Direct detection of exoplanets

An exoplanet is a planet that orbits a star other than the Sun. Direct detection means observing light from the planet separately from the light of its host star.

A planet can be seen through light it emits itself or light it reflects from its star. However, the planet emits far less light than the star and reflects only a small fraction of the star’s light. The star is therefore much brighter, and its light can overwhelm the planet’s faint signal.

A second difficulty is that exoplanetary systems are very distant. The planet and star usually appear very close together in the sky: their angular separation is small. Even if a planet is physically far from its star, their images may be difficult to resolve as separate objects.

Direct detection therefore requires the planet’s faint light to be distinguished from the much brighter starlight when the two appear close together.

Radial velocity method

A planet’s gravity pulls on its star, just as the star’s gravity pulls on the planet. As a result, both orbit their common centre of mass. The star’s motion repeats as the planet completes each orbit.

The radial velocity method detects the part of the star’s motion that lies along the observer’s line of sight. As the star moves, its radial velocity changes, producing a repeating pattern in its spectrum.

Radial velocity and spectral shifts

A star’s spectrum contains identifiable spectral lines. The Doppler effect shifts these lines to shorter wavelengths when the star moves towards the observer: this is a blueshift. Motion away from the observer shifts them to longer wavelengths, producing a redshift.

As the star moves around the common centre of mass, its radial velocity varies periodically. Measurements of the spectral lines can reveal this changing velocity. The star system may also have an overall motion relative to the observer, so the search is for a repeated shift relative to the star’s average velocity, not necessarily alternating absolute redshifts and blueshifts.

What the radial velocity variation reveals

A repeating radial velocity variation can reveal an orbiting planet. The time taken for the pattern to repeat is the planet’s orbital period.

The size of the observed velocity variation depends on the planet’s gravitational effect on the star and on the orbit’s orientation. An orbit viewed edge-on produces the largest line-of-sight component for the same stellar motion. If the orbit is viewed face-on, the stellar motion is across the line of sight, so it produces no radial velocity variation.

Exoplanet transit method

An exoplanet can be detected when it passes across the visible disc of its host star from our viewpoint. During this transit, the planet blocks a small fraction of the star’s light, so the star appears temporarily dimmer.

A light curve plots the star’s observed brightness against time. It shows a dip during each transit and approximately constant brightness between transits. Regularly recurring dips provide evidence that a planet is orbiting the star: the time from one dip to the next gives the planet’s orbital period.

Transit depth and planet size

The fractional depth of a dip is the decrease in brightness divided by the star’s normal brightness. It indicates the fraction of the stellar disc blocked by the planet. A larger planet relative to its star blocks a larger fraction and produces a deeper dip.

If the stellar disc is treated as uniformly bright and the planet is fully in front of it, the relationship is approximately:

Here, $$R_{\text{planet}}$$ and $$R_{\text{star}}$$ are the radii of the planet and star. For example, a dip of approximately $$1%$$ corresponds to a planet radius about one-tenth of the star’s radius.

Transit alignment

A transit is visible only if the planet’s orbit is suitably aligned with our line of sight, so that the planet passes in front of the star from our viewpoint. A planet can orbit a star without producing observable transits if its orbit is not aligned this way.