Analytic theory of Titan’s Schumann resonance: Constraints on ionospheric conductivity and buried water ocean

Abstract

This study presents an approximate model for the atypical Schumann resonance in Titan’s atmosphere that accounts for the observations of electromagnetic waves and the measurements of atmospheric conductivity performed with the Huygens Atmospheric Structure and Permittivity, Wave and Altimetry (HASI–PWA) instrumentation during the descent of the Huygens Probe through Titan’s atmosphere in January 2005. After many years of thorough analyses of the collected data, several arguments enable us to claim that the Extremely Low Frequency (ELF) wave observed at around 36 Hz displays all the characteristics of the second harmonic of a Schumann resonance. On Earth, this phenomenon is well known to be triggered by lightning activity. Given the lack of evidence of any thunderstorm activity on Titan, we proposed in early works a model based on an alternative powering mechanism involving the electric current sheets induced in Titan’s ionosphere by the Saturn’s magnetospheric plasma flow. The present study is a further step in improving the initial model and corroborating our preliminary assessments. We first develop an analytic theory of the guided modes that appear to be the most suitable for sustaining Schumann resonances in Titan’s atmosphere. We then introduce the characteristics of the Huygens electric field measurements in the equations, in order to constrain the physical parameters of the resonating cavity. The latter is assumed to be made of different structures distributed between an upper boundary, presumably made of a succession of thin ionized layers of stratospheric aerosols spread up to 150 km and a lower quasi-perfect conductive surface hidden beneath the non-conductive ground. The inner reflecting boundary is proposed to be a buried water–ammonia ocean lying at a likely depth of 55–80 km below a dielectric icy crust. Such estimate is found to comply with models suggesting that the internal heat could be transferred upwards by thermal conduction of the crust, while convective processes cannot be ruled out.

Introduction

Titan, Saturn’s largest satellite, is the only moon in the Solar System with a dense atmosphere and stable liquid hydrocarbon lakes on its surface. Its global properties (mass, radius, density) are similar to those of its cousin icy jovian satellites Ganymede and Callisto. The discovery by the Galileo mission of their own magnetic fields, partly intrinsically produced (Ganymede) and partially induced by the variations of the jovian magnetic field, has led to the interpretation that internal water oceans are present beneath their icy crust (Schubert et al., 2004). Discovering a buried ocean at Titan would mean that this moon is a likely world of organic molecules and liquid water, two of the necessary ingredients for life to form and develop. Unfortunately, the magnetic measurements from the Cassini orbiter (Dougherty et al., 2004) do not reach the sensitivity required for a similar detection at Titan. The reasons for that are manifold, namely: (i) a fainter signal, since Saturn’s magnetic field is weaker at Titan’s orbit than that of Jupiter at its moons, (ii) a larger safe flyby distance of the spacecraft above the surface, and more specifically, (iii) the shielding effect due to Titan’s ionosphere.

Thanks to Titan’s dense atmosphere, the presence of a buried ocean might be detected by measuring the non-synchronous rotation of the crust (i.e., the length of day) due to the periodical exchange of angular momentum between the atmosphere and the crust (Tokano and Neubauer, 2005). An initial analysis of the location of geological features at different times led the Cassini Radar team (Stiles et al., 2008, Lorenz et al., 2008) to propose a non-synchronous rotation rate of 1.1 × 10⁻³ degree/day that would have been consistent with this model. However, the discovery of an error in the data reduction led to reconsider the rate as being rather 3 × 10⁻⁴ degree/day (Stiles et al., 2010). Since this value is strongly correlated with the precession, it lies within the error bar of a non-synchronous rotation. Furthermore, a more elaborate model of angular momentum exchange (Tokano et al., 2011) predicts much smaller displacement, with amplitudes of polar motion from 100 to 1000 m for crustal thickness of 70–20 km, respectively. Given that the spatial resolution of the radar is several times larger than the 300 m surface sampling, it appears that the Cassini Radar observations could detect the non-synchronous component related to the presence of a buried ocean if the thickness of the crust is less than 20 km (Ö. Karatekin, Royal Observatory of Belgium, private communication).

Independently, the possibility to diagnose the shallow interior of planets, using the properties of Extremely Low Frequency (ELF) waves trapped within their atmospheric cavity, was suggested by Sentman (1990a) as a way to reveal the liquid metallic hydrogen surface of Jupiter. To date, the only observation that seems consistent with the presence of a subsurface water ocean at Titan is that of the ELF signal collected by the Huygens Probe (Béghin et al., 2010), as it descended through the atmosphere on January 14, 2005.

