A census of exoplanet discovery

On 16 October 2026 the NASA Exoplanet Archive listed 6,451 planets outside the Solar System. Of these, 4,785 were credited to transits, 1,204 to radial velocities, 292 to microlensing and 98 to direct imaging, with a few dozen more found by timing, astrometry and stranger signatures. Read naively, the numbers say that transits are the best way to find planets and that astrometry hardly works. Neither statement is quite right. The numbers say how many planets each method was first to report and how many of those survived vetting, follow-up, peer review and the archive’s inclusion rules. They say almost nothing by themselves about how common planets are, because they lack the denominator: how many stars were searched, and which planets around those stars could have been found.

This chapter is about both halves. The first is a history of discovery, told as a history of validation. It shows how a coherent-looking astrometric orbit, a clean pulsar-timing residual and a Doppler wobble each came to be believed or disbelieved. The second half is the machinery that turns a catalogue into a population: completeness measured by injection and recovery, reliability measured against false alarms, and the Poisson likelihood that combines them. The detection methods themselves belong to Chapters 29 to 34. Here the subject is what their outputs mean when added up, and why calibrating a search costs far more compute than running it.

Three numbers that are not the same

Three quantities are easily confused, and the rest of the chapter depends on keeping them apart.

Catalogue yield is the number of accepted detections, perhaps sorted by method and year. Occurrence is the expected number of planets per star in a stated region of parameter space. Host fraction is the probability that a star has at least one planet in that region. The last two coincide only under restrictive assumptions about multiplicity, and an occurrence above one is physically ordinary: a star can have several small planets.

Let $\theta$ denote planet properties, $z_j$ the properties of star $j$, and $\lambda(\theta \mid z_j, \phi)$ the intensity of planets per star, with population parameters $\phi$. The measure must be stated. A common choice for transits is

$\lambda(P, R \mid z, \phi) = \frac{d^2 N}{d\ln P\, d\ln R},$

the number of planets per star per natural-log interval of period and radius. The occurrence in a region $B$ is

$f_B(z) = \int_B \lambda(\theta \mid z, \phi)\,d\theta .$

If planets in $B$ are independent and Poisson distributed, the host fraction is $1 - e^{-f_B}$, not $f_B$. An occurrence of 1 means a host fraction of 63%, and an occurrence of 0.37 means about 31%. Real systems are correlated, and a full description is a distribution over whole architectures. Two “Earth occurrence” numbers also differ in kind. The local density at Earth’s period and radius,

$\Gamma_\oplus = \left.\frac{d^2 N}{d\ln P\, d\ln R}\right|_{P_\oplus, R_\oplus},$

is a density, whereas $\eta_\oplus$ is an integral over a defined habitable zone and size range. A density per decade is $\ln 10 \approx 2.3$ times a density per natural-log interval (Foreman-Mackey et al. 2014; Mulders et al. 2018). A quoted Earth occurrence is incomplete without its stellar sample, its radius or mass interval, its period or irradiation interval, and its completeness and reliability models.

The archive’s own rules add a fourth layer. It accepts objects with mass or minimum mass up to 30 Jupiter masses, excludes free-floating objects, and requires adequate validation or follow-up and a refereed publication (NASA Exoplanet Archive 2024). The census therefore does not implement any formation-based definition of a planet, nor the deuterium-burning limit sometimes used, and studies of free-floating planets need a different catalogue and a different denominator (Chapter 32).

A history of discovery, and of false discovery

Barnard’s star

The decisive evidence was a control field. Low residuals about a fitted orbit do not show that the noise model is right, and a calibration change shared by every star on the plate can imitate slow astrophysical motion. Planets reported around Barnard’s star in recent years concern different signals and do not rehabilitate the old claim.

Pulsars: a false planet and the first real ones

In July 1991 Matthew Bailes, Andrew Lyne and S. L. Shemar reported a companion of about 10 Earth masses in a nearly circular six-month orbit around PSR 1829−10, from timing with the 76-m Lovell telescope at Jodrell Bank (Bailes et al. 1991). In January 1992 Lyne and Bailes withdrew it. Their starting position for the pulsar was 7 arcmin from the true one. The software corrected arrival times for small position errors using a circular approximation to Earth’s orbit. At that unusually large offset, the eccentricity of Earth’s orbit left an 8-ms residual with a six-month period. Redoing the barycentric correction at the better position removed the planet. The story is often told as “they forgot Earth’s eccentricity”. The retraction tells a more useful one: a normally adequate approximation was used outside the regime where it was valid. The absence of similar residuals in their 300 other pulsars could not catch an error specific to one source (Lyne & Bailes 1992).

