The radial velocity method shows a marked preference for shortperiod massive planets

What do we know about other planetary systems? Very little, if we consider individually each of the planets so far discovered. The characteristics deduced using the radial velocities method (the only method that has so far yielded a good number of results) involve three parameters: the period of revolution of the planet (directly linked with the semimajor axis of its orbit, according to Kepler's Law); the ellipticity of the orbit; and the planet's mass, if the inclination of the orbit is known, involving the factor sin i. Under the right circumstances, the number of planets involved in the system may also be deduced. These parameters are decided on the basis of observed variations in velocity, and depend on the mass of the star involved, estimated using spectral type/ luminosity models. As for such a basic parameter as the radius of the planet, this is only known in the case of the objects observed by the transit method. With the available evidence we cannot really step into the realms of speculation about the individual nature of such planets or their composition or climate; but with more than 200 already known, statistical studies become possible, and the global properties of the population of exoplanets can be discussed.

As with any statistical study, we must take into account factors which might introduce bias into our interpretation. Not all planets are detectable. Far from it! Certainly, all observable solar-type stars come under scrutiny - the description 'observable' meaning that they are bright enough and stable enough to be studied using the radial velocity method. In practice this limits the search to stars nearer than 50 parsecs. Within this sample, a planet with a period longer than the time allotted for the search programme may not be detected. Currently, it is just possible to detect a planet of 1 Mj if it is, like Jupiter, at a distance of 5 AU from its star. This would give it an orbital period of 12 years, which is about the duration of searches, the earliest dating from 1995.

As far as planetary masses are concerned, the amplitude K of the perturbations of the star's velocity is directly proportional to the minimum mass of the planet, Mp sin i. Unsurprisingly, high-mass planets are the easiest to detect. Remember that the detection limit of the best instruments is around a few m/s, the goal being to attain 1 m/s. Detection of an 'Earth' would require better than 0.1 m/s. K also depends to a lesser extent on the planet's period of revolution, linked to its mean distance from the star (longer periods being the hardest to detect) and the eccentricity of the orbit. The cumulative effects of these parameters are therefore quite subtle. Lastly, it must be pointed out that the theoretical accuracy of 1 m/s could be achieved only in the case of a star with an absolutely calm atmosphere, without spots or prominences. In reality this is improbable, and care must be taken not to confuse the effects of stellar activity with signs of the presence of a planet.

B.I A very selective method of discovery 41

There is one more adjustment to consider - by no means the least important. What we know is the minimum mass of the exoplanet, since the method underestimates true masses by a factor 1/ sin i. This can be worked in only statistically, and on average the true mass of the planet will be 1.57 times greater than that arrived at through observation.

Limits of detection using the radial velocity method

The radial velocity method is sensitive to perturbations induced in the observed velocity of a star, but in practice the limit of detection of current instruments is of the order of a few m/s. For example, the ELODIE spectrograph attached to the 193-cm telescope at the Haute-Provence Observatory is accurate to 8 m/s. CORALIE, on the Swiss 1 -metre telescope at La Silla, in Chile, is accurate to 5 m/s. The HARPS instrument on the 3.6-m telescope at La Silla reaches a limit of about 1 m/s.

There is also the question of the length of time taken to observe the star. A )upiter-mass planet would induce an effect of 2.8 m/s if it orbited at 100 AU from its star; but it would not be detected, because its orbital period would be 1,000 years. Radial velocity measurements have been undertaken systematically since 1995 - which limits the detection of any planet with an orbital period shorter than 12 years, whatever its mass.

The minimum mass of planets Mp sin i as a function of the semimajor axis of their orbits, a. The amplitude K (in m/s) of the perturbations in the velocity of the star in question is directly proportional to the minimum mass of the planet orbiting it, but it also depends on the planet's orbital period P and the eccentricity e of the orbit, according to the equation:

The minimum mass of planets Mp sin i as a function of the semimajor axis of their orbits, a. The amplitude K (in m/s) of the perturbations in the velocity of the star in question is directly proportional to the minimum mass of the planet orbiting it, but it also depends on the planet's orbital period P and the eccentricity e of the orbit, according to the equation:

K = 28.4 (P/1 year) 1/3 (Mp sin i/Mj) (M. / M0) 2n (1 - e2) V2.

The High Accuracy Radial Velocity Planet Searcher (HARPS) spectrograph. With this instrument, mounted on the 3.6-metre ESO telescope, Michel Mayor's team is reaching an accuracy of 1 m/s in the measurement of radial velocities. Components of great accuracy and unusual size were needed in the construction of HARPS. This photograph -taken during laboratory testing, with the vacuum chamber of the spectrograph open -shows the large optical system which disperses starlight in such a way that its spectrum can be accurately measured. The dimensions of this system are 20 x 80 cm.

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