A planet can block 1% of the light from its host star while a telescope records a dip of only 0.8%. The difference is not necessarily a change in the planet. Light from an unresolved neighbouring star can dilute the fractional brightness drop and make an uncorrected planet radius look too small.
This Gold Standard guide works through a 20%-contamination example, translates depth into planet-to-star radius ratio, and tests wavelength, aperture and pipeline effects. The numbers are intentionally simple; the source-identification and measurement questions are treated rigorously.
eduKateSG · The Gold Standard of Astronomy
Choose your reading route
Understand the diluted dip · Chapters 1–3: photons, corrected depth and radius.
Validate the measurement · Chapters 4–6: wavelength, uncertainty and pipeline history.
Check and connect · Chapters 7–8: questions, related astronomy and sources.
Chapter index
Photons, depth and radius · Chapters 1–3
Bandpass, errors and pipeline · Chapters 4–6
Questions and sources · Chapters 7–8
CHAPTER 1 OF 8
1. What a telescope counts when more than one star is in the aperture
A telescope measures photons within a selected image region or extraction aperture. If that region contains the host star and a nearby source that is not resolved cleanly, the flux recorded outside a planetary transit contains more than light from the planet’s host. A planet can still block the same amount of its host’s light, but that missing light is now expressed as a smaller fraction of the total recorded flux.
The effect is called transit dilution or third-light contamination. It is distinct from the planet actually becoming smaller. A crowded aperture changes the denominator used to normalise a transit light curve, and the inferred planet-to-star radius ratio can be biased if the extra flux is ignored.
NASA’s TESS crowding documentation explains that excess light from neighbouring stars reduces the apparent transit depth and can systematically underestimate the planet radius. It also distinguishes the raw SAP light curve from the pipeline’s PDCSAP product, which can already include a crowding correction. The data product therefore matters as much as the correction equation.
Not every extra photon comes from a separate constant star. Blending, background-estimation failures and stellar variability can change how a measured light curve looks. Nor does a diluted dip prove that a planet exists: a blended eclipsing binary can imitate a transit candidate. The aim of this article is to understand one measurement effect without claiming the entire detection has been vetted.
Before doing any radius calculation, identify the target, other sources in the aperture, the observing filter, and the processing level of the light curve. The physical question is: how much light did the target lose, and how much other light was included when that loss was divided by the out-of-transit baseline?
Imagine a fictional host star contributing 80,000 detected flux units outside transit, with a second constant source contributing 20,000 units in the same aperture. The baseline total is 100,000 units. Define the host-light fraction f=Fhost/(Fhost+Fblend)=80,000/100,000=0.80.
Now suppose the true host-star transit depth is 1%, meaning the planet blocks 0.01×80,000=800 flux units from the host under a uniform-disk, small-planet teaching approximation. At mid-transit the aperture contains 79,200 host units plus 20,000 extra units, or 99,200 units.
The recorded fractional dip relative to the total aperture baseline is (100,000−99,200)/100,000 = 800/100,000=0.008, or 0.8%. The host alone truly fell by 1%, but the contaminated light curve shows only 0.8%.
Write δobs=δtrue×f, provided the contaminating light is constant during the event and the extraction and normalisation refer to that defined flux mixture. Then δtrue=δobs/f=0.008/0.80=0.010. This corrects the illustrative depth, not every other possible shape or source-identification problem.
If someone subtracts the contaminant’s 20,000 units only from the in-transit point and not from the baseline, they change the denominator inconsistently. Both the baseline and the in-transit measurement must be treated coherently. The same logic applies to a complete light curve, not only two individual flux samples.
The arithmetic does not assume that all target light enters the aperture: an aperture-loss factor can matter separately. A pipeline may account for both crowding and lost target flux, so readers should not apply a second correction before understanding the data product’s provenance.
| Toy measurement | Out of transit | At mid-transit |
|---|---|---|
| Host flux | 80,000 | 79,200 |
| Constant blended flux | 20,000 | 20,000 |
| Total aperture flux | 100,000 | 99,200 |
| Dip relative to host only | — | 1.00% |
| Dip relative to blended baseline | — | 0.80% |
For a simple fully transiting opaque disk across a uniformly bright star, the fractional transit depth is approximately δtrue=(Rp/Rstar)². Limb darkening, noncentral transit geometry, finite integration time and detailed modelling modify real light-curve inference, but the square-law relation is the standard starting approximation.
If an astronomer mistakes the diluted 0.8% depth for the intrinsic 1% depth, the naive radius ratio is sqrt(0.008)≈0.08944. Correcting the light dilution first yields sqrt(0.010)=0.10000.
