Observational Signatures of a Massive Distant Planet on the Scattering Disk
S. M. Lawler, C. Shankman, N. Kaib, M. T. Bannister, B. Gladman, J.J. Kavelaars
aa r X i v : . [ a s t r o - ph . E P ] N ov Draft version August 15, 2018
Preprint typeset using L A TEX style emulateapj v. 04/17/13
OBSERVATIONAL SIGNATURES OF A MASSIVE DISTANT PLANET ON THE SCATTERING DISK
S. M. Lawler , C. Shankman , N. Kaib , M. T. Bannister , B. Gladman , J.J. Kavelaars Draft version August 15, 2018
ABSTRACTThe orbital element distribution of trans-Neptunian objects (TNOs) with large pericenters has beensuggested to be influenced by the presence of an undetected, large planet at >
200 AU from the Sun.To find additional observables caused by this scenario, we here present the first detailed emplace-ment simulation in the presence of a massive ninth planet on the distant Kuiper Belt. We perform4 Gyr N-body simulations with the currently known Solar System planetary architecture, plus a10 M ⊕ planet with similar orbital parameters to those suggested by Trujillo and Sheppard (2014) orBatygin and Brown (2016), and 10 test particles in an initial planetesimal disk. We find that in-cluding a distant superearth-mass planet produces a substantially different orbital distribution for thescattering and detached TNOs, raising the pericenters and inclinations of moderate semimajor axis(50 < a <
500 AU) objects. We test whether this signature is detectable via a simulator with the ob-servational characteristics of four precisely characterized TNO surveys. We find that the qualitativelyvery distinct Solar System models that include a ninth planet are essentially observationally indistin-guishable from an outer Solar System produced solely by the four giant planets. We also find that themass of the Kuiper Belt’s current scattering and detached populations is required to be 3–10 timeslarger in the presence of an additional planet. We do not find any evidence for clustering of orbitalangles in our simulated TNO population. Wide-field, deep surveys targeting inclined high-pericenterobjects will be required to distinguish between these different scenarios. INTRODUCTION
The trans-Neptunian region contains far more struc-ture than the originally hypothesized flat vestigial disk(Edgeworth 1949; Kuiper 1951). While the bulk of theKuiper Belt’s mass is contained in the classical belt,which has trans-Neptunian objects (TNOs) on fairly cir-cular, low inclination orbits, TNOs on higher eccentricityorbits are plentiful. Resonant TNOs are protected fromclose Neptune encounters and can attain high eccentric-ity, allowing them to be more easily detected when nearperihelion. Scattering TNOs often approach the Suneven more closely, as by definition they are required tohave scattering encounters with Neptune or another gi-ant planet (Gladman et al. 2008) and thus have pericen-ters in the giant planet region. Though scattering TNOscan have very large semimajor axis orbits ( a ≫
50 AU)and only make up ∼
2% of the Kuiper Belt’s total pop-ulation (Petit et al. 2011), their very high eccentrici-ties boost detection rates, allowing detailed study ofthe population’s characteristics (Shankman et al. 2013;Adams et al. 2014; Shankman et al. 2016). DetachedTNOs make up a larger fraction of the Kuiper Belt to-tal population ( ∼
29% for D &
100 km; Petit et al. 2011),but never approach Neptune closely enough to have theirorbits affected by scattering encounters, and so are muchharder to detect, due to their high pericenter distances National Research Council of Canada, Astronomy & Astro-physics Program, 5071 West Saanich Rd, Victoria, V9E 2E7,Canada Department of Physics and Astronomy, University of Victo-ria, PO Box 1700, STN CSC Victoria, BC V8W 2Y2, Canada HL Dodge Department of Physics & Astronomy, Universityof Oklahoma, Norman, OK 73019, USA Department of Physics and Astronomy, University of BritishColumbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1,Canada and large semi-major axes.The history of the understanding of the a >
