arXiv:1603.05712v2 [astro-ph.EP] 9 Jun 2016 a rsn nteotrslrsse tsm time some or at is system either solar mass outer perturbing the large in ( a present that was clear been diinlpten ea oeeg.Ms impor- beyond axis, Most – (KBOs) semimajor objects with belt objects Neptune Kuiper of emerge. Sedna-like orbits determined to perihelion began tantly, high patterns third additional and ( ond VP113 2012 and high additional of lack a objects. of perihelion because possible how- not orbit, was perturbed ever, Sedna’s of cause the understanding ( 2006 h v ihtelretprhlo itne r likewise are distances perihelion largest the less with with KBOs is five all chance the of these to Importantly, de- of due 0.01%. 22 probability simply than of combined happening average The occurrences an ecliptic. two tilted the is to the which nearly grees very plane, each share orbital of also same longitude objects of these Moreover, degrees other. 94 within perihelion proach rae en’ ri aeicue iln tr in stars sibling have included ( to cluster known have required birth the sun’s orbit perturber of the placed the any Sedna’s other been for from created have all Proposals perturbation cannot unlike by it planets. orbit thus, interac- orbits, its planets, direct onto object to known belt immune the Kuiper essentially with is tions Sedna AU, 76 atpae nteotrslrsse ( 2006 system Chan solar & outer Gladman the in planet 2004 tant al. et Rickman obdli&Lvsn2004 Levison & Morbidelli 2004 al. et Brown BEVTOA OSRIT NTEOBTADLCTO FPLAN OF LOCATION AND ORBIT THE ON CONSTRAINTS OBSERVATIONAL boncleheu [email protected] [email protected], ic h ieo h icvr fSda thas it Sedna, of discovery the of time the Since ihtedsoeyo 00G14( GB174 2010 of discovery the With rpittpstuigL using 2016 typeset 13, Preprint June version Draft ; ue rmoz2012 Krumholz & Dukes ayi Brown & Batygin topsto,ismto,mil u oprla,cnesl edetecte be brig easily approximate can an parallax, with to ou aphelion due rule near mainly to likely motion, surveys on is its these and opposition, Nine use At previous Planet We and to orbit. detection ecliptic. Nine planet’s planet’s the Planet to the of degrees to brightness sensitive 30 to be estimated approximately similar masses and inclined planes and is AU, positions orbital have planet 980 generally the and have also that 380 AU, between 380 objects axes beyond confined axis Orbitally semimajor semimajor AU, with 350 Kuip and objects eccentric th distant belt the Nine reproduce of Kuiper Planet confinement can confine of orbital elements the mass of orbital and range eccentricity, of axis axis, range compatib semimajor narrow of statistically semim a combination are high only parameters eccentric that simulation aligned find which of the determine in population orbit observed and eccentric the distant a to in simulations perturber proposed recently the euea xesv ut fnmrclsmltost osri h m the constrain to simulations numerical of suite extensive an use We iiino elgcladPaeaySine,California Sciences, Planetary and Geological of Division 1. rjlo&Sepr 2014 Sheppard & Trujillo .Wt eieindsac of distance perihelion a With ). swl sasalfre rex- or former small a as well as ) A INTRODUCTION T E ; rw ta.2004 al. et Brown tl mltajv 5/2/11 v. emulateapj style X oe ta.2006 al. et Gomes ( 2016 ; eyn&Boly2004 Bromley & Kenyon a on u htalwell- all that out point ) ,asnl asn star passing single a ), agrta 2 Uap- AU 227 than larger , ihe .Bon&Kntni Batygin Konstantin & Brown E. Michael rw ta.2004 al. et Brown hne l 2013 al. et Chen ; .Pors on Progress ). rse tal. et Brasser > a h sec- the – ) rf eso ue1,2016 13, June version Draft 0 AU, 100 OA SYSTEM SOLAR ABSTRACT ) ; ; fti itn in lntadftr rset o its for prospects future and planet detection We giant discovery. the distant perturber. on this planetary the constraints of distant observational on the discuss constraints of then place and mass Nine, to and Planet orbit observations, of system effects the solar include that simulations previously had Centaurs origin ( perihelion whose mysterious low been orbits of strongly perpendicular collection is with the prediction the of by this Unexpectedly, rest supported a the with system. to objects predicts solar eccentric perpendicular Nine axis essentially KBOs. Planet semimajor inclinations perihelion high of high of like other existence collection the objects the the to creates Additionally, in addition objects naturally in of and Sedna, perihelia cluster the modulates anti-aligned – Nine Planet Brown & Batygin plane. orbital and region perihelion same the to confined n rismiti ogtr tblt yrsdn na on res- residing motion mean by onances. cross- phase-protected stability the of term web evolution, long