Radial Velocity (Doppler) Method

A star doesn't sit perfectly still while its planet orbits around it — the planet tugs back, and the star traces out a small wobble of its own. That wobble is far too small to see directly, but it leaves an unmistakable trace in the star's spectrum, and reading that trace is the second great technique for finding worlds around other stars.

The star isn't really stationary

It's tempting to picture a planet orbiting a perfectly fixed, stationary star, the way diagrams usually draw it. In reality, gravity is mutual: the planet pulls on the star exactly as hard as the star pulls on the planet (Newton's third law), so both bodies orbit their common centre of mass, not the centre of the star. Because the star is so much more massive than any planet orbiting it, its orbit around the shared centre of mass is tiny — a gentle back-and-forth wobble rather than a dramatic loop — but it is not zero.

This wobble means the star's velocity relative to Earth is not constant: over the course of one planetary orbit, the star alternately moves very slightly toward Earth and very slightly away from it, tracing out a small periodic variation in its radial velocity — the component of its velocity directly along our line of sight. It is this line-of-sight component, and only this component, that produces a Doppler shift; sideways motion across the sky does not.

Reading the wobble in the star's spectrum

A star's light contains sharp absorption or emission lines at specific, well-known wavelengths, produced by the elements in its outer layers. As covered in the earlier lesson on the Doppler effect and redshift, motion of a source along the line of sight shifts the observed wavelength of these lines: motion away from the observer stretches the light to longer wavelengths (redshift), and motion toward the observer compresses it to shorter wavelengths (blueshift). The fractional shift is related to the line-of-sight speed $v$ by the same relation used there:

As the star wobbles toward and away from Earth once per orbit, its spectral lines shift back and forth, cyclically, between very slightly redshifted and very slightly blueshifted, then back again. Monitoring a star's spectrum repeatedly over time and tracking the position of a known absorption line reveals this oscillation directly. Two things fall out of it:

• Orbital period. The time for one complete cycle of the wobble — from maximum redshift, through no shift, to maximum blueshift, and back — is simply the planet's orbital period.
• Planet mass (or a lower bound on it). The size of the star's wobble depends on how strongly the planet tugs on it, which depends on the planet's mass. Combining the measured wobble speed with the orbital period and some orbital mechanics allows the planet's mass to be estimated. Because the method is most sensitive to the line-of-sight component of the star's motion, an orbit seen close to edge-on gives the full wobble speed, while a system viewed at a shallower angle gives only a smaller, foreshortened line-of-sight component — so on its own the method usually yields a minimum mass, rather than pinning the mass down exactly. This dependence on orbital alignment is real, but noticeably less restrictive than the transit method's requirement, since even a partially inclined orbit still produces a detectable, if reduced, radial velocity signal.

Why the earliest discoveries were "hot Jupiters"

Because the radial velocity method's sensitivity depends on the size of the stellar wobble it produces, it favours planets that are massive (a bigger gravitational tug on the star) and orbiting close to their star (a faster orbit, producing a larger and more rapidly repeating wobble). A large planet in a distant, slow orbit produces only a tiny, slowly-changing wobble that is far harder to detect against the practical noise floor of the measurement.

This selection effect explains why many of the first exoplanets ever confirmed were so-called hot Jupiters: gas-giant planets, comparable in mass to Jupiter or larger, orbiting extremely close to their star with orbital periods of just a few days. These are not necessarily the most common type of planet in the galaxy — they are simply the type this particular detection method finds most easily. Recognising a method's detection bias like this is essential when interpreting what its results do, and don't, say about the true population of planets out there.