A recent proposal for the detection of a hypothetical gravitating body 500 AU from the Sun (termed Planet 9) calls for a fleet of near-relativistic spacecraft, equipped with high-precision clocks, to be sent to a region where the object is suspected to be. We show that the technological constraints of such a mission can be relaxed somewhat, while improving the sensitivity: high-precision clocks can be avoided when the transverse displacement induced by Planet 9 is measurable with Earth-based, or near-Earth, telescopes. Furthermore, we note that in the absence of Planet 9, these spacecraft still yield useful data by mapping gravitational perturbations in the outer parts of the solar system.
In the current paradigm of planet formation research, it is believed that the first step to forming massive bodies (such as asteroids and planets) requires that small interstellar dust grains floating through space collide with each other and grow to larger sizes. The initial formation of these pebbles is governed by an integro-differential equation known as the Smoluchowski coagulation equation, to which analytical solutions are intractable for all but the simplest possible scenarios. While brute-force methods of approximation have been developed, they are computationally costly, currently ma…
A distant, as yet unseen ninth planet has been invoked to explain various observations of the outer solar system. While such a 'Planet Nine', if it exists, is most likely to be discovered via reflected light in the optical, it may emit much more strongly at 3$-$5$μ$m than simple blackbody predictions would suggest, depending on its atmospheric properties (Fortney et al. 2016). As a result, Planet Nine may be detectable at 3.4$μ$m with WISE, but single exposures are too shallow except at relatively small distances ($d_9 \lesssim 430$ AU). We develop a method to search for Planet Nine far beyond…
Bailey et al.~(2016) and Gomes et al.~(2016) recently suggested that the 6 degree misalignment between the Sun's rotational equator and the orbital plane of the major planets may be produced by the forcing from the hypothetical Planet Nine on an inclined orbit. Here we present a simple but accurate calculation of the effect, which provides a clear description of how the Sun's spin orientation depends on the property of Planet Nine in this scenario.
The Radius, Composition, Albedo, and Absolute Magnitude of Planet Nine Based on Exoplanets with Teq less than 600 K and the Planet Nine Reference Population 3.0
Unexpected clustering in the orbital elements of minor bodies beyond the Kuiper belt has led to speculations that our solar system actually hosts nine planets, the eight established plus a hypothetical "Planet Nine". Several recent studies have shown that a planet with a mass of about 10 Earth masses on a distant eccentric orbit with perihelion far beyond the Kuiper belt could create and maintain this clustering. The evolutionary path resulting in an orbit such as the one suggested for Planet Nine is nevertheless not easily explained. Here we investigate whether a planet scattered away from th…
It has been proposed that mean motion resonances (MMRs) between Planet Nine and distant objects of the scattered disk might inform the semimajor axis and instantaneous position of Planet Nine. Within the context of this hypothesis, the specific distribution of occupied MMRs largely determines the available constraints. Here we characterize the behavior of scattered Kuiper Belt objects arising in the presence of an eccentric Planet Nine ($e_9 \in 0.1$, $0.7$), focusing on relative sizes of populations occupying particular commensurabilities. Highlighting the challenge of predicting the exact MM…
Recent estimates of the characteristics of Planet Nine have suggested that it could be closer than originally assumed. Such a Planet Nine would also be brighter than originally assumed, suggesting the possibility that it has already been observed in wide-field moderate-depth surveys. We search for Planet Nine in the Zwicky Transient Facility public archive and find no candidates. Using known asteroids to calculate the magnitude limit of the survey, we find that we should have detected Planet Nine throughout most of the northern portion of its predicted orbit -- including within the galactic pl…
The recent 'Planet Nine' hypothesis has led to many observational and archival searches for this giant planet proposed to orbit the Sun at hundreds of astronomical units. While trans-Neptunian object searches are typically conducted in the optical, models suggest Planet Nine could be self-luminous and potentially bright enough at ~3-5 microns to be detected by the Wide-field Infrared Survey Explorer (WISE). We have previously demonstrated a Planet Nine search methodology based on time-resolved WISE coadds, allowing us to detect moving objects much fainter than would be possible using single-fr…
Motivated by the report of a possible new planetary member of the Solar System, this work calculates cross sections for interactions between passing stars and this proposed Planet Nine. Evidence for the new planet is provided by the orbital alignment of Kuiper Belt objects, and other Solar System properties, which suggest a Neptune-mass object on an eccentric orbit with semimajor axis $a_9\approx400-1500$ AU. With such a wide orbit, Planet Nine has a large interaction cross section, and is susceptible to disruption by passing stars. Using a large ensemble of numerical simulations (several mill…
We evaluate the dynamical stability of a selection of outer solar system objects in the presence of the proposed new Solar System member Planet Nine. We use a Monte Carlo suite of numerical N-body integrations to construct a variety of orbital elements of the new planet and evaluate the dynamical stability of eight Trans-Neptunian objects (TNOs) in the presence of Planet Nine. These simulations show that some combinations of orbital elements ($a,e$) result in Planet Nine acting as a stabilizing influence on the TNOs, which can otherwise be destabilized by interactions with Neptune. These simul…
We significantly constrain the sky position, distance, and mass of a possible additional, distant planet in the solar system by examining its influence on the distance between Earth and the Cassini Spacecraft. Our preferred region is approximately centered on (RA, Dec) = ($40\arcdeg$, $-15\arcdeg$), extending approximately 20 degrees in all directions.
