencing Nongravitational
Accelerations)

At the time of 1I/‘Oumuamua’s discovery, there had been no asteroidal objects
discovered that exhibited nongravitational accelerations with no dust
activity. As discussed previously, nongravitational accelerations have been
measured on inactive asteroids due to the Yarkovsky effect and radiation
pressure. However, the magnitudes of these accelerations are typically much
lower than those discovered on 1I/‘Oumuamua. Since the detection of
1I/‘Oumuamua, a new population of inactive asteroids have been discovered that
exhibit stronger nongravitational accelerations and similarly lack dust comae.
We refer to these as dark comets.

Namely, [215], [216] and [214] reported statistically significant detections
of non-radial nongravitational accelerations in a sample of photometrically
inactive NEOs. The objects with nongravitational accelerations inferred from
astrometric data are (523599) 2003 RM, 1998 KY26, 2005 VL1, 2016 NJ33, 2010
VL65, 2006 RH120, and 2010 RF12. In Figure 5, we show a stack of VLT images of
one of these objects, 1998 KY26, taken during 2020 December. This image
contains a stack of exposures resulting in a composite image with a total of
3600 s exposure. The object quite clearly lacks a dust tail and, because of
this and the nongravitational acceleration, is reminiscent of 1I/‘Oumuamua.
The image corresponds to an upper limit of dust production of $\dot{M}_{\rm
Dust}<0.2$ g s-1.

Figure 6: Nongravitational accelerations measured in asteroids (teal) and dark
comets (purple), similar to Figure 1. Measured radial nongravitational
acceleration $A_{1}$ are due to solar radiation pressure (left) and transverse
acceleration $A_{2}$ are due to the Yarkovsky effect (middle). The out-of-
plane nongravitational acceleration $A_{3}$ measured in the objects (right)
are presumably due to polar outgassing events. Dark comet candidates with
anomalous $A_{2}$ values, 2003 RM and 2006 RH120, are shown in purple dashed
lines in the middle panel.

All of the dark comet nongravitational accelerations are inconsistent with
being caused by radiation pressure or Yarkovsky effect, demonstrated in Figure
6. The best fitting nongravitational acceleration parameters and their
significances are shown in Table 2. The significant $A_{2}$ and $A_{3}$ are
inconsistent in magnitude with radiation pressure and the Yarkovsky effect.
Therefore [214, 216] argued that these accelerations were caused by outgassing
with no (or low levels of) accompanying dust comae.

These dark comets may be Solar System analogues of 1I/’Oumuamua, in that they
have measured nongravitational accelerations and no (or low levels of) dust
comae. The lack of dust has been attributed to low levels of outgassing and
presumably a lack of surface dust. Although 1I/‘Oumuamua is now long gone,
investigating these dark comets may reveal similar physical processes that can
produce outgassing and nongravitational accelerations without significant dust
production. The JAXA Hayabusa2 extended mission will rendezvous with 1998 KY26
[217]. The instrument suite onboard Hayabusa2 can measure volatile and dust
production [218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229].
Therefore, the nature of the nongravitational acceleration of these possible
Solar System analogues of 1I/‘Oumuamua should be definitively identified in
the near-term future.

Table 2: Dark comets with nongravitational accelerations and no observed dust production. Best-fit nongravitational acceleration parameters for each object are shown with 1-$\sigma$ uncertainties. $P_{\rm Rot}$ is the rotational period and $H$ is the reported absolute magnitude. Reproduced from [214]. Object | $a$ | $e$ | $i$ | $q$ | $H$ | $r_{\rm n}$ | $P_{\rm Rot}$ | $A_{1}$ | $A_{2}$ | $A_{3}$
---|---|---|---|---|---|---|---|---|---|---
| [au] |  |  [∘] | [au] | [mag] | [m] | [h] |  [$10^{-10}$ au d-2] |  [$10^{-10}$ au d-2] |  [$10^{-10}$ au d-2]
|  |  |  |  |  |  |  |  Signif.[$\sigma$] |  Signif.[$\sigma$] |  Signif.[$\sigma$]
2003 RM | 2.92 | 0.60 | 10.86 | 1.17 | 19.80 | 230 |  |  -1.045$\pm$1.217 |  -0.0215 $\pm$0.0004 |  -0.0156$\pm$0.0543
|  |  |  |  |  |  |  | $<1$ | 56 | $<1$
1998 KY26 | 1.23 | 0.20 | 1.48 | 0.98 | 25.60 | 15 | 0.178 |  -1.73 $\pm$0.91 |  -0.00126$\pm$0.00061 |  -0.320 $\pm$0.115
|  |  |  |  |  |  |  | 2 | 2 | 3
2005 VL1 | 0.89 | 0.23 | 0.25 | 0.69 | 26.45 | 11 |  |  -6.66 $\pm$8.02 |  -0.00711$\pm$0.00592 |  -0.240 $\pm$0.041
|  |  |  |  |  |  |  | $<1$ | 1 | 6
2006 RH120 | 1.00 | 0.04 | 0.31 | 0.96 | 29.50 | 2-7 | 0.046 |  -1.38 $\pm$0.08 |  -0.507 $\pm$0.0637 |  -0.130 $\pm$0.032
|  |  |  |  |  |  |  | 18 | 8 | 4
2010 VL65 | 1.07 | 0.14 | 4.41 | 0.91 | 29.22 | 3 |  |  -6.57 $\pm$13.0 |  -0.00146$\pm$0.00534 |  -0.913 $\pm$0.130
|  |  |  |  |  |  |  | $<1$ | $<1$ | 7
2010 RF12 | 1.06 | 0.19 | 0.88 | 0.86 | 28.42 | 4 |  |  -0.488$\pm$0.597 |  -0.00136$\pm$0.00286 |  -0.168 $\pm$0.021
|  |  |  |  |  |  |  | $<1$ | $<1$ | 8
2016 NJ33 | 1.31 | 0.21 | 6.64 | 1.04 | 25.49 | 16 |  $0.41$-$1.99$ |  -9.28 $\pm$2.96 |  -0.00566$\pm$0.00193 |  -0.848 $\pm$0.163
|  |  |  |  |  |  |  | 3 | 3 | 5

##  3 2I/Borisov

Figure 7:  The second interstellar comet discovered, 2I/Borisov. The image was
taken with HST on 2019 October 12 [230]. 2I/Borisov displays a clear cometary
tail. $r_{H}$ corresponds to the heliocentric distance of the object when the
image was obtained. Reproduced from [230].

###  3.1 Discovery

The comet C/2019 Q4 (Borisov) was discovered on 2019 August 30 when it was
close to the sun with an angular separation of just 38∘. This object was
discovered by Gennadiy Borisov, an amateur astronomer using a 0.65 m
telescope. It is worth noting that the object was not discovered by the all
sky surveys searching for transient events, which intentionally do not observe
near the Sun.

