Planet Injection-Recovery Tests

Updated 24 August 2025

Planet injection-recovery tests are empirical experiments that insert synthetic planetary signals into observational data to quantify detection efficiency and survey completeness.
These tests use analytic models and logistic functions to assess recovery rates, reliability, and false-alarm metrics across transit, imaging, and phase curve surveys.
They provide critical quantitative corrections for exoplanet occurrence studies, influencing both pipeline validation and survey design improvements.

Planet injection-recovery tests are a class of empirical experiments central to calibrating the detection efficiency and reliability of planetary signals in both photometric and imaging surveys. They provide quantitative measurements of survey completeness, false-alarm rates, and sensitivity limits by inserting synthetic planetary signals into observational datasets, subjecting these signals to the same detection pipelines and systematic effects as the original data. These methodologies are foundational in exoplanet occurrence rate studies, the validation of new detection algorithms, and the rigorous assessment of survey limitations.

1. Methodological Foundation of Planet Injection-Recovery Tests

The core procedure is the artificial injection of planetary signals—either photometric transits, phase curves, or point sources—into authentic, often raw, observational data. These signals are constructed using established analytic models (e.g., Mandel & Agol formalism for transit photometry), parameterized by properties such as orbital period, planet radius, depth, epoch, and orbital geometry. The modified datasets are then processed through the full, standard reduction and detection pipeline—including all subsequent stages of detrending, systematics correction, and candidate vetting.

Upon completion, the outputs of the pipeline are analyzed to determine whether the injected planets are successfully detected. The detection criteria typically require the recovery of period and epoch within a fixed tolerance (e.g., within 3% in period and 0.5 days in epoch for the Kepler pipeline (Christiansen et al., 2016)). In the context of direct imaging, synthetic point sources are injected at known contrasts and separations into imaging sequences. These are then assessed for recovery at a given signal-to-noise threshold after post-processing, PSF subtraction, and application of matched-filter algorithms (Ruffio et al., 2017).

The completeness, $C$ , is modeled as a function of relevant parameters (e.g., $C(P, R_p)$ in transit surveys) and is often parameterized as a logistic function or similar empirical model of signal-to-noise metrics such as the Multiple Event Statistic (MES) (Zink et al., 2021). The true-positive rate, false-alarm rate, and parameter-dependent sensitivity maps resulting from these tests enable rigorous statistical correction of planetary population inferences.

2. Representative Implementations Across Modalities

Transit Surveys

Injection-recovery tests in Kepler and K2 campaigns involve the large-scale injection (over 100,000 stars) of modeled transits spanning a wide range of planet radii, orbital periods (typically 0.5–500 days), and impact parameters. For Kepler SOC pipeline v9.2, injected signals were added at the calibrated pixel level, bypassing any contamination of the cotrending basis vector construction (Christiansen et al., 2016). Analogous procedures in K2 involve injection at the raw aperture-integrated flux stage, propagating through all subsequent corrections, including EVEREST detrending and Gaussian process filtering (Zink et al., 2021). Recovery is dictated by congruence in period and epoch and successful passage through automated vetting software (e.g., EDI-Vetter).

Direct Imaging

In surveys such as GPIES, fake planets are injected into each image, using realistic point spread functions (PSFs) at selected separations and contrasts. The full imaging reduction pipeline, incorporating advanced PSF subtraction via Karhunen–Loève Image Processing (KLIP) and forward-modeled matched filters, is then executed. The SNR of the recovered synthetic planet in the final image is measured, yielding completeness and contrast curves as a function of angular separation and planetary spectrum (Ruffio et al., 2017).

Phase Curve and Variability Studies

When probing phase curve detectability in the presence of stellar variability, simulated light curves constructed with controlled noise and periodicity are used. Synthetic phase-curve sinusoids of known amplitude and phase are repeatedly injected into these light curves or directly into segments of real data (e.g., Kepler Q9). Recovery is tested over ensembles of orbital combinations, with successful detection typically defined via the interquartile range (IQR) of the recovered amplitude falling within 15% of the injected value (Hidalgo et al., 2018). When white noise and stellar variability are combined, different detrending approaches (e.g., local filtering, spline interpolation) are assessed for their impact on recovery performance.

3. Quantitative Performance Metrics

Detection Efficiency and Completeness

Completeness, $C$ , is empirically determined by binning injections in a relevant parameter space (e.g., MES, period, planet radius) and computing $C = N_\text{recovered} / N_\text{injected}$ . For Kepler and K2, completeness versus MES is well-fit by a generalized logistic model:

$f(x) = a / (1 + e^{-k(x - l)})$

where $a$ is the maximal completeness and $k$ , $l$ parameterize the slope and 50% completeness threshold (Zink et al., 2021). For planet imaging surveys, completeness contours are constructed in the space of contrast and separation. In some cases, the completeness as a function of planet radius and period is also modeled using logistic or cumulative gamma distributions (Christiansen et al., 2016, Zink et al., 2021, Dietrich et al., 2023).

