A High-School Exoplanet Claim With a Secondary Dip
A high-school observatory collects 40 nights of CCD photometry of a V = 11.3 Sun-like star using a 0.20 m telescope. The light curve shows a 1.2% dip every 3.71 days lasting 3.1 hours, plus a shallower 0.30% dip centered exactly halfway between the deep dips. Images were taken with a 1.1 arcsec per pixel scale and reduced with a 6 arcsec radius aperture; the Digitized Sky Survey shows a V = 14.8 star 5.5 arcsec from the target. The students compute a planet radius 1.1 times Jupiter's by assuming the dip is a transiting planet and the host star is 1 solar radius, and they write that they have a confirmed transiting exoplanet. Their mentor can obtain time on a 1 m telescope with an adaptive-optics imager and a spectrograph, and can access wide-field survey archive images of the field. The students must revise the paper before submission.
1. Check the radius calculation and evaluate whether the word 'confirmed' is justified.
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The arithmetic is fine: fractional depth equals (Rp/Rs)^2, so 0.012 gives Rp/Rs = 0.11, and 0.11 solar radii is about 1.1 Jupiter radii. The interpretation is not fine.
Three assumptions are doing all the work, and none is tested. The stellar radius is assumed rather than measured, and a 20% error in radius propagates to a 20% error in planet size. The depth is assumed to be diluted by nothing, yet a V = 14.8 star only 5.5 arcsec away falls inside a 6 arcsec aperture, so some of the recorded light may come from a source that never dims - making the true depth deeper and the planet larger, or revealing that the wrong star is being measured. And a grazing orbit also invalidates the simple depth-to-radius conversion.
'Confirmed' requires independent evidence, typically a radial-velocity mass measurement, plus a quantitative false-positive analysis. Photometry alone establishes a candidate, not a planet. The correct wording is candidate, with stated limits on the radius.
2. Interpret the 0.30% dip at phase 0.5. Why does it undermine the planet interpretation?
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A secondary eclipse occurs when the companion passes behind the star, and its depth is roughly (Rp/Rs)^2 times (Tp/Teff)^4. For a hot Jupiter with Rp/Rs = 0.11 and a dayside temperature near 1500 K around a 5800 K star, the temperature factor is about 0.26^4 = 0.0046, so the expected secondary depth is of order 0.012 x 0.0046, about 5 x 10^-5 - far below the 0.30% observed.
The observed dip is 25% of the primary depth. Ratios that large at phase 0.5 point to a self-luminous companion or a blended eclipsing binary, where the second dip is an occultation of two stars (or a grazing configuration), not a planet. Reflection, ellipsoidal distortion and Doppler beaming can all produce out-of-eclipse modulation, but at amplitudes well below 0.3% for a planetary companion.
So the two dips cannot both be planetary. Either the system is stellar, or the deep dip and the shallow one arise from different sources in the aperture. The planet claim fails until that is resolved.
3. Recommend the follow-up observations that would settle the interpretation, and say what result would support or refute the planet claim.
Read the worked answer
First, resolve the field. Use the adaptive-optics imager and archive survey frames to see whether the V = 14.8 star is bound to the target or just along the line of sight, and to search for closer companions. Then re-reduce with a smaller aperture or point-spread-function fitting so the neighbor's light is excluded. If the transit depth deepens on re-reduction, blending was inflating the stellar radius estimate and the planet size.
Second, test chromaticity. Take light curves in two well-separated filters. A genuine planetary transit is achromatic because the planet is opaque at both wavelengths; a blended eclipsing binary usually shows a depth that changes with wavelength. This is cheap and decisive.
Third, obtain spectroscopy. Radial-velocity monitoring should show a planetary-mass reflex motion at 3.71 days; a stellar companion would show tens of km/s. Line-bisector analysis can flag blends.
Finally, check archive photometry for rotational modulation that could mimic 3.71-day periodicity. Refutation comes from any chromatic depth difference, a stellar-mass velocity amplitude, or resolved contaminating light.