Nonthermal radio emission from the magnetospheres of Hot Jupiters

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Planetary parameters

Since 1995, more than 150 exoplanets were detected5, many of them in close orbits around G and K stars. In this section, relevant information on the state of detections concerning Hot Jupiters and terrestrial exoplanets is summarised, and some planetary parameters are provided for later use.

Presently known Hot Jupiters

Currently, 40 planets with orbital distances of less than 0.1 AU are known. Of these, 11 have minimum masses below 0.3MJ. The remaining 29 planets are potential Hot Jupiters. Unfortunately, only for a few planets both mass and radius are known, which are both needed to obtain information on the planetary structure. The mass is required to determine whether the stellar companion is a planet or a brown dwarf, see Section 2.2. For a given planetary mass, the radius is determined by its composition. The largest  planetary radius can be achieved by gas spheres composed of hydrogen. For other gases (e.g. helium), the maximum radius is strongly reduced (see Section 4.3.1). For planets composed of ices or rocks, the radius (for a given planetary mass) is again considerably smaller (Guillot et al. 1996). For the planets HD 209458b, OGLE-TR-10b, OGLE-TR-56b, OGLE-TR-111b, OGLE-TR-113b, OGLE-TR-132b and TrES-1b, the measurements of the planetary radii show hydrogen to be the main constituent. Thus, at least seven “Hot Jupiters” (as defined in Section 2.2.4) are known today6.
For all other planets, the radius is not known. However, while gaseous giants of approximately one Jupiter mass are consistent with various planet formation scenarios, the existence of Jupiter-mass terrestrial planets seems unlikely. For this reason, usually all Jupiter-mass planets in close orbits are denoted as Hot Jupiters. Nevertheless, this work will (with one exception, namely Bootes) focus on the “confirmed” Hot Jupiters mentioned above, because the planetary radius is required for the calculation of the tidal locking timescale as well as for the models used to estimate the planetary magnetic dipole moment.

Parameters for Hot Jupiters

For the calculation of the tidal locking timescale (Section 3.1.3), for the estimation of the planetary magnetic moment (Section 4.3), for the evaluation of the planetary stellar wind environment (Section 5.1.4), and for the calculation of the radio flux (Section 6.1) of Hot Jupiters (as defined in Section 2.2.4), various stellar and planetary values are required. The required stellar parameters include: the stellar radius R?, the stellar mass M?, the stellar age t?, and the distance s to the solar system. As for the planetary parameters, the following values are needed: the planetary radius Rp, the planetary mass Mp, the orbital frequency !orbit and the radius d of the planetary orbit. In this section, numbers are given for the stellar and planetary parameters.
Of the planetary values, the orbital frequency !orbit is the easiest one to measure. It can be obtained by various techniques: by radial velocity measurement, astrometric observation, transit detection, and observation in the infrared during a secondary transit. All these methods yield periodic signals, from which the orbital frequency can be determined very accurately. Once the orbital frequency (and the stellar mass) is known, the orbital radius d can be calculated from Kepler’s third law. For the mass Mp, projection effects due to the unknown inclination i of the planetary system limit most observation methods. For radial velocity measurements, for example, only the productMp sin(i) can be determined. Usually, two complementary methods have to be employed to obtain the planetary mass Mp. For example, if the inclination is known from detected transits, it is possible to calculate the planetary mass from radial velocity data. Similarly, astrometric observations can be combined with radial velocity measurements. The planetary radius Rp is even more difficult to obtain. Currently, it can only be determined from planetary transits, where the depth of the dip in the light curve can be used to estimate the relative radii of the star and the planet7. See Section 2.4 for a comparison of the different observation methods. In this work, only Hot Jupiters for which the radius is either known from transit observations or is reasonably well constrained by theoretical models ( Bootes b) are treated. This restriction is applied because information on the planetary radius is required in the following sections. For such planets, the observational data are summarised in Table 2.2. They were obtained in the following way:
• For HD 209458 (for which the first planetary transit was observed), the existence of a planetary companion was known from radial velocity measurements when the first transit observations were reported by Henry et al. (2000) and Charbonneau et al. (2000). From these measurements, the composition of an extrasolar planet could be deduced for the first time. It was shown that the planet HD 209458b is a gas giant with hydrogen as its main constituent (Burrows et al. 2000). Here, the more recent planetary data of Cody and Sasselov (2002) are adopted.
• For OGLE-TR-10b, for a long time, it was not clear whether the observed photometric signal was caused by a planet. Accordingly, early publications spoke of a “possible exoplanet” (Konacki et al. 2003b, Bouchy et al. 2005). Recent observations, however, were able to confirm the planetary nature of the companion to OGLE-TR-10 (Konacki et al. 2005). In this work, the parameters of Konacki et al. (2005) are used. These values are based on a combination of additional observations with the observational data of Bouchy et al. (2005).
• For OGLE-TR-56b (the first planet detected by transits), transits were first reported by Konacki et al. (2003a). Here, the planetary values from Bouchy et al. (2005) are used.
• The values for OGLE-TR-111b are taken from Pont et al. (2004). It is the exoplanet with the lowest mass discussed in this work.
• Transits of the planet OGLE-TR-113b were first analysed by Bouchy et al. (2004) and Konacki et al. (2004). Combining the data of these publications, Konacki et al. (2005) derived the planetary parameters with higher accuracy. These improved values are adopted in this work.
• For OGLE-TR-132b, a planetary transit was first announced by Bouchy et al. (2004). Here, the values found by the follow-up observation (Moutou et al. 2004) are taken.

