Complete reference for exoplanet detection methods, classification, atmospheric study,
habitability assessment, key missions, notable systems, and biosignatures.

## Key Points

- **Principle**: Star and planet orbit common center of mass. Star's reflex motion causes
- **Observable**: Radial velocity semi-amplitude K. Gives minimum mass (m sin i).
- **Key equation**: K = (2πG/P)^(1/3) × (m_p sin i) / (m_star + m_p)^(2/3) × 1/√(1−e²)
- **Sensitivity**: Modern spectrographs achieve ~0.3–1 m/s precision (HARPS, ESPRESSO).
- **Biases**: Favors massive planets on short-period orbits. Cannot determine true mass
- **Key instruments**: HARPS (ESO 3.6 m, Chile), ESPRESSO (VLT), HIRES (Keck),
- **Challenges**: Stellar activity (spots, convection, pulsation) mimics or masks signals.
- **First confirmed exoplanet around Sun-like star**: 51 Pegasi b (Mayor & Queloz, 1995),
- **Principle**: Planet passes in front of star, blocking a fraction of starlight.
- **Transit depth**: δ = (R_p/R_star)² — gives planet-to-star radius ratio.
- **Transit duration**: T ≈ (R_star × P) / (π × a) for central transit. Typically hours.
- **Geometric probability**: p = R_star/a. For Earth analog around Sun: ~0.47%.

Exoplanet Science — Detection, Characterization, and Habitability

Complete reference for exoplanet detection methods, classification, atmospheric study, habitability assessment, key missions, notable systems, and biosignatures.

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Detection Methods

Radial Velocity (Doppler Spectroscopy)

• Principle: Star and planet orbit common center of mass. Star's reflex motion causes periodic Doppler shift in spectral lines.
• Observable: Radial velocity semi-amplitude K. Gives minimum mass (m sin i).
• Key equation: K = (2πG/P)^(1/3) × (m_p sin i) / (m_star + m_p)^(2/3) × 1/√(1−e²)
• Sensitivity: Modern spectrographs achieve ~0.3–1 m/s precision (HARPS, ESPRESSO). Jupiter causes ~12.5 m/s on Sun. Earth causes ~0.09 m/s — below current detection limits.
• Biases: Favors massive planets on short-period orbits. Cannot determine true mass without inclination (from transit or astrometry).
• Key instruments: HARPS (ESO 3.6 m, Chile), ESPRESSO (VLT), HIRES (Keck), NEID (WIYN), HPF (HET, for M dwarfs in near-IR).
• Challenges: Stellar activity (spots, convection, pulsation) mimics or masks signals. Activity indicators (bisector span, log R'HK, Hα) help distinguish.
• First confirmed exoplanet around Sun-like star: 51 Pegasi b (Mayor & Queloz, 1995), hot Jupiter, K = 59 m/s, P = 4.23 days.

Transit Photometry

• Principle: Planet passes in front of star, blocking a fraction of starlight.
• Transit depth: δ = (R_p/R_star)² — gives planet-to-star radius ratio. Jupiter-size: δ ≈ 1%. Earth-size around Sun-like star: δ ≈ 84 ppm.
• Transit duration: T ≈ (R_star × P) / (π × a) for central transit. Typically hours.
• Geometric probability: p = R_star/a. For Earth analog around Sun: ~0.47%. Need to observe many stars to find transiting systems.
• Limb darkening: Star is dimmer at edges. Affects transit shape. Must be modeled.
• Key missions: Kepler, K2, TESS, PLATO (planned), CHEOPS.
• Ground-based: WASP, HATNet, MEarth, TRAPPIST, NGTS.
• Combined with RV: Gives true mass (inclination known to be ~90°) and radius → bulk density → constraints on composition.

