Searching the swath: the hunt for Planet Nine

Brown and Batygin’s search of the Zwicky Transient Facility archive ended with 103 candidate linkages that survived to a final orbit integration. One was real. It was Eris, a dwarf planet co-discovered by Brown, at about 96 au. The search had picked it up by accident, through 11 detections in 20 days near quadrature, the point where an outer body’s apparent motion is slowest and a nearby object can pass for a distant one. The other 102 were chance alignments of unrelated transients. Among 56,373 simulated planets that the archive should have recorded at least seven times, the pipeline linked 56,173. So the search was sensitive, and it found no Planet Nine (Brown & Batygin 2022).

That is the shape of every result in this chapter. A search for Planet Nine does not end with a planet. It ends with a measured probability of having found one, computed for a specified population of possible planets, and a statement that none was found. Three archival searches together would have caught 78% of the planets in the main reference population (Brown et al. 2024). The other 22% are farther, fainter, and mostly hidden where the northern Milky Way crosses the ecliptic.

Chapter 8 covered the reasons for thinking a planet exists and how its orbit is inferred. This chapter covers the hunt: the physics of the signal, each search in turn with its algorithm and its numbers, what remains, and what Rubin and image stacking may add. Thermal-infrared and millimetre searches are summarised here and treated fully in Chapter 24.

What makes the search hard

Not a streak, but a loop

Most moving-object pipelines look for things that move within a night: asteroids trail, or shift between exposures minutes apart (Chapter 12). Planet Nine barely moves within a night. A body at 500 au moves across the sky mainly because Earth does, and Earth’s orbital speed of about 30 km/s, seen from 500 au, is a fraction of an arcsecond per hour. In a typical exposure the planet is an ordinary point source, indistinguishable from a star. On the next night it has shifted by several arcseconds. Over a year it traces a loop, the reflection of Earth’s orbit scaled down by the distance.

This has three consequences. A pipeline that rejects sources lacking measurable motion within a night throws the planet away. Linking must work across nights, months and years, through a curved path. And the signal sits in the most crowded part of the problem, among stars, subtraction residuals and noise. A planet near the Galactic plane has many more neighbours to be confused with.

A target defined by a model

The second difficulty is that the target is a probability distribution, not a position. The dynamical inference constrains the orbit’s orientation, but hardly its phase, so the predicted planet is smeared along a band about $\pm12^\circ$ wide around a great circle (Brown & Batygin 2021). Its brightness depends on a radius and an albedo that no dynamical argument fixes. A search therefore excludes a fraction of a reference population: 100,000 sample planets drawn from the 2021 posterior, each with a sky position, distance, radius and albedo (Brown & Batygin 2022). Change the population and the exclusion changes.

History of the hunt

The hunt began before the hypothesis was public. Brown and Batygin report that they started a Subaru Hyper Suprime-Cam (HSC) search in the fall of 2015. Their 2016 paper on observational constraints identified the faint northern region near the predicted aphelion as particularly suited to HSC’s wide, deep field (Brown & Batygin 2016). In a 2021 update on their research blog, they said that the Subaru search had concentrated near the probability maximum around right ascension $60^\circ$, close to the Galactic plane (Brown & Batygin blog 2021). No completed, injection-calibrated exclusion from that program has been published.

The 2016 paper also took stock of what existing surveys already said, and it set the pattern for everything since. It predicted that the planet was probably near aphelion, with brightness $22 < V < 25$. It noted that most wide-field Kuiper belt surveys had been blind to motions slower than about 1 arcsec per hour, so they said nothing about a body at several hundred au. A handful of surveys had the right cadence. Brown and Batygin searched the transient stream of the Catalina Real-time Transient Survey for groups of four or more detections that fit Keplerian orbits. Out of about $10^{19}$ possible combinations, the filter left eight known Kuiper belt objects and no false positives, and the survey was essentially complete to $V\approx19.1$ in the north and 18.6 in the south. The Pan-STARRS transient stream, at a typical depth of $g=21.0$, excluded much of the sky within about $45^\circ$ of the predicted perihelion, except near the Galactic plane. A preliminary Pan-STARRS outer Solar System analysis reported no detections out to 600 au. WISE, which had ruled out Saturn-sized planets to about 30,000 au through their internal heat, was much weaker here. A planet of 10 Earth masses would lack the enhanced short-wavelength emission of a gas giant, and at the WISE W1 limit Neptune itself could be detected only to about 70 au (Brown & Batygin 2016). The bright, nearby part of the orbit was already being closed off. The faint aphelion, in the northern sky, was the open question, and it still is.