Relative to the correct illustrative ratio, the naive ratio is smaller by (0.10000−0.08944)/0.10000≈10.6%. The 20% contaminating fraction of aperture light did not produce a 20% radius error, because radius scales with the square root of transit depth.
The host-star radius must also be known to obtain the planet’s radius in kilometres or Earth radii. Even a perfectly corrected Rp/Rstar cannot produce an accurate absolute planet radius if Rstar is substantially uncertain.
The result can be expressed without choosing any specific stellar radius: (Rp/Rstar)corrected=(Rp/Rstar)naive/sqrt(f), under the adopted model. For f=0.80, divide the naive ratio by sqrt(0.80)≈0.8944, giving a correction factor of about 1.118.
This is why the direction of contamination is important: extra constant light reduces observed fractional depth and normally biases a naive radius low. Yet unresolved eclipsing contaminants may make the assumed host identity itself wrong, in which case applying a simple depth correction does not solve the planet-identification problem.
| Quantity | Naive blended interpretation | After known f=0.80 correction |
|---|---|---|
| Transit depth | 0.008 (0.8%) | 0.010 (1.0%) |
| Rp/Rstar | ≈0.08944 | 0.10000 |
| Radius-ratio difference | ≈−10.6% relative to corrected | Reference |
A companion can have a different stellar spectrum from the target. Even if both stars remain constant, their relative contribution to an aperture may change from one wavelength band to another. The same physical planetary occultation can consequently produce different observed depth dilutions in blue and infrared measurements.
Imagine an optical band in which the target contributes 80% of blended baseline flux, producing the 0.8% observed depth from a true 1% event. In another band let the target contribute only 60%, perhaps because the companion is relatively brighter in that band. Then δobs=0.010×0.60=0.006, or 0.6%.
The naive second-band radius ratio is sqrt(0.006)≈0.07746, whereas correcting by f=0.60 again recovers 0.10000 under the toy assumptions. The two observed depths differ by a third despite a constant planet and host radius in the model.
Do not interpret such a band-dependent change automatically as a planetary atmosphere. Transmission spectroscopy uses small wavelength-dependent variations of transit depth to infer atmospheric opacity, but uncorrected companion light, starspots and bright stellar regions can create or distort spectral features. Research reviewed by NASA’s Exoplanet Exploration Program explicitly warns about stellar contamination.
Aperture choice also matters. A smaller image aperture may exclude part of a contaminating star but lose some target light; a larger one may capture more of both. PSF shape, pointing variation and the data reduction influence the appropriate fractions. A factor determined for one extraction cannot simply be moved to another without checking.
A valid correction needs a time- and band-appropriate estimate of target and contaminant contributions and recognition of what the processing pipeline has already done. The same correction applied blindly to every wavelength can produce an attractive but misleading planetary spectrum.
| Band-specific toy case | Target fraction f | Observed depth | Naive radius ratio |
|---|---|---|---|
| Band A | 0.80 | 0.80% | ≈0.08944 |
| Band B | 0.60 | 0.60% | ≈0.07746 |
| Both after correct dilution removal | — | 1.00% | 0.10000 |
CHAPTER 5 OF 8
5. Uncertainty in the contaminating light enters the radius estimate
A crowding factor is often an estimate rather than an exact number. Neighbouring-star magnitudes, unresolved companions, variability and aperture response can affect the inferred target fraction. A depth correction reported with five decimal places is therefore not justified merely because the division is easy.
Hold the measured depth at δobs=0.008 and suppose f is estimated as 0.80, with a plausible sensitivity range from 0.75 to 0.85 for the toy exercise. If f=0.75, the corrected depth is 0.008/0.75≈0.010667 and its square-root radius ratio is ≈0.10328.
If f=0.85, corrected depth is 0.008/0.85≈0.009412 and radius ratio is ≈0.09701. Thus uncertainty in f translates into an approximate radius-ratio range of 0.0970 to 0.1033 when the observed depth and stellar radius are artificially held fixed.
This is a sensitivity range under chosen plausible inputs, not a statistical confidence or credible interval. The observed transit depth also has noise and modelling uncertainty. A physical planet-radius estimate additionally has stellar-radius uncertainty and possibly correlated fitting errors.
For small independent fractional uncertainties under the simple square-law model, the first-order propagation of Rp/Rstar=sqrt(δobs/f) can be approximated using one-half the fractional sensitivity of depth and target fraction. Correlations, limb darkening and uncertain source identity can require a fuller model.