The observed physical clustering of the orbits of small bodies in the distant Kuiper Belt (TNOs) has recently prompted the prediction of an additional planet in the outer solar system. Since the initial posing of the hypothesis, the effects of Planet Nine on the dynamics of the main cluster of TNOs - the objects anti-aligned with its orbit - have been well-studied. In particular, numerical simulations have revealed a fascinating phenomenon, referred to as "resonance hopping", in which these objects abruptly transition between different mean-motion commensurabilities with Planet Nine. In this w…
The six-degree obliquity of the sun suggests that either an asymmetry was present in the solar system's formation environment, or an external torque has misaligned the angular momentum vectors of the sun and the planets. However, the exact origin of this obliquity remains an open question. Batygin & Brown (2016) have recently shown that the physical alignment of distant Kuiper Belt orbits can be explained by a 5-20 Earth-mass planet on a distant, eccentric, and inclined orbit, with an approximate perihelion distance of ~250 AU. Using an analytic model for secular interactions between Planet Ni…
We use astrometry of Pluto and other TNOs to constrain the sky location, distance, and mass of the possible additional planet (Planet Nine) hypothesized by Batygin and Brown (2016). We find that over broad regions of the sky, the inclusion of a massive, distant planet degrades the fits to the observations. However, in other regions, the fits are significantly improved by the addition of such a planet. Our best fits suggest a planet that is either more massive or closer than argued for by Batygin and Brown (2016) based on the orbital distribution of distant trans-neptunian objects (or by Fienga…
We present results from a new pipeline custom-designed to search for faint, undiscovered solar system bodies using full-frame image data from the NASA Transiting Exoplanet Survey Satellite (TESS) mission. This pipeline removes the baseline flux of each pixel before aligning and co-adding frames along plausible orbital paths of interest. We first demonstrate the performance of the pipeline by recovering the signals of three trans-Neptunian objects -- 90377 Sedna ($V=20.64$), 2015 BP519 ($V=21.81$), and 2007 TG422 ($V=22.32$) -- both through shift-stacking along their known sky-projected paths a…
Planet 9 was proposed as an explanation for the clustering of orbits for some trans-Neuptunian objects. Recently, the use of a sub-relativistic spacecraft was proposed to indirectly probe Planet 9's gravitational influence. Here we study the effects of the drag and electromagnetic forces exerted on a sub-relativistic spacecraft by the interstellar medium (ISM) and compare these forces with the gravitational force induced by Planet 9. We find that the resulting noise due to density and magnetic fluctuations would dominate over Planet 9's gravitational signal at sub-relativistic speeds, $v\gtrsi…
We use an extensive suite of numerical simulations to constrain the mass and orbit of Planet Nine, the recently proposed perturber in a distant eccentric orbit in the outer solar system. We compare our simulations to the observed population of aligned eccentric high semimajor axis Kuiper belt objects and determine which simulation parameters are statistically compatible with the observations. We find that only a narrow range of orbital elements can reproduce the observations. In particular, the combination of semimajor axis, eccentricity, and mass of Planet Nine strongly dictates the semimajor…
The Planet Nine hypothesis has now enough constraints to deserve further attention in the form of detailed numerical experiments. The results of such studies can help us improve our understanding of the dynamical effects of such a hypothetical object on the extreme trans-Neptunian objects or ETNOs and perhaps provide additional constraints on the orbit of Planet Nine itself. Here, we present the results of direct N-body calculations including the latest data available on the Planet Nine conjecture. The present-day orbits of the six ETNOs originally linked to the hypothesis are evolved backward…
Studies of the clustering of the most distant Kuiper belt objects in the outer solar system have hinted at the possible existence of a planet beyond Neptune referred to as Planet Nine (P9). Recent efforts have constrained the parameter space of the orbital elements of P9, allowing for the creation of a synthetic catalog of hypothetical P9s. By examining the potential recovery of such a catalog within numerous sky surveys, it is possible to further constrain the parameter space for P9, providing direction for a more targeted search. We examine the ability of the full six years of the Dark Energ…
