Constraints on the location of a possible 9th planet derived from the Cassini data
AAstronomy & Astrophysics manuscript no. FiengaLaskar2016R7 c (cid:13)
ESO 2016February 24, 2016
Constraints on the location of a possible 9th planet derived fromthe Cassini data
A. Fienga , , J. Laskar , H. Manche , and M. Gastineau G´eoAzur, CNRS-UMR7329, Observatoire de la Cˆote d’Azur, Universit´e Nice Sophia Antipolis, 250 Av. A. Einstein,Valbonne, 06560, Francee-mail: [email protected] ASD/IMCCE, CNRS-UMR8028, Observatoire de Paris, PSL, UPMC, 77 Avenue Denfert-Rochereau, 75014 Paris,Francee-mail: [email protected]
Accepted 16 February 2016. Received 31 January 2016.
ABSTRACT
To explain the unusual distribution of Kuiper Belt objects, several authors have advocated the existence of a super-Earth planet in the outer solar system. It has recently been proposed that a 10 M ⊕ object with an orbit of 700 AUsemi major axis and 0.6 eccentricity can explain the observed distribution of Kuiper Belt objects around Sedna. Herewe use the INPOP planetary ephemerides model as a sensor for testing for an additional body in the solar system. Wetest the possibility of adding the proposed planet without increasing the residuals of the planetary ephemerides, fittedover the whole INPOP planetary data sample. We demonstrate that the presence of such an object is not compatiblewith the most sensitive data set, the Cassini radio ranging data, if its true anomaly is in the intervals [ − ◦ : − ◦ ] or [ − ◦ : 85 ◦ ] . Moreover, we find that the addition of this object can reduce the Cassini residuals, with a most probableposition given by a true anomaly v = . ◦ + ◦ − ◦ . Key words.
Celestial mechanics - Ephemerides - Kuiper belt: general -Planets and satellites: general - Planets andsatellites: detection
1. Introduction
The discovery in 2014 of the Kuiper Belt object (KBO)2012 VP (Trujillo & Sheppard 2014) in the inner Oortcloud revived the question of a planet X. With a relativelylarge radius (R ≈ > ω around 0 ◦ . As stressed in (Trujillo & Sheppard 2014; de laFuente Marcos & de la Fuente Marcos 2014), the recent ob-served distribution of ω for the inner Oort cloud objects isconcentrated around 0 ◦ . One proposed explanation for suchan unlikely spatial distribution is the existence of a super-Earth mass planet with mass between 2 to 15 M ⊕ and asemi-major axis of 200 to 300 AU (Trujillo & Sheppard2014).The existence of such object can have an important im-pact not only on the mass distribution of the material be-yond the limit of 50 AU but also on the spatial distributionof objects between 40 to 50 AU (Lykawka & Mukai 2008;Kenyon & Bromley 2015). The present mass distribution inthe outer edge of our solar system can be seen as a foot-print of the mechanism of formation of our solar system.Characterization of the orbit parameters of a super-Earthbeyond 200 AU can give some estimations of the mass andthe outer radius of the solar nebula (Bromley & Kenyon2014) as well as some clues to the scenario of formation.Low eccentric orbits is compatible with migrating scenario (Ward 1997; Crida et al. 2009), higher eccentricity for lowmass planet being more compatible with a gas drag for-mation model (Kenyon & Bromley 2015). Such an objecthas also been invoked to explain some periodicities in massextinction events (Raup & Sepkoski 1984; Whitmire 2016).The question of the existence of a massive object in theouter solar system thus becomes important for studyingthe present solar system’s architecture and understandingits formation. Very recently, this quest has reached a newlevel with the publication by Batygin & Brown (2016) of aproposal of a ninth planet to explain the clustering of thedistant KBO in the vicinity of 2012 VP . The gravita-tional interaction with this object (which we will call P9from now on) should have scattered the bodies that are notconfined in the vicinity of the central island of a pseudoresonance with P9. To be able to remove the bodies thatwere originally evenly distributed in a disk, P9 needs tobe massive enough and not too far, with high eccentricity.Batygin & Brown (2016) propose a M ⊕ planet with 0.6eccentricity and a 700 AU semi major axis. In the presentwork, we examine the contraints given by the analysis ofthe dynamics of the solar system on the possibility of sucha new planet. We denote this kind of resonance a pseudo resonance, becauseit does not involve the existence of separatrices in the phasespace (Batygin & Brown 2016) Article number, page 1 of 4 a r X i v : . [ a s t r o - ph . E P ] F e b &A proofs: manuscript no. FiengaLaskar2016R7