Direct Imaging

• Principle: Spatially resolve planet's light from star's light.
• Challenge: Extreme contrast ratio. Jupiter is ~10⁹× fainter than Sun in visible. Earth is ~10¹⁰× fainter.
• Techniques: Coronagraphy (block starlight), angular differential imaging (ADI), spectral differential imaging (SDI), vortex coronagraphs.
• Current capability: Young, massive, wide-orbit planets (self-luminous, still contracting). Separations >0.1–0.5 arcsec. Contrasts ~10⁵–10⁶.
• Instruments: GPI (Gemini), SPHERE (VLT), SCExAO (Subaru).
• Notable detections: HR 8799 b/c/d/e (4 planets imaged), Beta Pictoris b/c, 51 Eridani b, AF Leporis b.
• Future: Roman Coronagraph Technology Demonstration. Habitable Worlds Observatory (HWO) concept: 6+ m space telescope with 10¹⁰ contrast coronagraph for imaging Earth analogs.

Gravitational Microlensing

• Principle: Foreground star's gravity bends background star's light (Einstein ring). If foreground star has planet, additional perturbation in lightcurve.
• Advantages: Sensitive to low-mass planets at ~1–10 AU. Can detect free-floating planets. Works at kiloparsec distances.
• Disadvantages: One-time events, not repeatable. Limited characterization. Planet parameters often have degeneracies.
• Key surveys: OGLE, MOA, KMTNet. Roman Space Telescope microlensing survey planned.
• Statistics: Microlensing suggests planets are common beyond the snow line, including unbound planets (possibly ~1 per star).

Astrometry

• Principle: Measure star's positional wobble on the sky due to orbiting planet.
• Complementary to RV: Gives 2D on-sky motion (vs 1D radial). Determines true mass and full 3D orbit when combined.
• Sensitivity: Scales with (m_p/m_star) × (a/d). Favors massive planets at large separations around nearby stars.
• Gaia: Expected to detect ~10,000–70,000 giant planets via astrometry by end of mission. Requires multi-epoch observations over years. Full astrometric planet catalog expected with DR4/DR5.
• Historical note: Pre-Gaia ground-based astrometric planet claims were all spurious (van de Kamp's "planets" around Barnard's Star). Precision was insufficient.

Transit Timing Variations (TTVs)

• Principle: Additional planet gravitationally perturbs transiting planet, causing deviations from strict periodicity.
• Sensitivity: Strongest near mean-motion resonances. Can detect non-transiting planets. Sensitive to low-mass planets in resonant configurations.
• Notable: TRAPPIST-1 system masses refined primarily through TTVs. Kepler-9 first confirmed TTV detection.

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Key Missions

Kepler (2009–2013) / K2 (2014–2018)

• 0.95 m aperture. Stared at single field in Cygnus (Kepler) / ecliptic fields (K2).
• Monitored ~150,000 stars continuously for 4 years.
• Results: ~2,700 confirmed planets. Revealed that small planets (< 4 R⊕) are far more common than gas giants. Discovered that planets with P < 1 year are ubiquitous. Found the radius gap at ~1.5–2 R⊕ (Fulton gap).

TESS (2018–)

• 4 wide-field cameras, 24° × 96° field of view. Nearly all-sky survey.
• 27-day observing sectors (longer at ecliptic poles).
• Focuses on bright, nearby stars (V < 12) — amenable to ground-based follow-up.
• Results: >7,000 candidates, >500 confirmed as of 2026. Many nearby transiting planets for atmospheric characterization by JWST.

JWST (2021–)

• 6.5 m primary. Near- and mid-IR (0.6–28.5 μm). L2 orbit.
• Exoplanet capabilities: Transit and eclipse spectroscopy. NIRSpec, NIRCam grism, MIRI LRS and MRS for atmospheric spectra.
• Key results: First CO₂ detection in an exoplanet atmosphere (WASP-39b). Detailed atmospheric compositions of hot Jupiters and sub-Neptunes. Thermal emission maps. Constraints on terrestrial planet atmospheres (TRAPPIST-1 system under investigation).
• Photochemical products detected (SO₂ in WASP-39b's atmosphere).

Future Missions

• PLATO (ESA, launch ~2026): 26 cameras, bright star transit survey. Focus on Earth-size planets in habitable zones of Sun-like stars. Stellar seismology for precise stellar parameters.
• Roman Space Telescope (NASA, launch ~2027): 2.4 m, wide-field near-IR. Microlensing survey for cold exoplanets. Coronagraph technology demonstration.
• ARIEL (ESA, launch ~2029): Dedicated exoplanet atmospheric characterization. Survey of ~1,000 planets in transit spectroscopy.
• Habitable Worlds Observatory (HWO): NASA flagship concept from Astro2020 Decadal. 6+ m UV/optical/IR space telescope. Starshade or coronagraph for direct imaging of ~25 Earth analogs.