A responsible article reports the assumed contaminating-flux fraction, its derivation, which wavelength and aperture it applies to, and uncertainty. It should not say ‘we corrected third light’ without enough details to reproduce the calculation.
| Assumed target fraction f | Corrected depth | Corrected Rp/Rstar |
|---|---|---|
| 0.75 | ≈0.010667 | ≈0.10328 |
| 0.80 | 0.010000 | 0.10000 |
| 0.85 | ≈0.009412 | ≈0.09701 |
TESS light-curve files can provide different columns with different processing histories. NASA’s TESS documentation identifies a simple-aperture photometry product, SAP, and a processed product, PDCSAP, whose corrections can include treatment of crowding and aperture flux fraction. Applying an extra estimated dilution factor to an already corrected light curve can overcorrect the depth.
A complete provenance check records the mission, release, selected extraction, aperture mask, source list, estimated CROWDSAP and FLFRCSAP where available, and any user pipeline adjustments. These metadata are not optional decorations; they determine whether the raw observed depth still contains the modelled contamination.
A simple target fraction f is not necessarily identical to every crowding metric from every pipeline. Terms may involve target flux included in the aperture and how much of the target point-response function falls within that region. Read the exact data-product documentation instead of treating one metadata field as a universal correction formula.
Inspect raw and corrected light curves, baseline behaviour and centroid shifts. If the apparent transit changes with extraction aperture or if the source centroid moves significantly during the dip, consider whether a nearby eclipsing binary or variable source could be responsible.
Follow-up images with better angular resolution and independent photometry can help identify neighbouring stars and estimate their flux contributions. Multi-band and multi-epoch observations help challenge a blended interpretation, but additional data still require consistent modelling.
Do not conclude a planet radius is secure merely because applying a correction yields a neat percentage. The identity of the eclipsed star, orbital fit, stellar parameters and instrumental quality must all be supported. The companion transit-vetting article addresses those larger inference steps.
Does a neighbour’s constant light make the planet physically smaller? No. It changes the fraction of recorded aperture light lost during a host-star transit and can bias a naive radius estimate.
Why does 20% extra baseline contamination not mean a 20% radius error? In the simple uniform-star model, radius ratio scales with the square root of intrinsic transit depth, so the percentage effect differs.
Can dilution make a real transit undetectable? Extra light reduces fractional depth and may complicate detection, although photon statistics and noise determine the actual detection significance.
Does a diluted dip establish which star has the planet? No. The eclipse may occur on the target or a blended source. Source identification requires independent evidence.
Can the dilution factor differ with colour? Yes. The contaminant and host may have different spectra and therefore different flux ratios in different observing bands.
Should I always divide a TESS transit depth by CROWDSAP? No. The appropriate correction depends on the data product and its existing pipeline operations. PDCSAP may already include crowding correction.
Does a perfect light-ratio correction establish the absolute planet radius? No. The stellar radius and detailed transit geometry also affect the physical radius estimate.
Can spots on the host mimic wavelength-dependent dilution? Stellar spots and bright regions can bias transit depths, but their physical mechanism differs from flux supplied by a separate blended star.
Is an f range from 0.75 to 0.85 a confidence interval? Not unless derived using a defined uncertainty model. In this article it is only a sensitivity exercise.
CHAPTER 8 OF 8
8. Use the radius correction to strengthen the astronomical evidence chain
A transit-depth interpretation has several denominators: the host’s unobscured light, any additional aperture light, and the geometrical star area used to convert corrected depth into a radius ratio. Keeping each one explicit prevents a measurement error from being disguised as a planetary property.
As a transfer exercise, repeat the first calculation after changing the companion flux from 20,000 to 40,000 while holding host flux at 80,000 and its intrinsic transit depth at 1%. The target fraction becomes 80,000/120,000≈0.6667, so the measured dip becomes about 0.667%. Explain why the true toy planet remains unchanged.
Continue in The Gold Standard of Astronomy, Vetting an Exoplanet Transit Candidate, Aperture Photometry and Sky Counts, and Radial-Velocity Signals and Minimum Mass. For wider learning transfer use Learning Transfers into Life and How X Works.
Authoritative source references reviewed on 23 October 2026: NASA HEASARC: Understanding Crowding in TESS, Open University: From Dips to Planet Size Measurement, Astronomy & Astrophysics: Contamination Factors in TESS Transit Validation, and NASA Exoplanet Program SAG21: Stellar Contamination.
Every star flux, transit depth, f value and derived radius ratio above is invented for education. The simplified relation δ=(Rp/Rstar)² is not a substitute for a complete limb-darkened transit light-curve fit or validation of the transited star.