The Planet Nine Hypothesis (Part 14)

 February 23, 2026

and combine these results with the rate of stellar encounters to determine an optical depth, τ_s, for scattering (Adamsand Laughlin, 2001; Li and Adams, 2015; Adams et al., 2006; Proszkow and Adams, 2009). This quantity can be written in the form

τ_s = , n_∗ (v σ_int) dt , (19)

where n_∗ is the number density of stars in the system, v is the relative speed between the Sun and other systems, and σ_int is the interaction cross section. The angular brackets denote averages over both the velocity distribution and the stellar initial mass function for the cluster members.

For interactions in a cluster with velocity dispersion of v_c = 1 km/s, and a planet with an aphelion distance of 640 AU (comparable to our best-fit P9 orbital solution obtained in section 5), Li and Adams (2016) derive an ejection cross-section of σ_int

2.5 10⁶ AU². Adopting a stellar number density of n = 100 pc^–3 and a cluster lifetime of ∆t = 100 Myr, we obtain τ_s 0.4²², which translates to a P9 survival probability

of exp( τ_s) 2/3. In other words, integrated over the lifetime of the cluster, the probability of ejecting Planet Nine is of order 30%.

Once the solar system emerges from its birth cluster, the probability that Planet Nine can be stripped from the solar system by a passing star diminishes dramatically. In particular, for scattering interactions in the field (Binney and Tremaine, 2008), the stellar density is much lower ( n_∗ 0.1 pc^–3) and the velocity dispersion is higher (v_c 40 km/s). The higher interaction speeds lead to much lower ejection cross sec-

tions (see Li and Adams 2015), which more than compensates for the longer residence time (about 4.5 Gyr). As a result, the corresponding scattering optical depth for the ejection of Planet Nine in the solar neighborhood is essentially negligible – τ_s 0.002 – 0.02. In other words, once the solar system emerges from its birth cluster, and Planet Nine attains its required orbit, it has an excellent chance of continued survival.

In light of the fact that ejection of planets constitutes a distinct possibility within the early evolution of the solar system, the same reasoning applies to other members of the solar system’s birth cluster. This opens up the possibility that rather than originating within the solar system, Planet Nine was ejected from some other planetary system, and was subsequently captured by the sun’s gravitational field. This P9 capture scenario has been recently considered by a number of authors (Li and Adams, 2016; Mustill et al., 2016; Parker et al., 2017). However, a multitude of requirements must be met in order for successful capture to take place.

One limiting factor is that the scattering encounter must be sufficiently distant so that the cold classical population of the Kuiper Belt (which is likely primordial; Batygin et al. 2012) is not destroyed. This demand implies that the impact parameter exceeds b ^> 150 200 AU. More constraining is the requirement that the final orbital elements of the captured planet be consistent with those inferred for Planet Nine. For the condi- tions expected in the solar birth cluster, the probability for successful capture is of order a few percent, both for freely floating planets (Li and Adams, 2016), and for planets captured from other planetary systems (Mustill et al., 2016). More recent work (Parker

²²Following Li and Adams (2015), we have accounted for the fraction of single (vs binary) stellar encoun- ters by reducing τ_s by a factor of 2/3.

et al., 2017) finds even lower probabilities, with successful captures of freely floating planets estimated to be only 5 – 10 out of 10⁴. In addition, planet capture is enhanced for expanding, unbound clusters. In contrast, solar system enrichment of short-lived radiogenic isotopes is enhanced for subvirial (partially collapsing) clusters, so some tension exists between the requirement of capturing Planet Nine and explaining mete- oritic enrichment.

1. Conclusion

Over the past decade and a half, continued detection of minor bodies in the distant solar system has brought the intricate dynamical architecture of the distant Kuiper belt into much sharper focus. Staggeringly, the collective orbital structure of the current census of long-period trans-Neptunian objects offers a number of tantalizing hints at the possibility that an additional massive object – Planet Nine – may be lurking beyond the current observational horizon of the distant solar system. In this work, we have presented a comprehensive review of the observational evidence, as well as the analyti- cal and numerical formulation of the Planet Nine hypothesis. The emergent theoretical picture is summarized in section 8.1, followed by a discussion of alternate explanations for the observed orbital anomalies (section 8.2) and prospects for future work (section 8.3).

