February 21, 2026
employ a color-scale that is solely a measure of the perihelion distance, with blue points
19Equivalent i ∆Ω plots for the favorable m9 = 10 M⊕ solutions look quite similar to the top right panel of Figure 23, so we omit them to avoid redundancy.
m9 = 5M a9 = 500 AU e9 = 0.25 i9 = 20 deg 180 m9 = 5M a9 = 500 AU e9 = 0.25 i9 = 20 deg
120
10-1
60
0
10-2 180
120
10-3
0 90 180 270 360
2⌦ — $ — $9 (deg)
perihelion
distance (AU) 30 40 50 60 70 80 90 100 +
60
Figure 23: High-inclination dynamics induced by a m9 = 5 M⊕ Planet Nine. Akin to plots illustrated in Figure 11, the right panels show the orbital footprints of simulated KBOs on the (i, ∆Ω) plane for the two optimal P9 orbital solutions emphasized in Figure 20. Note that the a9 = 500 AU, e9 = 0.25 solution produces high-inclination objects more readily than its lower eccentricity counterpart. The panel on the left
shows a density histogram of particles footprints, projected into (θ, Θ) phase-space (see equation 11 and Figure 12). Unlike the color-scheme employed in Figures 14 and 17, here we adopt a blue-gray gradient to exclusively represent perihelion distance.
corresponding to q = 30 AU, and gray points signifying q ≥ 100 AU. The full census of observed a ≥ 250 AU TNOs is also shown on the panels, with high-inclination (i > 40 deg) Centaurs plotted as large orange points, and the KBO 2015 BP519 shown
with a pink dot, as in Figure 9.
Because we are showing only long-term stable particles in Figure 23, simulated orbits that achieve q < 30 AU are essentially absent from the plot. This renders the comparison between the numerical experiments and the present-day orbits of high- inclination Centaurs inexact, leaving 2015 BP519 as the only high-inclination TNO which conforms strictly to the depicted numerical results (recall that severe observa- tional biases exist against detecting high-inclination, high-perihelion KBOs). Nev- ertheless, it is very likely that the observed Centaurs originate as strongly inclined q > 30 AU Kuiper belt objects that are scattered inwards by Neptune, meaning that the numerical data depicted in Figure 23 represents the simulated source population of high-i KBOs from which the observed Centaurs are derived.
As can be deduced from examination of Figure 23, the simulation with e = 0.25 produces retrograde TNOs in much greater proportions than its lower eccentricity counterpart. Qualitatively, this can be attributed to the fact that the harmonic term responsible for orbit-flipping behavior is octupolar in nature (section 4.1) and thus ne- cessitates a significant eccentricity to drive high-inclination dynamics. In light of the strong observational biases that act against the detection of high-inclination TNOs, the
true occurrence ratio of distant high-i objects to low-i objects is not known. Unfor- tunately, this means that at present, we cannot observationally favor either of the two shown simulations, since they both produce strongly inclined TNOs in some propor- tion. To complement the discussion presented in section 4.4, the panel on the left-hand- side of Figure 23 presents the simulation results as a density histogram in phase-space, where the transparency of the cells corresponds to a logarithmic measure of the num- ber of orbital footprints contained within each cell and the color corresponds to typical values q of the constituent points. The regions of phase-space occupied by real TNOs is also heavily populated by simulated particles, suggesting that the agreement between the observed and synthetic populations of distant TNOs is satisfactory.
Although highly inclined long-period Centaurs embody an unexpected consequence of P9-induced dynamics, TNOs residing on nearly orthogonal and retrograde orbits are not confined to the distant edges of the Kuiper belt, and are observed on shorter- period orbits as well (Figure 9). As with the large semi-major axis Centaurs them- selves, these objects are envisioned to have acquired large inclinations through in- teractions with Planet Nine at large semi-major axes, and to have subsequently been scattered inwards by Neptune. N-body simulations that elucidate this process for a
m9 = 10 M⊕, a9 = 600 AU, e9 = 0.5 Planet Nine were reported in Batygin and Brown (2016b). Accordingly, let us now examine the generation of high-inclination TNOs with a ≤ 100 AU by a lower mass, lower eccentricity Planet Nine derived from the preceding analysis.