A parallel program by Scott Sheppard, Chadwick Trujillo, David Tholen and collaborators searched for distant bodies and possible planets with DECam and Subaru, while building the very sample of detached objects that motivates Planet Nine. By 2016 it covered 1,080 square degrees (Sheppard & Trujillo 2016). One discovery shows its cadence: 2015 TG387 was found at Subaru on 13 October 2015, at about 80 au and $r=24.0$, then recovered over later oppositions. By 2019 the survey had grown to about 2,130 square degrees (Sheppard et al. 2019).

The turning point for archival searches was the 2021 orbit posterior. It favoured a closer, lighter planet than the original illustration, with median $a_9=380$ au and $m_9=6.2M_\oplus$. Reflected flux falls as distance to the fourth power, so a closer, smaller planet can be brighter than a distant, larger one. Wide surveys of moderate depth became real discovery instruments. Brown and Batygin’s ZTF search appeared as a preprint in October 2021 and was published in 2022. Belyakov, Bernardinelli and Brown connected the reference population to the completed Dark Energy Survey search in 2022. Brown, Holman and Batygin added Pan-STARRS1 in 2024. Holman and collaborators broadened the Pan-STARRS search in 2025. Socas-Navarro and Trujillo took the opposite approach, acquiring purpose-designed observations of one crowded northern field, revised for publication in January 2026. Meanwhile, image-stacking methods matured to the point of forecasting what a stacked archive could add (Geringer-Sameth et al. 2025; Napier et al. 2026).

These are three strategies. One searches more sky in old catalogues. Another models the selection better. The third acquires the cadence the signal actually needs.

The physics of the signal

Brightness

For an unresolved body that reflects sunlight,

with $r$ the heliocentric distance and $\Delta$ the distance from the observer, both in au, $H$ the absolute magnitude, and $\Phi(\alpha)$ the phase function, normalised to one at zero phase angle $\alpha$. Near opposition at large distance, $r\simeq\Delta$ and $\Phi\simeq1$, so

At fixed geometric albedo $p$ and radius $R$, flux scales as $pR^2r^{-4}$. Doubling the distance makes the planet $10\log_{10}2=3.01$ magnitudes fainter. Going one magnitude deeper extends the reach in distance by only $10^{0.1}=1.26$ (Belyakov et al. 2022). This is the arithmetic behind the whole search. A survey a magnitude deeper than its predecessor reaches only a quarter farther, and the most probable positions, near aphelion, are also the faintest (Chapter 2).

The reference population fixes the physical properties by assumption:

a sub-Neptune radius law and a uniform albedo range. Mean anomaly is drawn uniformly, which means uniform time along the orbit and therefore extra weight near aphelion (Brown & Batygin 2022). Chapter 8 works through the resulting magnitudes: about $V\approx19$ at perihelion and $V\approx21$–22 near aphelion for the median planet.

Motion

Let the planet be at heliocentric position $\mathbf r(t)$ and the observer at $\mathbf R(t)$. The observed direction, allowing for light travel time, is

To first order in the inverse distance $\gamma=1/r$, the position on a tangent plane is

where $\boldsymbol\mu$ is the planet’s own slow angular motion and $\mathbf R_\perp$ is the component of the observer’s position perpendicular to the line of sight (Holman et al. 2025). The last term is the annual parallax. It dominates.

The sizes follow from Earth’s orbital speed, $v_\oplus\approx29.8$ km/s. Seen from distance $r$ near opposition, the reflex angular rate is $v_\oplus/(r\cdot1\,\mathrm{au})$ radians per second. Converting,

the second for a circular orbit, whose speed falls as $r^{-1/2}$. At 500 au the reflex motion is about 0.296 arcsec per hour, or 7.1 arcsec per day, while the orbital motion is about 0.013 arcsec per hour, twenty-two times smaller. These coefficients ignore projection and both orbits’ eccentricities. They are calculations made for this book, not values from the papers. At quadrature the reflex term passes through zero, so “it moves slowly, therefore it is distant” fails without the actual observing geometry. That is how Eris crept into the ZTF candidates.

Straightening the loop

The parallax term suggests the central trick of the archival searches. Guess a distance. For each detection, with observed direction $\hat{\mathbf u}$ and observer position $\mathbf R$, find the point at heliocentric distance $r$ along the line of sight:

If the guess is right, the detections of a real distant body, viewed from the Sun, move at nearly constant rate along a great circle. If the guess is wrong, a residual loop remains. Search over a grid of distances, and at each one look for detections that line up (Holman et al. 2025; Brown & Batygin 2022). This is the same idea as the heliocentric transformations of Chapter 12, applied to slower bodies over longer arcs.