1. Summary of Results

The case for the existence of Planet Nine can be organized into the following four primary lines of evidence.

Orbital Alignment of Long-Period KBOs. The observed collection of dynamically stable Kuiper belt objects with semi-major axes in excess of a ^> 250 AU (orbital peri- ods greater than P & 4000 years), reside on orbits that are clustered together in phys- ical space. This clustering is statistically significant at the 99.8% significance level, and ensues from the simultaneous alignment of the apsidal lines (equivalently, longi-

tudes of perihelion) as well as the orbital planes (which are dictated by the inclinations and the longitudes of ascending node). Because the orbits precess differentially under perturbations from the known giant planets, a sustained restoring gravitational torque is required to preserve the orbital grouping. Dynamical evolution induced by Planet Nine can fully account for the generation and maintenance of the observed alignment of long-period KBOs, while simultaneously allowing for their orbital stability.

Detachment of Perihelia. Long-period KBOs exhibit a broad range of perihelion dis- tances, with a substantial fraction possessing q > 40 AU. Such objects are dynamically decoupled from Neptune, and cannot be created during Kuiper belt formation via in- teractions with the known planets alone. As a result, this population of KBOs requires external gravitational perturbations to lift their perihelia. Within the framework of the Planet Nine hypothesis, the same dynamics that are responsible for the aforementioned apsidal alignment also provide a means of generating Neptune-detached Kuiper belt objects, thereby explaining their origins.

Excitation of Extreme TNO Inclinations. Trans-Neptunian objects with inclinations in excess of i & 50 deg are not a natural outcome of the solar system formation process. Nevertheless, several objects with inclinations well above 50 deg have been detected on wide (a > 250 AU) orbits, including the recently discovered KBO 2015 BP₅₁₉ which is the only known member of this class characterized by q > 30 AU. Despite their puz- zling nature, such highly inclined objects are routinely produced within the framework

of the P9 hypothesis, via a high order (octupolar) secular resonance with Planet Nine.

Production of Retrograde Centaurs. In addition to long-period TNOs with i > 50 deg, the solar system also hosts a multitude of highly inclined, and even strongly retrograde shorter-period (a < 100 AU) objects. As with their distant counterparts, the dynam- ical origins of such objects is inexplicable through perturbations from the known gi- ant planets alone. Although these objects are decoupled from Planet Nine’s gravita- tional influence today, numerical simulations demonstrate that an intricate interplay between P9-induced dynamical evolution and Neptune scattering can deliver highly inclined long-period TNOs onto shorter period orbits, polluting the classical region of the Kuiper belt with highly inclined Centaurs. More generally, this process allows for the injection of objects that trace through orbits in the retrograde direction, into the trans-Jovian domain of the solar system.

Each of the above dynamical effects can be understood from purely analytic grounds within the framework of the Planet Nine hypothesis. Simplified models of this sort, based on secular perturbation theory, are presented in section 4. Detailed comparison with the data, however, requires the fabrication of a synthetic population of long-period KBOs using large-scale N-body simulations. The results of thousands of such simu- lations are described in section 5, and collectively point to a revised set of physical and orbital parameters for Planet Nine. Specifically, compared to the original results

(Batygin and Brown, 2016a), where P9 was reported to have m₉ 10M_⊕ and occupy an a₉ = 700 AU orbit with e₉ = 0.6, the current simulations (reviewed in section 5), point towards a marginally lower-mass planet that resides on a somewhat more prox- imate and less dynamically excited orbit, with m₉ 5 10M_⊕, a₉ 400 800 AU, e₉ 0.2 0.5, and i₉ 15 25 deg. Perhaps counterintuitively, the increase in bright- ness due to a smaller heliocentric distance more than makes up for the decrease in brightness due to a slightly diminished physical radius, suggesting that Planet Nine is more readily discoverable by conventional optical surveys than previously thought.

