The Doppler Method and Proxima Centauri

by Hugh R. A. Jones, Centre for Astrophysical Research at University of Hertfordshire

Proxima Centauri is the closest star to the Sun, hence its name. Nonetheless, gravitationally speaking, it belongs to a triple system in which Proxima Centauri orbits a central binary system at a distance of 10 thousand times the Earth–Sun distance. The members of the inner binary are designated as Alpha Centauri A and B. They orbit one another with a distance 20 times that of the Earth–Sun distance. Both Alpha Centauri A and B are rather similar to our Sun. The components of a multiple star system are named by adding uppercase letters to the name of the star. Alpha Centauri A is the brightest component, Alpha Centauri B is the slightly fainter second star and Alpha Centauri C is the much fainter Proxima Centauri. Currently Alpha Centauri A and B are rather close together on the sky and present as the 2nd brightest night-time object in the Southern sky—after Canopus which is a hotter, more distant star. Proxima Centauri was not discovered until 1915 in part because its luminosity is only 0.1% that of the Sun. Despite being next door (astronomically speaking) it was not easily spotted near its brighter neighbours. Naturally people have long speculated the possibilities for the closest possible places for life beyond the Solar System. In 2012 a radial velocity or Doppler wobble search of Alpha Centauri B revealed the signal of an Earth-mass planet in a three day orbit. However, several subsequent studies have analysed exactly the same data and not confirmed the claimed signal. The 2012 discovery depended on a model accounting for the activity of Alpha Centauri B just as one might have to account for the effects of solar rotation, activity and the sunspot cycle if one were interested in detecting the Earth next to the Sun. A number of scientists have been working hard on accounting for the cycles of stellar activity but so far the evidence for an Earth-mass planet around Alpha Centauri B is unconfirmed.

One might ask why we and the 2012 study of Alpha Centauri B use the Doppler wobble technique at all when so many planets have been found by the Kepler space telescope. It is important to realize that detection by Kepler requires that the planet blocks the light from the star so while transit surveys have been hugely successful they can only deliver objects around the small fraction of stars whose alignment happens to give rise to a transit signal. On the other hand Doppler wobble or radial velocity signals can potentially be discerned for all stars with planets, unless they have face-on orbits. In principle, Proxima Centauri presents a better opportunity to search for planets because its mass and radius are only 10% that of Alpha Centauri B. The lower mass of Proxima Centauri means that the same mass planet in orbit could be proportionally easier to spot. Of course this will depend on the details! For our search, we measure the Doppler wobble induced by the planet on its host star through their gravitational pull on each other. In the case of Alpha Centauri B the claimed signal was 51 centimetres per second (1.8 km/hr), about the speed of a baby crawling and corresponding to a mass close to that of the Earth. However, if we found such a signal around the much lighter star Proxima Centauri it would correspond to an even lighter planet.

Example of measurements (in red) overplotted on the expected Doppler signal caused by an exoplanet on the Star. Changes in the velocity of the Sun-like star 51 Peg used by M. Mayor and D. Queloz to infer the presence of a gas-giant planet in a short period orbit around the star.
Example of measurements (in red) overplotted on the expected Doppler signal caused by an exoplanet on the Star. Changes in the velocity of the Sun-like star 51 Peg used by M. Mayor and D. Queloz to infer the presence of a gas-giant planet in a short period orbit around the star.

Previous work on Proxima gives us a constraint that any signals around Proxima will likely be no more than 10 Earth-masses. Proxima Centauri’s mass—of about a tenth that of the Sun—means the mass ratio between Proxima and any planet in orbit will be at least 3000. To put this is context think of the forces on you when you spin an object on a string around your body. In the case of an Olympic hammer thrower the hammer twirls around their gyrating body with the string keeping them together. This analogy with the hammer thrower as the star and the hammer as the planet serves to illustrate that although the planet does most of the moving a star with a planet in orbit around it will be tugged slightly to and fro as the planet orbits, and these subtle movements of the star show up as subtle shifts in the color of the star’s light we see from Earth.