2. Searching for planet X
The hunt for a planet X started in 1915 Lowell (1915),and some important limitations were provided by differ-ent approaches. The direct imaging survey of the far solarsystem by infrared space telescopes IRAS and WIZE didnot detect any massive objects of Jupiter size inside 25000AU and of Saturn size inside 10000 UA Luhman (2014).In 1993, Standish (1993) demonstrated that no anomalousresiduals can be seen in the residual of the outer planet or-bits. However since this work, no direct confrontation hasbeen performed between the perturbations induced by aplanet X on the orbits of the main planets of our solar sys-tem and the best fitted planetary ephemerides. The onlyestimates were made indirectly, based on the results of theephemerides, but without refitting the whole parameters ofthese ephemerides (Iorio 2012, 2016).Since 1993, very accurate observations of Saturn orbitwere obtained thanks to the tracking of the Cassini space-craft during its exploration of the Saturnian system. Asdescribed in (Folkner et al. 2014), (Hees et al. 2014) and(Fienga et al. 2016), the ten year positions of Saturn allowsignificant improvement in our knowledge of Saturn’s orbit,as well as of Jupiter, Uranus, and Neptune orbits. TheseCassini data have already been used very successfully toput some strict limits on the possibility of an anomalousPioneer acceleration (Anderson et al. 2002; Fienga et al.2010). Furthermore, thanks to the Cassini flyby of Jupiter,a supplementary accurate position of Jupiter is also used tobuild the ephemerides. Finally, the flyby of the New Hori-zons spacecraft of the Pluto-Charon system should bringsome supplementary information and constraints for the ex-istence of a super-Earth.We use here the dynamical model of the INPOP plan-etary ephemerides (Fienga et al. 2008, 2009, 2010, 2011,2016) for testing the possibility of an additional planet, fo-cussing on the proposed nominal planet P9 of Batygin &Brown (2016). In the dynamical model of INPOP planetaryephemerides, we add a super-Earth object of M ⊕ withdifferent orbital characteristics, in agreement with the pro-posed orbit of P9. We then build new ephemerides includ-ing these objects and perform a global fit of the perturbedplanet orbits to the whole data set that is used to con-struct the INPOP and DE430 JPL ephemerides (Folkneret al. 2014).
3. Method
Since (Fienga et al. 2008), the INPOP planetaryephemerides are regularly produced and used for testingalternative theories of gravity, studying variations in the so-lar plasma density, and estimating asteroid masses (Fiengaet al. 2009, 2010, 2011, 2016). The INPOP ephemerides ofthe eight planets of our solar system, of Pluto, and of theMoon, are obtained by numerically integrating the barycen-tric Einstein-Infeld-Hoffmann equations of motion (Moyer1971) in a suitable relativistic time-scale, and taking up to298 asteroids of the main belt into account.In 2015, we released the latest INPOP ephemerides,built over the whole sample of modern and ancient plan-etary observations, from ten years of Cassini round-triparound Saturn and its system, up to the first photographic -400-200 0 200 400-400-200 0 200 400 v = 60-400-200 0 200 400-400-200 0 200 400 v = 80-400-200 0 200 400-400-200 0 200 400 v = 85-400-200 0 200 400-400-200 0 200 400 v = 90-400-200 0 200 400 2004 2006 2008 2010 2012 2014 C a ss i n i r ange ( O - C ) m date-400-200 0 200 400 2004 2006 2008 2010 2012 2014 C a ss i n i r ange ( O - C ) m date v = 95 Fig. 1.