Like 1I/‘Oumuamua, the trajectory of the comet is definitively of interstellar
origin, with an escape velocity, $v_{\infty}=32.304\pm 0.001$ km/s, semimajor
axis of $a=-0.850$ au, eccentricity of $e=3.363$, inclination $i=44.0^{\circ}$
and perihelion of $q=2.009$ au. Because of the definitive interstellar
trajectory, it was renamed to 2I/Borisov. Unlike 1I/‘Oumuamua, the object was
discovered $\sim 3$ months prior to perihelia which left ample time for
characterization with subsequent telescopic observations. In Figure 7, we show
an image of 2I/Borisov taken with the Hubble Space Telescope [230].

###  3.2 Nucleus Properties

####  3.2.1 Size

The images of 2I/Borisov obtained with HST [231] provided empirical evidence
for a nuclear radius of 0.2–0.5 km. This was supported by upper limits from
ground-based infrared imaging [232]. The upper limit was derived from
modelling the brightness profile of the coma, and the lower limit was derived
from the measured nongravitational acceleration assuming a bulk density
representative of comets to prevent catastrophic disruption due to outgassing
forces [230]. This nuclear size is more in line with Solar System comets, and
provides a stark contrast to the very small size inferred for 1I/‘Oumuamua.

####  3.2.2 Colors

2I/Borisov displayed a distinct dust and gas coma and was unmistakably a comet
[231, 232, 233, 234, 235]. The measured colors of 2I/Borisov, unlike for
1I/‘Oumuamua, were representative of the color of the ejected dust which
dominate the images. The dust ejected from 2I/Borisov was reddened with
respect to that of the Sun, similar to 1I/‘Oumuamua. Early spectral
observations with the 10.4 m Gran Telescopio Canarias (GTC) revealed a visible
spectrum with a spectral slope that is roughly in the middle of the range of
visible spectral slopes observed for cometary nuclei in the Solar System
[236]. The dust in the cometary tail was measured to have a slightly reddish
color of $g^{\prime}-r^{\prime}=0.63\pm 0.03$ [233, 231, 232], later measured
as $g^{\prime}-r^{\prime}=0.68\pm 0.04$ and $r^{\prime}-i^{\prime}=0.23\pm
0.03$ [234].

####  3.2.3 Nongravitational Acceleration

With 10 months of astrometric positional data, it was evident that 2I/Borisov
exhibited nongravitational acceleration. Similar to 1I/‘Oumuamua, the dominant
component of the nongravitational acceleration was in the radial direction,
with $A_{1}=7.1\pm 0.8\times 10^{8}$ au d-2, $A_{2}=-1.4\pm 0.3\times 10^{8}$
au d-2 and $A_{3}=0.1\pm 1.5\times 10^{8}$ au d-2. These were consistent with
being recoil effects from measured production rates [234, 237, 238]. In Figure
8, we show the nongravitational accelerations measured in comets, asteroids,
dark comets, 1I/‘Oumuamua and 2I/Borisov. We limit to only objects that have
sizes measured.

Figure 8: Measured nongravitational accelerations of a variety of small
bodies. The three panels show measured components of nongravitational
accelerations in the radial A1 direction (left), transverse A2 direction
(middle) and out-of-plane A3 direction (right). In each panel, measured
nongravitational accelerations of comets (teal circles) asteroids (purple
hexagons), dark comets (orange diamonds), 1I/‘Oumuamua (dark purple star) and
2I/Borisov (magenta triangle) are shown. Only comets with measured nuclear
diameters are shown — many more comets exist for which nongravitational
accelerations have been measured (Figure 1). The size of the asteroids have
been approximated using Equation 3.

###  3.3 Coma Properties

####  3.3.1 Dust Properties

VLT and ALMA data of 2I/Borisov was reported by [239] showing that that the
dust in the coma contained a contribution from pebbles with sizes $\gtrsim 1$
mm. Dust production rates of $Q({\rm dust})=35$ kg s-1 (2019 November) and
$Q({\rm dust})=30$ kg s-1 (2019 December) were reported by [240] using
observations with the Telescopio Nazionale Galileo. The contributing dust
grains were consistent with sizes mostly larger than $100\,\mu\text{m}$ [241].

The presence of submicron sized conglomerates of magnesium-ferrous particles
were inferred from photometric observations for $\sim 2$ months before
periastron [242]. Polarimetric measurements of the object obtained by the ESO
Very Large Telescope intriguingly showed that the dust in the outflow
exhibited a high level of polarization compared to levels seen in dust
produced in typical Solar System comets [243]. This polarization was further
shown to be consistent with a high $\sim 80\%$ fraction of rough fractal
aggregates and $\sim 20\%$ of agglomerated debris, interpreted as 2I/Borisov
having a large percentage of small and porous pristine cosmic dust particles
[244].

