Looking For Planet X

There are some hints from the orbits of known objects in the solar system that there might be a Planet X out there that has not been discovered. A recent study by Siraj et al., analyzes a bigger data set (orbits of 51 objects v. 11 in previous studies) to work out where this Planet X should be based upon these hints. It concludes that:

We find that the unseen planet parameters that best fit the data are a mass of m(p) = 4.4 ± 1.1M⊕, a semimajor axis of a(p) = 290 ± 30 AU, an eccentricity of e(p) = 0.29 ± 0.13, and an inclination of i(p) = 6.8 ± 5.0∘ (all error bars are 1σ). 

Only 0.06% of the Brown & Batygin (2021) reference population produce probabilities within 1σ of the maximum within our quadrivariate model, indicating that our work identifies a distinct preferred region of parameter space for an unseen planet in the solar system. If such an unseen planet exists, it is likely to be discovered by LSST.

So, we are looking for a planet about 3-5 times the size of Earth, at the fringe of the solar system past Neptune (about 9-12 times as far away from the Sun as Neptune), in a rather strongly elliptical orbit comparable to Mercury whose orbit has e = 0.205 or Pluto whose orbit has e = 0.248 (as opposed to the nearly circular orbit of all of the other planets and most of the moons) but not nearly as non-circular as the well-known comets, and quite close to the plane in which the other planets of our Solar System orbit the Sun. It also can't have an exceptionally reflective surface (i.e. high albedo), since otherwise we would have seen it already. This narrows down the places we should look for it, and what we are looking for, dramatically.

As a reference: The distance from the Sun to Mercury is 0.39 AU, to Venus is 0.72 AU, to Earth is 1.00 AU, to Mars is 1.52 AU, to Jupiter is 5.20 AU, to Saturn is 9.54 AU, to Uranus is 19.22 AU, and to Neptune is 30.06 AU. Pluto averages 39 AU and ranges from 30-49 AU from the Sun. 

The mass of the Sun is roughly 333,000 times that of Earth. The gas giants have masses ranging from Jupiter at about 318 Earth masses to Saturn at about 95 Earth masses to Neptune at about 17 Earth masses to Uranus at about 14.5 Earth masses. Other of the other planets, dwarf planets, moons, and other objects in our solar system are less massive than Earth. So, Planet X, if it exists, would have a mass significantly greater than Earth, but significantly smaller than Uranus.

It might be a gas dwarf, an ice giant, a super-Earth, or  a super-puff.

The mass range suggests a radius larger than the 6,371 km  of Earth and less than the 24,622 km of Neptune (which has a smaller radius than Uranus despite being more massive than Uranus), realistically, a radius in the ballpark of 9,000 to 18,000 km, unless it is a super-puff (which would have a radius larger than Neptune despite having a much smaller mass).

The rather precise parameters for a potential Planet X means that it should be seen or ruled out in a matter of not all that many years. If it is ruled out, then another hypothesis for the hints attributed to Planet X needs to be established.

The paper lays out the hints that suggest a Planet X:

There is a long history of theoretically proposed planets in the outer solar system, dating back to the mid-1800s. Recently, the structure of the distant Kuiper belt has led to speculation regarding the possibility of an unseen planet. Some of these recent studies have been motivated by apparent clustering of distant trans-Neptunian objects (TNOs) in various orbital parameters, including longitude of perihelion (ϖ), longitude of the ascending node (Ω), argument of perihelion (ω ≡ ϖ−Ω) and inclination relative to the ecliptic (i). An unseen planet in the outer solar system could potentially shepherd the orbits of distant TNOs into clustered configurations. The observational search for such a planet has, to date, been unsuccessful. 

There is an ongoing debate over whether the claimed clustering of distant TNOs is real or spurious, perhaps arising from observational selection effects or limited statistics. Shankman et al. (2017) and Bernardinelli et al. (2020) could not conclude that distant TNOs were clustered in Dark Energy Survey (DES) data alone, and Bernardinelli et al. (2022) similarly could not conclude that distant TNOs were clustered in Outer Solar System Origins Survey (OSSOS) data alone. Brown & Batygin (2019) and Napier et al. (2021) examined larger samples of TNOs and reached opposite conclusions about the statistical significance of clustering in the orbital elements. In addition to clustering in angular orbital elements, an unseen planet could also produce a population of high-inclination Centaurs. 

Brown & Batygin (2021) ran a suite of 121 n-body simulations testing various parameters for an additional planet in the solar system. Each simulation contained several tens of thousands of test particles, whose orbital parameters were compared to the ϖ, Ω, and i distributions of 11 distant TNOs to identify a preferred region of parameter space for the additional planet. Additionally, Batygin et al. (2024) argued that an unseen planet may produce a population of Neptune-crossing TNOs significantly more consistent with the observed population of such objects than if no unseen planet were present. 

In this paper, we re-examine the question of whether or not the current distribution of distant TNO detections suggests clustering in ϖ, Ω, and i. Furthermore, we explore the parameter space of hypothetical unseen planets and ask what parameters are most likely given the current state of observations. 

A novel feature of this work is that we determine the long-term stability for a large set of distant TNOs– such stability is crucial for evaluating the plausibility of an unseen planet because it takes ∼ 1 Gyr for such a planet to induce clustering amongst TNOs. Using this information and new discoveries of distant TNOs in addition to a broader range of allowed semimajor axes we are able to expand the sample of TNOs that we search for clustering to 51 objects.

Finding a planet this big, so long after the last major discovery of a large object in the Solar System, would be remarkable.