interconnected chaotic maintain Despite posi- orbits perihelion come planet. ing the the objects from of away belt tion degrees giant Kuiper 180 the clustered perihelion the with to is, anti-aligned That are that perihelion planet. orbits high like have and orbits clustered perihelion objects high these with Surprisingly, lead the objects Sedna. in naturally of creation objects will the additionally, belt perihelion to and, Kuiper the distant observed, of of manner clustering planes orbital cause and will planet eccentric eew aedtie oprsn ewe dynamical between comparisons detailed make we Here Brown & Batygin h itn ceti etre tde in studied perturber eccentric distant The 2. nttt fTcnlg,Psdn,C 91125 CA Pasadena, Technology, of Institute OSRIT NMS,SMMJRAI,AND AXIS, SEMIMAJOR MASS, ON CONSTRAINTS rbl bet.Alwdobt,which orbits, Allowed objects. belt er ue oa ytm ecmaeour compare We system. solar outer prxmtl w-hrso the of two-thirds approximately t bevtos npriua,the particular, In observations. e togydcae h semimajor the dictates strongly on uvy hc ol be would which surveys going oe ta.2015 al. et Gomes we n 0Erhmasses. Earth 20 and 5 tween eiei ogl ewe 150 between roughly perihelia ewt h bevtos We observations. the with le hto h lnt suggesting planet, the of that ihn2 hours. 24 within d jrai uprbl objects belt Kuiper axis ajor s n ri fPae Nine, Planet of orbit and ass ( opr h loe orbital allowed the compare 2016 ( 2016 ECCENTRICITY teso 22 of htness hc erfrt as to refer we which – ) hwta itn massive distant a that show ) TNN NTEOUTER THE IN NINE ET ). < V < 25. 2
The inclined orbits of the aligned KBOs (and thus, pre- sumably, of the distant planet) render ecliptic-referenced orbital angles awkward to work in (particularly when we consider the Centaurs with perpendicular orbits later). Accordingly, we re-cast the three ecliptic-referenced pa- rameters – argument of perihelion, longitude of ascending node, and inclination – into simple descriptions of orbit 60 in absolute position on the sky: the ecliptic longitude 40 of the point in the sky where the object is at perihelion 20 (which we call the “perihelion longitude”, not to be con- 0 fused with the standard orbital parameter called “longi- -20 tude of perihelion” which, confusingly, does not actually perihelion latitude -40 -60 measure the longitude of the perihelion except for zero 360 270 180 90 0 inclination orbits), the latitude of the perihelion (“peri- perihelion longitude helion latitude”), and an angle which measures the pro- jection of the orbit pole onto the plane of the sky (“pole 360 angle” perhaps more easily pictured as the direction per- pendicular to the motion of the object at perihelion). 270 Figure 1a shows the perihelion longitude and latitude as well as the pole angle for all objects with q > 30 and a > 60 AU and well-determined orbits. The seven 180 objects with a > 227 AU are highlighted in red. The clustering in perihelion location as well as pole angle 90 is clearly visible. In Figure 1b we plot the perihelion perihelion longitude longitude of all well constrained orbits in the Kuiper belt which have perihelia beyond the orbit of Neptune 0 0 100 200 300 400 500 as a function of semimajor axis. The 7 objects with semimajor axis (AU) a > 227 AU cluster within 94 degrees of perihelion lon- gitude. Batygin & Brown (2016) showed that this clus- Fig. 1.— Orbital parameters of distant Kuiper belt objects. (a) tering, when combined with the clustering in pole angle, The standard orbital parameters argument of perihelion, longitude was unexpected at the 99.993% confidence level. The of ascending node, and inclination can be transformed into non- standard, but more readily interpretable ecliptic longitude and lat- clustering is consistent with that expected from a giant itude of the point where the object comes to perihelion and an planet whose perihelion is located 180 degrees in longi- angle which is a projection of the orbits pole position on the sky. tude away from the cluster, or an ecliptic longitude of In this representation, the collection of all objects with q > 30 and 241 ± 15 degrees. A closer examination of Figure 1b a > 60 AU is shown. The six objects with the highest semimajor axis are highlighted in red. The KBO 2000 CR105, which has the makes clear a possible additional unlikely phenomenon. seventh largest semimajor axis and has an elevated perihelion of While KBOs with semimajor axes out to 100 AU appear 44 AU, is shown in green. The blue points are all of the object with randomly distributed in longitude, from 100 to 200 AU, a > 227 AU and i> 50 degrees. All of these objects are Centaurs with perihelia inside of 15 AU. (b) A plot of the semimajor axis 13 