Detection statistics

An image $I_i$ can be written as background $B_i$ plus the planet’s flux times the point-spread function (PSF) $P_i$ at the position $\mathbf x_i(\vartheta)$ predicted by orbit $\vartheta$, plus noise:

Here $f$ is an overall flux and $a_i$ the relative throughput. With independent Gaussian pixel variances $\sigma^2_{ip}$, the matched-filter sufficient statistics over all images $i$ and pixels $p$ are

with flux estimate $\hat f=\Psi/\mathcal V$ and significance $S=\Psi/\sqrt{\mathcal V}$ (Geringer-Sameth et al. 2025). The sum keeps evidence from exposures in which the planet was too faint to detect alone. That is the case for stacking (Chapter 17, Chapter 20). For $N$ equal exposures with background-limited noise, the stacked SNR grows as $\sqrt N$, a depth gain of $2.5\log_{10}\sqrt N=1.25\log_{10}N$ magnitudes. With Rubin’s 800 exposures in one night (see below), the gain is $1.25\log_{10}800=3.6$ mag. Added to a single-exposure $5\sigma$ limit of $r=24.6$, that gives $r\approx28.2$ at $5\sigma$, or $28.2-2.5\log_{10}2\approx27.5$ at SNR 10. That is my check, and it reproduces the published forecast.

Every completed search so far worked instead from catalogues: lists of positions, magnitudes and uncertainties for sources above a threshold in single images. Linking then tests whether enough catalogue points fit an allowed orbit, typically through

The Gaussian form describes positional errors of real detections. It says nothing about the false sources that dominate the catalogues: bright-star halos, detector edges, cosmic rays, variable stars and subtraction residuals. Their correlations make a global false-alarm probability from multiplied Gaussian tails meaningless. Orbit fits, confirmation in independent images, injected test sources and explicit artifact handling do the real work (Bernardinelli et al. 2022).

Completeness and the meaning of a null

Let $C_s(z)$ be the probability that survey $s$ would have discovered a planet with parameters $z$. The exclusion of the reference population $\pi_{\rm ref}$ is

After a null result, assuming the planet exists under that prior,

This pushes the surviving population toward places and properties that are harder to detect. Several surveys combine through the union of reference planets each would have found. That is the actual procedure with deterministic discovery flags. The formula $1-\prod_s(1-C_s)$ is valid only if the surveys’ failures are independent, and they are not when they share sky, seasons or exposures (Holman et al. 2025).

The searches, one by one

ZTF: sparse transients, transformed

The Zwicky Transient Facility uses the 48-inch Samuel Oschin Schmidt telescope at Palomar, with a 47-square-degree camera field. Brown and Batygin searched its public transient archive, which the paper describes as three years of data (Brown & Batygin 2022). After removing sources that recurred at one fixed position, the predicted swath held about 13 million detections, 8.6 million of them near known Solar System objects.

Calibrating the selection. The transient feed does not record everything needed to reconstruct exposure-by-exposure completeness. The authors used numbered asteroids as moving calibration sources instead. JPL Horizons predicts where each asteroid was and how bright, so the archive’s detections and non-detections of asteroids map the probability of detection by sky cell, night and magnitude. The calibration used HEALPix NSIDE = 32 cells of about 1.8 square degrees, nightly sampling, and 0.25-magnitude bins. Predicted asteroid magnitudes scatter by about 0.2 mag RMS from the measured ones, which limits the calibration. Using predicted $V$ also assumes Planet Nine has average asteroid colours.

Requiring seven distinct detections balances completeness against chance associations and fitting cost. Over much of the swath, a planet brighter than about $V=20.5$ had a 95% chance of seven detections. The northern Galactic plane did reasonably well, because frequent revisits made up for confusion. The southern plane and low declinations did worse.

Linking. The sky was cut into 1,164 overlapping bricks of $3^\circ\times3^\circ$. Trial distances were spaced uniformly in $\gamma=1/r$ from zero to $1/200$ au⁻¹ in steps of $10^{-4}$ au⁻¹. At each trial distance, every detection was transformed to a heliocentric direction and paired with others to compute an implied angular velocity. A real body makes a tight cluster in velocity space, typically $5\times10^{-5}$ by $2\times10^{-5}$ degrees per day in longitude and latitude. Clusters with enough distinct dates went to an iterative distance fit, then a full orbit fit, with a final astrometric tolerance of 2 arcsec RMS.

for each overlapping 3x3 degree brick:
    load real transients plus blinded synthetic planet detections
    for gamma in 0 .. 1/200 au^-1 step 1e-4:
        transform detections to heliocentric directions
        for each anchor detection:
            compute angular velocities to compatible detections
            find velocity clusters with >= 7 distinct dates
            refine distance; fit full orbit if residuals pass
unblind synthetic identities; inspect surviving real candidates

The naive cost is $O(G\sum_bN_b^2)$ for $G$ distance hypotheses and $N_b$ detections in brick $b$, before clustering and fits. Geometric bounds cut the practical work, but contamination can restore the combinatorial growth, and passing false clusters to the orbit fitter costs more than the geometry. No CPU-hour or GPU-hour total was reported.