50 AUpopulation is an important context that frames both ourcurrent conception of these distant TNOs and their im-plications for an additional planet in this region. The a ≃ −
50 AU low- e Kuiper Belt initially seemed promisingas the long-sought source of the Jupiter-Family comets(JFCs). However, once the population was observation-ally constrained, the estimated escape rate from that re-gion was too low to allow it to serve as a JFC source(Duncan et al. 1995). It became clear that no near-circular belt in the trans-Neptunian region could feed inJFCs without creating a scattering structure of large- a TNOs once strong encounters with Neptune begin(Duncan and Levison 1997), and the discovery of thefirst member of this population, 1996 TL , was nearlysimultaneous with this theory (Luu et al. 1997). Dy-namical simulations (Duncan and Levison 1997) showedthe surprising possibility that a non-negligible fraction( ∼ q ≃ −
39 AU (Duncan and Levison 1997; Trujillo et al.2000; Morbidelli et al. 2004; Lykawka and Mukai 2007),steadily decreasing in number as a function of semi-major axis. TNOs are displaced outwards almost solelyby gravitational interactions with Neptune; TNOs with q <
35 AU are rapidly depleted, and thus relatively rare,while TNOs with q >
38 AU are extremely rare. Therecognition that TNOs with q >
38 AU existed, and inwhat must be great numbers (Gladman et al. 2002) ledto the realization that the perihelion distribution must beextended to larger values (Morbidelli et al. 2004). The Lawler et al.current terminology in the literature is to use the term‘detached’ for TNOs whose orbits are not today evolv-ing due to Neptune encounters (Gladman et al. 2008),and scattering for those which are. Unfortunately thisdoes not correspond to a simple perihelion cut, although q = 37 AU is sometimes used (Lykawka and Mukai2007).The existence of the detached population requiressome other major process, either historical or on-going, to produce TNOs on these orbits. Sedna(Brown et al. 2004) and recently-discovered 2012 VP (Trujillo and Sheppard 2014) are currently the highest-pericenter examples of detached TNOs. Possible ex-planations for the production of detached orbits in-clude close stellar flybys (e.g. Kenyon and Bromley2004; Brasser and Schwamb 2015), changes in galac-tic tides caused by different Solar position within theGalaxy (e.g. Kaib et al. 2011b), “rogue planets” whichwere ejected early in the Solar System’s history (e.g.Gladman and Chan 2006) and undiscovered, additionalplanets (e.g. Gladman et al. 2002; Brown et al. 2004;Soares and Gomes 2013). Lykawka and Mukai (2008)suggest the presence of a distant Earth-mass planet toexplain some of the structure of the Kuiper Belt, butone of their key arguments requires that there be no ob-jects in distant Neptune mean-motion resonances. Sev-eral distant resonances, including the 3:1, 4:1, and 5:1,have been shown by recent surveys to be heavily pop-ulated (Gladman et al. 2012; Alexandersen et al. 2014;Pike et al. 2015).Limits exist on the presence of distant Solar Systemplanets: analysis of data from the Wide-Field InfraredSurvey Explorer (WISE) has shown that Jupiter-massplanets can be ruled out within 26,000 AU of the Sun(Luhman 2014), though a superearth would be too faintin infrared wavelengths to be yet observed in the distantouter Solar System (5–20 M ⊕ ; Fortney et al. 2016).Trujillo and Sheppard (2014) have proposed a su-perearth on a circular orbit at roughly 250 AU to ex-plain the apparent clustering in argument of pericenter( ω ) of a half-dozen detached TNOs with large perihe-lia. The Kozai-Lidov effect and the inclination instabilityproposed by Madigan and McCourt (2016) both demon-strate mechanisms for the clustering of ω , but TNOs af-fected by either mechanism will continue to precess, andso naturally the orbits will separate over time. This ideais modified and