The outer solar system exhibits an anomalous pattern of orbital clustering, characterized by an approximate alignment of the apsidal lines and angular momentum vectors of distant, long-term stable Kuiper belt objects. One explanation for this dynamical confinement is the existence of a yet-undetected planetary-mass object, "Planet Nine (P9)". Previous work has shown that trans-Neptunian objects, which originate within the scattered disk population of the Kuiper belt, can be corralled into orbital alignment by Planet Nine's gravity over ~Gyr timescales, and characteristic P9 parameters have bee…
We present a numerical simulation of the dynamical interaction between the proposed Planet Nine and a debris disk around the Sun for $4{\rm Gyr}$, accounting for the secular perturbation of the four giant planets in two scenarios: (a) an initially thin circular disk around the Sun (b) inclined and eccentric disk. We show, in both scenarios, that Planet Nine governs the dynamics in between $1000{\rm -5000{\rm AU}}$ and forms spherical structure in the inner part ($\sim1000{\rm AU}$) and inclined disk. This structure is the outcome of mean motion resonances and secular interaction with Planet Ni…
A series of dynamical anomalies in the orbits of distant trans-Neptunian objects points to a new celestial body (usually named Planet Nine) in the solar system. In this draft, we point out that a mirror planet captured from the outer solar system or formed in the solar system is also a possible candidate. The introduction of the mirror matter model is due to an unbroken parity symmetry and is a potential explanation for dark matter. This mirror planet has null or fainter electromagnetic counterparts with a smaller optical radius and might be explored through gravitational effects.
The existence of Planet Nine has been suggested to explain the pericenter clustering of extreme trans-Neptunian objects (TNOs). However, the underlying dynamics involving Planet Nine, test particles and Neptune is rich, and it remains unclear which dynamical processes lead to the alignment and how they depends on the properties of Planet Nine. Here, we investigate the secular interactions between an eccentric outer perturber and TNOs starting in a near-coplanar configuration. We find that a large number of TNOs could survive outside of mean motion resonances at 4Gyr, which differs from previou…
Planet Nine is a hypothetical planet located well beyond Pluto that has been proposed in an attempt to explain the observed clustering in physical space of the perihelia of six extreme trans-Neptunian objects or ETNOs. The predicted approximate values of its orbital elements include a semimajor axis of 700 au, an eccentricity of 0.6, an inclination of 30 degrees, and an argument of perihelion of 150 degrees. Searching for this putative planet is already under way. Here, we use a Monte Carlo approach to create a synthetic population of Planet Nine orbits and study its visibility statistically i…
The longitudes of perihelia and orbital poles of the solar system's dozen or so most remote detected objects are clustered in a manner inconsistent with that of a random sample of uniformly distributed orbits. While small number statistics and observational biases may explain these features, the statistical significance of the clustering has led to the recent development of the "Planet Nine hypothesis." In the proposed scenario, orbits in the distant solar system are shepherded via secular perturbations from an undetected massive planet on an eccentric orbit. However, the precession of perihel…
The existence of a giant planet beyond Neptune -- referred to as Planet Nine (P9) -- has been inferred from the clustering of longitude of perihelion and pole position of distant eccentric Kuiper belt objects (KBOs). After updating calculations of observational biases, we find that the clustering remains significant at the 99.6\% confidence level. We thus use these observations to determine orbital elements of P9. A suite of numerical simulations shows that the orbital distribution of the distant KBOs is strongly influenced by the mass and orbital elements of P9 and thus can be used to infer t…
We report the detection of radial velocity variations in nine evolved G- and K-type giant stars. The observations were conducted at Okayama Astrophysical Observatory. Planets or planet candidates can best explain these regular variations. However, a coincidence of near 280-day variability among five of them prevents us from fully ruling out stellar origins for some of the variations, since all nine stars behave similarly in stellar properties. In the planet hypotheses to the RV variations, the planets (including one candidate) may survive close to the boundary of the so-called "planet desert" …
The observation that the orbits of long-period Kuiper Belt objects are anomalously clustered in physical space has recently prompted the Planet Nine hypothesis - the proposed existence of a distant and eccentric planetary member of our solar system. Within the framework of this model, a Neptune-like perturber sculpts the orbital distribution of distant Kuiper Belt objects through a complex interplay of resonant and secular effects, such that in addition to perihelion-circulating objects, the surviving orbits get organized into apsidally aligned and anti-aligned configurations with respect to P…