####  3.3.2 Volatile Composition

Table 3: The production rates of molecules CO, H2O and OH measured in the comae of 2I/Borisov. rH is the Heliocentric distance at observation. Adapted from [59]. Date | rH |  ${\rm Q({H_{2}O})}$ $10^{26}$ |  ${\rm Q({CO})}$$10^{26}$ |  ${\rm Q({OH})}$$10^{26}$ | Reference
---|---|---|---|---|---
| [au] | [molec s-1] | [molec s-1] | [molec s-1] |
9/27/19 | 2.56 | $<8.2$ |  |  | [245]
10/2/19 | 2.50 |  |  | $<0.2$ | [246]
10/11/19 | 2.38 | $6.3\pm 1.5$ |  |  | [247]
10/13/19 | 2.36 |  |  | $<0.2$ | [246]
11/1/19 | 2.17 | $7.0\pm 1.5$ |  |  | [245]
12/1/19 | 2.01 | $10.7\pm 1.2$ |  |  | [245]
12/3/19 | 2.01 |  | $3.3\pm 0.8$ |  | [239]
12/11/19 | 2.01 |  | $7.5\pm 2.3$ |  | [248]
12/15-16/19 | 2.02 |  | $4.4\pm 0.7$ |  | [249]
12/19-22/19 | 2.03 | $4.9\pm 0.9$ | $6.4\pm 1.4$ |  | [248]
12/21/19 | 2.03 | $4.9\pm 0.9$ |  |  | [245]
12/30/19 | 2.07 |  | $10.7\pm 6.4$ |  | [248]
1/13/20 | 2.16 | $<5.6$ | $8.7\pm 3.1$ |  | [248]
1/14/20 | 2.17 | $<6.2$ |  |  | [245]
2/17/20 | $2.54$ | $<2.3$ |  |  | [245]
Table 4: The production rates of molecules CN, C2 and C3 measured in the coma of 2I/Borisov. rH is the Heliocentric distance at observation. Adapted from [59].  Date | rH | ${\rm Q({CN})}$ | ${\rm Q({C_{2}})}$ | ${\rm Q({C_{3}})}$ | Reference
---|---|---|---|---|---
| [au] |  $10^{24}$[molec s-1] |  $10^{24}$[molec s-1] |  $10^{24}$[molec s-1] |
9/20/19 | 2.67 | $3.7\pm 0.4$ | $<4$ |  | [250]
9/20/19 | 2.67 | $<5$ | $<8$ |  | [251]
10/1/19 | 2.50 | $1.1\pm 2.0$ | $<2.5$ |  | [251]
10/1/19 | 2.51 | $1.8\pm 0.1$ | $<0.9$ | $<0.3$ | [246]
10/2/19 | 2.50 | $1.9\pm 0.1$ | $<0.6$ | $<0.2$ | [246]
10/9/19 | 2.41 | $1.59\pm 0.09$ | $<0.44$ |  | [251]
10/10/19 | 2.39 | $1.69\pm 0.04$ | $<0.162$ |  | [251]
10/13/19 | 2.36 | $2.1\pm 0.1$ | $<0.6$ | $<0.3$ | [246]
10/18/19 | 2.31 | $1.9\pm 0.6$ |  |  | [246]
10/20/19 | 2.29 | $1.6\pm 0.5$ |  |  | [246]
10/26/19 | 2.23 | $1.9\pm 0.3$ |  |  | [251]
10/31/19 | 2.18 | $2.0\pm 0.2$ |  |  | [252]
11/4/19 | 2.15 | $2.4\pm 0.2$ | $0.55\pm 0.04$ | $0.03\pm 0.01$ | [252]
11/10/19 | 2.12 | $1.9\pm 0.5$ |  |  | [253]
11/14/19 | 2.09 | $1.8\pm 0.2$ | $1.1$ |  | [253]
11/17/19 | 2.08 | $1.9\pm 0.5$ |  |  | [253]
11/25/19 | 2.04 | $1.6\pm 0.5$ |  |  | [253]
11/26/19 | 2.04 | $1.8\pm 0.2$ |  |  | [253]
11/26/19 | 2.04 | $1.5\pm 0.5$ | $1.1$ |  | [253]
11/30/19 | 2.01 | $3.36\pm 0.25$ | $1.82\pm 0.6$ | $0.197\pm 0.052$ | [254]
12/22/19 | 2.03 | $6.68\pm 0.27$ | $2.3\pm 0.82$ | $0.714\pm 0.074$ | [254]

The orbit and discovery of 2I/Borisov enabled several months of detailed
compositional measurements to be obtained. While the object was definitively a
comet unlike 1I/‘Oumuamua, its composition was different than those typically
seen in Solar System comets. These observations are summarized in Table 3 and
Table 4.

Initial measurements of the object showed that ${\rm H_{2}O}$ was active as
early as 6 au and inbound [250, 231, 255]. Subsequent observations revealed
carbon and nitrogen bearing species in the coma. Near-UV emission of CN from
2019 September 20 was presented by [250] presented, together with an upper
limit on the abundance of $\rm C_{2}$, based on observations with the
4.2-meter William Herschel Telescope and the ISIS spectrograph on La Palma.
Measurements of CN and $\rm C_{2}$ production were also reported by [251]
using the 2.3-meter Bok telescope at Kitt Peak National Observatory in
Arizona, the 6.5-meter MMT telescope located at Mount Hopkins, and the Large
Binocular Telescope at the DDT. Similar spectroscopic detections and upper
limits were reported by [246] using data from the 4.2-meter William Herschel
and 2.5-meter Isaac Newton telescopes on a range of dates from 2019 September
30 to 2019 October 13. Detections of $\rm C_{2}$ and of $\rm CN$ were reported
by [256] using data from the MDM observatory Hiltner 2.4-meter telescope and
the Ohio State Multi-Object Spectrograph from 2019 October 31 and November 4.
Additional observations were presented by [253] using the Multi-Unit
Spectroscopic Explorer (MUSE) at the 8.2-meter UT4 of the ESO/Very Large
Telescope (VLT) and the the 0.6-meter TRAPPIST North and South telescopes.

Production rates and upper limits of H2O were measured throughout the
trajectory. A production rates of $Q({\rm H_{2}O})=6.3\pm 1.5\times 10^{26}$
molecules s-1 was derived by [247] based on observations with the ARCES
instrument at Apache Point Observatory on 2019 October 11, while [254]
reported observations taken with the 2-meter Himalayan Chandra Telescope
located at the Indian Astronomical Observatory, Hanle (HCT) and the Mount Abu
Infrared Observatory (MIRO) from 2019 November 30 and December 22 that yielded
production rate ratios of $Q(C2)/Q(CN)=0.54\pm 0.18$ and $Q(C2)/Q(CN)=0.34\pm
0.12$ before and after perihelion respectively. Critically, [245] presented
observations of production rates both before and after perihelion with 6
epochs of observations with the Neil Gehrels Swift Observatory’s
Ultraviolet/Optical Telescope. These revealed that the H2O production
increased and decreased before and after perihelion, and they estimated an
active fraction of $\geq$ 55 $\%$ of the surface to account for the inferred
production.

While these previously discussed observations were in line with compositions
typically seen in Solar System comets, post perihelia observations
demonstrated that the object was enriched in the hypervolatile CO [249, 248].
Atacama Large Millimeter/submillimeter Array (ALMA) images were obtained on
2019 December 15 and 16, and revealed the presence of HCN and CO at high
abundances relative to H2O [249]. Similarly, [248] reported observations with
the Cosmic Origins Spectrograph (COS) on the HST between 2019 December 11 and
2020 January 13, that revealed high CO production rates with respect to H2O.
Additional measurements of CO production by [239] found that the CO/H2O mixing
ratio changed drastically before and after perihelion.

A spectroscopic detection of atomic nickel vapor in the coma of 2I/Borisov at
2.322 au was reported by [257] using observations with X-shooter spectrograph
at the ESO VLT on 2020 January 28, 30 and 31, when the object was at an
equilbrium temperature $\sim 180$ K. Atomic nickel vapor has been detected in
sun-grazing comets such as the case of C/1965 S1 (Ikeya–Seki) [258, 259].
However, this is typically observed at much warmer temperatures $>700$ K and
attributed to the sublimation of metal enriched dust grains. These authors
concluded that the nickel vapor was a photodissaociation product of a short-
lived nickel-containing molecule.

###  3.4 Breakup

2I/Borisov exhibited a stark brightening event [260] and subsequent breakup in
the spring of 2020 [261, 262, 263, 264]. HST observations of the breakup were
presented in [261]. The splitting event can be seen in March, where the
nucleus develops a two-lobed shape.

The evolution of the coma morphology of 2I/Borisov in the HST images was
interpreted as evidence of seasonal effects [241]. Specifically, the changes
in activity levels and breakup [261] could be explained by regions on the
northern hemisphere of the nucleus being exposed to the sun for the first time
(particularly, see Figure 7 in [241]). Seasonal effects and nucleus disruption
are typically seen in Solar System comets and have been attributed to cometary
fading [265].

