Radial velocities

The first exoplanet detected around a Sun-like star was found using an indirect method: the radial velocities ? method. This finding was made at the Haute-Provence Observatory, using the Elodie spectrograph by the Swiss astronomers Michel Mayor and Dider Queloz around star 51 Peg b, which is the 51st brightest star in the constellation of Pegasus.

 

Evolution of the radial velocity ?  of star 51 Pegasi, due to the presence of planet 51 Pegasi b
(Michel Mayor & Didier Queloz, Nature, 1995)

The history curve above presents the evolution of the radial velocity ?  of 51 Peg as presented by Mayor & Queloz in Nature review in 1995. The time here is given for one period of revolution of the star and the planet (see drawing below).

The radial velocity ? $R_V$ is the projection of the star’s velocity vector on the “line of sight” between the star and the observer. This curve shows the period of revolution of the planet and the product of the mass of the planet, $M_{\text{pla}} \text{ by } \sin\left({i}\right)$ where $i$ is the angle between the planet’s orbital plane and the reference plane of the sky.

Radial Velocity ?
(Emmanuel Précontal)

In this animation, we can see:

  • Left: the star and the planet, which orbit around their centre of gravity, are observed with a telescope?. To simplify, the orbital plane here is perpendicular to the reference plane of the sky
    ($i=90^{\circ} \text{ et } \sin\left({i}\right)=1$).
  • Bottom right: the light from the star, scattered by spectrograph. The spectral lines ? (here there are 4, in reality there are thousands) shift alternately to the red and to the blue as the star moves away from and comes closer to the observer. By comparing the wavelength of the lines observed in the star’s spectrum with the position of these same lines measured in the laboratory (blue lines), we can calculate the radial velocity ? of the star as its moves away/comes closer.
  • Top right: the curve represents the radial velocity ? of the star. It is a sinewave. When the planet’s orbit is elliptical, the sinewave is deformed. The amplitude of this curve and the period can be used to calculate $M_{\text{pla}} \times \sin\left({i}\right)$

When the orbital plane is in the reference plane of the sky, the radial velocity ? is nil, and this method cannot be used to measure the mass of the star.

If the star is observed using only the radial velocities ? method, the value of i cannot be found. We only have access to value of $M_{\text{pla}} \times \sin\left({i}\right)$ and thus to a lower-bound value for the mass of the planet.

So far 15/10/2026 this method has been able to discover

objects.

Advantages:

  • Gives a lower-bound value for the mass of the planet.
  • Can be used to study planets close to their star.
  • Enables telluric planets to be detected.

Drawbacks:

  • The mass is known to within a factor $\sin\left({i}\right)$ (depending on the inclination).
  • Cannot be used to detect planets far from their star with a period that is too long.
  • Requires very high-precision spectra, therefore very bright stars.