Correlations in the orbits of several minor planets in the outer solar system suggest the presence of a remote, massive Planet Nine. With at least ten times the mass of the Earth and a perihelion well beyond 100 AU, Planet Nine poses a challenge to planet formation theory. Here we expand on a scenario in which the planet formed closer to the Sun and was gravitationally scattered by Jupiter or Saturn onto a very eccentric orbit in an extended gaseous disk. Dynamical friction with the gas then allowed the planet to settle in the outer solar system. We explore this possibility with a set of numer…
The distribution of the orbital elements of the known extreme trans-Neptunian objects or ETNOs has been found to be statistically incompatible with that of an unperturbed asteroid population following heliocentric or, better, barycentric orbits. Such trends, if confirmed by future discoveries of ETNOs, strongly suggest that one or more massive perturbers could be located well beyond Pluto. Within the trans-Plutonian planets paradigm, the Planet Nine hypothesis has received much attention as a robust scenario to explain the observed clustering in physical space of the perihelia of seven ETNOs w…
Cosmology experiments at mm-wavelengths can detect Planet Nine if it is the size of Neptune, has an effective temperature of 40 K, and is 700 AU from the Sun. It would appear as a ~30 mJy source at 1 mm with an annual parallax of ~5 arcmin. The challenge is to distinguish it from the approximately 4000 foreground asteroids brighter than 30 mJy. Fortunately, these asteroids are known to the Minor Planet Center and can be identified because they move across a resolution element in a matter of hours, orders of magnitude faster than Planet Nine. If Planet Nine is smaller, colder, and/or more dista…
Batygin and Brown (2016) have suggested the existence of a new Solar System planet supposed to be responsible for the perturbation of eccentric orbits of small outer bodies. The main challenge is now to detect and characterize this putative body. Here we investigate the principles of the determination of its physical parameters, mainly its mass and radius. For that purpose we concentrate on two methods, stellar occultations and gravitational microlensing effects (amplification, deflection and time delay). We estimate the main characteristics of a possible occultation or gravitational effects: …
Co-orbital bodies are the byproduct of planet formation and evolution, as we know from the Solar System. Although planet-size co-orbitals do not exists in our planetary system, dynamical studies show that they can remain stable for long periods of time in the gravitational well of massive planets. Should they exist, their detection is feasible with the current instrumentation. In this paper, we present new ground-based observations searching for these bodies co-orbiting with nine close-in (P<5 days) planets, using different observing techniques. The combination of all of them allows us to rest…
The trans-Neptunian region of the solar system exhibits an intricate dynamical structure, much of which can be explained by an instability-driven orbital history of the giant planets. However, the origins of a highly inclined, and in certain cases retrograde, population of trans-Neptunian objects remain elusive within the framework of this evolutionary picture. In this work, we show that the existence of a distant, Neptune-like planet that resides on an eccentric and mildly inclined orbit fully accounts for the anomalous component the trans-Neptunian orbital distribution. Adopting the same par…
Complete sets of reference magnitudes in all 7 Johnson-Cousins bands (U, B, V, R, I, Rc and Ic) and the 5 principal Sloan bands (u', g', r', i', and z') are presented for the 8 planets. These data are accompanied by illumination phase functions and other formulas which characterize the instantaneous brightness of the planets. The main source of Johnson-Cousins magnitudes is a series of individualized photometric studies reported in recent years. Gaps in that dataset were filled with magnitudes synthesized in this study from published spectrophotometry. The planetary Sloan magnitudes, which are…
Zechmeister et al. (2009) surveyed 38 nearby M dwarfs from March 2000 to March 2007 with VLT2 and the UVES spectrometer. This data has recently been reanalyzed (Butler et al. 2019), yielding a significant improvement in the Doppler velocity precision. Spurred by this, we have combined the UVES data with velocity sets from HARPS, Magellan/PFS, and Keck/HIRES. Sixteen planet candidates have been uncovered orbiting nine M dwarfs. Five of them are new planets corresponding to radial velocity signals, which are not sensitive to the choice of noise models and are identified in multiple data sets ove…