Presently known terrestrial exoplanets

While currently over 150 exoplanets are known, Earth-like planets (as defined in Section 2.2.5) outside the solar system are not yet accessible to current detection techniques. The smallest planet detected until recently has a projected mass of 14 ME, where ME is the mass of the Earth (Santos et al. 2004). It orbits the star μ Arae (HD 160691), but until now its composition could not be determined. Recently, the detection of a planet with 7.5ME orbiting the M star GJ 876 was announced by Rivera et al. (2005). Neither a small gas planet, nor a rocky planet can be ruled out for these planets (an icy planet is excluded because of its small orbital distance and the resulting high equilibrium temperature). However, this situation is expected to improve in the near future, when the detection of terrestrial exoplanets will be possible with the transit missions CoRoT (CNES, launch scheduled for 2006) and Kepler (NASA, launch scheduled for 2007). According to Bordé et al. (2003), CoRoT is sensitive enough to allow the detection of exoplanets within the habitable zone of K and M dwarfs under the condition that their radius is at least twice that of the Earth. The detection of Earth-size exoplanets orbiting solar-like stars will be possible with Kepler (Jenkins 2002). With the simultaneous measurement of the planetary mass and radius provided by transit detections, it will be possible to deduce constraints for the planetary structure. Additional detections can be expected from the ESA mission Gaia (launch planned in 2011) which will combine precise astrometric measurements with photometric observations (Mignard 2005). Further analysis will be possible with missions like DARWIN (Fridlund 2004), for which launch is planned in 2015 (Perryman and Heinaut 2005).

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Parameters for terrestrial exoplanets

For terrestrial exoplanets (as defined in Section 2.2.5), the planetary mass Mp and radius Rp are required for later calculations (i.e. the estimation of the tidal locking timescale in Section 3.1.5, and the evaluation of the planetary magnetic moment in Section 4.5). In this section, these parameters are presented.
Within this work, only terrestrial planets for which structure models exist will be studied, treating the orbital distance of the planet and the mass of its host star as free parameters. The following model planets will be analysed:
• First, exact Earth analogues will be studied in environments different from that of the Earth. The required parameters of the planet Earth are taken from Cain et al. (1995).
• Within the same frame, smaller planets will be studied. The planet Mercury will serve as an example for small, terrestrial planets. Again, the parameters are taken from Cain et al. (1995).
• As an example for larger planets, a 6 Earth-mass planet (composed of 2 ME metals and 4 ME silicates) is studied. A simple model for the internal structure of such a planet was presented by Léger et al. (2004), in which the silicates form a thick mantle above the metallic core.
• Léger et al. (2004) suggested the existence of so-called “Ocean planets”, i.e. large terrestrial planets with a large mass fraction of water (6 ME, 1 ME of which are metals, 2ME silicates, and 3ME ices). The internal structure consists of the metallic core, the silicate mantle, a thick layer of ice, and a liquid water ocean (with a depth of 40 to 133 km, depending, for example, on the surface temperature). Such a planet would be especially interesting because of its larger radius, which makes detection easier.