Post fit residuals (in m) for the Cassini observations over [2004 . . . In blue are the nominal residuals of INPOP. Inred are the post fit residuals after the introduction of P9 in theINPOP model. plates of Pluto. Besides the differences in the dynamicalmodeling and in fitting choices explained in Fienga et al.(2016), this latest version of INPOP is very close to the JPLDE430 planetary ephemerides (Folkner et al. 2014). To test the possible presence of P9, we add it to the dynami-cal model of the solar system in INPOP. We then proceed toa complete fit of all the initial conditions and parameters forthe planetary orbits of INPOP, totalling 150 variable quan-tities. The fit is performed over the full set of about 150000 planetary and satellite observations that are currentlyused to determine the INPOP ephemerides, although theINPOP ephemerides also comprise the adjustment of theparameters of the Moon which will not be considered here.The presence of P9 is only possible if the post-fit residualsare not increased after the introduction of P9 in the IN-POP model. The increase of the residual will be a clue thatP9 cannot exist at the given location. In the same way, asignificant decrease in the residuals could be the signatureof P9.For P9, we use the ecliptic orbital parameters of Batygin& Brown (2016) (Table 1). In Batygin & Brown (2016), onlythe long term evolution is considered as a constraint for thedistribution of the KBO, so the true anomaly is left as an
Article number, page 2 of 4ienga et al.: Contraints on planet 9
Table 1.
Orbital elements of P9, as given in Batygin & Brown(2016), in ecliptic (IERS) orbital elements ( a , e , i , ω, Ω ) , respec-tively semi-major axis, eccentricity, inclination, argument of per-ihelion, and longitude of the node. a (AU) e i (deg) ω (deg) Ω (deg)700 0.6 30 150 113unknown. With a large eccentricity of e = . , the radiusvector from the Sun, r , can vary from 280 to 1120 AU,depending on the true anomaly v of P9. We thus samplethe possible values of v over a full orbit ( v ∈ [ − ◦ : 180 ◦ ] ).
4. Results P O S T F I T ( R m s - R m s ) / R m s ( % ) true anomaly (deg) 0 50 100 150 200 -150 -100 -50 0 50 100 150 P O S T F I T ( R m s - R m s ) / R m s ( % ) true anomaly (deg) 0 50 100 150 200 -150 -100 -50 0 50 100 150 P O S T F I T ( R m s - R m s ) / R m s ( % ) true anomaly (deg) 0 50 100 150 200 -150 -100 -50 0 50 100 150 P O S T F I T ( R m s - R m s ) / R m s ( % ) true anomaly (deg) 030012009002400 P R E F I T ( R m s - R m s ) / R m s ( % ) Fig. 2.
Relative change in the root mean square residuals of afitted INPOP solution including P9, with respect to those of thenominal INPOP, with respect to the true anomaly of P9 ( v in x axis). Pre-fit residuals are in blue with the right y-scale (in % ).Post-fit residuals are in red with the left y-scale (in % ). -8-6-4-2 0 2 90 100 110 120 130 140 150 160 ( R m s - R m s ) / R m s ( % ) true anomaly (deg)-8-6-4-2 0 2 90 100 110 120 130 140 150 160 ( R m s - R m s ) / R m s ( % ) true anomaly (deg)-8-6-4-2 0 2 90 100 110 120 130 140 150 160 ( R m s - R m s ) / R m s ( % ) true anomaly (deg)-8-6-4-2 0 2 90 100 110 120 130 140 150 160 ( R m s - R m s ) / R m s ( % ) true anomaly (deg)-8-6-4-2 0 2 90 100 110 120 130 140 150 160 ( R m s - R m s ) / R m s ( % ) true anomaly (deg) Fig. 3.