###  3.5 Borisov in the Context of Solar System Comets

Figure 9: The compositions of 2I/Borisov and C/2016 R2, analogous to Figure 2.
Note that there were no observations sensitive to CO2 obtained for 2I/Borisov.
Therefore, it is possible that the object had CO2 in its outflow that was
never measured as indicated with a question mark.

The composition of 2I/Borisov was anomalous compared to typical Solar System
comets due to the high abundance of the hypervolatile CO. Contemporaneous
observations sensitive to H2O and CO revealed a production rate ratio of
$Q({\rm CO})/Q({\rm H_{2}O})\geq$ 1\. It is important to note that this
production rate ratio is calculated only when near-contemporaneous
measurements of both species were obtained. As discussed previously in this
review (subsection 1.4 and 1.5), comets are typically composed primarily of
H2O, with average ratios of $Q({\rm CO})/Q({\rm H_{2}O})\sim$ 4$\%$ although
with a wide range [57].

This was interpreted as 2I/Borisov having formed in a carbon rich environment.
It was argued that 2I/Borisov likely formed in an M star system. In such a
system, the relatively cooler temperatures would lead to a CO snowline closer
to the star. This implies that the majority of the circumstellar solids lie
outside the CO snowline [248]. Alternatively, [249] argued that 2I/Borisov
formed close to or at the CO snowline and was possibly the remnant of an
impacted exo-Kuiper belt object. This scenario is similar to that suggested
for 1I/‘Oumuamua in which it is a fragment of an exo-Pluto analogue [166, 165,
168]. All of these interpretations of the hyerpvolatile content indicate that
the object formed exterior to the CO snowline in its original protoplanetary
disk [266].

Interestingly, the abundance of remnant hypervolatiles can inform the timing
of the ejection of 2I/Borisov from its host system. Even if it formed beyond
the CO snowline and remained there, prolonged heating from stellar irradiation
would have removed hypervolatiles at large stellocentric distances if exposed
for 100s of Myr. Therefore, [267] argued that the object must have been
ejected within $<20$ Myr of the formation in its host system.

An intriguing comparison object is C/2016 R2 [268, 269, 58], a highly
eccentric LPC that exhibits a CO to H2O production rate ratio $\gtrsim 100$
[58]. However, C/2016 R2 displayed a CO/H2O ratio much higher than that of
2I/Borisov, and an unexpectedly high abundance of N2 [268, 270]. It has been
suggested that C/2016 R2 is interstellar in origin because of its exotic
composition [58]. In Figure 9, we show the compositions of 2I/Borisov and
C/2016 R2. While not a direct analogue of 2I/Borisov, it is one of the few
Solar System comets enriched in hypervolatiles, and is certainly the most
extreme case. Relevant to this discussion, the Solar System comets C/2009 P1
Garradd [271, 272, 273, 274], C/2010 G2 Hill [275] and C/2006 W3 Christensen
[60] have high abundances of CO relative to H2O. C/1995 O1 (Hale-Bopp) had
$Q({\rm CO})/Q({\rm H_{2}O})>$ 12 measured at $r_{H}$ = 6 au [276] and the
Centaur 29P/SW1 exhibited $Q({\rm CO})/Q({\rm H_{2}O})=$ 10$\pm$1, measured at
$r_{H}\sim$ 6 au [276, 57]). However, at these further heliocentric distances,
H2O is typically not active. Therefore, the compositions measured at large
distances are not necessarily representative of the volatile inventories.

##  4 Galactic Population of Interstellar Objects

###  4.1 Number of Interstellar Objects

Prior to the detection of 1I/‘Oumuamua, several studies had estimated the
number density of interstellar comets from non-detections. These are
summarized in Table 5, dating back to 1976. Immediately before 1I/‘Oumuamua’s
discovery, several studies provided detailed simulations of the expected
galactic population of ejected comets and predicted the prospects for future
detections with existing and forthcoming surveys.

The discovery of 1I/‘Oumuamua implies that a much larger galactic population
exists than was previously estimated. The occurrence rate of detections was
estimated to be $0.2$ yr-1, with an average of $\sim 20$ $M_{\oplus}$ of
material ejected per star [277]. The number density was estimated to be $n\sim
10^{-2}\,{\rm au}^{-3}$ [278], implying a total number of $N\sim 2\times
10^{26}$ throughout the Milky Way and a galactic mass of $M\sim
10^{11}\,M_{\oplus}$. A more detailed analysis that incorporated the survey
sensitivities of observational facilities resulted in a number density $n\sim
2\times 10^{-1}\,{\rm au}^{-3}$ [279]. If we assume a mass of $M_{\rm
1I}=10^{12}\,\rm{g}$ in every 1I/‘Oumuamua-like object, this implies a total
galactic mass density of 0.3 $M_{\oplus}\,{\rm pc}^{-3}$. This translates to a
population of $N\sim 4\times 10^{26}$ in the Milky Way, or approximately
$1\,M_{\oplus}$ per stellar system. Based on the non-detection of similar
objects since these initial estimates, this number density has been revised to
$n\sim 1\times 10^{-1}\,{\rm au}^{-3}$ [167, 66]. Frustratingly, the detection
of 2I/Borisov does not constrain the number density of interstellar objects
due to its brightness and discovery method.

Table 5: Published estimates of the galactic space density of interstellar
interlopers.

Reference | Density | Density | Rate
---|---|---|---
| [$M_{\odot}$ pc-3] | [ au-3 ] | [ yr-1 ]
[280] | $6\times 10^{-4}$ | $\lesssim 0.07^{\rm a}$ |
[281] | 2$\times 10^{-5}$ | 10${}^{-3}\,{}^{\rm a}$ |  $\sim$0.6
[282] |  |  |  $<$0.01
[283] |  |  $\sim 10^{-3}$ a |
[10] | $3\times 10^{-6}$ | $3-4.5\times 10^{-4}$ |
[284] | $\sim 2\times 10^{-7}$ | 3$\times 10^{-5}$ a |
[285] |  | $<1.4\times 10^{-4}$ |
[286] |  | 10-8 \- 10${}^{-5}\,{}^{\rm a}$ |
[68] |  |  $\sim$ 0.1 |
[277] |  |  $\sim$ 0.1 |
[278] |  |  $\sim$ 0.2 |
[279] |  |  $\sim$ 0.2 |
[287] |  $\sim 3\times 10^{-7}$ (singles) |  |
[287] |  $\sim 1\times 10^{-6}$ (binaries) |  |
[288] |  |  $\sim 3\times 10^{-3}$ (Oort cloud) |

a Objects greater than 1 km.

