On the null detection of exoplanetary radio emission and magnetic field structures

Expected radio emission from the extra-solar planets due to physical phenomenon called "electron-cyclotron maser instability (ECMI)" requires two necessary conditions: right magnitude of stellar wind and existence of magnetic field structure of the planet. Assuming that stellar wind exists, in this study, we probe the second necessary condition for the existence of magnetic field structure of extra-solar planets from their observed radio fluxes. Even though observations show the null (statistically not significant) detection, it is interesting to examine whether there is any trend in the observed data such that clues regarding magnetic field structure can be obtained. Analysis of observational upto date emission of radio flux data of exoplanets from the literature survey yields the following results: (i) most of the observed planets have dimensions of solar Jupiter size whose magnetic diffusion time scales are estimated (assuming cores of all the exoplanets have similar core magnetic diffusivity of solar Jupiter ~ 3.5e+06 cm^2/sec) to be ~ million yrs, (ii) there are two types of planets with flux of radio emissions < 2 mJsky (let us call as type A) and  >=2 mJsky (type B) that follow different evolutionary paths, (iii) majority of type A groups of planets orbit very close ( < 10 AU) to the host stars, while type B group of planets are distributed uniformly between 0.02 AU to 2000 AU, (iv) independent of their ages (assuming that planets have similar ages as those of host stars), type A planets emit similar (~ 1 mJsky) radio fluxes, whereas type B planets emit very high radio fluxes (200-300 mJsky) during their early life times (within few million yrs) and emit very low radio fluxes ( ~ 2-6 mJsky) during their old ages ( ~ 10 billion years) and, follow a power law decay of radio flux emission with respect to ages, (v) majority of type A planets have near zero eccentricty and type B planets have varied eccentricity distribution , (vi) from the mass-density distribution, it is found that, on average, type A planets are denser compared to type B planets and, (vii) compared to solar metallicity, type A planets are metal rich, whereas type B planets are metal poor . Implications of these results suggest that, irrespective of their ages, type A planetary groups, due to their proximity and synchronization of rotation rates with their host stars, probably maintain dynamo like magnetic field structures and hence, irrespective of their ages emit constant radio flux of similar magnitude. Unfortunately, this implication is in contrast with the conventional wisdom that as planets slow down with respect to their ages, magnitude of magnetic field must vanish. It is conjectured that group B exoplanets might be rogue planets whose magnetic field structures might have decayed within few million years after their formation and while wandering in space successively might have been captured by the host stars. For all these results, there is a caveat such that the observed radio fluxes of both the groups have estimated large errors in their emitted
radio fluxes. Accurate estimation of observed planetary radio fluxes and more number of observations are needed in order to confirm these results.