Measuring Schumann Resonances on Titan: expected performances of future EFIELD/Dragonfly observations

I. Introduction

Many evidence suggest the presence of an internal global ocean on Titan [1,2]. Notably, the Permittivity, Wave and Altimetry (PWA) analyzer on board the Huygens’ probe in 2005 might have detected a Schumann-like resonance (SR) [3]. On earth, SR are extremely low frequency waves propagating between the Earth’s surface and the ionosphere [4]. Theoretically, SR could be observed on other planets and therefore, can be used as a tool to obtain information on the various planetary cavities [5]. Although the detection of SR by Huygens is still in doubt [6], the Dragonfly mission (NASA) to Titan, will embark an electrical-field sensor designed to detect the first three harmonics of SR, if any [7]. On Titan, SR are believed to propagate between the ionized atmospheric layer (60–70 km altitude) and a subsurface layer (40–80 km depth), presumably a subsurface salty water ocean. Thus, the detection of SR by Dragonfly would provide better constraints on the depth of this buried ocean and would therefore be key to better assess Titan’s habitability.

Fig.1: Structure and parameters of Titan’s cavity [8]

A numerical model has been develop to accurately approximate the behavior of Titan's planetary cavity (see figure 1) [8]. This model showed that the assumptions on SR made on Huygens observations, does not provide any specific constraint on the depth of Titan’s ocean in the range 5-200 km contrary to what is advanced in [3]. This work present the extension on what can be done with this model in order to investigate notably the uncertainty at estimating Titan's crust thickness. Current simulations are including the actual EFIELD electrodes along with the drone body of Dragonfly to study their effect on measurements of the location and polarization of the possible sources of SR.

II. Numerical simulations of the EFIELD experiment

With the current design of the EFIELD experiment, frequencies could be measured in the range 1-100 Hz which allows the measurement of the first three SRs with their corresponding quality factor. Considering the three input parameters of our model: the thickness of the ice crust z_c, its conductivity σ_c and its permittivity ε_c, their existing domains can be integrated into the model to compute the measurement uncertainty of the EFIELD experiment. 

Fig.2: Standard deviation of the EFIELD inversion against the thickness of the ice crust z_c for two different uncertainties on σ_c in percentage of z_c

For example on figure 2, the standard deviation at estimating z_c with the current uncertainties on the electromagnetic properties of the ice crust from Hamelin et al. [9] can be computed. This allows us to investigate the potential results from another experiment of the Dragonfly Geophysics and Meteorology Package (DraGMet): the DIEL experiment which aims at measuring the electrical properties of Titan's surface. On figure 2, a better constraint on σ_c (in red) which could be measured with DIEL compared to the existing constraint from [9] (in blue) would greatly decrease the measurement uncertainty on z_c.
The current simulations are taking into account the actual EFIELD electrodes accommodated on the Dragonfly (conductive) body. Similarly as with the electromagnetic properties of the surface, the drone could influence the inversion of the EFIELD experiment and thus the estimation of the thickness of the ice crust z_c. On figure 3, the deformation of the equipotentials and the differential potential between the two probes for a SR at f=36 Hz with a vertical polarization are shown around a simplification of the drone body. 

(a)

(b)

Fig.3: Influence of the drone body with a Schumann resonance at f=36 Hz} on the equipotential (a) and the differential potential between the two probes (b)

The EFIELD experiment will measure the electrical potential at the two probes. Given the vertical polarization of a single mode as shown on figure 3, the Schumann resonance can be accurately measured in both frequency and power and the effect of the metallic body properly quantified. But realistically, the wave polarization is unknown and the SRs are a spectrum with various modes instead of individual peaks. The next step is to include a full wave spectrum with various polarizations. Given the different orientation and altitude of the drone and the two EFIELD electrodes, at least two components of the electrical field could be measured with the third component captured by rotating the drone. Further studies could also include the sources of the SRs. Such further developments will be presented at EPSC2025.

References

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[3] C. Béghin et al., Icarus 218, 1028–1042 (2012).
[4] W. O. Schumann, Zeitschrift für Naturforschung A 7, 149–154 (1952).
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