A number of authors have proposed that the statistically significant orbital alignment of the most distant Kuiper Belt Objects (KBOs) is evidence of an as-yet undetected planet in the outer solar system, now referred to colloquially a "Planet Nine". Dynamical simulations by Batygin & Brown (2016) have provided constraints on the range of the planet's possible orbits and sky locations. We extend these investigations by exploring the suggestion of Malhotra et al. (2016) that Planet Nine is in small integer ratio mean-motion resonances (MMRs) with several of the most distant KBOs. We show that th…
We examine the possibility that icy super-Earth mass planets, formed over long time scales (0.1--1~Gyr) at large distances ($\sim$ 200--1000~AU) from their host stars, will develop massive H-rich atmospheres. Within the interior of these planets, high pressure converts CH$_4$ into ethane, butane, or diamond and releases H$_2$. Using simplified models which capture the basic physics of the internal structure, we show that the physical properties of the atmosphere depend on the outflux of H$_2$ from the mantle. When this outflux is $\lesssim 10^{10}$ [molec cm$^{-2}$ s$^{-1}$], the outgassed atm…
Over the course of the past two decades, observational surveys have unveiled the intricate orbital structure of the Kuiper Belt, a field of icy bodies orbiting the Sun beyond Neptune. In addition to a host of readily-predictable orbital behavior, the emerging census of trans-Neptunian objects displays dynamical phenomena that cannot be accounted for by interactions with the known eight-planet solar system alone. Specifically, explanations for the observed physical clustering of orbits with semi-major axes in excess of $\sim250\,$AU, the detachment of perihelia of select Kuiper belt objects fro…
HD 106906 is a 15 Myr old short-period (49 days) spectroscopic binary that hosts a wide-separation (737 au) planetary-mass ($\sim11\,M_{\rm Jup}$) common proper motion companion, HD 106906 b. Additionally, a circumbinary debris disk is resolved at optical and near-infrared wavelengths that exhibits a significant asymmetry at wide separations that may be driven by gravitational perturbations from the planet. In this study we present the first detection of orbital motion of HD 106906 b using Hubble Space Telescope images spanning a 14 yr period. We achieve high astrometric precision by cross-reg…
The existence of a hypothetical Planet 9 lurkng in the outer solar system has been invoked as a plausible explanation for the anomalous clustering in the orbits of trans-Neptunian objects. Here we propose that some meteoroids arriving at Earth could serve as messengers with the potential of revealing the presence of a hitherto undiscovered massive object. The peculiar meteor CNEOS 2014-01-08, recently put forward as the first interstellar meteor, might be one such messenger. The meteor radiant is in the maximum probability region calculated for the Planet 9 location in previous works. The odds…
We investigate the physical characteristics of the Solar System's proposed Planet Nine using modeling tools with a heritage in studying Uranus and Neptune. For a range of plausible masses and interior structures, we find upper limits on the intrinsic Teff, from ~35-50 K for masses of 5-20 M_Earth, and we also explore lower Teff values. Possible planetary radii could readily span from 3 to 6 R_Earth depending on the mass fraction of any H/He envelope. Given its cold temperature, the planet encounters significant methane condensation, which dramatically alters the atmosphere away from simple Nep…
The observational census of trans-Neptunian objects with semi-major axes greater than ~250 AU exhibits unexpected orbital structure that is most readily attributed to gravitational perturbations induced by a yet-undetected, massive planet. Although the capacity of this planet to (i) reproduce the observed clustering of distant orbits in physical space, (ii) facilitate dynamical detachment of their perihelia from Neptune, and (iii) excite a population of long-period centaurs to extreme inclinations is well established through numerical experiments, a coherent theoretical description of the dyna…
We investigate the formation of icy super-Earth mass planets within a gravitationally unstable ring of solids orbiting at 250-750 AU around a 1 solar mass star. Coagulation calculations demonstrate that a system of a few large oligarchs and a swarm of pebbles generates a super-Earth within 100-200 Myr at 250 AU and within 1-2 Gyr at 750 AU. Systems with more than ten oligarchs fail to yield super-Earths over the age of the solar system. As these systems evolve, destructive collisions produce detectable debris disks with luminosities of $10^{-5}$ to $10^{-3}$ relative to the central star.