1. Alternative Explanations

As a formulated dynamical model, the Planet Nine hypothesis provides a satisfac- tory account for the orbital anomalies of the distant solar system. Nevertheless, until the existence of Planet Nine is confirmed observationally, the possibility that the envi- sioned theory is incorrect will continue to linger. The history of proposed planets based on dynamical anomalies suggests that this option should be taken seriously. In this vein, it is useful to recall the cautionary tale surrounding the prediction and subsequent abandonment of planet Vulcan (see section 1.3), as it illuminates the vulnerability of even the most well-formulated theoretical models.

While it is unlikely that the asym- metries of the orbital structure of the distant solar system point to fundamentally new physics (as in the case of Vulcan), we must acknowledge alternative explanations for the observations that do not invoke the existence of Planet Nine. These ideas generally fall into two distinct categories, and we briefly discuss their attributes below.

Observational Bias. If the Planet Nine hypothesis proves to be unnecessary, perhaps the most likely explanation is that no explanation is required. One can envision a sce- nario where the observational strategy and serendipity conspire to produce the observed patterns in the data. In this case, the apparent clustering in longitudes of perihelion and orbital poles would be spurious, and the underlying distribution of orbital angles of the distant solar system objects would be uniform (e.g., Lawler et al., 2017; Shankman et al., 2017).

The upshot here is that this interpretation can be quantified by a well-defined sta- tistical likelihood. As discussed in section 3, the associated false-alarm probability is estimated to be less than one percent (Brown and Batygin, 2019). Beyond angular clustering alone, the statistical significance of the Planet Nine hypothesis is further re- inforced by the fact that multiple lines of evidence all point to the same Planet Nine model. Specifically, not only can the orbital alignment of the distant TNOs be under- stood in terms of a new planet, the existence of perihelion-detached objects, as well as the generation of the observed high inclination objects also naturally emerge within the framework of the same theoretical model. While observational bias can never be completely ruled out as an explanation for the data, continued detection of long-period Kuiper belt objects (e.g., Sheppard et al. 2018; Khain et al. 2018b, etc) will lead to further refinement of the false-alarm probability.

Self-Gravity of the Distant Kuiper Belt. A separate class of models posit that the ob- served structure of the distant solar system is real but is not sculpted by a planet, and instead arises from the collective gravity of the distant Kuiper belt. The first of these theories is due to Madigan and McCourt (2016), who propose that the distant solar sys-

tem contains 1 10M_⊕ of unseen material. Over Gyr timescales, this population of objects experiences coupled inclination-eccentricity evolution – a process the authors

refer to as the “inclination instability” (see Madigan et al. 2018 for further discussion). The development of this instability results in a clustered distribution of the arguments of perihelion of the constituent bodies, in agreement with the anomalous pattern first pointed out by Trujillo and Sheppard (2014). However, this model provides no ex- planation for the observed confinement in the longitudes of perihelion as well as the angular momentum vectors, and thus fails to reproduce the actual observed structure of the distant belt. Moreover, the inclination instability does not naturally manifest in numerical simulations of Kuiper belt emplacement that self-consistently account for self-gravity of the planetesimal disk, calling into question the specificity of initial con- ditions required for this model to operate (Fan and Batygin, 2017).

A different self-gravity model has been recently proposed by Sefilian & Touma (2018). In this theory, instead of the observed Kuiper belt contributing to the collective potential of the trans-Neptunian region, there exists a moderately eccentric (e ~ 0.2) shepherding disk that extends from a_in = 40 AU to a_out = 750 AU, comprising 10M_⊕ of material in total. The gravitational potential of this disk creates a stable, apsidally

anti-aligned secular equilibrium at high eccentricity that facilitates the confinement ofthe longitudes of perihelion of the observed long-period KBOs (which act as test par- ticles, enslaved by the disk’s potential). In light of the fact that the primary mode of dynamical evolution induced by Planet Nine itself is secular in nature (and in an orbit-averaged sense, the gravitational potential of Planet Nine is not different from a massive wire that traces its orbit), there are clear mathematical similarities that ensue between this model and the analytical formulation of the P9 hypothesis (section 4). Nevertheless, from the point of view of planet formation, the prolonged existence of the envisioned shepherding disk suffers from many of the same drawbacks outlined

in section 7.1 (e.g., radiative stripping of r & 50 AU protoplanetary disk material, disruptive perturbations due to passing stars in the birth cluster, etc.) as well as the ap-

parent incompatibility with the striking decrease in observed number of KBOs beyond

a & 48 AU.