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Planet Classification

Hot Jupiters

• Gas giants (> 0.3 M_J) with P < 10 days, a < 0.1 AU.
• Tidally locked. Dayside temperatures 1,000–3,000+ K.
• Inflated radii (many larger than predicted by models — radius anomaly).
• Atmospheres: Na, K, H₂O, CO, TiO/VO in hottest cases. Thermal inversions in ultra-hot Jupiters.
• Formation: likely formed beyond snow line and migrated inward (disk migration or high-eccentricity migration + tidal circularization).
• Occurrence rate: ~1% of Sun-like stars host hot Jupiters.

Super-Earths and Sub-Neptunes

• Super-Earths: 1–1.75 R⊕, likely rocky (possibly with thin atmospheres).
• Sub-Neptunes (mini-Neptunes): 1.75–3.5 R⊕, low density suggests H/He envelope or water-rich composition.
• Radius gap (Fulton gap): deficit of planets at ~1.5–2 R⊕. Explained by atmospheric mass loss: photoevaporation (XUV-driven) or core-powered mass loss strips envelopes from planets below a threshold core mass.
• Most common planet type detected by Kepler. No solar system analog.

Earth Analogs

• Rocky planet, ~0.5–1.5 R⊕, in habitable zone of Sun-like star.
• No definitive detection yet. Kepler provided statistical estimates.
• Detection requires extreme photometric precision (84 ppm transit) or radial velocity precision (~0.09 m/s) or direct imaging (10¹⁰ contrast).

Other Categories

• Warm/cold Jupiters: Gas giants at >0.1 AU. Analogous to our Jupiter/Saturn.
• Lava worlds: Ultra-short period rocky planets. Dayside surface may be molten. Example: 55 Cancri e (P = 0.74 d, dayside ~2,500 K).
• Water worlds / Hycean planets: Hypothesized water-rich sub-Neptunes with H₂-dominated atmospheres over liquid water oceans. Proposed as biosignature targets.

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Habitable Zone

Definition

• Orbital region where stellar flux allows liquid water on a rocky planet's surface (given appropriate atmospheric pressure).
• Inner edge (IHZ): Runaway greenhouse. For the Sun: ~0.95–0.99 AU (depends on model).
• Outer edge (OHZ): Maximum greenhouse (CO₂ condensation). For Sun: ~1.67–1.70 AU.
• Scales with stellar luminosity: a_HZ ∝ √L.

Complications

• Tidal locking: Planets in HZ of M dwarfs (most common stars) are likely tidally locked. One side permanent day, one side permanent night. Atmospheric circulation may redistribute heat, but depends on atmosphere thickness and composition.
• M-dwarf activity: Frequent flares, strong UV/XUV emission, especially when young. May strip atmospheres from close-in HZ planets.
• Atmospheric composition matters: A planet with a thick CO₂ atmosphere can maintain liquid water farther from the star. A planet with no atmosphere has no habitable zone.
• Optimistic vs conservative HZ: Conservative uses runaway greenhouse and maximum greenhouse limits. Optimistic extends to recent Venus (inner) and early Mars (outer).
• Habitable zone ≠ habitable: A planet can be in the HZ and be uninhabitable (no atmosphere, wrong composition, too much radiation). Habitability requires assessing multiple factors.

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Notable Exoplanet Systems

TRAPPIST-1

• Ultra-cool M dwarf, 12.4 pc, M8V, T_eff ≈ 2,566 K, 0.09 M☉, 0.12 R☉.
• Seven roughly Earth-sized transiting planets (b through h). All within 0.06 AU.
• Three planets (e, f, g) in habitable zone. Periods: 1.5 to 18.8 days.
• Mean-motion resonance chain (all seven in or near resonances).
• Masses from TTVs: 0.3–1.4 M⊕. Densities suggest rocky, some may have volatiles.
• JWST actively studying atmospheres: initial results suggest limited thick atmospheres on innermost planets (thermal emission consistent with bare rock or thin atmosphere for TRAPPIST-1 b and c).

