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The minimum size of instruments required for planetary imagery clearly shows that we will have to abandon the idea of monolithic instruments and instead examine the possibility of imaging via interferometry.

The concept of imaging via interferometry is quite old, and several different configurations have been suggested. However, to obtain a field around the target, only the so-called Fizeau form is suitable. It is, nevertheless, very difficult to implement because it requires an optical system that guarantees homothetic mapping of the entry pupil to the exit pupil, and the accuracy of which increases as the spatial resolution increases (i.e., as the number of pixels in the image increases). If this homothetic mapping is not attained, the field is limited to the target direction (the centre of the image).

In addition, if we consider the baselines required to image planets (several 100 km), we are faced with the necessity of using small-sized telescopes (a few metres in diameter), separated by great distances (unless we use a large number of telescopes). As a result, if we want to preserve the homothetic mapping between the instrument's entry and exit pupils, the image will be very poor, and not capable of being exploited in terms of spatial frequencies. (Coverage of spatial frequencies is given by the pupil's autocorrelation function, which introduces many gaps in the frequency space if we use small telescopes separated by large distances) In other words, the image will be of very poor quality because it will contain few spatial frequencies.

An elegant solution for obtaining very-high-spatial-resolution imagery has been suggested by Labeyrie (1996), and this consists of combining the imaging capabilities of classic telescopes with the angular resolution given by interferometers. This concept, which has been called a 'hypertelescope' (Fig. 2.28), consists of several small telescopes that lie on the fictional mirror of a larger telescope (like Fizeau interferometers). An arrangement called a 'densified pupil' enables the frequency

Fig. 2.28 A diagrammatic representation of the principle of a hypertelescope. Several small telescopes synthesize a larger aperture (shown schematically by a single lens). The intermediate image (FF) lacks spatial frequencies because the pupil is only weakly sampled. The densified-pupil combiner (Li + GT + L2) enables a PSF to be attained that is comparable to that of a monolithic telescope with a size equal to the sum of those of the small telescopes. This gain is at the expense of the field that is covered. A compromise must be made between field size and frequency coverage (After Labeyrie, 1996)

Fig. 2.28 A diagrammatic representation of the principle of a hypertelescope. Several small telescopes synthesize a larger aperture (shown schematically by a single lens). The intermediate image (FF) lacks spatial frequencies because the pupil is only weakly sampled. The densified-pupil combiner (Li + GT + L2) enables a PSF to be attained that is comparable to that of a monolithic telescope with a size equal to the sum of those of the small telescopes. This gain is at the expense of the field that is covered. A compromise must be made between field size and frequency coverage (After Labeyrie, 1996)

coverage to be increased by assuming an equivalence between the sub-pupils of the hypertelescope's entry pupil. Admittedly, one then loses the homothetic mapping of the pupil (and thus reduces the field observed), but the whole interest in this arrangement is to find the best compromise between field and frequency coverage. The other special feature of hypertelescopes is that the (virtual) primary mirror that is covered with the small, individual telescopes is spherical. (The reason being that it simplifies the problem.) An optical corrector (a Mertz corrector) is then used to re-establish a stigmatic configuration at infinity, and to restore a large field.

The hypertelescope concept is currently being investigated. The Carlina project (see Chap. 8) should, in a few years' time, allow it to be validated and allow the first actual instruments to be defined, with initial baselines of a few hundred metres. The extension of this concept to baselines measured in kilometres or even more, and particularly within the framework of a space-borne implementation, will need to be accompanied by complementary efforts into positioning in precise formation. A hypertelescope in space, with long baselines, cannot be designed as a rigid structure. The sampling telescopes will therefore need to be autonomous in operation and positioning. The overall instrument will need to be maintained in a precise position, most especially when being aimed at a target, and during the observation. Several studies are under way, most notably within the framework of the DARWIN project (a dark-fringe interferometer), to validate ideas about formation positioning. Be that as it may, imaging the surface of a terrestrial-like exoplanet remains an extremely difficult task, which will require several generations of instruments before it becomes a reality. Intermediate stages will be necessary, such as imaging a whole planetary system. Luckily, it is not necessary to image the surface of a planet to obtain spectroscopic information about the planet itself, and thus be able to study it. This less sensitive method will therefore be favoured initially.

