by Ludwig Scheibe (TU Berlin), September 2024
Because the direct imaging of planets around other stars is only feasible in select cases, the question arises: How, then, can we detect and study planets around other stars if we can’t see them? We need indirect methods to find them, and both the first successful method and one of the most common ones is radial velocity measurement, also known as the Doppler method.
Looking for the wobble
When a planet orbits a central star, that star does not stay perfectly motionless. What actually happens is that both planet and star orbit around a common center of mass. To illustrate this effect, imagine a hammer thrower spinning around. The athlete’s body does not just stay upright, but revolves around a point just outside it. Since the star is much, much heavier than the planet, the common center of mass is inside the star’s volume in most cases or just outside its surface.
So, the planet causes a periodic oscillation (“wobble”) in its host star. If we observe the system close to edge-on, the induced movement means that the star alternately moves away from us as observers and towards us. This is the movement we measure with this method. Because we measure the star’s movement along the line that connects us and it, so along the radius of our imagined “sky sphere”, we call this its radial velocity.
Star and planet orbit a common center of mass, where the star is always opposite the planet. So, as the planet moves away from us, the star moves towards us (upper panel) and vice versa (lower panel). Below the orbit configurations are the red- and blue-shift we use to measure it (see next paragraph). Credit: ESA
So how do we go about measuring it? When light is emitted from a light source moving towards oraway from us, we can measure a so-called Doppler-shift. Light from a source that moves towards us is “blue-shifted”, that means it is slightly shifted towards smaller wavelengths. Conversely, if a light source moves away from us, the radiation is red-shifted, i.e. shifted towards longer wavelengths.
Animated illustration of the radial velocity method. Upper left: top-down view of the planet and star, showing their orbit around the common center of mass. Lower left: edge-on view of the same system, from the point of view of the observer. Upper right: Change in the radial velocity of the star, i.e. its movement towards us or away from us. Lower right: Shift of the lines in a star’s spectrum towards shorter (bluer) and longer (redder) wavelengths. Credit: Alysa Obertas via Wikimedia Commons
So in the case of our star which moves periodically towards and away from us due to a planet, its light is alternately red- and blue-shifted. We can detect that by measuring the star’s spectrum, which has a large number of distinctive lines – see here for an introduction in spectroscopy.
If the lines shift periodically, we can conclude that the star performs the “wobble” we described here, and thus we can conclude the existence of a planet. Note that these line shifts are too small to see with the naked eye. They are even too small to measure on an individual line. Only by measuring the changes in thousands of lines can we actually calculate the radial velocity shift.
The first exoplanet orbiting a Sun-like star – discovered with the radial velocity method
Michel Mayor and Didier Queloz discovered the first exoplanet in 1995 using the radial velocity method (Mayor & Queloz 1995). Pegasi 51 b, also called “Dimidium”, is a hot Jupiter and orbits the Sun-like star Helvetios in the constellation Pegasus.
Artist’s impression of the hot Jupiter exoplanet 51 Pegasi b, sometimes called Dimidium or Bellerophon. It orbits a star about 50 light-years from Earth in the constellation of Pegasus. In 1995, this was the first exoplanet to be found around a sun-like star. Credit: ESO/M. Kornmesser/Nick Risinger
The Geneva research team received a Nobel Prize in 2019 for this discovery.
Swiss astronomers Didier Queloz and Michel Mayor in front of ESO’s 3.6-metre telescope at La Silla Observatory in Chile, which contains HARPS, ESPRESSO’s predecessor as the world’s premier radial velocity instrument. For their discovery, they were awarded the 2019 Nobel Prize in physics. Credit: L. Weinstein/Ciel et Espace Photos via ESO
More on the winding road humanity took to this point can be found here.
Interesting questions on the topic:
How can we measure the periodic motion of the star?
Through the so-called Doppler effect, the periodic motion of the star causes a recurring shift of the stellar spectrum to longer, red wavelengths when it is moving away from us, or to shorter, blue wavelengths when it is moving towards us.
The radial velocity method to detect exoplanet is based on the detection of variations in the velocity of the central star, due to the changing direction of the gravitational pull from an (unseen) exoplanet as it orbits the star. When the star moves towards us, its spectrum is blueshifted, while it is redshifted when it moves away from us. By regularly looking at the spectrum of a star – and so, measure its velocity – one can see if it moves periodically due to the influence of a companion.
What type of telescope is used to perform the radial velocity method?
The measurements are done with extremely high-precision spectrometers attached to large ground-based telescopes. An example is the ESPRESSO spectrometer at the Very Large Telescope in Chile
What can we learn about the planet via the radial velocity method?
We can learn the mass of the planet. How strong the star’s motion induced by the planet is, depends on the masses of both objects. So, if we have the mass of the star, we can calculate the mass of the planet from the Doppler measurement. However, this only works if we know the inclination of the planet, i.e. the angle of its orbit around the star. This parameter can not be obtained from a pure radial velocity measurement, so we only get a lower limit for the planet mass. However, an additional observation of the planet with the transit method will help to determine the inclination and thus makes the mass determination possible.
Additionally, the time it takes for the star to go through one cycle of red- and blue-shifted light directly gives us the planet’s orbital period.
Which planets are particularly suitable for the radial velocity method?
- The more massive a planet, the more it influences its central star and the easier it is for us to measure the variations. Therefore, for example, Jupiter-sized planets (300 times heavier than Earth) are easier to detect than Earth-sized ones.
- A star is more strongly influenced the lighter it is, so the method favors planets in orbit around small, light stars like M dwarfs.
- Finally, the fluctuations in the stars radial velocity can more easily be shown to be a periodic occurrence caused by a planet, if you have a lot of planetary orbits recorded. Thus, it is easier to find planets that have a very short orbital period and are therefore close to their star.
Recommended book on the topic:
Radial-velocity Searches for Planets Around Active Stars
Raphaëlle D. Haywood
Publisher: Springer Verlag
ISBN: 978-3-319-41273-3
Find more books to the topic exoplanets and astronomy for children, amateurs and scientists in our booklist.