In order to populate the inner trans-Neptunian region with a sufficient number of synthetic KBOs, we re-ran the m9 = 5 M⊕, a9 = 500 AU, e9 = 0.25, i9 = 20 deg numer- ical experiment, increasing the particle count to N = 20, 000. The simulated orbital dis- tribution of particles that attain a ≤ 100 AU throughout any point in the simulations is shown in Figure 24 as a density histogram, where once again transparency represents a
logarithmic measure of the density of points. Recalling that all initial conditions of our numerical experiments (including this one) are drawn from the a (100 AU, 800 AU) range, every particle that comprises the density histogram shown in Figure 24 has been emplaced into the a ≤ 100 AU region from a more distant orbital domain. The current
a ≤ 100 AU observational sample of TNOs is over-plotted on the Figure, and objects
with i ≥ 60 deg are emphasized.
Upon examination of Figure 24, two qualitative features are immediately evident.
First, P9-induced dynamics significantly boosts the inclination dispersion of compar- atively short-period TNOs, providing a natural explanation for the existence of nearly orthogonal orbits, such as those of Drac (Gladman et al., 2009) and Niku (Chen et al., 2016). Second, a distinct population of strongly retrograde particles with perihelion
distances in the 6 AU . q . 12 AU range is also produced. These synthetic objects seamlessly explain the almost planar, but backward orbits of the TNOs 2016 NM56 and 2017 KZ31. Comprehensively, the union of the two panels shown on Figure 24 demon- strates that the observed data is in excellent agreement with synthetic population of TNOs produced within the simulation.
More generally, the inability of standard Nice model simulations to produce KBOs with inclinations in excess of i & 40 deg has long been recognized as a shortcoming of the instability-driven scenario of outer solar system evolution (Levison et al., 2008; Nesvorny´, 2015b). Although the conflict between the observed aggregate of KBOs and
180
150 150
120 120
90 90
60 60
30 30
0 0
30 50 70 90 10 20 30 40
semi-major axis (AU) perihelion distance (AU)
Figure 24: Generation of a ≤ 100 AU high-inclination Centaurs by inward scattering of P9-perturbed distant objects. The current census of TNOs is shown with black points, and the i ≥ 60 deg objects that cannot be explained within the standard model of solar system evolution are emphasized. The underlying density
histogram delineates the regions of parameter space onto which long-period, P9-influenced particles are emplaced when they are scattered inwards by Neptune. The specific domains of a q i space most heavily populated by Planet Nine signal a strong consistency with the observational dataset.
the Nice model can in principle be resolved either by P9-facilitated pollution of the Kuiper belt with high-inclination objects that originate further out, or by inward deliv- ery of Oort cloud objects, the two hypotheses make distinct predictions regarding the orbital structure of the resulting high-inclination Kuiper belt. That is, while dynamical emplacement driven by Planet Nine generates a rather specific orbital architecture (as detailed in Figures 23 and 24), high-inclinations objects sourced from the Oort cloud should stem from a more uniform distribution of orbital elements. Continued map- ping of the high-i component of the Kuiper belt thus offers a direct avenue towards observational differentiation between these two hypotheses.
Solar Obliquity
A final piece of information that is readily informed by our aggregate of JSUNP9 simulations concerns the interactions between Planet Nine and the mean plane of the known eight-planet solar system (often referred to as the “invariable plane”; Souami & Souchay 2012). Shortly after the initial formulation of the Planet Nine hypothesis, it was pointed out by Bailey et al. (2016); Gomes et al. (2016); Lai (2016) that the sec- ular gravitational torque exerted by P9 upon the canonical giant planets would slowly perturb the orbital plane of the planets away from its initial state, thereby exciting a spin-orbit misalignment between the total angular momentum vector of the canonical giant planets and the spin-axis of the sun. Moreover, these authors found that given plausible P9 parameters (e.g., m9 = 15 M⊕, a9 = 500 AU, e9 = 0.5, i = 20 deg; Bai- ley et al. 2016), the entire 6-degree obliquity of the sun could be accounted for by P9 perturbations alone.
This effect is self-consistently captured in our simulations, and it is worthwhile to examine if the revised orbital properties of Planet Nine derived above remain consistent with a scenario where Planet Nine plays a dominant role in the excitation of solar obliquity. For the two best-fit P9 parameters combinations shown in Figures 17 and 18, the answer is a resounding ’no.’ Specifically, for m9 = 5 M⊕, a9 = 500 AU, e9 = 0.25,
i9 = 20 deg, P9’s secular torque only leads to a ψ = 1.1 deg change in the inclination
of the solar system’s invariable plane over 4 Gyr. For a m9 = 10 M⊕ perturber on a a9 = 800 AU, e9 = 0.45, i9 = 15 deg orbit, the induced solar obliquity is similarly small, evaluating to only ψ = 0.7 deg. This implies that some other process, unrelated
to the existence of Planet Nine, must be responsible the present-day obliquity of the sun.