Result. Linking efficiency was 99.66% for synthetic planets with enough detections, which made up about 56% of the reference population. The all-population recovery curve reaches 50% at $V=20.57$. The 103 real candidates reduced to Eris. No Planet Nine.

DES: deep, sparse, and confirmed in independent images

The Dark Energy Survey observed about 5,000 square degrees of southern sky with DECam on the 4-m Blanco telescope from 2013 to 2019. Its full search for outer Solar System bodies and its Planet Nine calculation are separate papers (Bernardinelli et al. 2022; Belyakov et al. 2022).

The search builds orbits from sparse detections. It finds single-night transients, forms compatible pairs within bins of inverse distance, searches the region where a third detection could lie, and grows the orbit by predicting further positions. An improved triplet search represents the allowed region as a parallelogram and uses a linear-algebra containment test instead of a kd-tree. It is reported to be about 100 times faster than the previous implementation. For bodies beyond 50 au, triplet dates can be up to 90 days apart. Orbit growth uses $4\sigma$ prediction ellipses and refits as detections are added. Cuts require seven unique nights, $\chi^2/(2N_{\rm det}-6)<4$, and an arc longer than six months even after dropping any one night. A chance-association diagnostic, $\mathrm{FPR}=\sum_jA_jn_j<0.02$, sums search-ellipse area times transient surface density over the extensions. It is a linkage diagnostic, not a “2% chance the discovery is false”.

The confirmation step is the most transferable idea in the chapter. Sub-threshold significance (STS) stacks the exposures along the fitted orbit, excluding the detections used to build it and every image from those nights. A chance linkage has no reason to produce flux in the independent images. A real object does. Candidates were accepted with at least nine unique nights, or if they passed $\mathrm{STS}>1.2\sqrt{N_{\rm images}}$.

The scale is unusually well documented: about $1.60\times10^{10}$ initial detections, $1.08\times10^8$ transients, at least about $10^{13}$ pairs and $10^{12}$ triplets, and 15–20 million CPU hours for the whole outer Solar System search. The final Y6 catalogue holds 817 objects, including 815 TNOs, with 50% completeness at $r_{50}=23.77$. That compute served the whole survey, not Planet Nine alone (Bernardinelli et al. 2022).

For Planet Nine, Belyakov and collaborators intersected each reference planet’s path with the DES exposures and applied the measured detection probability,

then a transient-selection efficiency of about 95.5% and the timing rules: at least seven unique nights, an arc of at least 180 days, and a suitable triplet. They did not rerun the linker, relying on its established near-complete linking of qualifying observations. Of 100,000 planets, 11,709 cross the DES footprint and 10,187 would have been recovered. That is 87.0% of those crossing, but only 10.2% of the whole population, and only 5,032 beyond those ZTF already excluded. The Planet Nine recovery curve reaches 50% at $g\approx24.1$ (Belyakov et al. 2022).

Pan-STARRS1, 2024: the same idea at billion-object scale

Pan-STARRS1 (PS1) surveyed the sky north of declination $-30^\circ$, with about 12 visits per filter in $grizy$ and single-epoch depths of about 22.0, 21.8, 21.5, 20.9 and 19.7 (Brown et al. 2024). Brown, Holman and Batygin worked from the DR2 catalogue, not the images.

The archival engineering is part of the story. They queried catalogue objects with fewer than 12 detections and at least one in $g$, $r$ or $i$, then kept those that appeared on only one date. Downloading in batches through the CasJobs service took months. The predicted swath held 1.26 billion single-night objects. Successive cuts left 772 million after PSF-quality and magnitude cuts, 428 million after detector masks, 314 million after bright-star masks, and 244 million after removing dense local clusters of five or more detections within 40 arcsec. The bright-star mask radius was an empirical function of the star’s magnitude,

Injected planets were extracted after these cuts, so the measured completeness includes their losses.

Linking used the same transform with a finer distance grid, $\Delta(1/r)=10^{-5}$ au⁻¹, velocity boxes of 0.052 and 0.026 arcsec per day, and nine detections required. With seven, false associations were overwhelming. Running about 50 sky blocks concurrently, processing still took several months. No hardware or core-hour figures were given. Of 69,082 injected planets with at least nine detections, 68,550 were correctly linked, 99.2%. Another 909 linkages mixed injected detections with each other or with real catalogue points. They were not discoveries.

The combined result is the headline of the field. Taking the union of reference planets found by ZTF, DES or PS1, 78% of the population is excluded. The combined efficiency is about 94% for $V<20.5$, falls to 50% at $V=21.5$, and has a tail to $V\approx23.5$ at about 20% efficiency, from DES alone. Outside the Galactic plane, the median local 95% limit of PS1 is $V=21.0$. If the unobserved low declinations and the poorly covered southern Galactic plane are excluded, the bright-object efficiency rises to 97% and 99.7% respectively (Brown et al. 2024).