expanded upon by Batygin and Brown(2016), who find that an eccentric superearth is capableof maintaining clustering among high-pericenter TNOs.Both Trujillo and Sheppard (2014) andBatygin and Brown (2016) rely on data from theMinor Planet Center (MPC) database, the repository ofthe orbital parameters for all known TNOs , but whichcontains no information about observational parametersof the surveys in which these objects were discovered.The MPC TNOs are from a multitude of differentsurveys, which largely have unreported pointings,limiting magnitudes, detection efficiencies, and trackingefficiency post-discovery; this masks the true number ofTNOs in different dynamical classes (Kavelaars et al. As of 16 May 2016, this database contains 1986 TNOs, Cen-taurs and scattering objects, ∼ a/e population. An effect such as the apparent clustering ofpericenters could be produced or significantly modifiedin non-intuitive ways (see Sheppard and Trujillo 2016,for a discussion).A survey with fully recorded observational biases canbe properly debiased, giving the true numbers of objectsrequired to exist in the unseen population in order tomatch the number of detections (Jones et al. 2006). Wetherefore select a subset of the published wide-field sur-veys, permitting highly precise tests of the effects of ob-servational bias on the observability of the distant-TNOorbital distributions. Our test suite is an ensemble offour well-characterized surveys (Section 3): the Canada-France Ecliptic Plane Survey (CFEPS; Petit et al. 2011),the HiLat Survey (Petit et al. 2016), the survey ofAlexandersen et al. (2014), and the first two sky blocksfrom the Outer Solar System Origins Survey (OSSOS;Bannister et al. 2016).Our goal is to see what dynamical signatures the addi-tion of a superearth-scale planet generates within the thescattering and detached populations, and test this pre-diction against published, well-characterized surveys. Inthis paper, we measure the effect a distant superearthwould have on the orbital distribution of the high- q ( q >
37 AU), moderate- a (50 < a <
500 AU) componentof the trans-Neptunian populations, using a detailed dy-namical simulation containing many thousands of testparticles. We consider this population because it orbitsbeyond the dynamical dominance of Neptune, will begravitationally sculpted by any potential ninth planet,and has still has pericenters within the detectable rangeof existing surveys.We show that although the differences between the in-trinsic distribution of high-pericenter TNOs in modelswith and without a ninth planet are substantial, afterobservational biases are applied, the differences are cur-rently indistinguishable. The fact that almost all knownscattering objects have q =35–38 AU has tended to beviewed as confirmation of the baseline scattering sce-nario; our results show that the detection biases in thescattering population are so strong that the q >
38 AUpopulation could be numerous, but so weakly detectablethat they are not represented in the observed sample.Also using the survey simulator, we compare the pre-dicted number of objects in the distant Solar System,and find that having an additional planet requires 3-10times as many objects in the moderate- a population. ORBITAL INTEGRATIONS
In order to make a realistic model of the distant TNOsas influenced by a possible superearth, we begin withthe framework for building a scattering TNO and OortCloud model used by Shankman et al. (2016), which is amodified version of the model from Kaib et al. (2011b).Our three dynamical simulations begin with a hundredthousand massless test particles distributed from 4-40AU, along with the 4 giant planets on their present-dayorbits. The “control” sample is identical to that usedby Shankman et al. (2016), while the other two simu-lations have an additional superearth with similar pa-rameters to what was suggested by Batygin and Brown(2016) (eccentric P9: M = 10 M ⊕ , a = 500 AU, e = 0 .
