What Is Radial Velocity? Measuring Motion Along the Line of Sight

Light from a star contains dark lines at specific wavelengths where atoms in its atmosphere absorb particular colours, and the wavelengths of those lines are known precisely from laboratory measurement. If the star is moving towards the observer the lines appear at shorter wavelengths and if it is moving away they appear at longer ones, by an amount proportional to the speed, which is the same effect that changes the pitch of a passing siren. Comparing the observed wavelengths with the laboratory values therefore gives the velocity along the line of sight directly. The great advantage is that the result does not depend on distance at all, since the shift is the same whether the star is near or far, which makes this one of the few astronomical quantities that can be measured without first solving the much harder problem of how far away something is.

The technique underlies a substantial portion of what is known about the universe:

• •The rotation of the galaxy, measured by the differing velocities of stars at different distances from the centre
• •The evidence for dark matter, since galaxies rotate faster at their edges than their visible mass allows
• •Binary stars, identified by lines shifting back and forth as two stars orbit each other
• •Stellar masses, since the orbital motion of a pair gives the masses directly
• •The expansion of the universe, from the systematic recession of distant galaxies
• •Planets around other stars, detected by the tiny wobble a planet imposes on its star

A star with a planet does not sit still, since both orbit their common centre of mass, so the star traces a small orbit of its own and its velocity along the line of sight varies periodically. Detecting that requires extraordinary precision, since a planet the mass of Jupiter moves a star like the sun at around twelve metres per second and an Earth-mass planet at around ten centimetres per second, against a star whose surface is turbulent and whose light travels for years. The first confirmed detection around an ordinary star, in 1995, used this method and found a giant planet orbiting extremely close to its star, which was not what anyone expected and forced substantial revision of theories about how planetary systems form. The method favours massive planets in close orbits, which is why the early catalogue was dominated by them, and that bias had to be corrected for before any conclusion about how common planets are.

Reaching the sensitivity needed for planet detection demanded instrumental developments that are interesting in their own right. Ordinary spectrographs drift as temperature and pressure change, which swamps a signal of a few metres per second, so the instruments are held in vacuum chambers at stabilised temperature and are calibrated against a reference light source recorded simultaneously with the star. Early work used a cell of iodine gas placed in the beam, imprinting a dense forest of known lines on the spectrum against which any shift could be measured. Later instruments use lamps with rich line spectra and, most recently, laser combs producing precisely spaced reference lines across the whole range. Each advance lowered the detectable signal by roughly an order of magnitude, and the limit is now set by the stars themselves rather than by the equipment, which is an unusual and satisfying place for a measurement technique to arrive.

The measurement is powerful and partial, and knowing the limits matters. It gives only the component of motion along the line of sight, so a star moving across the sky at any speed registers nothing, and obtaining the full three-dimensional motion requires combining it with a separate and much harder measurement of apparent movement across the sky. For planets it yields a minimum mass rather than a mass, since the shift depends on the tilt of the orbit and an orbit seen nearly face on produces almost no signal, so every mass from this method alone is a lower bound. It cannot give the size of a planet, which requires watching one pass in front of its star. And it is limited by the star itself, since surface activity produces velocity signals that mimic planets and has caused several claimed detections to be withdrawn.

Absorption lines shift to shorter or longer wavelengths depending on motion towards or away, and the shift gives speed directly without needing to know the distance. The method measured galactic rotation, revealed dark matter, weighed binary stars and found the first planet around an ordinary star. It gives only motion along the line of sight, and planet masses from it are lower bounds because the orbital tilt is unknown.