Enlargement of Fig.2 around the minimum (green bar,at v = . ◦ ). In the green zone, ∆ σ < − . In figure 1 we represented the post fit residuals of theINPOP ephemerides after the addition of P9 for variousvalues of the true anomaly v = ◦ , ◦ , ◦ , ◦ , ◦ . Forcomparison, the INPOP residuals are also plotted. We havenot plotted the residuals for values of v less than ◦ , as for v = ◦ , it is already obvious that P9 cannot exist. For v = ◦ the difference in the residuals is too small to besignificant, while these residuals already increase for v = ◦ . In figure 2, we have gathered the results computedfor all values of v by plotting, for the pre-fit ( ˜ ∆ σ , in blue) and post-fit ( ∆ σ , in red) residuals, the relative change inroot mean square residuals ( ∆ σ = ( σ − σ ) /σ ), where σ = . m is the standard deviation for the INPOP nominalephemerides over the Cassini data.The pre-fit residuals are differences between the obser-vations (here, radio ranging) and the computed values ofobserved quantities, for INPOP ephemerides, with the addi-tion of P9 to the INPOP model, without fitting the parame-ters. The variation in these residuals with the true anomalyreflects how much the perturbation of P9 on Saturn changeswith the geometry of the problem, and not only with thedistance of P9 from the Sun. The post-fit σ are the resid-uals after the fit of 56 planetary parameters in the INPOPephemerides after the addition of P9 in the model. Thisfit is performed over the whole set of more than 150000planetary observations.The shaded region corresponds to a relative increase inthe post-fit residuals of more than after the addition ofP9. This is about the level of precision of the INPOP σ , es-timated by comparison with DE430. We thus consider thatan increase of ∆ σ above is significant and denotes theimpossibility of fitting a P9 planet for this value of the trueanomaly v . The shaded regions ( [ − ◦ : − ◦ ] ∪ [ − ◦ :85 ◦ ] ) are thus the forbidden regions for P9. The ∆ σ curvepresents two minima. We do not believe that the minimumat v = − ◦ is really significant, since it also correspondsto a minimum of the pre-fit residuals and amounts to only ∆ σ = − . .The other minimum at v = . ◦ is more interesting. Itcorresponds both to the observed minimum of the residualscurve (Fig.3), with ∆ σ = − . , and to the result of a di-rect fit of the mean anomaly over the Saturn Cassini rangedata sample that provided an uncertainty at 2- σ of ± . ◦ on v . Owing to the relatively flat behaviour around the min-imum in Fig.3, we prefer a conservative approach here, andwe defined an empirical uncertainty by the zone (in greenin Fig.3) for which ∆ σ < − , which gives v = . ◦ + ◦ − ◦ .
5. Extrapolation of Cassini data
Although the INPOP ephemerides were fitted to all 150000 planetary observations, we have shown here only theresiduals with the Cassini data because they are most sen-sitive to the presence of an additional perturber P9. Wehave only used the data available up to 2014.4, but newdata will be available until the end of the mission, whichis programmed for 2017, unless the mission is extended.To evaluate the impact of an increase in the time span ofthe Cassini mission, we have simulated additional data, byadding to the INPOP prediction (without P9) a Gaussiannoise of 200m sigma, which is slightly pessimistic with re-spect to the already analysed data set. As previously, P9 isthen added, and the ephemerides are fitted to all observa-tions, including the extrapolated Cassini data, through sev-eral iterations (Figs.4, 5). Extending Cassini mission until2020 would thus allow to state for the non existence of P9on the interval v ∈ [ − ◦ : 106 . ◦ ] (Fig.5). The respectivearea of exclusion of a possible P9 from the present data andfrom the extrapolated Cassini data up to 2020 are displayedin Fig.6, together with the most probable zone for findingP9. At this point, no false alarm probability has been associatedto this range of values. Article number, page 3 of 4 &A proofs: manuscript no. FiengaLaskar2016R7 -400-200 0 200 400-400-200 0 200 400 v = 60-400-200 0 200 400 2004 2006 2008 2010 2012 2014 2016 2018 2020 C a ss i n i r ange ( O - C ) m date-400-200 0 200 400 2004 2006 2008 2010 2012 2014 2016 2018 2020 C a ss i n i r ange ( O - C ) m date v = 120 Fig. 4.