50 100 150 200 250 300 350 400 450 500 a [AU] q [ A U ] controlcirc. P9ecc. P9
50 100 150 200 250 300 q [AU] i [ ◦ ] Fig. 1.—
Orbital elements of all simulated TNOs with q >
37 AUand 50 < a <
500 AU from the control dynamical model (orange),the circular superarth dynamical model (blue), and the eccentricsuperearth dynamical model (gray). Left panel shows semi-majoraxis a vs. pericenter distance q , right panel shows pericenter q vs.inclination i . The presence of a superearth on either a circular oreccentric orbit dramatically raises both the pericenter distributionand the inclination distribution of the distant TNOs. i = 5 ◦ ), and in the interest of completeness, what wassuggested by Trujillo and Sheppard (2014) (circular P9: M = 10 M ⊕ , a = 250 AU, e = 0 . i = 5 ◦ ). Thesetest particles and planets are evolved forward in time for4 Gyr, under the influence of stellar flybys and Galac-tic tides (for details, see Kaib et al. 2011b). In order toensure that the scattering and detached populations arenot contaminated by the initial 4-40 AU disk, any objectsthat have q >
34 AU and a <
42 AU at 3.5 Gyr into thesimulation are removed (this is the same procedure usedin Shankman et al. 2016), as we are not here interestedin the classical belt region.What makes this simulation much more powerful thanprevious analyses is the sheer number of particles. Asa result, this dynamical simulation was computation-ally expensive to run. Previous integrations of Kuiperbelt and Oort cloud formation were able to be sped upthrough a combination of adaptive timestepping and theexclusion of planetary perturbations on very distant par-ticles (e.g., Kaib et al. 2011a). However, the inclusion ofa distant ninth planet prevents this shortcut. Conse-quently, our integrations consumed over 10 core-hours.Figure 1 shows the orbital element distributions for thehigh- q population in the control dynamical model (the a [AU] f r a c t i o n p e r b i n controlcirc. P9ecc. P9 a = A U a = A U Fig. 2.—
Semimajor axis distribution from 50 to 100,000 AU atthe ∼ . currently known Solar System; Shankman et al. 2016)and our nine-planet dynamical models after 4 Gyr of in-tegration. The scattering TNO disk visible in the controldynamical model (orange) is the expected population of q =30-38 AU particles extending smoothly out to large a (the classic scattering disk). At no semi-major axes(except a few rare resonant locations which can producea few lower- e particles via resonance sticking) do perihe-lia get raised into the detached region. The introductionof a superearth results in frequent perihelion lifting for a >
150 AU scattering objects, destroying the confine-ment and thus potentially offering a production methodfor the entire detached population all the way out toSedna.Figure 2 shows the distribution of semimajor axesat the end of each of the three simulations. Thecontrol shows the number of moderate- a objects perlog( a ) bin steadily drops with larger distances from Nep-tune; the scattering physics is poor at retaining a =200-2000 AU objects over 4 Gyr (Dones et al. 2004). Fur-ther out, there is a climb to a peak at the inner OortCloud, starting at roughly a ∼ q ∼
200 AU peak, just in-side q of both superearths ( q = 250 AU).These simulated orbital distributions are very differentfrom the control case with no additional planet; the nextstep is to determine whether or not these stark differencesare observable with current surveys. SIMULATING OBSERVATIONS WITHWELL-CALIBRATED SURVEYS
Lawler et al.We use the OSSOS survey simulator (Bannister et al.2016; Shankman et al. 2016), which offers some improve-ments on the CFEPS survey simulator (Jones et al. 2006;Petit et al. 2011). The survey simulator works by draw-ing objects from a dynamical model, applying survey bi-ases for surveys where all the pointings, tracking efficien-cies, and detection efficiencies are well-known, and de-termining whether or not a given simulated object couldhave been detected.When each object is drawn from our dynamical model,its major orbital elements ( a , e , and i ) are randomizedwithin a small percentage of their model values, and itsangular orbital elements ( ω , Ω, and M ) are random-ized. The object is also given an absolute H r magni-tude using either the best-fit divot size distribution foundby Shankman et al. (2016) for the scattering population,or the knee size distribution preferred by Fraser et al.(2014), but we find that this choice has no statisticaleffect on the analysis presented here. The object’s sim-ulated instantaneous on-sky position, distance, and re-sulting r -band magnitude determine whether or not thisparticular object would have been detected and trackedby any of the included surveys. Simulated objects aredrawn until the number of simulated detections specifiedby the user is met.In this analysis, we use characterizations from fourpublished surveys . A wide range of longitudes alongthe ecliptic are sampled by three surveys: CFEPS(Petit et al. 2011), Alexandersen et al. (2014), and theOSSOS O and E blocks (Bannister et al. 2016). Highecliptic latitudes are sampled by the HiLat survey(Petit et al. 2016). We focus on the high- q , moderate- a population ( q >