Table of contents :

List of Figures
List of Tables
List of symbols and constants
1 Introduction 
2 Extrasolar planets: An overview 
2.1 Historical development
2.2 Definitions
2.2.1 Extrasolar planets: working definition of the IAU
2.2.2 Extrasolar planets: alternative definition of G. Basri
2.2.3 Extrasolar planets: definition used in this work
2.2.4 Hot Jupiters
2.2.5 Terrestrial Exoplanets
2.3 The habitable zone
2.4 Overview of current observation methods
2.5 Chromospheric heating
2.6 Planetary parameters
2.6.1 Presently known Hot Jupiters
2.6.2 Parameters for Hot Jupiters
2.6.3 Presently known terrestrial exoplanets
2.6.4 Parameters for terrestrial exoplanets
3 Tidal interaction 
3.1 Tidal locking
3.1.1 Tidal locking timescale
3.1.2 Imperfect tidal locking
3.1.3 Parameters for gas giants Structure parameter Tidal dissipation factor Q0 p Initial rotation rate !i Final rotation rate !f Overview of the parameters
3.1.4 Results for gas giants
3.1.5 Parameters for terrestrial planets Structure parameter Tidal dissipation factor Q0 Initial rotation rate !i Final rotation rate !f Overview of the parameters
3.1.6 Results for terrestrial planets
3.2 Orbital circularisation
3.3 Obliquity damping
4 Planetary magnetic moments 
4.1 Magnetic moment scaling laws
4.1.1 Blackett’s law
4.1.2 Busse’s geostrophic scaling law
4.1.3 Scale analysis by Jacobs
4.1.4 Stevenson’s scaling based on heat flow
4.1.5 Scaling law of Curtis & Ness
4.1.6 Mizutani’s scaling law
4.1.7 Sano’s scaling law
4.1.8 Scaling law based on the Elsasser Number
4.1.9 Overview over the scaling laws
4.2 Limits of the scaling law concept
4.3 Input parameters for gas giants
4.3.1 The hydrostatic model
4.3.2 Size of the dynamo region rc
4.3.3 Density of the dynamo region c
4.3.4 Planetary rotation rate !
4.3.5 Conductivity within the dynamo region
4.3.6 Known planetary parameters
4.4 Scaling results for gas giants
4.5 Input parameters for terrestrial planets
4.5.1 Planetary models
4.5.2 Size of the dynamo region rc
4.5.3 Density of the dynamo region c
4.5.4 Planetary rotation rate !
4.5.5 Conductivity within the dynamo region
4.5.6 Planetary structure
4.6 Scaling results for terrestrial planets
5 Formation of magnetospheres by stellar winds 
5.1 Stellar winds
5.1.1 Radial dependence Stellar wind model of Parker Stellar wind model of Weber and Davis
5.1.2 Long term time dependence
5.1.3 Influence of the orbital velocity
5.1.4 Resulting stellar wind parameters
5.2 Stellar coronal mass ejections
5.2.1 Density, velocity and temperature
5.2.2 Occurrence rate
5.2.3 Comparison to stellar wind parameters
5.3 Planetary magnetospheres
5.3.1 Magnetospheric model
5.3.2 Pressure equilibrium Stellar wind kinetic pressure Stellar wind magnetic pressure Stellar wind thermal pressure Planetary magnetic pressure Planetary plasma thermal pressure Pressure balance
5.3.3 Size of the magnetosphere of gas giants
5.3.4 Size of the magnetosphere of terrestrial planets
6 Nonthermal radio emission from the magnetospheres of Hot Jupiters 
6.1 Planetary radio emission
6.1.1 Planetary radio emission in the solar system
6.1.2 Model of exoplanetary radio emission
6.1.3 Influence of the stellar system age
6.1.4 Influence of stellar CMEs
6.2 Solar and stellar radio emission
6.2.1 Solar radio emission
6.2.2 Stellar radio emission
6.2.3 Comparison of solar, stellar and exoplanetary radio fluxes
6.3 Observation of exoplanetary radio emission
6.3.1 Observational attempts
6.3.2 Estimated radio flux
7 Protection of terrestrial exoplanets against galactic cosmic rays 
7.1 Galactic cosmic rays
7.2 Cosmic ray calculation
7.2.1 Calculation of particle trajectories
7.2.2 Cosmic ray impact area
7.2.3 Cosmic ray energy spectrum
7.3 Cosmic rays in exomagnetospheres
7.3.1 Impact of cosmic rays on Earth-like exoplanets
7.3.2 Influence of tidal locking
7.3.3 Influence of the stellar system age
7.3.4 Influence of the type of planet
7.4 Implications for habitability
8 Conclusions 


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