The men’s Olympic hammer throwing event involves a 7.3kg steel ball attached to a wire with a handle. Since the ball is 7.3kg this takes some strength and technique to throw so hammer throwers tend to be fairly large and strong. The force on the hammer thrower from the hammer is quite substantial because the mass of the hammer is high relative to the thrower. When Yuriy Sedykh set his world record for the hammer throw he was some 110 kg—a mass ratio of 15. The substantial force experienced by the athlete is not a particularly close analogy though, since a planet around Proxima Centauri would have a mass ratio of at least 3000. A better analogy needs something with a bit less mass. A golf ball weighing 45g serves as a better analogy but to get a mass ratio of 3000 we need the hammer thrower to be a bit heavier. The average sumo wrestler weighs in at 150kg so an appropriate analogy would be a sumo wrestler whizzing a golf ball around them. Or alternatively the force felt on a toddler (8.1 kg) swinging a ping pong ball (mass 2.7g) around.

Hammer thrower Mike Mai practices at Fort Lewis, July 1. Mai finished third at the U.S. National Championships and will soon compete at the World Track and Field Championships in Berlin, Germany. Image credits : Phil Sussman.
Hammer thrower Mike Mai practices at Fort Lewis, July 1. Mai finished third at the U.S. National Championships and will soon compete at the World Track and Field Championships in Berlin, Germany. Image credits : Phil Sussman.

When we look for the Doppler wobble of stars due to unseen planets we are actually looking to detect the small change in the light that results from the periodic stretching and compressing of the light from Proxima Centauri due to the motion induced on it by the planet. It might also be instructive to think about the Doppler effect in terms of other phenomena one experiences. Listen while a fast car moves past you or stand on the platform while a high speed train whizzes through the station. In these cases it is only possible to perceive these changes in sound when they are moving fast. While a vehicle moving at 100km/h (about 30 m/s) is only moving about ten times faster than Proxima Centauri might be moving, the change that our ears perceive is happening over much less than a second. However, we do not expect a planet in orbit around Proxima Centauri to make the change in period over less than a few days to appear to move from being slightly blue-shifted to slightly red-shifted. If we think in terms of sound waves the frequency ratio between two adjacent notes on a piano is approximately 1.06 which happens to be equivalent to the world record hammer throw ratio . The smallest shift in sound waves we can perceive is approximately 3.6 Hz, which at middle C corresponds to a rather modest ratio of 75. Thus even the smallest changes we can perceive in the frequency of sound are not really close to being representative of the level of effect we are trying to measure.

A star orbited by an exoplanet wobbles around the center of mass of the system as viewed in line with the orbital plane of the system. Image credits : Reyk
A star orbited by an exoplanet wobbles around the center-of-mass of the system as viewed in line with the orbital plane of the system. Image credits : Reyk

We are fortunate that modern technology, along with data handling ingenuity built up by successive generations of astronomers and instrument builders, allows us to reliably measure the frequency or wavelength of light over long periods of time. Rather than gazing into the sky and enjoying the mysterious wonder of all the far away specks of light; if we have access to a telescope and a sensitive digital camera we can collect enough light from the star that we can disperse the light so that rather than looking at a broad range of wavelengths—white light as we perceive it—we seek to measure the subtle changes in light from a star as a function of wavelength. This is equivalent to putting the starlight through a very powerful prism which enables us to split the white light into the full rainbow of colors. In practice this is achieved by putting the star light onto an echelle grating. This is a piece of glass (like a microscope slide) which has hundreds of lines ruled on it per millimetre. This enables the light to be dispersed a lot more than a prism, which in turn enables the resolution of individual atomic species and molecules that undergo particular transitions at precise energies. Since Proxima Centauri is comparatively nearby and space is very empty it can be seen that when a spectrum is taken, the atomic and molecular lines which we see correspond to the expected intensities for Proxima Centauri’s temperature; and move together as it moves relative to us and so we can be sure that our instrument is observing the atmosphere of Proxima Centauri.