As mentioned above, the number density of interstellar objects is higher than
expected, if we assume that 1I/‘Oumuamua is representative of a population
that is uniformly distributed. Population studies that have tackled this
discrepancy have estimated the number density of interstellar planetesimals
based on the observed number of stars per unit volume of space and an
estimated number of ejected planetesimals per star.

####  4.1.1 Contribution from Protoplanetary Disks Around Single Stars and
Close Binaries

Feasible sources of planetesimal ejection are dynamical instabilities and
orbit readjustment that occur as a result of interactions between planetesimal
and growing planets. These interactions lead to planetary migration, as is
thought to have occurred in the early Solar System [289, 42]. Numerical
simulations show that these episodes of dynamical instability and planetesimal
ejection are common in many planetary configurations [139]. In the Solar
System, there is evidence that the planetesimal belts were heavily depleted
and that the primordial Kuiper and asteroid belts were significantly more
massive. The two pieces of evidence are the existence of Kuiper belt objects
larger than 200 km (which formation by pairwise accretion must have required a
number density of objects about two orders of magnitude higher than today),
and the strong depletion in the asteroid belt region with respect to the
minimum mass solar nebula.

Ejection occurs when the giant planets in the Solar System have close
encounters with planetesimals. Some of these close encounters would impart
sufficient energy to eject the planetesimal. Based on theoretical models of
the timing of giant planet migration and/or instability in the Solar System,
it seems likely that this occurred within the first $<10$ Myr after the disk
dispersed [290, 291, 292, 293, 294, 295, 296, 297, 298]. Moreover, the recent
report of an excess of free-floating planets in the newly formed ($<10$ Myr)
Upper Scorpius stellar association [299] is consistent with ubiquitous early
ejection of debris.

For a giant planet to eject an interstellar comet, the planet must impart
sufficient energy via a close encounter to scatter the comet onto an unbound
trajectory. The Safronov number $\Theta=V_{e}^{2}/(2V_{K}^{2})$ is useful to
quantify the efficiency of this process, where $V_{e}$ is the escape velocity
and $V_{K}$ is the orbital velocity. Only objects with $\Theta>1$ are capable
of ejecting objects. The Safronov number may be written as,

$\Theta=\left(\frac{M_{\rm P}}{M_{*}}\right)\left(\frac{a_{\rm P}}{R_{\rm
P}}\right)\,.$ (6)

In Equation 6, $M_{*}$ and $M_{\rm P}$ are the mass of the star and planet,
while $a_{\rm P}$ and $R_{\rm P}$ are the semimajor axis and radius of the
planet. Because the ejection is more efficient beyond the snowline (as the
Safronov number for a planet of a given mass increases with orbital distance),
the majority of the ejected planetesimals are expected to be icy. However,
objects subject to multiple close passages by their host star could be ejected
from closer in [103]. In the Solar System, all of the giant planets have
$\Theta>$ 1 while the interior terrestrial planets have $\Theta<$ 1\.
Therefore, the material ejected from the Solar System mostly came from the
outer regions, with Jupiter and Neptune responsible for most of the ejections
and the population of the Oort Cloud and Kuiper belt. It has been argued that
if interstellar planetesimals come from a ubiquitous and isotropic
distribution, it is possible that Jupiter and Neptune analogues are typical in
extrasolar systems [278].

The estimate shown in Table 5 by [287] labeled singles corresponds to the
contribution to the interstellar object population from the ejection of
planetesimals from protoplanetary around single stars and close binaries, as a
result of the planetesimal and planet formation process. In this calculation,
it is assumed that the disk mass is 1% that of the stellar mass, that 1% is in
the form of solids, and that most of the solids are ejected.

####  4.1.2 Contribution from Circumbinary Disks

Intriguingly, circumbinary systems can also be a source of ejected material.
Importantly, this material would be ejected from much closer into the
potential well of the system. This has implications for the composition of the
ejected bodies. In [300], it was estimated that approximately $\sim 1/3$ of
the ejected material would be icy. The remaining fraction would have spent
significant time close to the binary stars prior to ejection, becoming
devolatized. This was used initially as an explanation for the lack of
outgassing activity in 1I/‘Oumuamua [301, 302]. It is intriguing that some
interstellar comets may come from circumbinary systems, and be representative
of material that formed at closer stellocentric distances. Moreover, [303]
demonstrated that misaligned circumbinary disks are even more efficient at
ejecting interstellar comets.

The estimate shown in Table 5 labeled binaries [287] corresponds to
interstellar objects ejected from circumbinary disks. This estimate assumes,
based on [300], that the mass of the circumbinary disk is 10% of the binary
system, that 10% of that material migrates due to gas drag and crosses the
unstable radius at which point the objects are ejected, and that 1% of that
material is solids.

####  4.1.3 Contribution from exo-Oort clouds

Another potential source of interstellar planetesimals are exo-Oort clouds.
These are swarms of planetesimals that, like the Solar System Oort cloud, are
thought to be weakly bound to the central star. The detection of these Oort
clouds lies beyond our current observational capabilities, even for the Solar
System Oort cloud. Based on the observed flux of LPCs in the Solar System, it
is estimated that the Oort Cloud harbors $\sim$1012 objects larger than 2.3 km
([11] and references therein). Oort clouds are thought to be a source of
interstellar planetesimals because, as the central star reaches the end of its
lifetime, it loses mass in its transition to a white dwarf. This mass loss and
the subsequent winds can release the weakly-bound Oort cloud objects into the
interstellar medium [304, 305, 306]. Exo-Oort cloud objects can also be
released via close encounters with other stars [307] or the galactic tide
[308, 309, 310].

The estimate shown in Table 5 labeled Oort cloud [288] corresponds to the
contribution to the interstellar object population from the release of these
putative exo-Oort clouds. Because we lack exo-Oort cloud observations, it is
not clear whether or not typical stars harbor exo-Oort clouds. A study by [47]
found that the Oort cloud formation efficiency is similar at a wide range of
Galactocentric distances. However, [311] found that the parameter space (in
terms of planetary architecture) to form an Oort cloud is quite restricted.
The estimate shown in Table 5 labeled Oort Cloud [288] adopts the simplifying
assumption that exo-Oort clouds are ubiquitous, that they have a population
similar to that of the Oort cloud, but scaled to the stellar mass,
10${}^{12}\,{{\it M_{*}}/{M_{\odot}}}$, and that they are located at distances
similar to that of the Oort cloud, but scaled to Hill radius of its parent
star in the Galactic potential. The calculation further assumes exo-Oort cloud
clearing is caused by post-main sequence mass loss for stars with 1–8 M⊙ and
stellar encounters for stars that are still on their main sequence. It assumes
varying ejection efficiencies as a function of the stellocentric distances
based on previously published dynamical models [308, 309, 310].

However, these post-main sequence stars are necessarily old, and have been
subject to dynamical heating. Therefore, their ejected objects are expected to
have very large velocities as they enter the Solar System. This contrasts with
the low velocity of 1I/‘Oumuamua, indicating that this object is unlikely to
have originated as ejecta from a post main-sequence system. The same is true
for 2I/Borisov, given its hypervolatile composition.