objects are loosely clustered within 223 degrees of each versus the ecliptic longitude at which the object comes to perihe- other. While this clustering is not as visually striking, lion for all KBOs with well determined orbits and with q > 30 AU the probability of such a loose clustering of 13 objects shows that the seven KBOs with the largest semimajor axes are occurring in randomly distributed data is smaller than clustered within 94 degrees of each other. The green points ad- ditionally highlight all objects with a > 100 AU and q > 42 AU, 5%. As will be seen, such a loose clustering of smaller showing that these objects, too, are similarly clustered. The weaker semimajor axis objects can indeed be explained as a con- potential clustering of objects ∼180 degrees away is also evident sequence of some orbital configurations of a Planet Nine. between 100 and 200 AU. To understand how these observations constrain the mass and orbit of Planet Nine, we performed a suite and e9 = 0.1 − 0.9 in increments of ∆a9 = 100 AU of evolutionary numerical integrations. Specifically, we and ∆e9 = 0.1 (here, and subsequently, the 9 subscript initialized a planar, axisymmetric disk consisting of 400 refers to the orbital parameters of Planet Nine, while eccentric planetesimals, that uniformly spanned semi- unsubscripted orbital parameters refer to the test par- major axis and perihelion, q, distance ranges of a = ticles). The a9 − e9 grids of synthetic scattered disks 150 − 550 AU and q = 30 − 50 AU, respectively. The were constructed for Planet Nine masses of m9 = 0.1, planetesimal population (treated as test particles) was 1, 10, 20 and 30 Me (Earth masses), totaling a suite of evolved for 4 Gyr under the gravitational influence of 320 simulated systems. All calculations were performed the known giant planets, as well as Planet Nine. using the mercury6 N-body integration software pack- Perturbations due to Planet Nine and Neptune were age (Chambers 1999), employing the hybrid symplectic- accounted for in a direct N-body fashion, while the sec- Bulirsch-Stoer algorithm with a timestep equal to a tenth ular effects of the remaining giant planets were mod- of Neptune’s orbital period. eled as a suitably enhanced quadrupolar field of the Sun. We assess the success of each simulation with two sim- As shown in Batygin & Brown (2016), such a numerical ple metrics. First, we collect the orbital elements of all setup successfully captures the relevant dynamical phe- remnant objects at each 0.1 Myr output time step from nomena, at a substantially reduced computational cost. 3 to 4 Gyr after the start of the simulation (in order In these integrations we varied the semimajor axis and to assure that the objects we are considering are stable eccentricity of Planet Nine from a9 = 200 − 2000 AU over at least most of the age of the solar system), and 3 we restrict ourselves to objects with instantaneous peri- helion q < 80 AU (to restrict ourselves to objects which 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 are most likely to be observable). In this fashion we are 0.8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 examining stream functions of orbital elements which fit 0.00 0.00 0.00 0.00 0.00 0.94 1.88 0.00 0.00 into an observable range of parameter space, rather than 0.6 0.00 0.00 0.00 3.32 0.00 0.00 0.00 0.17 0.02 examining individual objects at a single time step. This 0.00 0.00 0.00 0.00 5.14 0.00 0.04 0.15 0.16 approach is used in all subsequent discussions of simu- 0.4 0.00 0.00 0.00 3.17 0.00 0.05 0.04 0.02 0.02 lations below. We then select 13 objects at random in eccentricity the a = [100, 200] AU range and 7 objects at random in 0.00 0.00 0.00 4.75 0.09 0.00 0.01 0.00 0.02 the a = [227, 600] AU range and calculate the smallest 0.2 0.00 0.00 0.00 2.33 0.17 0.02 0.05 0.01 0.00 angles that can be used to confine the two populations. 0.00 0.00 0.00 0.11 0.13 0.03 0.01 0.02 0.00 We perform this random selection 1000 times and cal- 200 400 600 800 1000 culate the joint probability that, like the real data, the semimajor axis (AU) 13 objects in a = [100, 200]AU range are confined within 223 degrees and the 7 objects a = [227 − 600] AU range Fig. 2.— Only a limited set of simulated 10 Me Planet Nine are confined within 94 degrees. Additionally, we examine orbits provide an adequate fit to the known orbits of the distant any KBOs. For each semimajor axis - eccentricity combination, we whether objects exist in the range a = [200, 300] AU, calculate the probability that 7 objects selected at random with as many simulations remove all objects in this range. We 227 360 360 a=500 AU a=700 AU 270 e=0.6 270 e=0.3 180 180 90 90 perihleion longitude perihleion longitude 0 0 0 200 400 600 800 1000 0 200 400 600 800 1000 semimajor axis (AU) semimajor axis (AU) Fig. 4.