1. Future Directions

One result of this review is that numerical simulations containing Planet Nine can produce orbits that are in good agreement with the observed structure of the distant Kuiper belt. Nonetheless, a number of theoretical questions remain unanswered, and their resolution may help illuminate the path toward the direct detection of the most distant planetary member of the solar system. As a result, we conclude this article with a brief (and incomplete) discussion of some problems that remain open within the broader framework of the Planet Nine hypothesis.

The Inclination Dispersion of Jupiter-Family Comets. The inward scattering of TNOs that have been strongly influenced by Planet Nine constitutes a dynamical pathway through which highly inclined icy bodies can be delivered to much smaller heliocen- tric distances. In this way, Planet Nine can affect not only the orbital properties of the Kuiper belt itself, but the inclination dispersion of Jupiter-Family comets, which are sourced from the trans-Neptunian region (Duncan et al., 1988). In a recent study, Nesvorny´ et al. (2017) carried out detailed simulations of the generation and evolution

of short-period comets, and found that inclusion of a m₉ = 15M_⊕ Planet Nine that resides on a a = 700 AU, e = 0.6 orbit leads to a simulated inclination dispersion of Jupiter-Family comets that is broader than its observed counterpart.

Importantly, however, the simulation suite presented in section 5 of this work fa- vors a lower mass, more circular Planet Nine over the parameters adopted by Nesvorny´ et al. (2017). Because the inclination excitation of long-period TNOs is driven by octupole-level secular interactions with P9, we can reasonably expect that our revised P9 parameters would significantly diminish both the rate, and the efficiency of high-i comet generation, potentially eliminating any discrepancy between the observed and modeled orbital distributions. A quantitative evaluation of the possibility is of substan- tial interest.

Contamination of the Distant Kuiper Belt. Within the current observational sample of distant KBOs, orbital clustering exhibited by long-term (meta)stable KBOs is consid- erably tighter than that of the unstable objects. Qualitatively, this disparity is sensible since unstable objects actively interact with Neptune, and can be 

rapidly perturbed away from P9-sculpted dynamical states. Moreover, given their rapid excursions in

The Planet Nine Hypothesis (Part 13)

 February 22, 2026

consider an upper limit to the mass of Planet Nine, the most distant acceptable orbit has a₉ = 800

AU, e₉ = 0.45, and an aphelion of 1160 AU. Such an object would have an aphelion magnitude between 23.0 and 24.0 (perihelion magnitude between 19.9 and 20.8).

Counterintuitively, a lower mass Planet Nine is brighter owing to its requirement for a smaller heliocentric distance to have the same dynamical effect. To this end, a 5 M_⊕ Planet Nine, for example, is bright enough to be detectable by wide-field surveys such as Pan-STARRS throughout most of its orbit. It is not yet known how complete the moving object search for Pan-STARRS is, but with the survey still ongoing a discovery

could in principle happen at any time. An important complication, however, lies in that the inferred aphelion of Planet Nine’s orbit is close to the intersection between P9’s orbital path and the galactic plane, where higher source density can impede detection (see Figure 25).

A higher mass and thus more distant Planet Nine will require a dedicated survey along the predicted orbital path (Brown and Batygin, 2016), but with a lower limit to the brightness of 24th magnitude, such an object is readily observable by the cur- rent generation of telescopes with wide field cameras such as the Dark Energy Camera on the Blanco 4m telescope in Chile and the Hyper-Suprime Camera on the Subaru telescope in Hawaii. Finally, all but the very faintest possible Planet Nine will be ob- servable with the Large Scale Synoptic Telescope (LSST), currently under construction in Chile and scheduled for operations in 2022. Therefore, Planet Nine – if it exists as described here – is likely to be discovered within a decade.