The comparison with the surviving population is sobering. The survivors’ median brightness, $V=22.0$, is at or beyond the PS1 single-epoch depths in $g$, $r$ and $i$. Roughly half of what remains would not appear in the PS1 catalogue on a typical visit, however good the linker. A catalogue search of the same data cannot reach it. A stack of the same data might.

Pan-STARRS, 2025: broader motions and a learned selection function

Holman, Napier, Payne and Kurlander went back to Pan-STARRS with a broader search and a more explicit selection model (Holman et al. 2025). They used 708,554 source catalogues from unsubtracted images, from April 2009 to November 2017, covering about 80% of the sky. By filter: 62,098 in $g$, 106,270 in $r$, 226,912 in $i$, 68,064 in $z$ and 245,210 in the broad $w$ band. The $y$ band and the Medium Deep fields were left out.

The calibration improved on asteroid-based methods. A control population of 10,000 isotropic synthetic orbits was propagated into each exposure, with detector gaps, local detection efficiency, and astrometric and photometric errors modelled before the catalogue-level injection. That characterises places where real asteroids are sparse. It is still a model of source extraction, not injection into pixels.

Linking works in stages. At each assumed distance, sources are transformed to barycentric directions, and same-night detections are put in a three-dimensional kd-tree. Neighbours must be separated by no more than a bound orbit allows. The maximum barycentric angular rate is

the escape speed divided by distance. Tracklets, short same-night groups, are extended if residuals stay below 0.4 arcsec and magnitudes within one magnitude. Across nights, observations are transformed with an assumed inverse distance and zero radial velocity so that motion is nearly linear. The distance grid has 20 points from 80 to 1,600 au, uniform in inverse distance. Pairs of compatible tracklets seed bound orbits, which are extended, deduplicated and cleaned. A minimum of six tracklets was needed, because lower thresholds flooded the results with false associations.

The search took several days on about 100–200 CPU cores of Harvard’s Cannon cluster. That is far less than the months of the 2024 search, but the datasets, filters, motion assumptions, code and hardware all differ, so it is not a controlled benchmark. It found 692 objects, 642 with $a>30$ au and 109 not then known to the Minor Planet Center, and no new object beyond 60 au.

The selection function was learned. Detection counts in 10-day bins fed a logistic model, trained on 80% of the control sample and validated on 20%, predicting whether an object would be linked. Accuracy was about 90%, and the probabilities were checked for calibration. A recurrent neural network did no better. This is machine learning for the selection function, not a neural detector. Applied to the reference population with TNO-like colours, it predicts that 75,769 of the 100,000 planets would have been found. The authors decline to combine this with the 78% union, because the data overlap and the efficiency treatments differ. The two numbers must not be added, or merged into an invented combined percentage.

Dedicated fields: Subaru and DECam

Two kinds of targeted program must be kept apart. Brown and Batygin’s HSC program targets the predicted path itself, especially the northern aphelion region. The Sheppard–Trujillo program searches for distant bodies in general, and so can both find a planet and add to the evidence for or against one.

The 2016 Sheppard–Trujillo survey documents 1,080 square degrees: 970 from DECam, 40 from Subaru Suprime-Cam, 60 from Magellan and 11 from Kitt Peak. DECam exposures of about 330–700 s targeted $r\approx24$, and Subaru and Magellan fields $r\approx25.5$. Most fields had three images over 3–5 hours (Sheppard & Trujillo 2016). The crucial selection number is motion acceptance. Injections showed that about 90% of fields accepted motion faster than about 0.3 arcsec per hour, which corresponds to about 500 au at opposition. About 25% had enough baseline for 700 au or more, and 14% had about a day between first and last exposure. The survey generally kept about 15° from the Galactic plane. A deep image can still be blind to the slowest, most crowded Planet Nine possibilities.

By 2019 the program had added about 1,050 square degrees, mostly with HSC’s 1.5-square-degree field (about 300 s exposures to $r\approx25.5$) and DECam’s 2.7-square-degree field (about 420 s in a broad $VR$ filter, to an $r$-equivalent near 25). The paper tabulates field centres, depths and baselines (Sheppard et al. 2019). Those tables could feed a Planet Nine forward simulation. Nobody has published the resulting exclusion, and reading the depth column does not supply one.

