3.4.1. The Emission Mechanism
 Similarly to Jupiter's magnetospheric radio emission described in the previous section, all magnetized planets of the solar system emit radio waves from their magnetospheres [e.g., Zarka, 1998]. The emission is caused by a Cyclotron Maser Instability, which leads to radio waves with a frequency close to the local gyrofrequency. Thus, the maximum emission frequency fmax is given by
where me and e are the electron mass and charge, and BPmax is the maximum magnetic field strength close to the polar cloud tops. Because the other planets of the solar system have magnetic field strengths much lower than Jupiter, their maximum emission frequency is below the terrestrial ionospheric cutoff (∼10 MHz), which makes their emission unobservable from the ground. This is even true for the Earth's auroral kilometric radiation, which can usually only be observed using satellites.
 For a certain class of extrasolar planets (the so-called “Hot Jupiters”), an analogous, but much more intense radio emission is expected. When either the planet or the star has a sufficiently strong magnetic field,equation (1) shows that the maximum emission frequency is above the terrestrial ionospheric cutoff, and the emission is potentially observable from the ground.
3.4.2. Recent Studies
 In the last few years, the field of exoplanetary radio emission has become an active field of research, with a number of both theoretical studies and observation attempts. The theoretical studies are important not only because they indicate that the anticipated radio flux is strong enough to allow ground-based detection, but they also serve to guide the observation programs and select the most promising targets. A few recent results should be mentioned here:
 2. Because the stellar wind parameters strongly depend on the stellar age, the expected radio flux is a function of the age of the exoplanetary host star [Stevens, 2005; Grießmeier et al., 2005]. The radio flux of a planet around a young star may be orders of magnitude higher than for a planet in an older system.
 3. For the same reason, the uncertainty on the estimated radio flux at Earth is dominated by the uncertainty in the stellar age [Grießmeier et al., 2007a], which is usually considerable.
 4. For a small, but nonzero number of planets the plasma frequency in the stellar wind is expected to be of the same order of magnitude as the maximum emission frequency. In these cases, escape of the radio emission from its source toward the observer may not be possible [Grießmeier et al., 2007b].
 5. Even a purely planetary signal will be partially modulated by the stellar rotation period [Fares et al., 2010]. This will complicate the discrimination between a stellar and a planetary radio signal.
 6. Not only planets hosted by main sequence stars are interesting targets. More “exotic” environments have been studied, including terrestrial planets around white dwarfs [Willes and Wu, 2005], planets around evolved cool stars [Ignace et al., 2010], and planets around T Tauri stars [Vidotto et al., 2010]. Interstellar rogue planets (i.e., planets not bound to a star) were studied by Vanhamäki .
 8. The planetary magnetic moment is an ill-constrained, yet important quantity for estimating exoplanetary radio flux. Different theoretical arguments have led to two main approaches:Farrell et al.  and Grießmeier et al.  assume the planetary magnetic moment can be calculated by a force balance, and find a planetary magnetic field which depends on the planetary rotation rate. On the other hand, Reiners and Christensen  assume the planetary magnetic moment to be primarily driven by the energy flux from the planetary core. Thus, they find no dependence on the planetary rotation rate; however, they obtain stronger magnetic fields and more favorable observing conditions for young planets. Planetary radio observations may be one way to discriminate between these models.
 9. Most models favor close-in planets, especially “Hot Jupiters” [see, e.g.,Zarka, 2007; Grießmeier et al., 2007b]. However, rapidly rotating planets with strong internal plasma sources can also produce radio emission at detectable levels at orbital distances of several AU from their host star [Nichols, 2011].
 10. Hess and Zarka recently performed simulations to study how physical information on the star-planet system can be extracted from radio observations. In particular, they show that the interaction mode (i.e., exoplanet-induced stellar emission versus planetary radio emission) and the orbital inclination can be obtained through repeated radio observations.
 In addition to those theoretical studies, a number of observation attempts were carried out. Maybe surprisingly, the first attempts at observation of exoplanetary radio emission go back at least to Yantis et al. . At the beginning, such observations were necessarily unguided ones, as exoplanets had not yet been discovered. Later observation campaigns concentrated on known exoplanetary systems. While up to now no detection has been achieved, studies are ongoing or planned at the VLA, GMRT, with UTR-2 and with LOFAR.
3.4.3. Radio Predictions
 The first predictive studies [e.g., Zarka et al., 1997; Farrell et al., 1999] concentrated on only a few exoplanets. Comparative studies of expected exoplanetary radio emission from a large number of planets were performed by Lazio et al. , who compared expected radio fluxes of 118 planets (i.e., those known as of 2003, July 1) and by Grießmeier et al. [2007b], who examined 197 exoplanets (i.e., those known as of 2007, January 13). As the number of planetary detections has continued to grow rapidly over the last four years, it is worth while to update these predictions.