1. Infrared and Microwave Surveys

While detecting sunlight reflected at optical wavelengths might seem like the natu- ral method for searching for Planet Nine, the 1/r⁴ dependency of the flux of reflected sunlight makes the brightness of any object drop precipitously with distance. At long wavelengths, thermal emission, on the other hand, drops as only T /r², where T could be approximately constant with distance (or drop as 1/r² if the planet is in thermal equilibrium with the sun). For sufficiently distant planets, thermal emission constitutes a potentially preferable avenue towards direct detection. While current cosmological experiments at millimeter wavelengths have sufficient sensitivity to detect Planet Nine (Cowan et al., 2016), a systematic search would require millimeter telescopes with both high sensitivity and high angular resolution to robustly detect moving sources. The proposed CMB S-4, a next-generation cosmic microwave background experiment (Abazajian et al., 2016) could fulfill these requirements. Such an observatory would be sensitive not only to Planet Nine, but to putative even more distant bodies that might be present in the solar system.

It is worth noting that Planet Nine could emit more strongly than a blackbody at some wavelengths. Fortney et al. (2016) found that in extreme cases the atmosphere of Planet Nine could be depleted of methane and have order of magnitude more emis- sion in the 3-4 µm range. Meisner et al. (2017b) exploited this possibility to search for Planet Nine in data from the Wide-field Infrared Survey Explorer (WISE) dataset. In particular, they examined 3u steradians and placed a strongly atmospheric-model- dependent constraint on the presence of a high-mass Planet Nine at high galactic lati- tudes.

2. Gravitational Detection

A separate approach towards indirect detection of Planet Nine was explored by Fienga et al. (2016). Employing ranging data from the Cassini spacecraft, these au- thors sought to detect Planet Nine’s direct gravitational signature in the solar system ephemeris (somewhat akin to the technique Le Verrier 1846a,b used to discover Nep- tune; section 1.1). Adopting the P9 parameters from (Batygin and Brown, 2016a), they were able to immediately constrain P9 to the outer ~ 50% of the orbit (in agreementwith observational constraints; Brown and Batygin 2016). Moreover, the calculations of Fienga et al. (2016) point to a small reduction in the residuals of the ranging data if the true anomaly of P9 is taken to be u₉ 118 deg. This line of reasoning was further explored by Holman and Payne (2016a,b), who additionally considered the long base- line ephemerides of Pluto to place additional constraints on the sky-location of Planet Nine.

The reanalysis of the ephemeris carried out by Folkner et al. (2016), however, high- lights the sensitivity of Fienga et al.’s results to the specifics of the underlying dynam- ical model, suggesting that the gravitational determinations of Planet Nine’s on-sky location are in reality considerably less precise than advocated by Fienga et al. (2016); Holman and Payne (2016a,b). An additional complication pertinent to this approach was recently pointed out by Pitjeva & Pitjev (2018), who caution that failure to prop- erly account for the mass contained within the resonant and classical Kuiper belt (which

they determine to be on the order of 2 10^–2 M_⊕) can further obscure P9’s gravitational signal in the solar system’s ephemeris. Particularly, Pitjeva & Pitjev (2018) find that the anomalous acceleration due to a 0.02 M_⊕ Kuiper belt is essentially equivalent to that arising from a m₉ = 10 M_⊕ planet at a heliocentric distance of r = 540 AU (for orbits around Saturn), further discouraging the promise of teasing out Planet Nine’s

gravitational signal from spacecraft data.