— One of the successful simulations showing the orbital Fig. 5.— A low probability simulation. Clear anti-alignment does evolution of all objects with q < 80 AU at times t> 3 Gyr. A col- not develop until beyond 400 AU, while aligned orbits appear only lection of resonant stable high semimajor axis objects anti-aligned from approximately 300 to 400 AU. with Planet Nine (centered at ∆ longitude of 180 degrees) appears beyond 200 AU, while from 100-200 AU there is a slight preference for aligned orbits. 150 degrees. the low semimajor axis KBOs to high perihelia, while Unlike the planar suite of calculations, here we start higher semimajor axes fail to cluster the high semima- all planetesimals with their longitude of perihelia anti- jor axis KBOs appropriately. Higher mass simulations aligned to that of Planet Nine. The starting values of cannot match the observations at all. planetesimals’ longitudes of ascending node, on the other In Figure 4 we show, as an example, the Planet Nine- hand, are taken to be random. As demonstrated by centered perihelion longitudes as a function of a of all Batygin & Brown (2016), dynamical sculpting of such objects that have q< 80 AU and which have survived at a planetesimal population yields a configuration where least 3 Gyr, for the case of M9 = 10Me, a9 = 500 AU, long-term stable objects have longitudes of ascending and e9 = 0.6, one of the simulations along the accept- node roughly equal to that of Planet Nine. In turn, able locus. Objects anti-aligned with the planet have a this ties together ω9 and Ω9 through a fixed longitude longitude of 180 degrees in this simulation, while those of perihelion (which is the sum of these parameters). aligned will be at 0 degrees longitude. This simulation Upon examination of these simulations, we find that shows the major effects that we have previously identified efficiency of confinement of the distant population drops in the real data. Inside of 100 AU little perturbation is dramatically with increased inclination of Planet Nine. visible. From 200 to 600 AU the longitudes are confined To quantify this efficiency, we sample each simulation around 180 degrees, that is, they are anti-aligned with 1000 times, picking 7 random objects from the sample Planet Nine. And from 100 to 200 AU there is a slight of all objects in the range a = [300, 700] AU (as pre- tendency for a broad cluster centered on the longitude of viously shown, these a9 = 700 AU simulations do not the planet. begin strong perihelion confinement until a ∼300 AU; as As a counter example, Figure 5 shows a simulation with we are more interested in understanding the cluster than M9 = 10Me, a9 = 700 AU and e9 = 0.3 which depicts in specifically simulating our data at this point we in- many of the same general phenomena, but these phe- crease our semimajor axis range of interest). As before nomena do not develop until larger semimajor axes. For we restrict ourselves to time steps after 3 Gyr in which example, the anti-alignment does not begin until 400 AU, an object’s orbit elements have q < 80 AU, and we add while a broad aligned cluster can be seen from about 300 the constraint that i < 50 degrees, to again account for to 400 AU. Even with the crudeness of these simulations observability biases. We calculate the fraction of times these basic effects are clear. The semimajor axis at which that the 7 randomly selected objects are clustered within anti-alignment begins and the range where broad confine- 94 degrees (Figure 6). The confinement efficiency drops ment is evident are strong indicators of the combination smoothly until, at an inclination of 60 degrees and higher, of semimajor axis and the eccentricity of Planet Nine. it scatters around 20%. These results suggest, but do not demand, that Planet Nine has only a modest inclination. 3. CONSTRAINTS ON INCLINATION AND ARGUMENT OF One of the striking characteristics of the 7 aligned dis- PERIHELION tant Kuiper belt objects is the large value of and tight The planar simulations provide no constraints on incli- confinement in the pole angle (22 ± 6 degrees; Figure nation, i9, argument of perihelion ω9, or longitude of as- 1). In examining the simulations that exhibit good con- cending node, Ω9, of Planet Nine. To examine the effects finement in longitude, we note that the polar angles of these orbital elements on the Kuiper belt, we perform of the simulated orbits are approximately perpendicu- a second, fully three dimensional suite of simulations. In lar to the plane of Planet Nine, particularly for objects these simulations we fix the semimajor axis and