The fact that this was doable doesn’t surprise me. A spectrometer essentially outputs an intensity as a function of wavelength. The output is a combination of the signal plus a background from the star plus mostly additive noise. The researchers knew what signal they wanted to find, and standard statistical techniques are very good at this.

The data used in this paper came from an instrument called HARPS North. This is an amazing spectrometer. Forget finding a signature from iron — HARPS North can detect a Doppler shift of a bright spectral line or less than 1 cm/s. This lets it detect planets by measuring the degree to which they wiggle their star.

(For an old classic example, there’s a device called a lock-in amplifier that looks for a specific sine wave modulation of a noisy signal. They are extremely sensitive.)