There are many uncertainties in the calculations shown for the different
potential sources. However, the population studies generally find that there
is a discrepancy between the estimated number density of interstellar
planetesimals and that inferred from the detection of 1I/‘Oumuamua. This
discrepancy indicates that there is much to learn about the population of
interstellar planetesimals and their origin. One solution proposed by [287]
could be that 1I/‘Oumuamua was not representative of an isotropic distribution
of interstellar planetesimals. This could be explained if the object
originated in a nearby planetary system. As discussed below, this scenario
would be consistent with 1I/‘Oumuamua’s kinematics.

###  4.2 Kinematics

The incoming velocities of interstellar objects provide critical information
regarding their ages and galactic histories. However, meaningful
interpretations of the kinematics of interstellar objects with regards to
their provenance most likely will require a larger statistical sample.

In the Milky Way, gravitational interactions with Giant Molecular Clouds
(GMCs) and other substrucutures tends to gradually increase the velocity
dispersions of stars [312, 313]. This process is colloquially referred to as
dynamical heating, and manifests most obviously in the out of plane
z-component of galactic velocities. The thin disk of the Milky Way contains
younger stars with lower z-dispersion, while older stars that have experienced
more dynamical heating populate the thick disk and have larger excursions out
of the galactic plane. Younger stars like B0 stars have typical dispersions of
10s of km s-1, while older stellar populations exhibit higher dispersions
[314]. Transient structures like GMCs are much younger and have much lower
dispersions $\sim 1$ km s-1 [315]. However, these estimates are complicated by
a large systematic uncertainty in the velocity of the Sun with respect to the
Local Standard of Rest (LSR) [316, 317].

1I/‘Oumuamua exhibited a surprisingly low hyperbolic velocity of 26 km s-1
when compared to the 15$\pm$2 km s-1 velocity of the Sun relative to the LSR
[318]. 2I/Borisov exhibited a larger relative velocity of 32 km s-1. This is
indicative that 2I/Borisov has been subject to substantially more dynamical
heating than 1I/‘Oumuamua, which is presumably due to an older galactic age.
The approximate dynamical ages of these objects have been inferred to be
$\tau_{s}\sim 10^{8}$ yr for 1I/‘Oumuamua [318, 319, 320, 321] and for
2I/Borisov $\tau_{s}\sim 10^{9}$ yr [320]. It should be noted that these ages
are only statistical in nature.

Another indicator of a young age for 1I/‘Oumuamua is its suggested tumbling
state with [73] hypothesizing that the tumbling state could be related to a
collision in its parent system. This would suggest that the object is younger
than $\sim$ 1 Gyr, corresponding to the damping timescale due to stresses and
strains resulting from complex rotation for an object with 1I/‘Oumuamua’s
inferred properties. A recent ejection is also consistent with the fact that
1I/‘Oumuamua’s surface did not seem to be heavily processed based on its
color. As mentioned in subsection 2.3.2, unlike the cold classical Kuiper belt
objects that are ultra-red because of billions of years of exposure to cosmic
rays, plasma and radiation, 1I/‘Oumuamua’s surface was not ultra-red.

###  4.3 Tracing Interstellar Objects to Progenitor Systems

The statistical nature of stellar dynamics makes it difficult to infer a home
system for a single interstellar object based on the galactic kinematics.
Moreover, the chaotic nature of the galactic motions and the uncertainty in
stellar kinematic measurements complicates this task further. In [318], it was
suggested that 1I/‘Oumuamua’s trajectory was sufficiently distinct from all
local stars such that it was not co-moving with any single one and therefore
not associated with any local exo-Oort clouds. However, [319] suggested that
the kinematics of 1I/‘Oumuamua pointed to its formation in a protoplanetary
disk in the Carina or Columba young stellar associations.

Rigorous analysis of the galactic history of 1I/‘Oumuamua concluded that it
likely originated within 1 kpc of the Earth, based on its young dynamical age
[320]. While identification of a home system is not possible, they reported
that 1I/‘Oumuamua likely passed through a large subset of the Carina and
Columba moving groups at the time that those groups were forming. A similar
set of dynamical simulations performed by [321] were consistent with these
results, pointing towards formation within a Giant Molecular Cloud. As for
2I/Borisov, [320] demonstrated that identifying its home system is effectively
impossible.

As pointed out earlier, it is critical to note that if 1I/‘Oumuamua had a
local origin, the implied $n\sim$ 0.1 au-3 number density based on its
detection may not apply to the entire Galaxy. Furthermore, [287] argued that
if 1I/‘Oumuamua was ejected from a young nearby star, the spatial density may
be highly anisotropic. This would somewhat resolve the discrepancy between the
expected number density of interstellar objects and that inferred from the
detection of 1I/‘Oumuamua which had assumed an isotropic distribution.

Other attempts to trace 1I/‘Oumuamua to a home system were unsuccessful. In
[322], the search for previous stellar close encounters with 1I/‘Oumuamua
resulted in none. They noted a $\sim 2.2$ pc close encounter with the nearby
planet-bearing star Gliese 876 [323], but this distance is too far to provide
a definitive association. A different study by [324] broadened this analyses
and identified 109 potential close encounters but no definitive home system.
Another study by [325] presented a generalized method to estimate the
probability that an interstellar object is associated with a stellar system, a
methodology that should be useful when a statistical sample of interstellar
object kinematics is available. They noted a slight association with the
binary star system HD200325. Even with accurate stellar kinematics from the
European Space Agency (ESA) mission Gaia [326], [327] and [328] reported
unlikely prospects to trace a single interstellar object to a host system.

###  4.4 Size-Frequency Distribution of Interstellar Comets

Constraining the size-frequency distribution of the galactic population of
interstellar objects is difficult at the large end of the spectrum because
there are only two detections of macroscopic interstellar objects. However,
there is a long history of studies focusing on the size-frequency distribution
of interstellar dust, showing a well-established power-law. Extrapolations of
these distributions are tentatively consistent with the implied occurrence
rate of 1I/‘Oumuamua [66], although caution should be used when extrapolating
based on such small number statistics.

Measurements of interstellar dust date back to the Ulysses and Galileo
spacecrafts. Combined cumulative results from both of these spacecrafts were
reported in [329] and individual spacecraft measurements were reported in
[330], [331] and [332]. A controversial detection of an interstellar meteor
with the Arecibo Observatory was reported in [333]. Subsequent radar
measurements with the Arecibo UHF (430 MHz) were reported by [334] and [335].
The first radar-based detection of micron-sized hyperbolic meteors with the
Advanced Meteor Orbit Radar (AMOR) was attributed to the debris-disk host star
$\beta$ Pic [336, 337, 338]. The lower limit from the Canadian Meteor Orbit
Radar (CMOR) from twelve possible interstellar events from 1.5 million
measured orbits were reported by [339].