eccen- which come to perihelion in the plane of the planet. The tricity to be 700 AU and 0.6, respectively, values which implication of this phenomenon is that a pole angle of are within our acceptable range of parameter space. The 22 degrees suggests a minimum planet inclination of ap- inclination dynamics are unlikely to be unique to the spe- proximately 22 degrees, and an orbital plane (which is cific values of a9 and e9, so we deem these simulations controlled by Ω9) similar to the plane of the observed to be representative. We allow the inclination of Planet objects. To quantify this observation, we plot the me- Nine to take values of i9 = 1, 10, 20, 30, 60, 90, 120, and dian pole angle of our simulation objects which meet the 5 becomes improbable, which, based on an interpolation 1.0 of the data from Figure 5, occurs approximately around 40 degrees. For inclinations of ∼22 degrees, ω must be 0.8 quite close to 150 degrees. For inclinations of 30 degrees, the allowable range for the argument of perihelion ap- 0.6 pears to be ω9 ∼ 120 − 160 degrees. While this analysis yields useful constraints, we quan- 0.4 tify these results further by again sampling each of the simulations 1000 times and determining the probability 0.2 of 6 randomly selected objects (300 AU The inclination is between approximately 22 < i9 < 180 40 degrees, and the argument of perihelion is between 150 120 <ω9 < 160 degrees. We fix the perihelion longitude at 241±15 degrees. While these choices of parameter 120 ranges have been justified in the analysis of the simu- lations above, they cannot be considered a statistically 90 rigorous exploration of parameter space. Indeed, any at- inclination 60 tempt at such statistical rigor is not yet warranted: sub- stantial uncertainty comes not just from the statistics 30 of the objects themselves, but from the currently small number of simulations in the best fit region of parameter 0 space. Clearly, significantly more simulation is critical 360 270 180 90 0 perihelion longitude for a better assessment of the path of Planet Nine across the sky. Fig. 8.— For simulations with a9 = 700 AU, e9 = 0.6, and i9 = The last parameter we consider is the mass of Planet 30 deg, examination of all objects with 300 of 4 or more detections to Keplerian orbits. The Keple- rian filter is strong. From ∼ 1019 potential combinations, 40 we narrowed the detections down to eight known Kuiper 20 belt objects and zero false positives. Every bright Kuiper 0 belt object in the survey fields was detected, often dozens -20 of times. The survey was determined to be essentially declination -40 100% complete to V ∼ 19.1 in the north and V ∼ 18.6 2000 in the south. For some of the smaller potential values 1500 for semimajor axis and larger values of planetary radius, 1000 for example, Planet Nine would have been visible to this 500 survey over a substantial portion of its orbit, though it distance (AU) 0 26 was not detected. 24 22 5.3. The Pan-STARRS 1 Survey 20 18 The Pan-STARRS 1 telescope has surveyed large 16 amounts of sky multiple times to moderate depths at V magnitude 14 declinations greater than -30 degrees. We consider the 0.8 analysis of the data in two stages. 0.6 The Pan-STARRS Survey for Transients. Like the 0.4 earlier, CRTS, the Pan-STARRS Survey for Transients 0.2 speed ("/hr) 0.0 (PST) (Smartt et al. 2014) quickly disseminates detec- 360 270 180 90 0 tions of transients sources detected in the sky. We have RA performed a similar analysis on the reported PST data, searching for viable Keplerian orbits. As of 15 May 2016, no series of transients can be found which fit an outer so- lar system body on any bound Keplerian orbit. Typical transient depths reached are g = 21.0, and, based on Fig. 10.— Using all constraints on the orbital and physical pa- the collection of reported transients, the survey appears rameters of Planet Nine, we can predict the location, distance, brightness, and speed of the planet throughout its orbit. Regions to efficiently cover the sky north of -30 declination and within 10 degrees of the galactic plane are outlined in red, and the at galactic latitudes greater than about 10 degrees. This ecliptic plane is shown in blue. The colored portions show regions survey rules out much of the sky within about 45 degrees where Planet Nine would have been or should be detected by pre- of the predicted perihelion point, with the exception of vious or ongoing surveys. Light blue shows limits from the CRTS reanalysis, yellow shows Dark Energy Survey limits and cover- the region near the galactic plane. age, dark blue shows Pan-STARRS transient analysis limits, green The Pan-STARRS Outer Solar System Key Project. shows Pan-STARRS