A&A 522, A13 (2010) Astronomy DOI: 10.1051/0004-6361/201014251 & c ESO 2010 Astrophysics A magnetic field evolution scenario for brown dwarfs and giant planets A. Reiners1, and U. R. Christensen2 1 Universität Göttingen, Institut für Astrophysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany e-mail: [email protected] 2 Max Planck Institute for Solar System Research, Max-Planck-Strasse 2, 37191 Katlenburg-Lindau, Germany e-mail: [email protected] Received 12 February 2010 / Accepted 1 July 2010 ABSTRACT Very little is known about magnetic fields of extrasolar planets and brown dwarfs. We use the energy flux scaling law presented by Christensen et al. to calculate the evolution of average magnetic fields in extrasolar planets and brown dwarfs under the assumption of fast rotation, which is probably the case for most of them. We find that massive brown dwarfs of about 70 MJup can have fields of a few kilo-Gauss during the first few hundred Million years. These fields can grow by a factor of two before they weaken after deuterium burning has stopped. Brown dwarfs with weak deuterium burning and extrasolar giant planets start with magnetic fields between ∼100 G and ∼1 kG at the age of a few Myr, depending on their mass. Their magnetic field weakens steadily until after 10 Gyr it has shrunk by about a factor of 10. We use observed X-ray luminosities to estimate the age of the known extrasolar giant planets that are more massive than 0.3 MJup and closer than 20 pc. Taking into account the age estimate, and assuming sun-like wind-properties and radio emission processes similar to those at Jupiter, we calculate their radio flux and its frequency. The highest radio flux we predict comes out as 700 mJy at a frequency around 150 MHz for τ Boo b, but the flux is below 60 mJy for the rest. Most planets are expected to emit radiation between a few Mhz and up to 100 MHz, well above the ionospheric cutoff frequency. Key words. planets and satellites: magnetic fields – stars: activity – stars: magnetic field – brown dwarfs – stars: low-mass 1. Introduction sensitive enough to observe the expected weak radio flux (but see Lazio & Farrell 2007). The discovery of hundreds of extrasolar planets during the last Both the frequency and the total radio flux critically depend two decades has enabled us to investigate the physical properties on the magnetic field strength of the planet, the latter primarily of these objects and to compare them to the known planets of our because it controls the cross section of the magnetosphere inter- own solar system. The discoveries of brown dwarfs, on the other acting with the stellar wind. In addition, the energy flux of the hand, have opened our view for this interesting class of objects wind, which depends on the planet’s distance from the host star placed between stars and planets and sharing physical properties and on stellar activity, plays an important role for the total radio with both groups. Particularly interesting questions are whether flux. The spectrum of the radio emission is expected to show a planets, brown dwarfs, and stars share the same physical prin- sharp cutoff at the electron cyclotron frequency corresponding ciples with regard to their magnetic dynamos, and what typical to the maximum magnetic field strength close to the planetary field strengths must be expected at objects for which a positive surface. Future observations of the radio spectrum of extrasolar field detection is missing so far (brown dwarfs and exoplanets). planets can therefore constrain the field strength very reliably. Radioemissions from magnetized planets result from the in- Usually, one assumes that radio emission can be generated teraction of their magnetospheres with the stellar wind. This ac- at extrasolar planets in much the same way as they are generated celerates electrons to several keV, which emit radio waves at the at Jupiter. Recent estimates of radio fluxes from known extra- local cyclotron frequency (e.g., Zarka 1992, 1998; Farrell et al. solar planets were presented by Farrell et al. (1999), Lazio et al. 1999; Zarka 2007). A similar mechanism, the electron cyclotron (2004), Stevens (2005), Grießmeier et al. (2007a), and Jardine & maser, was identified as the dominant source of radio emission Cameron (2008). One of the large uncertainties in the prediction for a number of very-low mass stars and brown dwarfs (Hallinan of radio emission is the magnetic moment of extrasolar planets. et al. 2008). Radio emissions from extrasolar planets are par- Grießmeier et al. (2004) discussed the different magnetic mo- ticularly interesting because they can outshine the radio emis- ment scaling laws that were available at that