The Doppler effect to the rescue

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Let us return to the exoplanets which interest us most: those orbiting stars in the vicinity of the Sun. The negative conclusion of the work on Barnard's Star dashed the hopes of classical astronomy that sufficiently accurate measurement of tiny oscillations in central stars might be possible. However, in the 1990s another method came into its own: velocimetry.

How does this technique work? The procedure is based on measuring very accurately the radial velocity of the star (its velocity vis-à-vis the observer) as a function of time, in order to identify any periodic movement of the star around the common centre of gravity of the star and its planet. The movement of the companion cannot be measured, as it is not bright enough to be detectable. The method can be used if the orbit of the planet to be detected is not perpendicular

2.5 The key to success: velocimetry 23

The Doppler effect

Virgo distance fron» Earth PB.lfl6 i.y.

Corona Borealis distance from Earth 1,4.109 I.y.

Hydra distance from Earth 4.U0q I.y

H and K spectral lines of calcium

H and K spectral lines of calcium velocity of recession Í 200 km.s-1 \

velocity of recession Í 200 km.s-1 \

Corona Borealis distance from Earth 1,4.109 I.y.

velocity of recession 21 EDO km.s 1 \

velocity of recession 21 EDO km.s 1 \

velocity of recession 61 200 km.s velocity of recession 61 200 km.s source at rest source receding approaching

• m/wvg sample spectral line

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The principle of the Doppler effect. If an object moves relative to the observer, the spectral lines are shifted from their initial rest position: towards the red in the case of a receding object, and towards the blue in the case of an approaching object. By using large numbers of known lines, accuracy to within a few m/s can be achieved.

Light from approaching astronomical sources is shifted towards the blue end of the spectrum, and light from receding sources is shifted towards the red. in observing that all distant galaxies seem to be moving away from us, astronomers use this as evidence of the expansion of the Universe. Here on Earth it is easy to experience the Doppler effect by listening to the sound emitted by a passing vehicle such as a motorcycle or ambulance. The sound appears to be higher in piLch as the vehicle approaches, and lower as it recedes. The frequency of the sound waves is therefore lower as the vehicle recedes, implying that the wavelength is greater (frequency has an inverse relationship to wavelength). Light-waves behave in the same way: the wavelengths of the light from a receding object appears lengthened (redshifted), compared with that from an object at rest.

to the line of sight from the observer to the star. If it is, the radial velocity of the star is zero. It is worth mentioning that this infrequent case is favourable for astrometry. It remains only to measure the radial velocity of the star with sufficient accuracy. The rate of the periodic movement of the Sun due to the presence of Jupiter is 12.5 m/s. If we wish to find an exojupiter we will need to measure velocities to an accuracy better than a few metres per second, requiring high-resolution spectroscopy in the visible region. We know that if a luminous body is moving relative to an observer, the lines in its spectrum appear to be shifted towards the red end if it is receding, and towards the blue end if it is approaching. This is the Doppler effect. Stellar spectra exhibit a great number of well-known spectral lines, and their Doppler displacement can be accurately measured. If many lines are studied, accuracy can be increased to reveal movements of a few metres per second only.

In addition to accuracy we must include consistency over a long period. If another 'Jupiter' is to be found in some distant system, the search will take 12 years as the planet pursues its full orbit, causing one complete oscillation of that star. Only patient astronomers need apply.

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