moving object analysis current limits, and red A survey for objects in the outer solar system was shows eventual Pan-STARRS expected limits. Orange shows the one of the initial goals of the Pan-STARRS survey. region exclusively ruled out by lack of observed perturbation to Saturn (Fienga et al. 2016; Holman & Payne 2016). The black re- Holman et al. (2015) have now completed a preliminary gions show regions of phase space where Planet Nine could not analysis of the survey data and report no detections out have been or will not be detected in previous or currently planned to 600 AU. While detailed sensitivity studies have yet to surveys. be completed, it is estimated that the survey is complete of those images are coadded, Neptune could be detected to approximately r ∼ 22.5, though limits in the galactic ∼ with a S/N of 10 only to 63 AU, consistent with our plane are worse. An extended analysis is currently un- estimate above. Fortney et al. (2016) suggest that the derway which will have the same brightness limits, but W1 brightness of Planet Nine could be enhanced above will remove the artificial restriction to objects closer than its blackbody level and thus potentially observable to a 600 AU (Holman, private communication). If these sen- greater distance, but the sensitivity of the WISE data sitivity estimates are correct, the Pan-STARRS 1 moving to Neptune-sized planets except at the closest possible object survey has or will rule out a substantial fraction distances remains low. The Luhman (2014) results thus of the non-aphelion sky. provide no constraints on the position or existence of Planet Nine. 5.4. The Dark Energy Survey 5.2. The Dark Energy Survey (DES) is performing the Catalina real time transient survey largest deep southern hemisphere survey to date. Some While near earth object searches are performed at ca- of the DES region covers the orbital path of Planet Nine dences poorly matched to the detection of objects in the (indeed one of the 7 cluster objects, 2013 RF98, was de- outer solar system, they cover the sky multiple times in tected in the DES). While cadences are not designed for a year, allowing the possibility of detecting objects by ease of outer solar system detection, it is clear that the their weekly or monthly motion. In Brown et al. (2015), data will be sensitive to Planet Nine if it is in the survey we performed such an analysis from the Catalina real area. The DES team estimates a Planet Nine detection time transient survey (Drake et al. 2009, CRTS), which limit of r ∼ 23.8. (Gerdes, private communication). The itself repurposed the Catalina Sky Survey near earth as- survey should be completed in 2018. teroid search into a transient survey. We collected all 5.5. one-time transients over an 8 year period, that is, all Additional surveys instances in which an object was detected at a spot in Additional surveys covering wide areas of the sky have the sky only once, and attempted to fit all combinations been performed, but in all cases they are insensitive to 8 the slow expected speeds of Planet Nine, they have too within its orbit. Specifically they assume that the four low of a survey efficiency to consider the region effectively most distant KBOs are in N:1 and N:2 resonances, and surveyed, or they cover little or none of the region of the examine the implications for Planet Nine. Such an ap- predicted orbital path. The large community surveys proach could, in principle, work in the circular restricted which are concentrating on specific areas of the sky, such three-body problem, but, as shown in (Batygin & Brown as the VISTA surveys in the southern hemisphere and 2016), highly elliptical orbits are required to explain the the Subaru Hyper-SuprimeCam survey along the celestial spatial confinement of the orbits, and no specific reso- equator unfortunately do not overlap with the required nances dominate the disturbing function in this elliptical search region. problem. Indeed, no particular preference for type of In the future, the Large-Scale Synoptic Telescope is critical angle or even resonance order can be identified expected to survey much of the sky observable from in the dynamical simulations shown here. Rather, the its Chilean site to a single-visit depth of approximately crossing orbits evolve chaotically but maintain long term r ∼ 24.5 magnitude. The current survey strategy does stability by residing on a interconnected web of phase- not include visits to fields as far north as those at the protected mean motion resonances. The assumption of extremes of the predicted Planet Nine orbital path, but simple low order resonance is thus unlikely to be justi- if Planet Nine has not yet been found by the