Aleksander Wolszczan and Dale Frail’s paper had appeared on 9 January 1992, a week before the retraction. Timing the 6.2-ms pulsar PSR 1257+12 with the 305-m Arecibo telescope, they found two planets with periods of 66.6 and 98.2 days and minimum masses of 3.4 and 2.8 Earth masses (Wolszczan & Frail 1992). The accepted history of exoplanets therefore begins with planets around a dead star, and the census still lists only eight planets found by pulsar timing. Chapter 31 covers the method.

51 Pegasi

Michel Mayor and Didier Queloz began monitoring 142 G and K dwarfs with the ELODIE spectrograph at Haute-Provence in April 1994. ELODIE reached about 13 m/s, by cross-correlating each spectrum against a template of about 5,000 absorption lines. Observations of 51 Pegasi began in September 1994. A 4.23-day orbit was computed in January 1995 and checked in intensive runs in July and September. The companion had a minimum mass of $0.47 \pm 0.02$ Jupiter masses at about 0.05 AU (Mayor & Queloz 1995). The paper did not rest on a periodogram peak. It argued from low chromospheric activity, a rotation period inconsistent with the velocity period, photometric checks, and the absence of any phase variation in the line bisectors, so that the star’s own surface could not be producing the signal.

Why was the first planet around a Sun-like star a giant in a four-day orbit, when the instrument had been built partly with Jupiter analogues in mind? The Doppler semi-amplitude is

which for a circular orbit around a solar-mass star is 28.4 m/s for a Jupiter mass at one year, scaling as $M_p P^{-1/3}$ (Cumming et al. 2008). For a solar-mass host, a 0.47-Jupiter-mass planet at 4.23 days gives $K \approx 28.4 \times 0.47 \times (365.25/4.23)^{1/3} \approx 59$ m/s, more than four times ELODIE’s precision, and repeats its full cycle every four days. Jupiter itself, at 11.9 years, gives about 12.4 m/s and needs a decade to show one orbit. The first objects found were the ones the instruments responded to fastest, not a fair sample of planetary systems. That is the census’s original selection effect.

Independent observables

HD 209458 b joined two methods. David Charbonneau, Timothy Brown, David Latham and Michel Mayor observed two complete transits in 1999 with the small STARE camera, at times predicted by the Doppler orbit, and measured a radius of $1.27 \pm 0.02$ Jupiter radii for the adopted stellar properties. Gregory Henry and colleagues independently observed a partial transit (Charbonneau et al. 2000). The planet is still credited to radial velocities: in the census, each planet has one discovery method, and a later detection by another method does not create another planet. Small discovery counts for a method therefore say nothing about its role in measuring masses or confirming candidates.

In 2004 the first secure microlensing planet appeared, OGLE 2003-BLG-235/MOA 2003-BLG-53, with mass ratio 0.0039 (Bond et al. 2004; Chapter 32). In the same year Gaël Chauvin and colleagues imaged, with VLT/NACO, a planetary-mass candidate about 780 mas from the young brown dwarf 2M1207, with a model-dependent mass of $5 \pm 2$ Jupiter masses (Chauvin et al. 2004). It was rightly called a candidate, and it was a companion to a brown dwarf, not an image of a planet beside a Sun-like star (Chapter 33).

Kepler and validation at scale

Kepler changed both the scale and the meaning of “confirmed”. Most Kepler candidates orbit stars too faint for precise radial velocities, so their masses cannot be measured one by one. Timothy Morton and colleagues instead computed, for 7,056 Kepler objects of interest, the probability that each was an astrophysical false positive, using the vespa package. They found 1,935 with false-positive probability below 1%, including 1,284 newly validated planets (Morton et al. 2016). This was statistical validation without a mass for every planet. Morton and colleagues also describe the earlier approach of validating planets in multi-planet systems, which relies on the fact that false positives rarely come in multiples. Validation campaigns of this kind explain the steps in the curves below: the archive assigns 872 discoveries to 2014 and 1,504 to 2016, of which 1,432 are transits. A burst of validation produces a burst of “discoveries” with no burst in data.

The final Kepler catalogue, Data Release 25, made the selection process itself measurable. Susan Thompson and colleagues ran a fully automated vetting code, the Robovetter, on 8,054 objects of interest and classified 4,034 as candidates. They ran the same code on simulated data (injected transits, and real light curves inverted or scrambled in time so that no real transit could survive) and so measured both its completeness and its reliability (Thompson et al. 2018). The intellectual change was from removing suspicious objects to measuring what each removal does.