Reliability and False-Alarm Rate

Reliability is assessed via analysis of inverted (transit-free) light curves or via offset signal injections (e.g., background binaries). The false positive rate is quantified as the number of systematic/veto-passing signals in these control samples, relative to the number of candidates found in the unaltered sample, with corrections for the vetting routine's efficiency (Zink et al., 2021). For imaging, Receiver Operating Characteristic (ROC) curves mapping true/false positive rates for varying algorithm thresholds are used for similar purposes (Ruffio et al., 2017).

Statistical Uncertainty

Uncertainties in completeness are derived using binomial statistics:

$\sigma_C = \sqrt{C(1 - C)/N}$

where $N$ is the number of injections in a given bin (Dietrich et al., 2023).

4. Survey-Dependent Effects and Caveats

Injection-recovery tests elucidate systematic effects that would otherwise bias occurrence rate estimates. For example, in Kepler pipeline SOC 9.2, a period-dependent detection efficiency drop arises from an incorrectly implemented statistical bootstrap cut, breaking the previous monotonic relationship between MES and completeness and introducing a sharp efficiency decrease for $P > 40$ days—even for high-MES signals (Christiansen et al., 2016). K2's detrending pipeline suppresses transit signals more readily, capping maximal completeness at about 61% due to residual motion systematics (Zink et al., 2021).

Stellar variability, as in the detection of planetary phase curves, can drastically diminish recovery rates; in the presence of uncorrected stellar variation, even repeated orbits may not yield a detectable signal, and filtering techniques only partially restore recoverability (Hidalgo et al., 2018).

5. Implications for Occurrence Rate Calculations and Survey Design

Injection-recovery testing provides necessary corrections for incompleteness and sample bias in planet candidate catalogs. Its outputs are essential for translating observed candidate lists into robust exoplanet demographic statistics. In occurrence rate inference, the observed number of detections in a given regime is divided by the average completeness derived from injection-recovery results:

$N_\text{intrinsic} \sim N_\text{detected} / C$

This enables corrections for both false negatives (due to incomplete pipeline sensitivity) and, when combined with reliability analyses, false positives.

Survey design and target selection are directly affected; for instance, the suboptimal recoverability of phase curves from stars with $T_\text{eff}$ outside $5500\,\text{K} < T_\text{eff} < 6000\,\text{K}$ improves observational efficiency by narrowing target selection (Hidalgo et al., 2018).

Advanced pipeline development, such as forward-model matched filtering in direct imaging, is informed and calibrated by extensive injection-recovery analysis, revealing operational trade-offs (e.g., between SNR gain, aggressiveness of PSF subtraction, and template selection) (Ruffio et al., 2017). These quantitative frameworks guide both algorithmic optimization and the establishment of detection thresholds.

6. Extensions, Limitations, and Future Directions

The completeness functions and statistical corrections derived from injection-recovery tests are made publicly available in several major surveys via dedicated archives (e.g., NASA Exoplanet Archive for Kepler (Christiansen et al., 2016, Zink et al., 2021)). This facilitates target-specific completeness correction and enables robust population studies beyond the initial catalog constraints.

A notable limitation is the dependency of completeness and reliability on pipeline implementation details; changes in detrending, systematics correction, and vetting logic often require fully new injection-recovery experiments. For surveys targeting new stellar populations or instrument modalities (e.g., late M dwarfs, ground-based photometry), the detection parameter space must be fully remapped (Dietrich et al., 2023).

Ongoing and future exoplanet missions (TESS, CHEOPS, PLATO) and sophisticated imaging surveys require continual expansion of injection-recovery paradigms, including multi-wavelength, multi-instrument, and temporally segmented injection strategies, to capture both instrumental and astrophysical complexity.

Summary Table: Key Aspects of Planet Injection-Recovery Tests in Recent Surveys

Survey / Modality	Signal Injection Stage	Completeness Measurement
Kepler (SOC 9.2)	Calibrated pixel data	2D function of MES and period; gamma/logistic fit (Christiansen et al., 2016)
K2 Campaigns	Raw aperture sum	Logistic fit to MES; capped by detrending bias (Zink et al., 2021)
GPI Imaging	Reduced images	ROC, contrast curves, completeness map (Ruffio et al., 2017)
Phase Curve Detectability	Simulated/real lightcurves	IQR-based amplitude recovery, orbit stacking (Hidalgo et al., 2018)
EDEN (late M dwarfs, ground)	Time series photometry	Logistic completeness in $(R_p, P)$ ; binomial errors (Dietrich et al., 2023)

The rigorous application and statistical modeling of planet injection-recovery tests form the methodological backbone for contemporary exoplanet demographic studies and detection pipeline validation across all detection techniques.