expected fied. Not surprisingly, the Planet Nine orbits produced start of the LSST survey operations in 2023, a simple ex- by these assumptions do not produce the spatial confine- tension could quickly rule out nearly all but the faintest ments of the KBOs that are observed. Thus, it appears and most distant Planet Nine predictions. that no useful constraint on the orbit or position can be At its most distant predicted locations, Planet Nine drawn from this method. is faint and in the northern hemisphere. Subaru Hyper- Suprime Cam will be the instrument of choice for detect- 5.7. Joint constraints ing the planet at these locations. We began a survey of these regions in the fall of 2015 and will attempt to cover In Figure 10 we show the regions of the potential orbits all of this part of the predicted orbital path. of Planet Nine that have been ruled out by the above con- straints (or, in the case of the ongoing DES and final Pan- 5.6. Additional constraints: STARRS analysis, where the planet might still be found Fienga et al. (2016) perform full fits to the locations by these surveys). The existence of Planet Nine can be of all planets and nearly 300 asteroids observed from an- ruled out over about two thirds of its orbit. The vast ma- jority of the orbital region in which Planet Nine could be cient times to the present with and without a 10 Me Planet Nine at various positions along an orbit with located is beyond about 700 AU and within about 60 de- grees of its aphelion position. For the eccentric orbits a9 = 700 AU and e9=0.6, consistent with the nominal orbit suggested in Batygin & Brown (2016). They find considered here, Planet Nine spends greater than half of that the strongest constraint on the existence of Planet its time at these distances, so finding it currently at these Nine comes from the very precise measurements of the locations near aphelion would be expected. At its most distance to Saturn as measured by the Cassini spacecraft distant allowed location and with a Neptune-like albedo, over the past decade. With no Planet Nine, their best a 20 Re Planet Nine is approximately V = 25. While fit to the position of Saturn has Earth-Saturn distance faint, such an object would be well within the limits of residuals which roughly follow a sinusoid with a 12-year 10-m class telescopes. ∼ period and a full amplitude of 70 m. Previous fits to 6. the ephemeris of Saturn using the identical data, how- CONCLUSIONS ever, found smaller residuals and no evidence of system- The existence of a distant massive perturber in the atic variation (Hees et al. 2014), while even more recent outer solar system – Planet Nine – explains several hith- fits, leading to the creation of the DE435 JPL planetary erto unconnected observations about the outer solar sys- ephemeris, put even tighter constraints on any remaining tem, including the orbital alignment of the most distant residuals. It thus remains unclear whether any residual Kuiper belt objects, the existence and alignment of high is present in the Earth-Saturn distance. We remain ag- perihelion objects like Sedna, and the presence of per- nostic about the existence of residuals in the distance to pendicular high semimajor axis Centaurs. These specific Saturn, but instead assume that the signal apparently observations have been compared to suites of numerical detected by Fienga et al. (2016) is at or near the level integrations in order to constrain possible parameters of of the systematic errors in this type of analysis and that Planet Nine. The current constraints must be considered larger signals from Plant Nine could be detected. At its preliminary: our orbital simulations needed to cover sub- the nearest possible locations, in particular, Planet Nine stantial regions of potential phase space, and so were, of would cause such a large effect on the Earth-Saturn dis- necessity, sparsely populated. At present, the statistical tance that the Fienga et al. (2016) analysis and an ex- reliability of our constraints are limited as much by the tension by Holman & Payne (2016) (which assumes the limited survey nature of the simulations as by the small same residuals) can rule out any of the Planet Nine solu- number of observed objects themselves. Continued simu- tions near perihelion over the range of Right Ascension lation could substantial narrow the potential search area of RA9 > 255, RA9 < 2 deg. required. In addition, continued simulation is required A recent paper (Malhotra et al. 2016) makes no at- in order to understand one effect not captured in the tempt to explain spatial alignments, but instead at- current models: the apparent alignment of argument of tempts to simplistically look for mean-motion