The census today

The counts are aggregates of a frozen query to the archive’s table-access service, retrieved at 03:57 UTC on 17 October 2026, which was still 16 October in California. Two independent extractions, one from the composite-parameters table and one from the default rows of the planetary-systems table, agree in every method and year, and agree with the archive’s own statistics page (NASA Exoplanet Archive 2026a; 2026c).

Three features of the annual curve stand out. Radial-velocity discoveries rose through the late 1990s and have run between 21 and 115 a year since 2005. Transit discoveries are dominated by the Kepler validation years, and have run between about 90 and 460 a year since. Microlensing discoveries, a handful a year before 2016, reached 51 in 2022 as the KMTNet survey matured and its archive was searched systematically (Chapter 32). The curves are today’s catalogue sorted by discovery year. They are not snapshots of what astronomers believed in each year, because retractions, delayed ingestion and reclassification all change a retrospective count. Discovery year is also not publication date: some discoveries assigned to 2025 have discovery papers published in 2026.

Reading the catalogue

The archive has two main tables, and they answer different questions. The Planetary Systems table, ps, has one row per planet per published solution, so counting its rows counts papers, not planets. Its default_flag = 1 subset gives one chosen solution per planet. The Planetary Systems Composite Parameters table, pscomppars, has one row per planet with columns filled from several papers. It is more complete but explicitly not necessarily self-consistent, which suits descriptive plots better than physical inference (NASA Exoplanet Archive 2026b). The census query is short:

SELECT disc_year, discoverymethod, COUNT(*) AS n
FROM pscomppars
GROUP BY disc_year, discoverymethod
ORDER BY disc_year, discoverymethod

The work in a reproducible census is not the query. It is freezing the response, checking unique names, summing the aggregates against the row-level download, and filling empty method-year cells with explicit zeros.

Masses need more care. Of the planets in the snapshot, 3,035 have masses estimated from a mass–radius relation rather than measured, 2,477 have provenance “Mass”, 924 “Msini” and 15 “Msin(i)/sin(i)”. “Mass” is itself heterogeneous: for imaged planets it is usually an evolutionary-model estimate from luminosity and age, not a dynamical measurement. A plot of mass against period that includes the imputed masses shows the mass–radius relation, not the planets.

The figure removes the imputed masses and keeps 3,035 planets that have both a measured mass or minimum mass and a period. Its shape is the classic discovery-space diagram, and every boundary in it is a selection effect before it is anything else. Transits pile up at short periods. Radial velocities reach longer periods and lower masses around bright, quiet stars. Imaging finds young, massive planets far out. And microlensing, with 292 planets, is nearly invisible, because 280 of them have no catalogue period at all. Microlensing measures a mass ratio and a projected separation, not an orbit, and an honest plot does not invent periods for it.

Why each method sees what it sees

Each method’s catalogue is a projection of the planet population through its own response. A short summary of each response explains most of the structure in the figures above.

Radial velocity. The amplitude scales as $M_p \sin i\, P^{-1/3}$, and short periods accumulate many cycles quickly. The historical Keck sample had measurement errors of 3–5 m/s and stellar jitter of 1–5 m/s for quiet stars (Cumming et al. 2008). Noise models matter in both directions: a noise model flexible enough to absorb a planet lowers completeness, and one that mistakes stellar rotation for a planet lowers reliability (Chapter 29).

Transits. The flux drop is $\delta \simeq (R_p/R_\star)^2$. The probability that an orbit is aligned to transit is

and the multiple-event statistic, the signal-to-noise of all transits folded together, is

where $\Delta$ is the template-averaged depth, $\sigma_{\rm CDPP}(\tau)$ the photometric noise on the transit duration $\tau$, and $N_{\rm tr}$ the number of transits observed (Burke et al. 2015). For a circular orbit, $p_{\rm tr} \propto P^{-2/3}$ and, with uniform coverage, $N_{\rm tr} \propto T_{\rm obs}/P$. Around the Sun, a planet at 0.05 AU transits with probability about 9%, and one at 1 AU with probability about 0.5%. In four years the first transits about 345 times and the second four times. A raw period histogram multiplies falling geometry, falling signal accumulation and window losses, so it is steep even if the true population is flat (Chapter 30).

