Planetary and Space Science 55 (2007) 1978–1989 A new numerical model for the simulation of ELF wave propagation and the computation of eigenmodes in the atmosphere of Titan: Did Huygens observe any Schumann resonance? F. Simo˜ es a,Ã , R. Grard b , M. Hamelin a , J.J. Lo´pez-Moreno c , K. Schwingenschuh d , C. Be´ghin e , J.-J. Berthelier a , B. Besser d , V.J.G. Brown c , M. Chabassie`re e , P. Falkner b , F. Ferri f , M. Fulchignoni g , R. Hofe d , I. Jernej d , J.M. Jeronimo c , G.J. Molina-Cuberos h , R. Rodrigo c , H. Svedhem b , T. Tokano i , R. Trautner b a CETP/IPSL-CNRS 4, Avenue de Neptune, 94107 Saint Maur, France b RSSD, ESA-ESTEC, European Space Agency, Keplerlaan 1, 2200 AG Noordwijk, The Netherlands c Instituto de Astrofı´sica de Andalucı´a IAA-CSIC, Camino Bajo de Hue´tor 50, 18008 Granada, Spain d Space Research Institute, Austrian Academy of Sciences (IWF), Schmiedlstrasse 6, 8042 Graz, Austria e LPCE-CNRS 3A, Avenue de la Recherche Scientifique, 45071 Orle´ans cedex 2, France f CISAS ‘‘G. Colombo’’, Universita` di Padova, Via Venezia 15, 35131 Padova, Italy g LESIA, Observatoire de Paris, 5 Place Janssen, 92195 Meudon, France h Applied Electromagnetic Group, Department of Physics, University of Murcia, Murcia 30100, Spain i Institut fu ¨ r Geophysik und Meteorologie, Universita ¨t zu Ko¨ln, Albertus-Magnus-Platz, 50923 Ko¨ln, Germany Accepted 13 April 2007 Available online 27 April 2007 Abstract The propagation of extremely low frequency (ELF) electromagnetic waves in the Earth’s ionospheric cavity and the associated resonance phenomena have been extensively studied, in relation with lightning activity. We perform a similar investigation for Titan, the largest moon of Saturn. There are important differences between Earth and Titan, as far as the cavity geometry, the atmospheric electron density profile, and the surface conductivity are concerned. We present an improved 3D finite element model that provides an estimate of the lowest eigenfrequencies, associated quality factors (Q-factors), and ELF electric field spectra. The data collected by the electric antenna of the Permittivity, Waves, and Altimetry (PWA) instrument reveals the existence of a narrow-band signal at about 36 Hz during the entire descent of Huygens upon Titan. We assess the significance of these measurements against the model predictions, with due consideration to the experimental uncertainties. r 2007 Elsevier Ltd. All rights reserved. Keywords: Titan; Huygens probe; Atmospheric electricity; ELF electric field; Schumann resonance 1. Introduction The propagation of low frequency electromagnetic waves within the cavity formed by two, highly conductive, concentric, spherical shells, such as those formed by the surface and the ionosphere of Earth, was first studied by Schumann (1952) and was subsequently observed by Balser and Wagner (1960). When a cavity is excited with broadband electromagnetic sources, a resonant state can develop provided the average equatorial circumference is approximately equal to an integral number of wavelengths of the electromagnetic waves. This phenomenon is known as the Schumann resonance; it provides information about thunderstorm and lightning activity at Earth and acts, for example, as a ‘‘global tropical thermometer’’ (Williams, 1992). We shall apply the same approach to Saturn’s satellite. Titan and Earth are both wrapped up in thick atmo- spheres and conductive ionospheres (Schwingenschuh ARTICLE IN PRESS bwww.elsevier.com/locate/pss 0032-0633/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2007.04.016 Ã Corresponding author. Tel.: +33 1 4511 4273; fax: +33 1 48 89 44 33. E-mail address: Fernando.Simoes@cetp.ipsl.fr (F. Simo˜es).