commen- perihelion of the 16 KBOs with the largest semimajor surabilities in the distant KBOs, in hopes of being able axes (Trujillo & Sheppard 2014). Some of this apparent to constrain both a9 and the location of Planet Nine alignment may come from yet unmodeled observational 9 biases related to the close proximity of the perihelion po- axis perpendicular objects (whether Centaurs or Kuiper sitions of the most distant objects to the galactic plane, belt objects) has the possibility of placing the strongest while some may be a true as-yet-unmodeled dynamical constraints in the near term. While we have currently effect. only used the existence of these objects as a constraint, As important as continued simulation, continued de- their perihelion locations and values of ω change strongly tection of distant solar system objects is the key to re- with ω9 and i9 and so can be used to better refine these fining the orbital parameters of Planet Nine. Each addi- estimates. Though there are only currently 5 known of tion Kuiper belt object (or Centaur) with a > 100 AU these objects, they are being discovered at a faster rate tightens the observational constraints on the location of than the distant Kuiper belt objects, so we have hope of Planet Nine (or, alternatively, if significant numbers of more discoveries soon. As with the distant Kuiper belt objects are found outside of the expected cluster location, objects, of course, detection of these objects also has the the objects can refute the presence of a Planet Nine). strong possibility of entirely ruling out the existence of Interestingly, the detection of more high semimajor Planet Nine if they are not found with perihelia in the locations predicted by the hypothesis. REFERENCES Batygin, K. & Brown, M. E. 2016, AJ, 151, 22 Hees, A., Folkner, W. M., Jacobson, R. A., & Park, R. S. 2014, Brasser, R., Duncan, M. J., & Levison, H. F. 2006, Icarus, 184, 59 Phys. Rev. D, 89, 102002 Brown, M. E. 2008, in The Solar System Beyond Neptune, ed. Holman, M. J., Chen, Y.-T., Lin, H.-W., Lackner, M., Payne, M. A. Barucci, H. Boehnhardt, D. P. Cruikshank, & M. J., & Alcock, C. 2015, in AAS/Division for Planetary A. Morbidelli, 335–344 Sciences Meeting Abstracts, Vol. 47, AAS/Division for Brown, M. E., Bannister, M. T., Schmidt, B. P., Drake, A. J., Planetary Sciences Meeting Abstracts, 211.12 Djorgovski, S. G., Graham, M. J., Mahabal, A., Donalek, C., Holman, M. J. & Payne, M. J. 2016, ArXiv e-prints Larson, S., Christensen, E., Beshore, E., & McNaught, R. 2015, Kenyon, S. J. & Bromley, B. C. 2004, Nature, 432, 598 AJ, 149, 69 Luhman, K. L. 2014, ApJ, 781, 4 Brown, M. E., Trujillo, C., & Rabinowitz, D. 2004, ApJ, 617, 645 Malhotra, R., Volk, K., & Wang, X. 2016, ArXiv e-prints Burgdorf, M., Orton, G. S., Davis, G. R., Sidher, S. D., Millis, R. L., Buie, M. W., Wasserman, L. H., Elliot, J. L., Kern, Feuchtgruber, H., Griffin, M. J., & Swinyard, B. M. 2003, S. D., & Wagner, R. M. 2002, AJ, 123, 2083 Icarus, 164, 244 Morbidelli, A. & Levison, H. F. 2004, AJ, 128, 2564 Chambers, J. E. 1999, MNRAS, 304, 793 Petit, J.-M., Kavelaars, J. J., Gladman, B. J., Jones, R. L., Chen, Y.-T., Kavelaars, J. J., Gwyn, S., Ferrarese, L., Cˆot´e, P., Parker, J. W., Van Laerhoven, C., Nicholson, P., Mars, G., Jord´an, A., Suc, V., Cuillandre, J.-C., & Ip, W.-H. 2013, ApJ, Rousselot, P., Mousis, O., Marsden, B., Bieryla, A., Taylor,M., 775, L8 Ashby, M. L. N., Benavidez, P., Campo Bagatin, A., & Drake, A. J., Djorgovski, S. G., Mahabal, A., Beshore, E., Larson, Bernabeu, G. 2011, AJ, 142, 131 S., Graham, M. J., Williams, R., Christensen, E., Catelan, M., Rickman, H., Froeschl´e, C., Froeschl´e, C., & Valsecchi, G. B. Boattini, A., Gibbs, A., Hill, R., & Kowalski, R. 2009, ApJ, 2004, A&A, 428, 673 696, 870 Smartt, S. J., Smith, K. W., Wright, D., Young, D. R., Kotak, R., Dukes, D. & Krumholz, M. R. 2012, ApJ, 754, 56 Nicholl, M., Polshaw, J., Inserra, C., Chen, T.-W., Terreran, Fienga, A., Laskar, J., Manche, H., & Gastineau, M. 2016, A&A, G., Gall, E., Fraser, M., McCrum, M., Valenti, S., Foley, R., 587, L8 Lawrence, A., Gezari, S., Burgett, W., Chambers, K., Huber, Fortney, J. J., Marley, M. S., Laughlin, G., Nettelmann, N., M., Kudritzki, R. P., Magnier, E., Morgan, J., Tonry, J., Morley, C. V., Lupu, R. E., Visscher, C., Jeremic, P., Khadder, Sweeney, W., Stubbs, C. W. C., Kirshner, R., Metcalfe, N., & W. G., & Hargrave, M. 2016, ArXiv e-prints Rest, P. D. A. 2014, The Astronomer’s Telegram, 5850 Gladman, B. & Chan, C. 2006, ApJ, 643, L135 Trujillo, C. A. & Sheppard, S. S. 2014, Nature, 507, 471 Gomes, R. S., Matese, J. J., & Lissauer, J. J. 2006, Icarus, 184, 589 Gomes, R. S., Soares, J. S., & Brasser, R. 2015, Icarus, 258, 37