Same as Fig.1 with the addition of simulated Cassinidata over [2014 . , for v = ◦ and v = ◦ . P O S T F I T ( R m s - R m s ) / R m s ( % ) true anomaly (deg) 0 50 100 150 200 250 300 -150 -100 -50 0 50 100 150 P O S T F I T ( R m s - R m s ) / R m s ( % ) true anomaly (deg) 0 50 100 150 200 250 300 -150 -100 -50 0 50 100 150 P O S T F I T ( R m s - R m s ) / R m s ( % ) true anomaly (deg) 0 50 100 150 200 250 300 -150 -100 -50 0 50 100 150 P O S T F I T ( R m s - R m s ) / R m s ( % ) true anomaly (deg) 010002000300040005000 P R E F I T ( R m s - R m s ) / R m s ( % ) Fig. 5.
Same as Fig.2 with extrapolated Cassini data (wihoutP9) up to 2020.
6. Conclusions
The Cassini data provides an exceptional set of measuresthat acts as a very sensitive device for testing the possibilityof an additional massive body in the solar system. With thedata accumulated until 2014.4, we can exclude the possibil-ity that P9 is in the section of the orbit depicted in red inFig.6, with a true anomaly v in [ − ◦ : − ◦ ] ∪ [ − ◦ : 85 ◦ ] .We thus contradict the affirmation of Iorio (2016), whostates that a body of 10 M ⊕ is excluded if it resides closerto 1000 AU of the Sun. Iorio (2016) does not properly con-sider how much the presence of an additional body can beabsorbed by the fit of all the other parameters in the so-lar system ephemerides. The global fit that we present hereavoids this drawback. Moreover, we found that the presenceof P9 could significantly decrease the Cassini residuals if v isin the interval [108 ◦ : 129 ◦ ] , with a most probable positionat v = . ◦ + ◦ − ◦ .Since the Cassini data is at present the most precisesensor for testing the possibility of an additional body inthe solar system, it is essential that Cassini continues toprovide ranging data, since there will not be very soon anadditional spacecraft around one of the planets beyond Sat-urn. Extending the Cassini data up to 2020 will already al-low to state for the existence of P9 for v ∈ [ − ◦ : 106 . ◦ ] .Juno will soon arrive around Jupiter and will thus allowus to improve the orbit of Jupiter. This may not directlyimprove the constraints on P9, because Jupiter is less sen- -800-600-400-200 0 200 400 600 800-1200 -1000 -800 -600 -400 -200 0 200 400 Sun C20C14C14Uncertaintyzone P9(AU)(AU) C20
Fig. 6.
Allowed zone for P9. The red zone (C14) is excludedby the analysis of the Cassini data up to 2014 (Sec.4). The pinkzone (C20) is how much this zone can be enlarged by extendingthe Cassini data to 2020 (Sec.4). The green zone is the mostprobable zone for P9 ( v ∈ [108 ◦ : 129 ◦ ] ), with maximum reductionof the residuals at v = . ◦ (blue dot P9). The white zone isthe uncertainty zone where the P9 perturbation is too faint tobe detected. sitive than Saturn to the perturbations of P9. Nevertheless,constraining Jupiter more tightly will allow us to improvethe determination of P9, because less flexibility will existfor absorbing the perturbations due to P9. References