1. Formation Scenarios

In terms of both physical and orbital characteristics, the inferred properties of Planet Nine are certainly unlike those of any other planet of the solar system. Re- cent photometric and spectroscopic surveys of planets around other stars (Borucki et al., 2010; Batalha et al., 2013), however, have conclusively demonstrated that m

5 10 M planets are exceedingly common around solar-type stars, and likely repre- sent one of the dominant outcomes of the planet conglomeration process²⁰. A moder- ately excited orbital state (and in particular, a high eccentricity) is also not uncommon among long-period extrasolar planets, and is a relatively well-established byproduct of post-nebular dynamical relaxation of planetary systems (Juric´ & Tremaine, 2008). Nevertheless, the formation of Planet Nine represents a formidable problem, primarily due to its large distance from the sun.

To attack this speculative issue, several different origin scenarios have been pro- posed and are discussed in this section. The first option is for the planet to form in situ, via analogous formation mechanism(s) responsible for the known giant planets (section 7.1). Another option is for Planet Nine to form in the same annular region as the other giant planets, and then be scattered outward into its present orbit (section 7.2). Yet another possibility is for the planet to originate from another planetary sys- tem within the solar birth cluster, and then be captured during the early evolution of the solar system (section 7.3). While all of these scenarios remain in play (Figure 26), each is characterized by non-trivial shortcomings, as discussed below.

²⁰Jovian-class objects like Jupiter and Saturn, on the other hand, are comparatively rare and are believed to reside within 20 AU in only ~ 20% of sun-like stars (Cumming et al., 2008).

1. In Situ Formation

Perhaps the most straightforward model for the origin of Planet Nine is for it to form in situ, at its present orbital location. An attractive feature of this scenario is the fact that it does not require any physical processes beyond conglomeration itself. The advantages, however, stop there. Generally speaking, the timescale over which plan- etary building blocks (pebbles, planetesimals) amass into multi-Earth mass objects²¹ is set by the orbital period at the location of the forming planet (Johansen & Lam- brechts, 2017). With a 10, 000 year orbital period (corresponding to a 500 AU), a forming Planet Nine would only complete 300 revolutions around the sun within the typical lifetime of a protoplanetary disk (Hernandez et al., 2007). The corresponding impedance of growth by the slowness of the orbital clock is illuminated by the calcula- tions of Kenyon and Bromley (2016), who find that even under exceptionally favorable conditions, formation of super-Earths at hundreds of AU requires billions of years.

Another shortcoming of in situ formation concerns the availability of planet-forming material at large heliocentric distances. Various lines of evidence indicate the solar sys- tem did not originate in isolation, and instead formed within a cluster of 10³ 10⁴ stars (Adams and Laughlin 2001; Portegies Zwart 2009; Adams 2010; Pfalzner et al. 2015). Such a cluster environment can be highly disruptive to the outer regions of circum- stellar disks and hence to planet formation. At minimum, a number of authors have shown that over a timescale of 10 Myr, passing stars are expected to truncate the disk down to a radius of 300 AU, about one third of the minimum impact parameter (Heller, 1995; Ostriker, 1994). More importantly, these clusters also produce intense FUV radiation fields that evaporate circumstellar disks, removing all of the material beyond 30 40 AU over a time scale of 10 Myr (Adams et al., 2004). Observational evidence supports this picture and indicates that disks in cluster environments expe- rience some radiation-driven truncation (e.g., Anderson et al. 2013). Moreover, even in regions of distributed star formation, where external photoevaporation is unlikely to play a defining role, observations find that typical disk radii are only of order 100 AU (Haisch et al., 2001; Andrews et al., 2009, 2010). As a result, both observational and theoretical considerations suggest that the early Solar Nebula was unlikely to have

extended much farther than the current orbit of Neptune at a ~ 30 AU (see also Kretke et al. 2012). Forming Planet Nine at a radius of ~ 500 AU is thus strongly disfavored.