A third Subaru program is instructive but is not a Planet Nine search. Fraser and collaborators’ New Horizons survey used GPU shift-and-stack with KBMOD and a residual-network classifier in crowded fields, finding 239 multi-night TNOs to about $r\approx26.5$ (Fraser et al. 2024). Its rate grid, 35 rates from 0.5 to 4 arcsec per hour, covers about 30–300 au and misses most of the Planet Nine regime. The network cut bogus candidates by a factor of 500–1,000 at a cost of about 0.2 mag. That technology could transfer, with a slower rate grid, tests of how template subtraction treats slow sources, and multi-night confirmation (Chapter 17, Chapter 22).

A purpose-built parallax search: JAST/T80

Héctor Socas-Navarro and Ignacio Trujillo designed a search around the parallax itself (Socas-Navarro & Trujillo 2026). They observed a field of about 98 square degrees near the high-probability northern region with the 80-cm JAST/T80 telescope at Javalambre. Its camera has $9200\times9200$ pixels covering $1.4^\circ\times1.4^\circ$. The useful observations came on 24 and 25 September 2023, with 180 s exposures.

The method is simple. Detect sources on each night with SExtractor. Keep “orphans”, sources present on one night but absent at the same position on the other. Pair orphans whose displacement lies on a short segment, from $(-2.05,-0.91)$ to $(-8.25,-3.69)$ arcsec in RA and declination, which corresponds to distances of 270–1,100 au for that date and field. Require magnitudes to agree within one magnitude. This produced 939 candidate pairs. Visual inspection, and further images where needed, rejected them all. The false pairs were bright-star structures, pairs of cosmic rays, satellites combined with cosmic rays, and faint stars detected on only one night.

Completeness was estimated from the source counts, not from injected moving sources. If $m_i(r)$ is the fraction of sources of magnitude $r$ missed on night $i$, extrapolated from the count power law beyond its turnover, then both detections succeed with probability

The 85% limits range over about $r=21.0$–21.4, averaging 21.3. The authors estimate a 0.4% chance of losing a candidate to scattered light from bright stars. The extrapolation and the independence assumption deserve injection tests in a crowded field. Matching two catalogues with a spatial index costs about $O(N\log N+K)$ for $K$ candidate pairs. The hard part is the rare artifact coincidences, and a third epoch would remove most of them.

Beyond reflected light

Three other kinds of search have targeted Planet Nine, and each is owned by another chapter. In the thermal infrared, a planet’s own heat falls as $r^{-2}$, not $r^{-4}$. Meisner and collaborators searched 31,480 square degrees, 76.3% of the sky, with time-resolved WISE coadds, reaching 90% completeness at $W1=16.70$ at high latitude, and found no planet (Meisner et al. 2018). In the millimetre, Naess and collaborators searched about 18,000 square degrees of Atacama Cosmology Telescope maps from 2013–2019 with 25,837 distance–velocity templates. They found no significant detection and set limits of about 4–12 mJy at 150 GHz for 300–600 au. Through a planetary thermal model that corresponds to detection distances of 325–625 au for five Earth masses (Naess et al. 2021). Archival IRAS and AKARI searches have produced candidates, notably Phan and collaborators’ 2025 pair of far-infrared detections, which remain unconfirmed recovery targets (Phan et al. 2025). These are all covered in Chapter 24. Rice and Laughlin’s shift-and-stack search of TESS images in the northern Galactic plane produced 17 candidates, none confirmed (Rice & Laughlin 2020). That search is in Chapter 23.

What remains

After the three-survey null, the surviving members of the reference population have semimajor axis $500^{+170}_{-120}$ au, mass $6.6^{+2.6}_{-1.7}M_\oplus$, aphelion $630^{+290}_{-170}$ au, current distance $550^{+250}_{-180}$ au and $V=22.0^{+1.1}_{-1.4}$ (Brown et al. 2024). These are reweighted model predictions, not measurements. They are most useful for planning the next search.

The surviving sky is concentrated in three places. The largest is a swath near the northern Galactic plane, where the predicted orbit reaches aphelion. There the planet would be faint, the stars dense, and PS1’s sparse coverage weak. A smaller region lies in the poorly covered southern Galactic plane, and a strip lies below declination $-30^\circ$, outside PS1. Brown and collaborators note that the ephemeris analysis of Fienga and collaborators suggests a planet near perihelion, as the southern positions are, would already have shown up in Saturn’s orbit. How best to combine that with the optical limits is unresolved (Chapter 7).

The exclusion also depends on assumptions that could be wrong in a direction that makes the planet harder to find:

• Colour and albedo. Changing the assumed colours, albedos and radii shifts the covered fraction by only about 10%, judging by the DES models (Brown et al. 2024). A dark, icy “super-Eris”, however, would be about 3 magnitudes fainter than the sub-Neptune assumption (Brown & Batygin 2021).
• The source population. The 2021 fit assumed the clustered objects came from an early extended scattered disc. If many came instead from the inner Oort cloud, the cluster’s width would no longer imply a low mass. The planet could be more massive and more distant, and so much fainter (Batygin & Brown 2021).
• The dynamical model. The lower-inclination Planet X of Siraj, Chyba and Tremaine has 90% of its sky probability within $\pm10^\circ$ of the ecliptic and a peak near RA $55^\circ$ (Siraj et al. 2025). The 78% does not apply to it. Each new reference population needs its own pass through the survey simulators.