Microlensing. The natural coordinates are the mass ratio $q$ and the projected separation $s$ in Einstein radii. Sensitivity peaks near $s \approx 1$, a few AU for typical lenses. Converting to mass and semimajor axis needs the lens distance and host mass and a model of orbital projection, which is more than relabelling the axes (Cassan et al. 2012; Suzuki et al. 2016).

Imaging. Selection starts in angular separation and contrast, not in mass and semimajor axis. The Gemini Planet Imager reaches contrasts of about $10^{-5}$ to $10^{-6}$, and converting contrast to mass requires evolutionary models and an age, whose uncertainties the occurrence inherits (Nielsen et al. 2019; Chapter 33).

Astrometry and timing. Astrometry measures the angular reflex motion $\alpha_\star \simeq (M_p/M_\star)\,a/d$, projected onto the scanning law of the instrument. Timing measures a light-travel-time amplitude $a_\star \sin i / c$. Their selection functions depend on the baseline, orientation, nuisance model and sampling, not on amplitude alone. They also carry the lessons of Barnard’s star and PSR 1829−10 (Chapter 31; Chapter 34).

The selection function

Define the complete inclusion probability for a planet with properties $\theta$ around star $j$:

where $\mathcal{A}$ stands for everything done to the data: observing, searching, vetting and any validation rules. It factorises into conditional probabilities,

These are conditional probabilities, not a claim that the stages are independent. A homogeneous analysis of all candidates can drop the follow-up factor by modelling contamination explicitly. An analysis restricted to confirmed planets cannot drop it silently (Thompson et al. 2018). A 2026 study of TESS candidates shows how large that factor can be. Michael Collier and colleagues assessed 443 candidates, 264 with high-resolution imaging. Of 68 planets they validated using adopted contrast curves, 72% would have failed their validation criteria without that imaging, and in all they validated 64 new planets (Collier et al. 2026). That is a controlled experiment within one selected sample, not a law for all of TESS, but it makes the point: whether a transiting planet reaches the census depends on whether someone could follow it up.

Completeness is $\Pr(D \mid \text{planet}, \theta)$, the probability of detection given a planet. Reliability is $\Pr(\text{planet} \mid D, y)$, the probability that a detection with data $y$ is a planet. Confusing the two is a serious error, because reliability depends on how common contaminants are relative to planets in that part of parameter space, and completeness does not.

Methods

Injection and recovery

Completeness is measured by experiment. Freeze the target list, the inputs, the pipeline version, the search limits, the vetting and the definition of recovery. Draw synthetic planets from a known proposal distribution $g(\theta, j)$, with appropriate epochs and orientations, and inject them before the operations whose effect is to be measured. A transit injected into an already detrended light curve measures neither the losses of pixel-level extraction nor the way the detrending would have reacted to the signal.

for each injection batch:
    choose target and planet from the recorded proposal g
    generate signal with geometry, epoch, dilution, exposure integration
    inject into pixels, or into flux at an explicitly documented stage
    rerun the frozen extraction, detrending, search and vetting chain
    match recovered period and epoch to truth, allowing declared aliases
    store injected parameters, outputs, recovery flag, stage of failure
fit recovery probability as a function of target and signal properties
validate on held-out injections; marginalise calibration uncertainty

Two distinctions matter. “Triggered something” is not “recovered this planet”: a detection at a harmonic of the period, a lost individual transit or an assignment to a neighbouring star can all trigger the search without yielding a usable planet. And if the real catalogue excludes ambiguous solutions, the injections must face the same exclusion.

Erik Petigura, Andrew Howard and Geoffrey Marcy injected 40,000 synthetic transits into real Kepler photometry of 42,557 selected stars, searched with their own pipeline, TERRA, at a threshold of SNR > 12, and reported 603 candidates after vetting. Correcting for completeness, they found that $11 \pm 4\%$ of Sun-like stars have an Earth-size planet (1–2 Earth radii) receiving one to four times Earth’s insolation (Petigura et al. 2013). Jessie Christiansen and colleagues injected 10,341 transits at the pixel level into a year of Kepler data. For FGK stars at an expected MES of 7.1, the nominal threshold, the measured recovery was only 25.8%, against the 50% an ideal Gaussian detector would achieve at its threshold (Christiansen et al. 2015). Christopher Burke and colleagues adopted a smooth model of recovery,

a regularised incomplete gamma function with $a = 4.65$ and $b = 0.98$ in their analysis (Burke et al. 2015). The offset of 4.1 is essential, and neither historical curve should be transplanted into a different catalogue.