Proxima Centauri

• Closest star to Sun (1.30 pc). M5.5V, 0.12 M☉.
• Proxima b: m sin i ≈ 1.07 M⊕, P = 11.2 d, in habitable zone. Detection via radial velocity (HARPS). Transit not confirmed.
• Proxima d: m sin i ≈ 0.26 M⊕, P = 5.12 d, inside HZ.
• Proxima c: possible ~7 M⊕, P ~ 5.2 yr, cold. Under investigation.
• Proxima is active flare star — habitability concerns regarding atmospheric retention.

Kepler-186

• M1V star, ~179 pc. Five known transiting planets.
• Kepler-186f: First validated Earth-size planet in habitable zone (1.04 R⊕, P = 130 d). Mass unknown (too faint for RV). Receives 32% of Earth's insolation.

55 Cancri (Copernicus)

• G8V star, 12.3 pc. Five known planets (RV + transit for e).
• 55 Cancri e: Super-Earth, 1.88 R⊕, 8 M⊕, P = 0.74 d. Ultra-short period. JWST secondary eclipse data suggest possible volatile atmosphere (CO₂ or CO) rather than bare rock. Dayside ~2,500 K.
• System spans 0.015 to 5.7 AU — broad architecture.

Other Notable Systems

• Kepler-11: Six transiting sub-Neptunes, compact. Demonstrated prevalence of multi-planet flat systems.
• HR 8799: Four directly imaged giant planets (b, c, d, e) at 15–70 AU. Young system (~30 Myr).
• TOI-700 d and e: Earth-sized planets in habitable zone of M dwarf, discovered by TESS.
• LHS 1140 b: Potentially rocky super-Earth in HZ of M dwarf. Possible water world. JWST target for atmospheric characterization.

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Exoplanet Statistics and Occurrence Rates

• Total confirmed exoplanets: >5,700 (as of early 2026).
• Detection method breakdown: ~75% transit, ~18% RV, ~3% imaging, ~2% microlensing.
• Occurrence rates (Kepler):
  • Hot Jupiters: ~0.5–1% of FGK stars.
  • Cold gas giants (Jupiter analogs): ~5–10%.
  • Super-Earths/sub-Neptunes (1–4 R⊕, P < 100 d): ~30–50% of Sun-like stars.
  • Small planets (< 2 R⊕) more common around M dwarfs than FGK stars.
• Eta-Earth (η⊕): Fraction of Sun-like stars with Earth-size planet in HZ. Estimates range from ~5–25% depending on definitions and extrapolations. Key Kepler result, but significant uncertainties in extrapolation to long periods.
• Multiplicity: Most planetary systems are flat and compact (low mutual inclinations, periods of days to months). "Peas in a pod" pattern: adjacent planets tend to have similar sizes and regular spacing.

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Atmospheric Characterization

Transmission Spectroscopy

• During transit, starlight filters through planet's terminator atmosphere.
• Wavelength-dependent transit depth reveals atmospheric absorption features.
• Signal scales with atmospheric scale height: H = kT/(μg). Larger for hot, low-gravity, low-mean-molecular-weight atmospheres.
• Hot Jupiter signals: ~100–1000 ppm. Temperate Earth: ~5–20 ppm (extremely challenging).

Emission Spectroscopy

• Measure planet's thermal emission during secondary eclipse (planet passes behind star).
• Gives dayside spectrum. Constrains temperature structure and composition.
• JWST MIRI: thermal emission of rocky planets possible for nearest, hottest targets.

Phase Curves

• Continuous monitoring over full orbit. Maps brightness vs orbital phase.
• Reveals day-night temperature contrast, heat redistribution, atmospheric dynamics.
• Hot-spot offset from substellar point indicates superrotating winds.

Detected Atmospheric Species (as of 2026)

• Hot Jupiters: H₂O, CO, CO₂, Na, K, TiO, VO, FeH, SO₂, SiO, HCN.
• Sub-Neptunes: H₂O, CH₄, CO₂ (K2-18b — debated), hints of DMS.
• Rocky planets: Limited. TRAPPIST-1 b/c consistent with bare rock or very thin atmosphere. 55 Cancri e may have volatile atmosphere.