The Permittivity, Wave and Altimetry (PWA) experiment (Grard et al., 1995), a subsystem of the Huygens Atmospheric Structure Instrument (HASI) (Fulchignoni et al., 2002), was designed to perform measurements of electron and ion conductivities, ELF and VLF (Very Low Frequency) waves during the descent through Titan’s atmosphere (Lebreton et al., 2005). One of the most exciting but speculative goals of the PWA experiment dealt with the possible existence of lightning activity in Titan’s atmosphere and the associated Schumann resonance (Schumann, 1952, Sentman, 1995), hereinafter referred to as “SR”. Subsequently, the presence of a ground or subterranean conductive surface, such a liquid water ocean predicted by theoretical models (e.g., Grasset and Sotin, 1996), was expected to be a major scientific return of the mission. Preliminary data analyses revealed indeed that the 36 Hz signal observed with the PWA instrument (Grard et al., 2006) might satisfactorily fit the range of values predicted by models to be the second eigenmode of the SR (Nickolaenko et al., 2003, Simões et al., 2007). Given the absence of any acknowledged lightning activity on Titan after 72 flybys from 2005 to 2010 (Fischer and Gurnett, 2011), it was proposed that the ELF turbulence generated within the ionospheric currents driven by the co-rotating plasma flow of Saturn’s magnetosphere (e.g., Sittler et al., 2009) might be the power source able to excite a “Schumann-like” resonance (Béghin et al., 2007). After reanalyzing the characteristics of the 36 Hz signal in term of height profile and spin modulation, including a few attempts at identifying possible source regions from the measurements performed by the plasma and wave instruments on board the Cassini orbiter, the proposed powering mechanism was further developed in follow-up articles (Béghin et al., 2009, Béghin et al., 2010).

In the latter papers, because of the absence of any detectable radial electric field component of the 36 Hz signal, we were led to consider a mode of propagation with horizontal polarization. This assumption must be revisited and we consider instead the properties of waves with mixed horizontal and radial polarizations, called Transverse Electric and Magnetic (TEM) modes, known to be those of Earth’s SR (Wait, 1962). However, in a stratified cavity, bounded by an icy crust instead of a conductive ground and a multi-layered profile of atmospheric conductivity, the TEM waves are known to degenerate into Longitudinal Section Magnetic (LSM) modes (Collin, 1991), whose properties are shown below to be notably different from those of Earth’s SR.

We first establish the basic equations relevant to Titan conditions in Sections 2 and 3, referring to previous works and to Appendix A for some mathematical developments. After deriving the expressions of field components in Section 3 and the modal equations in Section 4, the formalism is subsequently applied to the PWA observations in Section 5 in order to constrain the parameters of the cavity. Making use of the Huygens Probe dynamics data deduced from the Descent Imager Spectral Radiometer (DISR) observations (Karkoschka et al., 2007), we retrieve in Section 5.4 a few case-studies of electric field strength profiles which compare favorably with Huygens measurements throughout the descent.

Section 6 contains discussions regarding the two main results of our study, the first one being the constrained upper atmosphere electron conductivity profile above the Galactic Cosmic Ray (GCR) layer at around 60 km revealed by the PWA-MIP (Mutual Impedance Probe) and PWA-RP (Relaxation Probe) instruments (Hamelin et al., 2007, López-Moreno et al., 2008). We invoke a probable relationship with thin aerosol layers and we consider a possible correlation with the zonal wind profile measured by the Doppler Wind Experiment (DWE) during the descent (Bird et al., 2005). The second major result concerns the crust characteristics and the presence of a buried conductive ocean, whose constrained parameters are discussed in terms of Titan’s interior thermal dynamics. Although only few ground truth and remote sensing measurements support the relevance of the constraints derived from our work, we are able to conclude in Section 7 that our interpretation of PWA-ELF data is consistent with recent models of Titan’s interior. The cavity appears to be bounded upwards by thin ionized layers of aerosols, at least up to an altitude of 140 km (López-Moreno et al., 2008) and downwards by a water–ammonia ocean buried beneath a semi-rigid icy crust, most likely 55–80 km thick.

We revisit, in Appendix B, a few experimental open points that have been subject of recurring questions regarding the validity of the PWA measurements, such as: (i) the absence of multi-SR modes that should have been observed in addition to the 36 Hz line, (ii) the disappearance of the signal 16 s after landing, and (iii) a presumably artifact induced by boom-antenna vibrations at 36 Hz possibly triggered by wind-blasts or by the descent velocity airflow (Béghin et al., 2007).