Velocimetry

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Velocimetry, which has enabled the detection of most of the known exoplanets, should continue to provide a series of results in future, all the more so, given that the technique has not yet been pushed to its limits. In addition, long-term monitoring of stars is essential to detect long-period planets. There are about ten current instruments or instrumental projects to detect planets by the radial-velocity method (cf. Chap. 2). Although each instrument is based on specific technical choices and consequently achieves different results, there are certain similarities between all the instrumental concepts. Before discussing the principal projects more specifically, let us consider how, in practice, one measures radial velocities.

The radial velocity of an object is measured from the Doppler shift of its spectral lines. These lines are all shifted towards the blue (short wavelengths) when the object is approaching the observer and shifted towards the red (long wavelengths) when it is receding. The formal description of this effect in given in Chap. 2. In practice, the shifts are extremely small, and it is for this reason that it is necessary to have many spectral lines to detect the overall effect on the whole spectrum. This equally supposes that any stellar variability is not too significant, which is why this technique is difficult to apply to hot stars. In the case of the ELODIE instrument at the Observatoire de Haute Provence (OHP), the shift of the lines to be detected is about 0.002 pixel on the CCD.

Measurement of radial velocities therefore implies being able to measure accurately the spectrum of the source and to compare the wavelengths of emission lines and their evolution over time, with a reference spectrum that is believed to be stable and invariant over time. In practice, the instrument capable of this operation is a high-resolution spectrograph (typically with a spectral resolution of several tens of thousands), linked to a spectral reference (Fig. 8.1). The light from the star is captured at the focus of the telescope by an optical fibre, and then sent to the spec-trograph. The latter also receives the flux from the reference source through another optical fibre, such that the spectrum of the star is recorded simultaneously with that from the reference source.

Fig. 8.1 Schematic diagram of a spectrograph for measuring radial velocities (see the main text for a description of the principles involved)

Telescope lamps

Optical fibers

Fig. 8.1 Schematic diagram of a spectrograph for measuring radial velocities (see the main text for a description of the principles involved)

Fig. 8.2 A schematic diagrams of the optics of the ELODIE spectrograph. The spectral dispersion is produced by the diffraction grating, while the orders are superimposed on the CCD by a grism (grating-prism) giving cross dispersion (After Baranne et al., 1996)

To obtain such high spectral resolutions, the spectrograph consists of a diffraction grating and a crossed-dispersion system which allows the various orders from the grating to be superimposed on a CCD. (Sometimes several tens of orders are involved.) A schematic diagram of the principles behind the ELODIE instrument is given in Fig. 8.2.

The reference source is generally one of the two following types:

• a cell containing iodine vapour,

• a thorium-argon spectral lamp.

The spectrum of these two references is shown in Fig. 8.3. These two reference sources are used independently, or sometimes, as with the AFOE spectrograph, simultaneously, to guarantee stability of the reference spectrum in the short term (with the spectral lamp) and in the long term (with the iodine cell).

The advantage of the spectral lamp over the iodine cell is that the emission spectrum covers a wider spectral range.

The level of accuracy required to measure the Doppler shift efficiently in the radial-velocity method requires perfect stabilization of the instrument during the measurement, and the possibility of being able to guarantee effective calibration from one measurement to the next.

In practice, spectrographs dedicated to the measurement of radial velocities are both thermally and mechanically controlled. (The spectrograph is placed in a temperature-controlled enclosure, generally in a vacuum to avoid distortions caused by variations in atmospheric pressure.) One of the keys to stability also lies in the fact that the conditions determining the illumination of the entrance pupil of the

Iodine Spectral Line
Fig. 8.3 Left: reference spectrum of iodine vapour; the structure of the spectrum corresponds to the spectral lines and not to noise. Right: emission spectrum of a thorium-argon lamp

spectrograph should be as stable as possible, and in any case, independent of the telescope's guidance, and of atmospheric turbulence (and thus of the position of the image spot). This stability is obtained by an image scrambler on each of the optical fibres in the instrument (Fig. 8.1).

The highest precision available with current instruments (with the HARPS instrument on ESO's 3.6 m telescope at La Silla) is about 0.8 m.s-1. Stellar noise (movement of the stellar surface) is generally regarded as the ultimate limit of this method. The temporal frequencies at which the effect appears are, however, very different from those at which extrasolar planets are detected. So it is not unreasonable to think that by increasing the stability of spectrographs still further, it may be possible, in the near future, to obtain accuracies of about 10cm.s_1, and thus detect large terrestrial-type exoplanets with this method (cf. Chap. 2). Finally, the size of the telescope itself is involved in evaluating the stability of measurements of the light flux that reaches the spectrograph.

Processing of the spectra is carried out by complex programs which take account of the various perturbing factors, and which subtract the Earth's motions from the radial-velocity measurements (cf. Chap. 6).

Table 8.2 lists the principal spectrographs currently in use or shortly to be commissioned. Each of the teams has drawn up a list of sample stars which it will undertake to monitor for radial velocities. The choice of the sample sets, more-or-less selectively chosen, meet certain criteria (proximity of parent stars to Earth, spectral type, magnitude, metallicity, etc.). It is estimated that several thousands of stars are followed by the different teams. Some stars are included in several samples. We therefore have data from several instruments, all with different limitations, which allows comparisons to be made.

The Keck Exoplanet Tracker (KET) is a new type of instrument, allowing relative radial velocity measurements. Instead of classical high resolution spectroscopy coupled with reference spectrum correlation, the KET is based on a fibre-fed, dispersed, fixed-delay interferometer. This instrument is a wide-angle Michelson interferometer followed by a medium-resolution spectrometer (R = 7000). The interferometer creates an interference pattern within each spectral channel, which allows the measurement of phase shift. With an accuracy of about 20 m/s on 8th magnitude stars, this low-cost instrument is designed for all-sky surveys.

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