To elaborate on this result further, it is useful to contextualize the sun’s spin-orbit misalignment within its broader, galactic context. Over the last decade, observations of the Rossiter-McLaughlin effect (see for example Winn et al. 2010; Triaud 2017) and doppler tomography (e.g., Marsh 2001; Johnson et al. 2017) have revealed that exo- planetary systems around sun-like stars generically exhibit a very broad range of spin- orbit misalignments, with projected stellar obliquities ranging from 0 to 180 deg. Importantly, this finding applies both to singly-transiting planets as well as to multi- transiting systems wherein the planets themselves are almost exactly coplanar, but are cumulatively inclined with respect to the spin-axis of their host star (e.g., the inner planets of Kepler-56, Li et al. 2014; Li & Winn 2016). Although the exact mechanism through which extrasolar spin-orbit misalignments are excited remains an active area of research, viable theories for the generation of planet-star misalignments include tur- bulence within the protostellar core (Bate et al., 2010; Spalding et al., 2014; Fielding et al., 2015), gravitational torques arising from primordial stellar companions (Batygin et al., 2012; Batygin & Adams, 2013; Lai, 2014; Spalding & Batygin, 2014, 2015), as well as magnetohydrodynamic interactions between the stellar magnetospheres and the inner edges of their circumstellar disks (Lai et al., 2011). In light of these results, we can comfortably attribute the 6-degree obliquity of the sun to the same primordial pro- cess that shapes the broad distribution of spin-orbit misalignments of generic sun-like stars throughout the Galaxy, decoupling it from the Planet Nine hypothesis.
Prospects for Detection
Optical Surveys
An important aspect of the Planet Nine hypothesis is that all of its theoretical at- tributes are directly testable, through the astronomical detection, and characterization of P9 itself. Arguably, the most straightforward approach towards direct detection of Planet Nine is via conventional observations in reflected visible light. The reference Planet Nine envisioned by Batygin and Brown (2016a,b) and (Brown and Batygin, 2016) had a moderately high semi-major axis, eccentricity, and mass, making Planet Nine potentially as faint as 25th magnitude. The more detailed model comparisons shown here suggest a Planet Nine that is lower in all of these parameters. Let us exam- ine the effect of this refinement on the expected brightness.
0
20
0
-20
-40
23
21
19
360 270 180 90 0
right ascension (deg)
Figure 25: On-sky properties of a typical P9 orbital fit. The top panel depicts an example path of Planet Nine, along with the RA-DEC projection of the ecliptic and galactic planes. The bottom panel reports the expected range of the visual magnitude of Planet Nine as a function of the right ascension. While ongoing observational surveys such as Pan-STARRS yield important limits on the location of P9 along its orbit, such constraints are absent from the galactic plane, which remains scarcely explored by solar system surveys.
The brightness of Planet Nine depends on its size, albedo, and distance. For a mass range between 5 and 10 M⊕, exoplanets follow an approximate power law where R R⊕(M/M⊕)0.55, suggesting radii of 2.4 and 3.5R⊕, respectively (Weiss and Marcy, 2014). Such estimates are further consistent with the interior modeling efforts of Linder and Mordasini (2016) who compute physical radii of ~ 1.9 – 3.7R⊕ for an isolated 10 M⊕ object (see also Ginzburg et al. 2016). The albedo of Planet Nine is unknown, but modeling by Fortney et al. (2016) suggests that at the inferred heliocentric distance,
the planetary H/He envelope will be free of all potential condensibles, rendering the atmosphere an essentially pure Rayleigh scatterer with a V-band albedo of almost unity. Neptune, in contrast, has an albedo of approximately 40%, which we take as a plausible lower limit.
As discussed above, for 5 M⊕, the best-fit orbital solution is characterized by a9 = 500 AU and e9 = 0.25 which corresponds to an aphelion distance of 625 AU, where it would be between magnitude V ≈ 21.2 and 22.2 (it would be between magnitude 19.0 and 20.0 at perihelion), depending on the albedo. For 10 M⊕, which we Part
No comments:
Post a Comment