2. Formation Among the Giant Planets

A somewhat more natural origin scenario is for Planet Nine to form within the region that produces the known giant planets (i.e., the annulus defined roughly by

5 AU _~^< a _~^< 30 AU), and to be scattered out later. The physics of the planet forma-

tion process is notoriously stochastic, and the number of planets produced in a given planet-forming region cannot be calculated in a deterministic manner (Morbidelli & Raymond, 2016), meaning that additional ice giants other than Uranus and Neptune

²¹While gravitational instability of the early solar nebula provides an alternate means of forming planets, it is irrelevant to the problem at hand, since the mass scale for objects generated through this channel is of order 10 M_J (or higher, e.g., Rafikov 2005)

Figure 26: Above, we show not-to-scale schematics for the three possible mechanisms by which Planet Nine could have been formed and placed in its current orbit in the solar system. (top panel) In in situ formation, Planet Nine forms in its current distant orbit while the protoplanetary disk is still present, and resides there throughout the history of the solar system. (middle panel) If Planet Nine forms among the outer planets in the solar system, it could subsequently be scattered outwards onto a high-eccentricity orbit through interactions with the other solar system planets. Then, its orbit could be circularized through interactions with passing stars. (bottom panel) If Planet Nine originally formed around a host star other than the sun, a subsequent close encounter between this other star and the sun could result in Planet Nine being captured into its current- day long-period orbit around the sun.

 may have occupied the outer solar system during its infancy. To this end, analytic ar- guments put forth by Goldreich et al. (2004) suggest that the outer solar system could have started out with as many as five ice giants. Along similar lines, numerical models for the agglomeration of Neptune and Uranus through collisions among large plane- tary embryos find that 5 M_⊕ objects routinely scatter away from the primary planet

forming region (Izidoro et al., 2015). Calculations of ancillary ice giant ejection during

the outer solar system’s transient epoch of dynamical instability are also presented in Nesvorny´ (2011); Batygin et al. (2012); Nesvorny´ & Morbidelli (2012).

It is important to recognize that this model of Planet Nine formation must neces- sarily involve a two-step process. This is because outward scattering of Planet Nine facilitated by the giant planets places it onto a temporary, high-eccentricity (q 5 AU) orbit, which must subsequently be circularized (thus lifting its perihelion out of the planet-forming region) by additional gravitational perturbations arising from the clus- ter. The difficulty with this scenario, however, is that the likelihood of producing the required orbit for Planet Nine is low. Li and Adams (2016) estimated the scattering probability for this process by initializing Planet Nine on orbits with zero eccentricity and semi-major axis a 100 200 AU, and found that stellar fly-by encounters pro- duce final states with orbital elements a = 400 1500 AU, e = 0.4 0.9, and i < 60 deg only a few percent of the time. We note however, that the calculations of Brasser et al. (2006, 2012) obtain considerably more favorable odds of decoupling a scattered plan- etary embryo from the canonical giant planets and trapping it in the outer solar system, with reported probability of success as high as 15%, depending on the specifics of the adopted cluster model.

As an alternative to invoking cluster dynamics, Ericksson et al. (2018) considered the circularization of a freshly scattered Planet Nine through dynamical friction arising from a massive disk of planetesimals, extending far beyond the orbit of Neptune. Un- like the aforementioned cluster calculations, in this scenario the chances of producing a favorable Planet Nine orbit can be as high as 30%. An important drawback of this model, however, is that it suffers from the same issues of disk truncation outlined in the previous sub-section. Moreover, simulations of the Nice model (Tsiganis et al., 2005) require the massive component of the solar system’s primordial planetesimal disk to end at a 30 AU, to prevent Neptune from radially migrating beyond its current orbit. Therefore, within the framework of Ericksson et al. (2018), some additional physical process would be required to create an immense gap ranging from 30 AU to 100 AU in the solar system’s primordial planetesimal disk.

1. Ejection and Capture Within the Solar Birth Cluster

Although gravitational perturbations arising from passing stars can act to alter the orbital properties of Planet Nine, as discussed above, the possibilities do not end there – the birth environment of the solar system can also lead to the disruption of Planet Nine from its wide orbit. Several groups have worked to quantify the effects of scattering encounters in young stellar clusters using N-body methods over the last decade (e.g., Portegies Zwart 2009; Malmberg et al. 2011; Pfalzner 2013; Pfalzner et al. 2015, 2018). Another way to study this class of disruption events is to separately calculate the cross sections for fly-by encounters to ionize the solar system,