A distant star can remain a single bright dot in an image. How can we know it has a planet, rather than merely drawing a wished-for world in the glare?
Exoplanets are found through testable changes in light and motion produced by a planet. The transit method looks for periodic reductions in stellar flux; the radial-velocity method looks for Doppler shifts in the star’s spectrum. A signal alone is not a confirmed planet: its origin, uncertainties and alternatives must be checked. Some planets are observed through their own light, but “discover” need not mean “resolve a disk”. NASA: search methods.
A planet blocks some of the light
If an orbit is viewed nearly edge-on, its planet can cross the stellar disk. This is a transit. A telescope measures total received light over time; a dip appears in the light curve. The planet need not be a separate visible dot: measuring the starlight it blocks is sufficient.
Repeating dips help determine the orbital period. Their depth primarily yields the planet’s size relative to the star. Obtaining a radius in kilometres requires the stellar radius. Revising that estimate can change the inferred planetary size even when the measured dip stays the same. Winn: geometry and dimensions, §2 and §3.1.
At a different inclination, the planet passes above or below the stellar disk in our projection. It continues to exist, but does not transit. A flat light curve therefore does not prove an empty system.
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Half the radius gives a dip four times weaker
For an opaque planet, its disk fully overlapping a uniformly bright star, and negligible planetary light:
δ = (F_(out) − F_(in))/(F_(out)) ≈ (((R_(p))/(R_(⋆))))^(2).
F is flux in matching units outside and during transit; R_(p) and R_(⋆) are radii in matching units. The depth δ is dimensionless. At R_(p)/R_(⋆) = 0.10, it is 0.01, or 1%; at 0.05, it is 0.0025, or 0.25%. As radius tends to zero, the dip disappears. These are teaching ratios, not measurements of a particular system. Winn: equation 22 and limb darkening, §2.5.
A real star is usually dimmer near its edge, so a precise model accounts for the patch being hidden. A neighbouring star’s light also matters: if it equals the target’s light, the observed fractional depth is halved. Attributing all the flux to one star makes the planet appear smaller. A weak dip can therefore indicate either a small planet or a diluted signal. Kepler DR25: extra light and radii, §VII.6.
The planet also makes its star move
A star and planet orbit a shared centre of mass. The star follows a smaller orbit, but its motion can be sought in its spectrum—light separated by wavelength. When the star approaches, its spectral lines shift to shorter wavelengths; when it recedes, to longer wavelengths. Radial velocity is the velocity component along the observer’s line of sight. The instrument measures line shifts, and a model converts them to this velocity. NASA: Doppler searches.
The method is sensitive to companion mass, but also orbital inclination. In the usual small-planet-mass approximation, with stellar and orbital parameters known, it yields M_(p)sini, often called the minimum mass. Here i = (90)^(∘) means edge-on and i = (0)^(∘) means face-on. In the latter limiting case there is no orbital motion along our line of sight, and this Doppler signal vanishes. Gravity has not vanished. Winn: mass and inclination, equation 25.
When both methods are available, periods and orbital models can be compared. The transit constrains inclination, and velocities help determine mass. With a radius, this gives mean density, narrowing possible compositions; it is not a detailed map of the interior.
From a measurement to an inference
Transit
- Measure
- Received light decreases as a planet passes in front of its star.
- Infer with a model
- Planet-to-star radius ratio; period from repeated events.
- What else is needed
- Stellar size, transit geometry, contaminating light and false-event checks.
Radial velocity
- Measure
- The stellar spectral lines shift periodically.
- Infer with a model
- Orbital motion along the line of sight; a constraint on companion mass.
- What else is needed
- Stellar mass, orbital parameters, inclination and stellar-activity checks.
What else could produce the signal?
A dip can be produced by an eclipsing binary, including a faint background pair whose light blends with the target. Stellar activity and instrumental effects also produce misleading events. Researchers therefore check dip shapes and repetitions, alternating depths, additional eclipses and whether the variable light originates at the intended star. Higher angular-resolution images help identify neighbours. Original Kepler vetting description, §III.1 and §VII.6.
In spectra, surface changes can distort lines and imitate motion. Periodicity alone does not guarantee a planet: stellar activity, instrumental stability and alternative models must be checked. Fischer and colleagues: sources of spurious radial velocities.
After initial selection an object may remain a candidate. Subsequent status rests on additional dynamical evidence or statistical tests of plausible false-positive scenarios. Not every confirmed planet necessarily has both a transit and measured radial velocity. The strength of the conclusion depends on available data and validation conditions.
Easiest to find does not mean most common
A large planet blocks more light. A short period gives more repetitions within a survey, and close orbits are more likely to transit for random orientations. Radial velocities also generally favour more massive, close companions with other conditions equal. Noise, observing duration and sampling add their own selection. The fraction of a planet type in a discovery list therefore differs from its fraction in nature. Winn: geometric selection, §2.2, and survey limitations, Kepler: detection efficiency, §VIII.
Other methods complement this picture. Direct imaging separates planetary light from stellar glare; it need not reveal the surface. Astrometry looks for stellar motion on the sky. Microlensing looks for a planet’s contribution to changes in the magnification of a distant background star. Each has its own sensitivity range and uncertainties. ESA: different observable signals.
Branch · testing the searchOptional · you can skip this
How do we estimate what a survey missed?
Artificial signals with known parameters can be added to the data and passed through the same search. If a hypothetical experiment recovers 10 out of 20 signals of a given class, the estimated efficiency under those conditions is 50%. A detected object of that class can receive a statistical weight near two, but this does not confirm its individual authenticity.
The number of false events passing selection is estimated separately. Completeness and reliability ask different questions: what was missed and what was wrongly included. Planet occurrence also needs corrections for geometry and stellar selection. Kepler performed such experiments at both pixel and light-curve levels; efficiency varied between stars. The 20 and 10 here are educational, not Kepler results. Thompson and colleagues, §VIII.1.
A discovery is a tested inference about a system
We find distant planets by combining a measured signal with a physical model and checks of alternatives. Transits and spectral shifts impose different constraints; orientation can hide a planet from one method, and survey properties can hide it from the whole search. Knowing these limits strengthens discoveries and helps us read a catalogue without a false impression of completeness.
Next time you read exoplanet news, look for three things: what signal was measured, what parameter was inferred and how other explanations were tested. For the physical basis of collecting faint light, see how a telescope works.