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. Image credits : ESO
The radial velocity method to detect exoplanets is based on the detection of variations in the velocity of the central star, due to the changing direction of the gravitational pull from the (unseen) exoplanet as it orbits the star. When the star moves towards us, its spectrum is blue-shifted, while it is red-shifted when it moves away from us. By regularly looking at the spectrum of a star—and by so, measuring its velocity—one can see if it moves periodically due to the influence of a companion. Image credits : ESO

Another key ingredient of many required to precisely record Doppler wobble is a stable reference source for the spectrograph . In the case of our experiment the instrument HARPS (High Accuracy Radial velocity Planet Searcher) has a Thorium Argon lamp as its reference source. A standard light bulb works when a voltage is applied to heat a tungsten filament to glow and emit light. In a reference source lamp the voltages applied are larger so that the electrons in the atoms are ionized. Suitable elements are chosen, which are those that have large number of different energy states. When excited electrons in the atom move between the many possible energy states, they emit photons of light, which can then be detected as a relative forest of emission lines across a broad wavelength range.

On the left, we can see emission lines of a Thorium Argon lamp (extracted from http://tdc-www.harvard.edu/instruments/tres/). On the right a small chunk of the spectrum of Proxima Centauri is shown for comparison (Image credits : G.Anglada-Escude). Sharp features like the ThAr lines and the hundreds of narrow absorption features in Proxima's spectrum are ideal to measure accurate Doppler velocities.
On the left, we can see emission lines of a Thorium Argon lamp (extracted from http://tdc-www.harvard.edu/instruments/tres/). On the right a small chunk of the spectrum of Proxima Centauri is shown for comparison (Image credits : G. Anglada-Escude). Sharp features like the ThAr lines and the hundreds of narrow absorption features in Proxima’s spectrum are ideal to measure accurate Doppler velocities.

The heavy element Thorium and the buffer gas of Argon are the best combination found so far. Whenever we take a spectrum of Proxima Centauri we compare it to the Thorium Argon lamp reference spectrum to determine how much the lines in Proxima Centauri’s spectrum have moved. All the time the temperature and the pressure of the Thorium Argon lamp, and the spectrograph as a whole, are carefully controlled in order that nothing changes. The idea is that nothing in the experimental procedure should be altered from one measurement of Proxima Centauri to the next. This means that we can use the recorded data to infer the motion of Proxima Centauri and thus any Doppler wobble that it has due to any planets in orbit around it.

Hugh R. A. Jones

About the author. Professor Hugh Jones is the Director of Bayfordbury Observatory at the University of Hertfordshire and teaches astrophysics and maths to undergraduates. He is also Director of Research for the University’s Science and Technology Research Institute, one of three multi-disciplinary research facilities in the University. His research is focused on our stellar neighbourhood and has led to the discovery of a number of extra-solar planets using the Doppler wobble method including the first long-period circular one, the 100th discovered and the one with the most eccentric orbit. He received his BSc in Physics from the University of Leeds, followed by an MSc in astrophysics from the University of Alberta in 1990. After working at Blackwell Scientific and setting up an educational electronics company (MadLab) he moved into academia gaining his PhD in astrophysics from the University of Edinburgh in 1995. He then moved to the University of Tokyo as a European Commission research fellow to work with Professor Takashi Tsuji on the model atmospheres of cool dwarf stars working on the inclusion of dust in model atmospheres finding the first empirical evidence for dust in cool dwarf stars. At this time he co-founded the Anglo-Australian Planet Search using the Doppler wobble technique. In 1997, he moved to Liverpool John Moores University and in 2000 a position at the University of Liverpool being closely involved with founding and running a joint Physis degree, a suite of ten online distance learning courses and the the Liverpool Robotic Telescope. He moved to Hertfordshire in 2004, led the Institute of Physics accreditation of the Physics degree and set up the inaugural European Week of Astronomy and Space Science. Hertfordshire is now host to a number of researchers involved in the discovery and characterisation of nearby stars and their companions. The group is unusual in finding planets by a number of different complementary methods and is particularly active in the systematic discovery of the coolest stars including most of the coolest known examples.