37 AU, 50 AU < a <
500 AU). Theseare the objects most strongly perturbed by the distantsuperearth (Figure 1). 15 real TNOs have been detectedin this a / q cut in the above surveys, which allows esti-mation of absolute population numbers (Section 3.2). Possible Superearth-Induced Structure in theKuiper Belt Region Can’t Yet be Observed
Figure 1 highlights the differences in orbital elementsof the high- q , moderate- a population expected for nosuperearth, a circular superearth, and an eccentric su-perearth in the form of scatterplots. The very obviousdifference is that the distant planet provides perturba-tions that raise inclinations and perihelia, potentiallyaddressing two puzzles in Kuiper Belt science (Gomes2003; Gladman 2005). For comparative analysis, it ismore straightforward to measure the differences betweenthese distributions as cumulative distributions than scat-terplots. Figure 3 shows a comparison between the threedifferent dynamical models as cumulative distributionsin three different orbital parameters: a , i , and q . Hereeach distribution has been cut at the same minimum andmaximum values for each parameter.The strong differences between the three model dis-tributions are immediately apparent in Figure 3. Bothsuperearth dynamical models result in more uniform dis-tributions in a : <
10% of the surviving high- q populationhave orbits with a <
100 AU, while in the control dynam-ical model about 50% have orbits with a <
100 AU. The Available for use as an ensemble at http://dx.doi.org/10.5281/zenodo.31297 fraction of the intrinsic distributions with a <
100 AU isa clear diagnostic of the presence of a distant superearth.The control dynamical model has essentially no test par-ticles with inclinations higher than ∼ ◦ , while the cir-cular superearth dynamical model has ∼
20% of objectswith i > ◦ , and the eccentric superearth dynamicalmodel has ∼
40% of objects with i > ◦ and ∼ q , lacking the q <
40 AU concentration ofthe control dynamical model where the q -distribution isdominated solely by interactions with Neptune.These dynamical models produce clear predictions forwhat the orbital distributions of the high- q populationshould look like in the absence of any observational bi-ases. However, we are not able to detect all TNOsequally. In order to compare these models using presentsurveys, we must use a survey simulator (Section 3) toapply the known biases of the surveys to our simulatedpopulations.Figure 4 shows the biased distributions in six orbitalparameters. Immediately notable is that the three dy-namical models which differ strongly are, when biasedby the surveys, nearly indistinguishable from each other.This underscores the peril of using TNOs at the fringeof detectability and where the discovery biases are sub-stantial and complex to assess the underlying population.We confirmed that these biased distributions are consis-tent with currently published TNO detections from thesesurveys.Because these surveys are all flux-limited, detectabil-ity of these objects drops sharply with distance ( d ), pro-portional d − . Due to this effect, as q increases, theprobability of detection drops dramatically, and the biastowards detection of the numerous small and also low-est q objects becomes overwhelming. The flux bias effectcompletely overwhelms the superearth induced signatureof a significant population with highly inclined orbits athigh- q .Using the survey simulator, we estimate that a deepwide-field, off-ecliptic survey of several thousand squaredegrees, sensitive to TNOs with i > ◦ and q >
37 AU,will be needed to distinguish between these dynami-cal models of the distant Solar System. In our surveyset, only the HiLat survey (480 deg to m g = 23 . A Distant Ninth Planet Requires a Much LargerHigh- q Population
The survey simulator draws a large number of unde-tectable, large q , TNOs before “detecting” the requirednumber of simulated objects (in this case, 15, as that isthe number of real detected TNOs in the four surveysinside this a / q cut). By keeping track of the number ofdrawn simulated objects, we measure the absolute num-ber of objects required by a model to produce the samenumber of detections as in the observed sample, down toistant Giant Planet? 5
100 200 300 400 a [AU] i [ ◦ ]controlcirc. P9ecc. P9
40 50 60 70 80 90 q [AU]
Fig. 3.—
Cumulative histograms showing the intrinsic orbital distributions for moderate- a orbits in each of the three dynamical models,to the same minimum and maximum values in each parameter: semi-major axis a , inclination i , and pericenter distance q . The baselineSolar System dynamical model is shown in orange, the circular 9-planet dynamical model in blue and the eccentric 9-planet dynamicalmodel in gray. Only test particles with q >
