--- title: "Why do large planets fill a discovery catalog?" description: "Planet catalogs favour signals a search can find. Follow transit geometry, observing gaps and noise to separate discoveries from the true population." canonical_url: "https://sandboxphysics.com/stories/planet-populations/why-big-planets-fill-the-catalog/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/planet-populations/why-big-planets-fill-the-catalog/" last_modified: "2026-11-03" --- [From planet catalogs to populations](https://sandboxphysics.com/stories/planet-populations/) AC24 · L1 # Why do large planets fill a discovery catalog? Sandbox Physics · 2026-11-03 A small planet can circle a star for years without making it into a discovery catalog. Its orbit may never take it across the star, or its tiny shadow may be lost in noise. A catalog full of large planets therefore tells us about both the planets and the search that found them. ## Before you begin No astronomy background is needed. Think of a planet as a dark disk crossing a bright circular lamp. ## A small shadow is easier to lose Watch a distant star through a telescope. You cannot usually separate the planet from the star in the image. You can measure their combined light. When a planet passes across the star, a small amount of that light disappears for a few hours. Astronomers call this passage a transit. Doubling a planet’s radius makes its disk cover four times as much area. Around an otherwise identical star, a large planet produces a much deeper dip. A smaller planet can make a real dip that is less obvious than the fluctuations in a detector or in the star itself. Finding the deeper dips first is an expected feature of the measurement. In the simplest picture, both disks are circular and the star has uniform brightness. The lost fraction of light is the planet’s area divided by the star’s area. Here the two radius symbols name the planet and the star. Actual stellar surfaces become dimmer near the edge, so careful transit analyses also calculate where the planet crosses. $$ \delta=(R_p/R_\star)^2 $$ The fractional loss of light is the squared radius ratio when the planet lies wholly inside a uniformly bright stellar disk. Reading: Christiansen 2017, Pixel-Level Transit Injection Tests of Pipeline Detection Efficiency for DR25 · NASA Exoplanet Archive DR25 completeness/reliability and simulated products ## Most orbits never put a shadow in our direction A planet can be large and still produce no transit. Imagine turning its orbital plane slowly away from an edge-on view. Its path across the sky climbs above the star. The planet is still there; we simply stop seeing it block starlight. Planets closer to their stars have a wider range of orbital directions that permit transits. A distant orbit has to line up more precisely. This geometric preference helps short-period planets enter a transit catalog. A short period also gives a telescope more chances to see the same dip repeat. A star with no detected planet must stay in the searched sample. Removing it would erase the very cases where geometry or weak signals hid a planet. The number of stars searched is the denominator needed to estimate how common planets are. Reading: About 30 percent of Sun-like Stars Have Kepler-like Planetary Systems ## The telescope needs to be watching at the right time Suppose a planet crosses its star once every twenty days. A thirty-day observing season might catch only one passage. Repetition helps distinguish a transit from a one-off fluctuation, but the season may end before the next useful event. A long season can also contain interruptions. An event during an interruption supplies no measurement. Extending the calendar span and reducing the interruptions can recover different planets. Two observing plans with the same total number of clear days need not catch the same repeated events. These effects form a selection probability: the chance that a particular planet would reach the final catalog under a specified search. It includes orbital alignment, available observations and the decision made from the noisy data. Each factor concerns the same possible discovery. If a measured recovery fraction already includes the observing interruptions, adding the same interruption penalty again would count the loss twice. Reading: Burke and Catanzarite 2017, Per-Target Detection Contours for DR25 · Measuring Transit Signal Recovery in the Kepler Pipeline IV ## Put test planets into the search Kepler researchers tested recovery by adding artificial transit signals to observed data and processing them through the search. They knew which planets they had inserted. A failed recovery was useful information: it showed that a planet with those properties could be missed. Those tests contain artificial planets embedded in real instrumental and stellar data. They are different from the discovered planets in the sky. Comparing the inserted and recovered signals helps calibrate the search before interpreting the discovery catalog. The final question is planets per searched star. A telescope might find ten planets in a region where its effective search covered only twenty stars. The implied population is much larger than ten planets divided by every star in the sky. It is also different from the fraction of stars with any planet, because one star can host several. A dip in the discovered radius distribution becomes especially interesting when it survives a careful description of the search and the radius errors. That is the route from a collection of detections to a physical question about how planets form and lose atmospheres. The first step is to keep the full searched-star sample and account for planets that can remain hidden. Reading: Christiansen 2017, Pixel-Level Transit Injection Tests of Pipeline Detection Efficiency for DR25 · A Probabilistic Approach to Kepler Completeness and Reliability for Exoplanet Occurrence Rates ## Exercises and explanations 1. A quieter detector reveals many new small-radius planets. Must the large planets have become less common? Read the explanation The sky population can remain unchanged. Lower noise increases the recovery probability of shallow transits, so small planets occupy more of the catalog even when the number of large planets stays fixed. ## Try the prediction ### [Change the detector and watch the missing planets](https://sandboxphysics.com/labs/planet-survey-selection/) 1. Predict what will happen to small-radius detections when noise decreases. 2. Choose A quieter detector. Compare the orange generating population with the blue catalog. 3. Extend the observing season next. Explain why this second change helps some longer-period planets. [Next: Keep the stars with no detected planet](https://sandboxphysics.com/stories/planet-populations/keep-stars-without-detections/) ## Sources and calculation scope 1. [NASA Exoplanet Archive DR25 completeness/reliability and simulated products](https://exoplanetarchive.ipac.caltech.edu/docs/Kepler_completeness_reliability.html) Official DR25 product roles and the INJ1 source tables. 2. [Christiansen 2017, Pixel-Level Transit Injection Tests of Pipeline Detection Efficiency for DR25](https://exoplanetarchive.ipac.caltech.edu/docs/KSCI-19110-001.pdf) KSCI-19110-001, sections 2–4 and pp. 9–12: ephemeris matching, aperture-corrected depth, expected MES and original table columns. 3. [Burke and Catanzarite 2017, Per-Target Detection Contours for DR25](https://exoplanetarchive.ipac.caltech.edu/docs/KSCI-19111-002.pdf) KSCI-19111-002, Equations 1–2, sections 3.5–3.6 and 4–7: OSD, windows and target-dependent transfer. 4. [Measuring Transit Signal Recovery in the Kepler Pipeline IV](https://arxiv.org/html/2010.04796v1) Version 2010.04796v1, sections II–IV: pixel-injection design and pooled recovery response. 5. [A Probabilistic Approach to Kepler Completeness and Reliability for Exoplanet Occurrence Rates](https://arxiv.org/html/1906.03575v4) Version 1906.03575v4, sections II–VI, Equations 10–12 and Appendix B: externally weighted integer catalogs and occurrence likelihoods. 6. [About 30 percent of Sun-like Stars Have Kepler-like Planetary Systems](https://arxiv.org/html/1802.09526v2) Version 1802.09526v2, section III.1, Equations 1–4, sections III.4–III.5 and Figures 7–9: planets per star, host fraction and system architecture.