 In this section, we update and extend the analysis of Grießmeier et al. [2007b], including all currently known extrasolar planets (i.e., 547 planets as of 2011, April 28, taken from http://exoplanet.eu/). The results are shown in Figure 1. Rather than showing three different models separately (as was done by Grießmeier et al. [2007b]), we combine the results of the magnetic energy model, the kinetic energy model and the CME model in one graph, showing the maximum radio flux that can be expected from each planet (denoted by open triangles). The typical uncertainties within these models (approximately one order of magnitude for the flux density, and a factor of 2–3 for the maximum emission frequency [see Grießmeier et al., 2007a]) are indicated by the arrows in the upper right corner. For comparison, we show the expected sensitivity of different detectors (for 1 hour integration and 4 MHz bandwidth, or any equivalent combination): The upgraded UTR-2 is represented by the lower dashed line, the NDA is shown by the upper dashed line, the VLA corresponds to the upper solid square, the WSRT is shown as a fine dotted line, the GMRT is indicated by the lower solid square, and two solid lines are used for the low band and high band of LOFAR, respectively. For a given instrument, a planet is observable if it is located either above the instrument's symbol or above and to its right.Figure 1shows that up to eight of the currently known planets should be observable by the upgraded UTR-2. For LOFAR, the number of potential targets is approximately twelve. Considering the uncertainties of the estimate, these numbers should not be taken literally, but should be seen as an indicator that while observation seem feasible, the observed targets must be selected carefully. It can be seen that the maximum emission frequency of many planets lies below the ionospheric cutoff frequency, making ground-based observation of these planets impossible. Interestingly, the number of potential targets has approximately increased by the same ratio as the number of known planets when compared toGrießmeier et al. [2007b]. This may indicate that more good targets can be expected to join this list in the future.
Figure 1. Maximum emission frequency and expected radio flux for known extrasolar planets for a rotation-dependent planetary magnetic field (adapted and updated from Grießmeier et al. [2007b]). Open triangles, predictions for planets. For comparison, the approximate sensitivity of the arrays described in the text is shown (for 1 h of integration time and a bandwidth of 4 MHz, or an equivalent combination): the upgraded UTR-2 (lower dashed line), the NDA (upper dashed line), the VLA (upper solid square), the WSRT (fine dotted line), the GMRT (lower solid square), LOFAR (two dash-dotted lines, one for the low band and one for the high band antenna). Frequencies below 10 MHz are not observable from the ground (ionospheric cutoff).
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 It has been mentioned above that the planetary magnetic field plays an important role, especially for the maximum emission frequency. In particular, close-in exoplanets, which receive the highest amount of energy by their host star and are thus believed to have the strongest radio emission, are tidally locked [Grießmeier et al., 2007b]. For Figure 1, the corresponding slow planetary rotation was assumed to lead to a small planetary magnetic moment, and thus a low maximum emission frequency (in many cases below 10 MHz, and thus unobservable). If however, as Reiners and Christensen suggest, planetary rotation has little influence on the planetary magnetic field then a different picture arises: Close-in planets still have a high radio flux density, but their emission frequency is higher, bringing it above the threshold of ground-based detectability. As shown inFigure 2, this leads to a considerably higher number of potentially observable planets (over 20 for both UTR-2 and LOFAR). Note, however, that we do not account for the age-dependence of the planetary magnetic moment considered byReiners and Christensen .
Figure 2. Maximum emission frequency and expected radio flux for known extrasolar planets for a rotation-independent planetary magnetic field. All lines and symbols are as defined in Figure 1.
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 The different approaches of Figures 1 and 2 are also reflected in Table 2, which shows the best candidates for ground-based radio observations of exoplanets. The second and third column contain the maximum emission frequency and the maximum expected radio flux density at Earth for the case of a rotation-independent planetary magnetic moment. Columns four and five contain the same numbers for the case where the planetary magnetic moment strongly depends on the planetary rotation. The table is sorted by decreasing values in column three. When the maximum emission frequency lies below 10 MHz, the numbers are shown in brackets, as an Earth-based observation is not possible. It can be seen that the model without rotational influence systematically has a considerable higher emission frequencyfc, but that the flux Φ is slightly reduced. This results from the fact that fc and Φ have a very different dependency on the planetary magnetic moment : In a simple approximation [e.g., Grießmeier et al., 2005, equations (9) and (12)], one finds Φ ∝ −1/3, whereas fc ∝ . All good candidates being close-in planets, they are all tidally locked and rotate slowly, which explains the large differences between both models. In particular, the rotation-dependent model leads to emission frequencies below ionospheric cutoff in many cases (also can be seen inFigure 1), leading to the more favorable results in the rotation-independent model.
Table 2. Expected Radio Emission Frequencies and Flux Densities for Exoplanetary Observationsa
|Planet||fcnorot (MHz)||Φmaxnorot (mJy)||fcrot (MHz)||Φmaxrot (mJy)|
|HD 41004 B b||170||610||70||820|
|HD 189733 b||21||560||(6.0)||(860)|
|tau Boo b||57||180||11||300|
|HD 73256 b||34||98||(8.2)||(160)|
|HD 63454 b||10||95||(2.3)||(150)|
|51 Peg b||11||93||(1.9)||(170)|
|HD 179949 b||19||90||(4.1)||(150)|
|ups And b||15||74||(2.5)||(140)|
|HD 46375 b||(6.3)||(69)||(1.4)||(113)|
|HD 75289 b||10||52||(2.0)||(89)|
|HD 209458 b||(2.9)||(51)||(0.6)||(88)|
|HD 212301 b||10||51||(2.8)||(77)|
|HD 20782 b||38||44||(0.2)||(270)|
|HD 102195 b||11||38||(2.0)||(68)|
 This question can also be inverted: planetary radio observations may be one way to discriminate between these models of planetary magnetic fields. The best test cases are planets which have radio emission above 10 MHz in one of the models, but not in the other. According to Table 2, good candidates for this test include HD 189733 b and HD 73256 b. However, as all numbers are to some extent model-dependent, caution is advised, and conclusions should not be based on one or two planets only.
 In addition to the information about the planetary magnetic field, direct radio detection of exoplanets could also yield information about their rotation periods [Farrell et al., 1999], about their stellar wind environments, including stellar coronal mass ejections [Grießmeier et al., 2007b], and on their orbital inclinations [Hess and Zarka, 2011].