37 AU and 50 < a <
500 AU are shown.
50 100 150 200 250 a [AU] i [ ◦ ]controlcirc. P9ecc. P9
21 22 23 24 25 m r
36 38 40 42 44 46 48 q [AU] distance [AU] H r Fig. 4.—
Cumulative histograms showing comparison between the three dynamical models biased by the survey simulator in semi-major axis a , inclination i , r -band magnitude m r , pericenter distance q , distance at detection, and absolute r -band magnitude H r . Thestandard Solar System dynamical model is shown in orange, and the 9-planet dynamical models are shown in blue and gray. Here we usethe Shankman et al. (2016) divot size distribution, but a knee size distribution produces statistically and qualitatively indistinguishableresults. Despite the huge differences in intrinsic distributions (Figure 3), after applying survey biases, the three dynamical models areindistinguishable from each other. Lawler et al.a given H r magnitude limit. Using our control dynami-cal model with just the currently known planets, we findthat the high- q , moderate- a population for H r < . . × TNOs. The population required by includ-ing a circular superearth is almost three times larger,at 3 × , while an eccentric superearth requires nearlyan order of magnitude larger high- q population than thecontrol simulation, at 9 × . These population valuesall use the divot size distribution found to be most ap-propriate for the scattering population (Shankman et al.2016). If we instead use a size distribution with a knee(similar to that favored by Fraser et al. 2014), this ap-proximately doubles all three required populations, whilethe relative population ratios remain the same.By assuming an albedo (0.04) and density (1 g/cm ),we can use the size distribution to convert the popula-tion numbers to mass estimates. The control dynam-ical model requires a present-day disk of q >
37 AU,50 < a <
500 AU TNOs with a mass of 0.02 M ⊕ ,while the circular superearth model requires a mass of0.06 M ⊕ , and the eccentric superearth model requires amass of 0.2 M ⊕ . For comparison, even the control modelrequires a mass that is larger than the entire classicalKuiper belt (0.01 M ⊕ ; Fraser et al. 2014). It is importantto note that current observations are rather insensitiveto this high- q population (Section 3.1), so it is unknownwhether these mass estimates violate any observationalconstraints. The possibility exists that a large high- q population could be hidden at the edge of observability. A Distant Ninth Planet Produces no AngularClustering
While this work is not focused on the clus-tering of orbital angles originally suggested byTrujillo and Sheppard (2014), our dynamical simulationscontain this information. We remind the reader that thisis a scattering disk that has been emplaced in the pres-ence of a massive ninth planet. The surviving TNOsat the end of the simulation exhibit no clustering of ar-gument of pericenter ω , longitude of pericenter ̟ , orlongitude of the ascending node Ω (Figure 5).While the shepherding of orbital angles has beendemonstrated to be a possible dynamical effect of aneccentric, distant, massive ninth planet on a subset ofTNOs by Batygin and Brown (2016), their simulationsdo not show how strong this clustering signal is ex-pected to be in a realistic scattering disk. Our simu-lations contain particles that do not uniformly precess,but the sample as a whole does not exhibit any cluster-ing; this result is also seen in the work of Shankman et al.(2016b). The N-body integrations in Batygin and Brown(2016) started with a flat distribution of a few hundredparticles on scattering disk-like orbits, while our simu-lation emplaced many thousands of particles into thescattering disk and Oort Cloud in the presence of thefour giant planets and a ninth planet. Further analy-sis of this theory must demonstrate if (and how) theclustered TNOs are preferentially retained, as well asremove possible observational biases (Shankman et al.2016b; Sheppard and Trujillo 2016). DISCUSSION AND CONCLUSION
We find that a superearth on either a circular or eccen-tric orbit in the outer Solar System strongly affects the ω [ ◦ ] Ω [ ◦ ]
50 100 150 200 250 300 350 400 450 500 a [AU] ϖ [ ◦ ] Fig. 5.—