time and applied sion from a quiet host star (e.g., Farrell et al. 1999; Grießmeier them to estimate the field of extrasolar planets. Christensen & et al. 2005), and may therefore be utilized to discover extraso- Aubert (2006) derived a magnetic field scaling relation for plan- lar planets. So far, none of the searches for radio emission from ets based on dynamo simulations that cover a broad parameter extrasolar planets could present a positive detection. This is not range. Recently, Christensen et al. (2009) generalized the scaling too surprising because currently available facilities are hardly law and showed that its predictions agree with observations for a wide class of rapidly rotating objects, from Earth and Jupiter to Emmy Noether Fellow. low-mass main sequence (spectral types K and M) and T Tauri Article published by EDP Sciences Page 1 of 7 A&A 522, A13 (2010) stars (see also Christensen 2010). Here, we revisit the question 2.1. Rotation of the planets of magnetic field strength at brown dwarfs and giant planets and the estimate for the radio flux from extrasolar planets, using this We implicitly assume that the objects are rotating above a crit- scaling law, which we believe to be on more solid grounds both ical rotation velocity, so that our scaling law can be applied. theoretically and observationally than previously suggested scal- This seems to be the case in most of the solar-system giant plan- ing laws. ets (Christensen 2010, Sect. 4) and in brown dwarfs (Reiners & Basri 2008). Giant planets with semimajor axes less than about 0.1–0.2 AU are expected to be slowed down to synchronous rota- 2. Magnetic flux estimate tion by tidal braking on time scales of less than 1 Gyr (Seager & Hui 2002). However, for planets that are very close to their host Here we use this scaling law in the form given by Reiners et al. star the synchronous rotation rate may still lie above the criti- (2009b), who expressed the magnetic field strength in terms of cal limit for our scaling law to apply; the value of the latter is mass M, luminosity L, and radius R (all normalized with solar somewhat uncertain. M-dwarfs with rotation periods of up to at values): least four days are generally found to fall into the magnetically 1/6 saturated regime (Reiners et al. 2009a) for which our scaling ML2 law applies. We emphasize that our results can be considered as B = 4.8 × [kG], (1) dyn R7 upper limits and would be lower if for some reason the objects would rotate substantially slower. where Bdyn is the mean magnetic field strength at the surface of the dynamo. In its original form (Christensen et al. 2009), the scaling rela- 3. Radio flux calculation tion connects the strength of the magnetic field to the one-third We estimate the magnetospheric radio flux from extrasolar giant power of the energy flux (luminosity divided by surface area). planets following the work of Stevens (2005). This means we as- ffi It is independent of the rotation rate, provided the latter is su - sume that the input power into the magnetosphere is proportional / ciently high. A weak 1 6-power dependence on the mean density to the total kinetic energy flux of the stellar wind. Grießmeier ffi and a factor describing the thermodynamic e ciency of mag- et al. (2007a) discussed different mechanisms depending on the netic field generation also enter into the scaling law. The latter source of available energy. They also calculate radio emission factor is found to be close to one for a large class of objects for the case where the input power is provided by magnetic en- (Christensen et al. 2009), and this value has been used in Eq. (1). ergy of the interplanetary field, for unipolar magnetic interac- Aside from this assumption, the value of the numerical prefactor tion, and for stellar flares. In general, stellar activity of planet in these equations is only based on the results of dynamo simu- host stars is relatively weak, so that we concentrate on the ki- lations. netic energy flux as source for the power input. For massive brown dwarfs and stars the top of the dynamo is close to or at the surface of the object and the value of Bdyn is directly relevant for observations that relate to the magnetic field 3.1. Radio flux scaling law < strength. In giant planets, with M 13 MJ (13 Jupiter masses), In order to calculate the radio flux of a giant extrasolar planet at the surface of the dynamo region is at some depth, for example the location of the Earth, we relate it to the radio flux of Jupiter in Jupiter at approximately 83% of the planet’s radius and the using Eq. (14) from Stevens (2005) neglecting the dependence field at the surface is somewhat smaller (Christensen et al. 2009).