Brown, Holman and Batygin weigh the null result candidly. One explanation is that Planet Nine does not exist, but that would require new explanations for several phenomena. Until those exist, they continue to regard the planet as the most likely hypothesis (Brown et al. 2024). Readers of Chapter 8 will know that others weigh the same evidence differently.

Rubin and the next decade

The survey itself

The Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) reaches about $r\approx24.3$–24.5 in a single visit over the southern sky (Brown & Batygin 2021; Holman et al. 2025). That is deep enough for much of the surviving population where Rubin looks. Brown and collaborators expect it to cover much of the remaining parameter space, except the faintest and most northern positions (Brown et al. 2024). That statement is qualitative. Nobody has published a completed Rubin exclusion of the reference population. The 2025 integrated forecast of Rubin’s Solar System yield did not include Sednoids or Planet Nine as populations (Chapter 15).

Two caveats matter. The first is the footprint. The predicted aphelion and the surviving swath are in the north, and Rubin’s survey plan does not extend as far north as the whole predicted path (Brown & Batygin 2021). An older study by Trilling, Bellm and Malhotra found geometrically useful coverage over about 61% of the sky under the cadence and ideal-detection assumptions of the time (Trilling et al. 2018). The second is motion. Rubin’s standard pipeline links detections within a night and across a few nights, which limits ordinary discovery to roughly 150–200 au. That is a limit of the linking algorithm, not of the images. A planet at 500 au needs a custom search of the kind described above, using the parallax arc over months.

A dedicated deep night

Geringer-Sameth, Golovich and Iwabuchi worked out a more aggressive option: one night of dedicated Rubin time on one field (Geringer-Sameth et al. 2025). Over 8 hours Rubin can take about 800 exposures of 30 s on its 9.6-square-degree field, each with a $5\sigma$ limit near $r=24.6$ and seeing of 0.7 arcsec. Stacking along the exact trajectory would detect a moving object at SNR 10 at $r=27.5$. Covering every proper motion slower than Neptune’s mean motion, 21.6 arcsec per day, takes about $1.4\times10^9$ trial orbits at a mismatch allowance of $m=1$. At that spacing an object is typically recovered at $e^{-1}$ of its best SNR, so the search is complete to $r=26.4$. More trials push it toward 27.5.

There is a catch in the geometry. An 8-hour continuous view from Cerro Pachón at airmass below 2 requires declination below $-8.3^\circ$, which includes the ecliptic only between ecliptic longitudes $201^\circ$ and $339^\circ$. The northern surviving swath, near the predicted aphelion around RA $45$–$60^\circ$, lies well outside that range. By my reading of that geometry, a deep night could probe the southern Galactic-plane remnant, but not the main northern one.

Stacking the archives

Catalogue searches throw away information. A planet that never rises above the single-image threshold cannot be linked, however good the linker. Stacking along trial orbits recovers it. Geringer-Sameth and collaborators built the machinery for ZTF: a metric on orbit space that sets how densely trial orbits must be placed. For small pixels and Gaussian PSFs of width $b_i$, the fractional SNR retained at an orbit error $\Delta\vartheta$ is

where $J_i$ maps orbit errors to position errors in image $i$, and the weights $c_i$ sum to one. Locally the mismatch $m=\Delta\vartheta^{\mathsf T}g\,\Delta\vartheta$ gives $\mathrm{SNR}/\mathrm{SNR}_{\max}\simeq e^{-m}$, and the number of trial orbits scales as $\sqrt{\det g}/m_{\max}^{d/2}$ in $d$ dimensions (Chapter 38).

The ZTF data comprise 849,750 exposures, about 50 million quadrant images over six years. In a blind test on the known TNO binary Mors–Somnus, the search covered a predicted $2.3\times10^9$ trials twice over, combining 780 image intersections. The true orbit gave SNR 60.3 and the best sampled orbit 46.1. For Planet Nine they computed, planet by planet, the limiting magnitude for a stacked ZTF search. Of the 22% of the reference population still allowed, about 18 percentage points would be detectable at SNR 10, about 80% of what remains. About 1% cross at least ten ZTF images but would be too faint, and 2.7% cross fewer than ten. This is a sensitivity forecast. The search has not been run. An exhaustive six-year northern search for all bound bodies beyond 100 au would need about $10^{19}$ trial orbits, but a search restricted to the Planet Nine prior is a much smaller problem.