Distribution of argument of pericenter ω , longitude ofthe ascending node Ω, and longitude of pericenter ̟ versus semi-major axis a for the eccentric P9 simulation. At the end of oursimulation emplacing scattering TNOs in the presence of an eccen-tric ninth planet, there is no clustering of any of these angles. Thisis also true for the circular P9 simulation. Points are color-codedaccording to pericenter distance q , as this dominates detectability.The most easily detected TNOs with q <
40 AU are black, themost difficult to detect with q >
100 AU shown in grey, and mod-erate q (40 < q <
100 AU) in red. This demonstrates there is alsono clustering in the most easily detected low- q population. orbital distribution of the distant Kuiper belt ( q >
37 AUand 50 < a <
500 AU) when compared to a control dy-namical model containing only the currently known plan-ets. However, because flux-limited survey detections willalways be dominated by the lowest q objects, the strongdifferences between the predicted distributions are unde-tectable in the well-characterized surveys we examinedhere.In order to match observations, the predicted mass ofthis high- q population is 3 × higher for a Solar Systemcontaining a circular superearth, and nearly 10 × higherfor an eccentric superearth. This is higher than otherpublished estimates of the size of the population in thisregion, but we note that this high- q population is notwell constrained by current observations and thereforethe uncertainties are large.We do not find evidence for clustering of TNO orbitalangles ( ω , Ω, or ̟ ) caused by either an eccentric or circu-lar ninth planet. Future analyses of this effect must notonly demonstrate that this apparent clustering is not duemerely to observational bias, but also provide an expla-nation for how TNOs are preferentially emplaced or re-tained in a portion of the ninth planet’s dynamical phasespace that allows this shepherding effect to dominate de-tected TNOs.The presence or absence of an additional superearth-mass planet also has important implications for theistant Giant Planet? 7structure of the scattering TNO disk and inner OortCloud. We find that the fraction of test particles thatend up in the Oort Cloud population ( q >
45 AU and a > ∼ q and moderate- a population( q >
37 AU, 50 < a <
500 AU), however, is significantlydifferent for the three simulations. With an eccentricsuperearth, the fraction is three times higher than thecontrol simulation’s value of 0.1% while a circular su-perearth produces a fraction that is nine times higher.These population ratios are largely beyond the currentrealm of detectability, but could provide an importantdiagnostic of our Solar System’s true planetary archi-tecture in the future when compared with other TNOpopulations.Using the simulations in this work, we find that a wide-field, relatively deep, off-ecliptic survey will have greatpower in constraining the presence or absence of an ad-ditional massive planet in our Solar System because ofthe widely differing inclination distributions of scatter-ing TNOs produced by different solar system scenarios.This survey must be meticulous about recording detec-tion and tracking biases, and must take care not to pref- erentially lose high-inclination, large a/e
TNOs due totracking difficulties. In particular, since the full a and q distribution contains so much information, placing a con-straint on the presence of a superearth requires trackingall large- a objects to high-quality orbits; this is expen-sive because getting a to converge for highly eccentric or-bits requires many astrometric observations, over a longtime period. Making sure that the survey is sensitiveto TNOs with inclinations greater than 30 ◦ and pericen-ters outside the immediate dynamical dominance zone ofNeptune ( q &
37 AU) is vital for distinguishing betweenthe dynamical models presented in this work.The authors wish to thank an anonymous referee forsuggestions which improved this manuscript. SML grate-fully acknowledges support from the NRC-Canada Plas-kett Fellowship and would like to dedicate this paperto Fern May Bongarzone Lawler, born three days af-ter manuscript submission. This research was sup-ported by funding from the National Research Councilof Canada and the National Science and Engineering Re-search Council of Canada. This research used the facil-ities of the Canadian Astronomy Data Centre and theCanadian Advanced Network for Astronomical Researchoperated by the National Research Council of Canadawith the support of the Canadian Space Agency.
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