Observations of clustering among the orbits of the most distant trans-Neptunian objects (TNOs) has inspired interest in the possibility of an undiscovered ninth planet lurking in the outskirts of the solar system. Numerical simulations by a number of authors have demonstrated that, with appropriate choices of planet mass and orbit, such a planet can maintain clustering in the orbital elements of the population of distant TNOs, similar to the observed sample. However, many aspects of the rich underlying dynamical processes induced by such a distant eccentric perturber have not been fully explor…
Trans-Neptunian Objects (TNOs) in the scattered disk with 50 < a < 100 au are thought to cluster near Neptune's n:1 resonances (e.g: 3:1, 4:1, and so on). While these objects spend lengthy periods of time at large heliocentric distances, if their perihelia remain less than around 40 au, their dynamical evolution is still largely coupled to Neptune's. Conversely, around a dozen extreme TNOs with a > 250 au and detached perihelia seem to exist in a regime where they are too distant to be affected by the giant planets, and too close for their dynamics to be governed by external forces. Recent wor…
Uranus' startlingly large obliquity of 98 degrees has yet to admit a satisfactory explanation. The most widely accepted hypothesis involving a giant impactor that tipped Uranus onto its side encounters several difficulties with regards to the Uranus' spin rate and its prograde satellite system. An obliquity increase that was driven by capture of Uranus into a secular spin-orbit resonance remains a possible alternative hypothesis that avoids many of the issues associated with a giant impact. We propose that secular spin-orbit resonance could have excited Uranus' obliquity to its present day val…
We show that an equal-mass, temporary binary companion to the Sun in the solar birth cluster at a separation of $\sim 10^3 \; \mathrm{\; AU}$ would have increased the likelihood of forming the observed population of outer Oort cloud objects and of capturing Planet Nine. In particular, the discovery of a captured origin for Planet Nine would favor our binary model by an order of magnitude relative to a lone stellar history. Our model predicts an overabundance of dwarf planets, discoverable by LSST, with similar orbits to Planet Nine, which would result from capture by the stellar binary.
Several papers have recently suggested the possible presence of a ninth planet (Planet X) that might explain the gravitational perturbations of a number of detached Trans-Neptunian objects. To analyze the possibility further, we have applied celestial mechanics, engineering physics and statistical analysis to develop improved estimates of the planet's primary orbital elements and mass from first engineering principles, using the orbital characteristics of both the original group of 6 objects analyzed and also a second group comprising the original 6 together with 6 additional long-period aster…
Nine transiting Earth-sized planets have recently been discovered around nearby late M dwarfs, including the TRAPPIST-1 planets and two planets discovered by the MEarth survey, GJ 1132b and LHS 1140b. These planets are the smallest known planets that may have atmospheres amenable to detection with JWST. We present model thermal emission and transmission spectra for each planet, varying composition and surface pressure of the atmosphere. We base elemental compositions on those of Earth, Titan, and Venus and calculate the molecular compositions assuming chemical equilibrium, which can strongly d…