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Biosignatures

Atmospheric Biosignatures

• Oxygen (O₂): On Earth, produced by photosynthesis. But abiotic sources exist (photolysis of H₂O or CO₂). Context-dependent.
• Ozone (O₃): UV-detectable proxy for O₂. Strong spectral feature at 9.6 μm.
• Methane (CH₄): Biological on Earth, but also produced abiotically (serpentinization). CH₄ + O₂ together is thermodynamically disequilibrium → strong biosignature when paired.
• Nitrous oxide (N₂O): Produced by denitrifying bacteria. Weak abiotic sources.
• Disequilibrium chemistry: Co-presence of thermodynamically incompatible species (e.g., O₂ + CH₄) maintained by biological fluxes.
• Dimethyl sulfide (DMS): Produced by marine phytoplankton on Earth. Tentative detection in K2-18b atmosphere (JWST, 2023) — heavily debated.

False Positives and Caution

• Abiotic O₂: photolysis of water on desiccated planets, CO₂ photolysis.
• Methane from serpentinization (olivine + water at ocean floor).
• Context is critical: need to assess stellar type, planetary bulk properties, atmospheric redox state, and multiple gases simultaneously.
• No single gas is a definitive biosignature. The "triplet" of O₂ + H₂O + CH₄ in an N₂-dominated atmosphere is considered strongest.

Surface Biosignatures

• Vegetation Red Edge (VRE): sharp increase in reflectance at ~700 nm from chlorophyll. Could be detected via direct imaging of Earth-like planet.
• Pigment absorption features from photosynthetic organisms.
• Seasonal variations in atmospheric composition (Earth's CO₂ cycle).

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Mass-Radius Relationships

• Pure iron: R ∝ M^0.27 (very compact).
• Earth-like (32% Fe core + 68% silicate mantle): R ∝ M^0.27 (R ≈ M^0.27 R⊕ for M in M⊕).
• Pure water: R ∝ M^0.24 (larger than rocky at same mass).
• With H/He envelope: Even 1% H/He by mass dramatically increases radius.
• Radius gap: Planets with R < 1.5 R⊕ are predominantly rocky. Above 2 R⊕, most require significant volatile envelope.
• Degeneracy: A given mass-radius pair can be fit by multiple compositions (e.g., large iron core + thick water layer vs small core + thin H/He envelope). Additional constraints (atmospheric characterization, formation context) needed.

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Anti-Patterns

• Claiming a planet is "habitable" based solely on HZ location: The habitable zone is a necessary but not sufficient condition. Atmosphere, magnetic field, stellar activity, tidal effects, and composition all matter. Say "in the habitable zone" not "habitable."
• Treating all exoplanet detections as equal confidence: Candidates require validation or confirmation. Kepler candidates have false positive rates of ~5–15%. TESS candidates need ground-based follow-up. Distinguish confirmed vs validated vs candidate.
• Ignoring detection biases in occurrence rate discussions: Transit and RV methods are biased toward short periods and large planets. Occurrence rates at long periods involve significant extrapolation. Always note the parameter space being constrained.
• Overstating atmospheric detections for small planets: As of 2026, no definitive atmosphere has been confirmed for an Earth-sized planet around another star. Results for TRAPPIST-1 planets are constraints and upper limits, not detections.
• Confusing minimum mass (m sin i) with true mass: Radial velocity alone gives minimum mass. The true mass could be significantly higher for low inclinations. Only transiting or astrometrically characterized planets have true masses.
• Presenting biosignature detection as proof of life: Even the strongest biosignature detections will require extensive analysis of false positive scenarios. Discovery of extraterrestrial life will require ruling out abiotic explanations — a process that could take years.
• Ignoring stellar host properties: Planet habitability is inseparable from its star. M-dwarf planets face different challenges (flares, tidal locking, XUV) than planets around G-type stars. Always discuss the star.
• Treating the Fulton gap as a sharp boundary: The radius gap is a statistical feature in a population distribution, not a hard physical boundary. Individual planets can exist within the gap.