At the larger end of the spectrum, [340] analyzed the extant video data
(multi-station photographic and television techniques) to constrain the flux
of large interstellar meteoroids. An upper limit using optical data with the
Canadian Automated Meteor Observatory (CAMO) was reported by [341]. An
extensive analysis of the IAU Meteor Data Center photographic database showed
that the vast majority of the apparent hyperbolic meteors were a consequence
of measurement error [342, 343].

These data are broadly compatible with a $r_{n}^{-3}$ size distribution for
interstellar particles, including for 1I/‘Oumuamua and free-floating planets
[288, 344, 66]. Larger particles in principle could produce interstellar
meteors. These would have large excess velocities and trajectories with
eccentricies $e>1$. However, these interstellar meteors are notoriously
difficult to identify because planetary perturbations can scatter particles
onto hyperbolic trajectories [345, 346]. Therefore, extremely precise
measurements of the incoming velocity vector would be required to verify a
meteor as interstellar [347]. Recently, there have been claims of interstellar
meteors detected in the CNEOS database [348, 349]. However, it is well
established that these observations are susceptible to poor accuracy of data.
The reported velocity vectors are most notoriously untrustworthy, which are
instrumental in aquiring pre-impact trajectories and meteorite fall positions
[350]. Moreover, the number of apparently hyperbolic events in databases,
which have been routinely detected for decades, is used primarily as an
estimation of the typical error in the detection method. The claims of the
interstellar nature of meteorites are largely disproven due to the poor
quality of the data and the nondisclosure of error bars [351].

As discussed in subsection 4, the comparison of the expected mass budget of
ejected planetesimals from extrasolar planetary systems, based on population
studies, to the mass budget of interstellar planetesimals, inferred from the
detection of 1I/‘Oumuamua, shows a significant discrepancy [287]. A critical
assumption in the calculation of the latter is the albedo and size of
1I/‘Oumuamua, and the expected size distribution of interstellar objects.
Given the large uncertainties in the latter, the size distribution that is
adopted is based on the small body population of the Solar System. This allows
for a wide range of possible values that define a broken power-law [287]. Even
when adopting this wide range of values, the discrepancy in the mass budget is
still present.

###  4.5 Captured Interstellar Objects in the Solar System?

It has been hypothesized that the Solar System could capture unbound objects
from the Galaxy via its gravitational perturbations. This process requires
some external force to modify the hyperbolic trajectory of an interstellar
object to make it bound by the Solar System. This capture process could be
driven by external stellar flybys of the tidal galactic gravitational field.
Alternatively, it may be driven by more localized perturbations from a Solar
System planet. It has also been hypothesized that some of the Oort cloud
comets in the Solar System were captured from other Oort clouds around other
stars. This would require the tidal galactic field to impart torques on
passing objects. This process may have been more efficient during the earliest
phases of the formation of the Solar System, when it was in a birth cluster
containing many stars [352]. More recent calculations have estimated that the
Solar System harbors $\sim 10^{7}$ trapped 1I/’Oumuamua-size interstellar
objects within $\sim$ 20 000 au [353].

The interstellar objects that pass interior to Neptune could in theory come
close to one of the planets and be captured into the Solar System. Since the
discovery of 1I/‘Oumuamua, several studies have performed detailed
calculations to quantify the effectiveness of this process [354, 355]. By in
large these studies agree that it is a relatively ineffective process, and
only $\simeq 10^{-9}\,M_{\oplus}$ of interstellar material should be present
in the Solar System [356]. With a different set of assumptions, [357]
estimated that $\sim 8$ captured interstellar objects would exist within 5 au
of the Sun.

There was a claim that Centaurs and Trojans with high inclination, retrograde
orbits were captured interstellar objects [358]. However, this was quickly
disproved, when [359] pointed out that these objects are more likely to come
from transient capture of Oort cloud comets. It therefore seems unlikely that
captured interstellar objects will be detected in the Solar System.

###  4.6 Interstellar Planetesimals Seeding Planet Formation

A long standing obstacle in the theory of planetary formation is the so-called
“meter barrier”. The formation of cm-sized particles is efficient and has been
well studied [360, 361]. At the meter size, however, collisions between
particles have increasing collisional energies and are prone to trigger
shattering events [362]. Moreover, these larger objects are subject to rapid
inward drift timescales as the protostellar gas provides a drag force which
removes angular momentum and causes the particles to quickly inspiral. This
process significantly limits the lifetime of growing planetesimals in the
disk. Several theoretical advances have been proposed to alleviate this
problem: the streaming instability which rapidly agglomerates particles into
larger objects on secular timescales [363]; the direct formation via
gravitational instability [364]; the presence of low-velocity collisions in
the velocity distribution of the dust particles, favoring growth ([365]; the
trapping of dust grains in pressure maxima [366]; and the effect of low
porosity and the electric charging of dust aggregates to favor sticking over
fragmentation [367, 368].

The discovery of the first interstellar objects led to an additional proposal
to alleviate the “meter barrier”: the capture of interstellar objects by gas
drag into star- and planet-formation environments. This could occur during an
early stage, when the objects are trapped into Giant Molecular Clouds. The
captured objects tracing the collapse of the prestellar core may subsequently
become incorporated into fragmenting star- and planet-forming regions [369,
370]. Moreover, interstellar objects may also be captured by already formed
protoplanetary disks [371]. These ideas were further explored by [372] who
considered the efficiency of capturing and incorporating interstellar
planetesimals into star- and planet-forming regions, as a function of their
velocity dispersion, size distribution and number density. They found that,
when assuming a background number density of 0.2 au-3 (derived from [279]), a
velocity dispersion of 30 km s-1 (characteristic of the young stars in the
Galaxy from where interstellar objects likely originated), and an equilibrium
size distribution of $q^{\prime}$ = 3.5, the number of interstellar objects
captured by a Giant Molecular Cloud and expected to be incorporated into each
protoplanetary disk during their formation would be $\mathcal{O}$(109) (50
cm–5 m), $\mathcal{O}$(105) (5–50 m), $\mathcal{O}$(102) (50–500 m),
$\mathcal{O}$(10-2) (500 m–5 km). During a later stage, when the
protoplanetary disk is formed, the number of interstellar objects that could
be captured from the interstellar medium during its lifetime would be
$\mathcal{O}$(1012) (50 cm–5 m), $\mathcal{O}$(108) (5–50 m),
$\mathcal{O}$(105) (50–500 m), $\mathcal{O}$(101) (500 m–5 km). In an open
cluster where $\sim$1% of stars have undergone planet formation, these values
would increase by a factor of $\mathcal{O}$(102–103). These trapped
interstellar objects might be large enough to rapidly grow into larger
planetesimals via the direct accretion of the subcm-sized dust grains in the
protoplanetary disk before they drift inwards due to gas drag. This provides a
promising alternative avenue to overcome the meter barrier, with interstellar
planetsimals acting as “seeds” for planet formation.