The companion computing paper describes the implementation on LLNL’s Lassen: nodes with 44 Power9 cores, four 16-GB V100 GPUs, 256 GB of memory and a 1.2-TB SSD each. GPUs compute orbit–image intersections, and SSDs serve local image patches (Golovich et al. 2025). In an instrumented test, intersection and pixel-retrieval times were 44.33 and 9.31 s on one node, and 45.71 and 37.37 s on 128 nodes, with communication excluded. These are not the wall time of the Mors–Somnus recovery or of a full search.

Napier and collaborators’ 2026 heliostack takes a different route (Napier et al. 2026). For a Keplerian orbit, the radial evolution does not depend on the orbit’s orientation. So one can assert a radial history, warp whole images onto a common barycentric canvas, and accumulate trajectories for many sky positions at once. A demonstration on archival Hubble images spanning about 15 days recovered the known faint objects and found two new ones. The authors name Planet Nine as a future application. No Planet Nine result has been reported (Chapter 20, Chapter 21).

Limitations and open problems

The exclusion inherits a dynamical model. Every percentage in this chapter is conditional on one orbit family, one radius law and one albedo range. A null result along a restricted path is powerful against that family and silent about the rest.

“Nearly perfect linking” is conditional. The 99%+ linking efficiencies apply after a planet already has enough acceptable detections. Detector gaps, catalogue cuts, blends, the number of distinct nights and the orbital phase all act earlier. DES shows the difference starkly: 11,709 planets crossed the footprint, but a footprint crossing is far easier than earning seven nights over six months.

Crowding is an extraction problem. Dense star fields raise both blending losses and non-Gaussian artifacts. ZTF’s repeated visits made the northern plane usable at brighter magnitudes, while PS1’s sparse visits did not. The plane is not uniformly unsearchable, and a deeper catalogue does not automatically fix it. Static-template subtraction may partly remove a very slow source near its stationary point, which needs time-dependent injection tests.

Slow motion makes adversarial cases. Rejecting stationary sources, defining “one-night objects”, demanding a minimum motion, and fixing radial velocity can all reject real orbits. Short arcs can mimic quite different distances, as Eris showed. Injections should deliberately include orbits near quadrature, at field edges, and in the tails of radial velocity.

Global significance is expensive. A count of catalogue candidates is not a false-discovery rate. A Gaussian matched-filter SNR is not a global significance after a search over $10^9$ orbits. Image stacks full of artifacts need empirical null trials and genuinely independent confirmation, like the DES sub-threshold test. No transferable false-alarm probability yet exists for an all-sky image-level search.

Where the room is

The catalogue searches already link nearly every planet that leaves enough detections. Their costs lie in false clusters and in thresholds chosen to keep those false clusters manageable. Their sensitivity limit comes from the per-image detection threshold. Both are algorithmic, not physical. The following proposals are assessments, motivated by the published bottlenecks. None has been demonstrated as an order-of-magnitude gain at equal sensitivity. The broader picture is in Chapter 42.

Reducing association combinatorics comes before optimising orbit propagation. Conservative bounds on distance, rate, time and reachable position cut candidate pairs. Grouping nearby distance hypotheses lets transforms and catalogue tiles be reused. Radix-sorted velocity bins can replace repeated pair traversal where occupancy allows. The DES parallelogram test shows the pattern: a better representation of the allowed region gave about a factor of 100, more than low-level tuning typically does. The right figure of merit is the number of fit proposals and end-to-end completeness, not transforms per second.

Template reduction has a price that should be stated. In a six-dimensional orbit space, trial density scales as $m_{\max}^{-3}$. Demanding at most a 10% local SNR loss, $m=-\ln0.9$, instead of the convenient $m=1$ multiplies the number of trials by about 855. Conversely, blurring images or shortening the coherent baseline cuts trials sharply but loses sensitivity. Such trades can be worth making. They are not equal-sensitivity speedups (Chapter 38).

Telescope time is an optimisation too. Once the bright sky has been searched, more visits at the same depth have diminishing returns unless they repair cadence or confusion losses. A northern program should rank fields by the surviving weighted population divided by observing and analysis cost, with colour, seeing, extinction and the minimum parallax baseline included, and with the probability map propagated to the observing epoch.

The physical limits are missing photons, unobserved sky, and blending or saturation that no reprocessing can undo. No GPU finds a planet that was never imaged, or infers its albedo from a null result. The engineering limits are subthreshold information thrown away by cataloguing, transformations repeated needlessly, conservative cuts, approximate motion families and expensive artifact rejection. Most of the surviving 22% is reachable in principle. It needs either stacking of archives that already exist or deep, well-planned northern observations, and in both cases a selection function measured with planets injected before extraction.

References

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