2.3.5 Detection by Radio

The problem of direct detection of exoplanets is generally described in terms of contrast and angular separation. This is, after all, the way in which we have initially attacked the subject. There is one spectral region where the contrast between the stellar flux and the planetary flux may be very low: this is a radio wavelengths, in particular at decametric wavelengths. In fact, planets with magnetic fields produce non-thermal auroral emissions (i.e., interactions between charged particles and the magnetic field in the polar regions as in the aurorae that occur on Earth). The intensity of these emissions is comparable, at these frequencies, with the emission from the star itself. The auroral emissions are very specific (Zarka et al., 1997):

• they have a typical duration of 30-300 ms on the planets in our Solar System,

• their frequency spectrum is relatively uniform and broad (from less than 20 kHz to more than 40 MHz), with a typical spectral power that lies between 0.1 and 100 W Hz-1, corresponding to a flux density that varies between 0.4 and 400 Jy.7

Detecting auroral emission from the Solar System's planets or from exoplanets is, however, rather tricky because of the presence of two main sources of parasitic signals:

• fluctuations in the sky background, of galactic origin, which have a very high brightness temperature (30 000-50 000 K at 25 MHz)

• parasitic signals of terrestrial (and human) origin. Such signals have the characteristic of being limited to relatively narrow frequency bands; and this obviously depends on the properties of the transmitter. Take, for example, CB8 signals, which completely saturate a frequency band around 27 MHz. On the other hand, the bands allotted to these emissions are numerous, spread out, and constantly being developed (Denis and Zarka, 1996).

In addition, at these wavelengths, the angular resolution is very low: the antenna's lobe is relatively broad (about 1° for an antenna 1 km in diameter, so the signals from both the star and the planet are detected simultaneously within the lobe). This breadth tends to increase the contribution of the galactic background in the signal that is detected. It is interesting to note that in this case it is not the noise in the detection chain that limits the sensitivity of the method, but the galactic contribution and any parasitic signals. Any detector, for example, can work at ambient temperatures.

Radio astronomers have suggested an observational strategy appropriate to these signals, and its specific features are as follows (Zarka et al., 1997):

• a receiving surface with a large area, so that the angular size of the antenna's lobe is reduced. In practice, the UTR-2 array at the Radio Astronomy Institute at Kharkov (Ukraine), which is currently the largest, and which is being used pending the commissioning of the future LOFAR (LOw Frequency ARray) and SKA (Square Kilometric Array) systems. The north-south arm of UTR-2 has an effective area of about 50 000 m2;

• the use of an acousto-optic spectrograph, which would enable time-frequency diagrams to be obtained with a temporal resolution (integration time) of about 250 ms, and spectral resolution of a few dozen kHz. The short duration of auroral emissions forbids the use of long integration times, because these would distinctly increase the contributions from parasitic signals and from the galactic background in every sample. It appears more sensible to integrate for short periods with durations that are comparable with those of the emission, and to eliminate empty samples so that only samples containing a signal are retained for integration;

8 Radio transmitting equipment, generally employed on vehicles. The development of mobile telephony (in a higher frequency region), however, is tending to marginalize their use, which appears to be restricted to professional drivers.

• handling the data with thorough observational and computational procedures, designed to eliminate parasitic signals (Zarka et al., 1997). In crude terms, this means detecting signals of terrestrial origin by observing two neighbouring areas of the sky, one on axis (and thus containing the astrophysical target), and the other off-axis. This technique may be used at Kharkov because the array's set of delay lines enables the array to be pointed in two different directions with an angular separation of 1°, and observations carried out in both lobes simultaneously.

Given the level of the background and parasitic signals, and using the method just described, it may be shown that, using UTR-2, it would be possible to detect Jupiter at about 0.2 parsec. This is, unfortunately, insufficient to even offer the hope of detecting extrasolar planets (remember that the star closest to the Sun, Proxima Centauri, lies at a distance of about 1.3 parsecs). On the other hand, Zarka has also shown that, in the case of giant planets close to their parent star (i.e., hot Jupiters), one could expect a mechanism that generated radio emission 103-105 times as strong as that produced by Jupiter. Under such circumstances, we could hope to detect emissions out to about 20-25 parsecs, which makes the method distinctly more attractive.

A series of observations has been made with UTR-2, but the complex processing to which the data are subject means that, to date, no candidates have yet been identified. When the SKA array is commissioned, it should increase the sensitivity of the method by reducing the size of the antenna's lobe and, as a result, the level of the galactic background.

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