The estimates above by [372] are very uncertain because, as discussed in
subsections 4.1 and 4.4, the number density and velocity and size distribution
of interstellar objects are uncertain. These estimates will be substantially
refined as the population of interstellar objects becomes better
characterized. However, these preliminary studies have shown that as the
number density of interstellar planetesimals in the Galaxy increases with
time, their trapping in star- and planet-formation environments may be
significant. Therefore, future star- and planet-formation models should take
into account the presence of this population of captured objects to assess if
it can significantly influence planet formation, particularly in cluster
environments.

##  5 Future Prospects

###  5.1 Orbits of Interstellar Objects in the Solar System

There has been significant interest in identifying the future prospects for
the detection and characterization of interstellar objects. As discussed
previously (subsection 4.1), the discovery of 1I/‘Oumuamua, if representative
of an isotropically distributed population, might imply that a galactic
population of similar objects exists with spatial number density of $n\sim
0.1~{}{\rm au}^{-3}$. There has therefore been significant efforts invested
into identifying the expected orbital distributions of interstellar objects
that travel through the Solar System.

The kinematic distribution of local stars in the local stellar neighborhood is
well measured (see subsection 4.2). Moreover, interstellar objects should
represent a better realization of the kinematics of the gravitational
potential of the Milky Way since there are estimated to be orders of magnitude
more of them than stars in the Galaxy. Assuming that the incoming interstellar
objects trace this velocity distribution, the distribution of orbits expected
for the interstellar objects that pass through the Solar System can be
calculated.

This is straightforward to implement numerically via a Monte Carlo method.
This was performed by [286] and [285] prior to the detection of 1I/’Oumuamua.
After its discovery, with updated number densities, these simulations were re-
performed and modified by [373] and [374]. With an elegant mathematical
analysis, [375] provided an entirely analytic method to calculate the
distribution of interstellar object orbits. They showed comparisons of their
analytic method (which they label the probabilistic method) – with the
numerical method previously performed (that they refer to as the dynamical
method), demonstrating that the probabilistic method is orders of magnitude
more computationally efficient and also more accurate. The resulting
distribution of perihelia is shown in Figure 10, for interstellar comet
populations with galactic velocity dispersions of various stellar populations.
In all cases, the number of interstellar objects passing through the Solar
System varies linearly with perihelia.

Figure 10:  Predicted perihelia distribution of interstellar objects from the
probabilistic method generated by [375]. Distributions are shown assuming
incoming kinematics of various stellar populations. Reproduced with permission
from [375].

###  5.2 Ground Based Prospects

The forthcoming Rubin Observatory Legacy Survey of Space and Time (LSST) [376,
377] will be efficient at detecting transient objects [378, 379, 380, 381].
Literature estimates based on survey detection efficiency and criteria and
number densities estimate that the survey will detect $\sim$1-3 1I/‘Oumuamua-
like interstellar object per year [284, 285, 286, 277, 373, 374, 375].

The most recent study of the of the expected distribution of interstellar
objects by [374] included a calculation of the distribution of orbital
elements and close approaches to the Earth of interstellar objects that will
be detected by the LSST. They incorporated a set of LSST detection criteria in
this analysis that required that the elongation angle and phase be such that
the the LSST would be able to detect the object. The results of this
simulation are shown in Table 6, and show that the LSST should detect 1-2
interstellar objects per year.

###  5.3 Space Based Prospects

The forthcoming NEO Surveyor [382] may also detect interstellar objects. NEO
Surveyor has a 50 cm diameter telescope and will be located interior to
Earth’s orbit at L1. The mission has been optimized to find small bodies out
to Jupiter that could be potentially hazardous. Moreover, the mission will
provide thermal infrared measurements of these objects. NEO Surveyor and
possibly JWST will be able to characterize both the sizes and albedos of these
objects.

Recently, ESA selected the Comet Interceptor [383] which will fly in 2029.
Comet Interceptor has a low $\Delta V\sim$ 1 km s-1 budget, and is designed to
rendezvous with a LPC. If an interstellar object is detected with a
serendipitously fortuitous orbit, then it is possible that Comet Interceptor
will reroute and rendezvous with it. For example, [373] showed that an
impactor mission to 1I/‘Oumuamua sent from Earth would have been achievable
with a $\Delta V\sim$ 4 km s-1 impulse given an earlier detection and
sufficient lead time. About 10% to 30% of the interstellar interlopers to be
detected by the LSST (Table 6) should be reachable by a mission with $\Delta$V
$<$ 15 km s-1 [374]. There has been ample work done to design such a dedicated
mission to an interstellar object [384, 373, 385, 386, 383, 387, 388, 389,
390, 391, 392, 393, 394, 395, 396, 397, 398], and it seems likely that a
handful of reachable targets will be detected.

The study of interstellar objects, still in its infancy, will experience a
revolution with upcoming ground-based and space-based observations. These will
not only help us understand the origin(s) of this new component of the
interstellar medium and the clues it unveils regarding planet formation, but
will also allow for the extraordinary opportunity to study a fragment from
another planetary system at close-range.

Table 6: The frequency that interstellar objects are detectable by the LSST and reachable with a range of $\Delta$V criteria. These calculations assume that each interstellar object has the same absolute magnitude as that of 1I/‘Oumuamua. Reproduced from [374].  Criterion | Percent | Conservative Rate | Optimistic Rate
---|---|---|---
|  | per Year | per Year
$m\leq 24$ |  $\sim$7.0% | $\sim 2.3$ | $\sim 4.6$
Detectable with the LSST |  $\sim$2.8% | $\sim 0.9$ | $\sim 1.9$
Detectable, $\Delta V<30$ km/s |  $\sim$1.1% | $\sim 0.35$ | $\sim 0.7$
Detectable, $\Delta V<15$ km/s |  $\sim$0.4% | $\sim 0.1$ | $\sim 0.3$
Detectable, $\Delta V<2$ km/s | 0.002% | $\sim 7\times 10^{-4}$ | $\sim 0.001$

## Acknowledgement(s)

We thank Dušan Marčeta for providing simulation results for Figure 10. We
thank Davide Farnocchia and Marco Micheli for detailed reviews of the
manuscript prior to submission. We thank Jennifer Bergner, Aster Taylor, Lisa
Kaltenegger, Dave Jewitt, Adina Feinstein, Fred Adams, Dong Lai, Nikole Lewis,
Greg Laughlin and Juliette Becker for useful suggestions and conversations.

## Funding

DZS acknowledges financial support from the National Science Foundation Grant
No. AST-2107796, NASA Grant No. 80NSSC19K0444 and NASA Contract NNX17AL71A
from the NASA Goddard Spaceflight Center.

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