International audienceAfter six years of a thorough data analysis of the data collected by the Permittivity, Wave and Altimetry (PWA/HASI) experiment during the descent of the Huygens Probe through Titan's atmosphere in January 2005, we report the major findings inferred from the measurements of low frequency waves and atmospheric conductivity. The observations display a Schumann resonance trapped within Titan's atmospheric cavity. In this presentation, we describe the characteristics of the observed mode, that allow us to constrain the parameters of the ionospheric cavity and to infer the presence of a conductive water-ammonia ocean buried below the surface, at a likely depth of 70 ± 10 km

Berthelier, Jean-Jacques

Béghin, Christian

Grard, Réjean

Hamelin, Michel

Simões, F.

Sotin, C.

Whitten, R.C.

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Constraints on Titan's atmospheric conductivity and buried ocean depth, disclosed by the Schumann resonance

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Constraints on Titan’s atmospheric conductivity and
buried ocean depth, disclosed by the Schumann
resonance
Christian Béghin, Michel Hamelin, C. Sotin, R.C. Whitten, Jean-Jacques
Berthelier, Réjean Grard, F. Simões
To cite this version:
Christian Béghin, Michel Hamelin, C. Sotin, R.C. Whitten, Jean-Jacques Berthelier, et al.. Con-
straints on Titan’s atmospheric conductivity and buried ocean depth, disclosed by the Schumann
resonance. EPSC-DPS Joint Meeting 2011, Oct 2011, Nantes, France. ￿insu-01555780￿
Constraints on Titan’s atmospheric conductivity 
and buried ocean depth, disclosed by the Schumann resonance 
 
 
 C. Béghin (1), M. Hamelin (2), C. Sotin (3), R.C. Whitten (4), J.J. Berthelier (2), R. Grard (5) and F. Simões  (6) 
(1) LPC2E-CNRS-Université d’Orléans, 3A, Ave. Recherche Scientifique, 45071 Orléans Cedex 2, France 
(2)  LATMOS-IPSL, Université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris cedex 05, France 
(3)  Jet Propulsion Laboratory and California Institute of Technology, Pasadena, CA 91109, USA 
(4)  SETI Institute, 189 Bernardo Ave., Mountain View, CA 94043, USA 
 (5)  RSSD, ESA-ESTEC, European Space Agency, Keplerlaan 1 2200 AG Noordwijk, The Netherlands 
 (6)  NASA-GSFC, Heliophysics Science Division, Greenbelt, MD 20771, USA 
 
Abstract 
After six years of a thorough data analysis of the data 
collected by the Permittivity, Wave and Altimetry 
(PWA/HASI) experiment during the descent of the 
Huygens Probe through Titan’s atmosphere in 
January 2005, we report the major findings inferred 
from the measurements of low frequency waves and 
atmospheric conductivity. The observations display a 
Schumann resonance trapped within Titan’s 
atmospheric cavity. In this presentation, we describe 
the characteristics of the observed mode, that allow 
us to constrain the parameters of the ionospheric 
cavity and to infer the presence of a conductive 
water-ammonia ocean buried below the surface, at a 
likely depth of 70 ± 10 km.   
1. Introduction 
On Earth, the Schumann resonance is triggered by 
lightning activity and it was anticipated that a similar 
observation on Titan would reveal the presence of a 
reflecting inner surface requisite to sustain such a 
resonance in addition to a sharp ionospheric 
boundary. However, given the absence of any 
acknowledged lightning activity on Titan (Fischer 
and Gurnett, 2011), we interpret the observed signal 
at 36 Hz, as the second spherical harmonic of the  
Titan’s cavity, triggered and sustained by intense 
electric currents induced in the ionosphere through 
the Saturn’s magnetospheric plasma flow.  
2. Model and PWA measurements 
After ruling out several possible artefacts (Béghin et 
al., 2009) the observed signal is presently 
unambiguously interpreted as the second harmonic of 
a Longitudinal Section Magnetic (LSM2) mode of 
atypical Schumann resonance in an inhomogeneous 
and radially layered cavity. Although the triggering 
current sources and the ground conductivity are 
strongly different from conditions encountered for 
the terrestrial TEM modes, the analytical expression 
of the modal equation of the eigenmodes can be 
written in a similar way, as a function of a small 
number of cavity parameters, such as 
 
   
2/1
22
1
1
)4/1(ln
Re/)1( ⎥
⎦
⎤
⎢
⎣
⎡
++
+
+=
ζζ
εω
kzh
zhll
a
c
c
cC
l
        (1) 
1
22
11 )4/1(ln
2/
Re/
2/Re/2Q
−
⎥
⎦
⎤
⎢
⎣
⎡
++
+
+
+
=
ζζ
πζ
ε
πζεδ
kzhzh
z
ccC
cC    (2) 
where ωl is the eigenfrequency for the harmonic l 
(here l = 2), Q is the quality factor, c and k are the 
free-space light velocity and the wave vector, 
respectively, a is the Titan’s radius (2575 km), h1 is 
the altitude of the ionospheric conduction boundary, 
zc and εc are the subsurface crust thickness and 
permittivity, respectively, δ is the loss tangent of the 
crust material, and ζ is the scale height of ionospheric 
conductivity.  
As on Earth, the altitude of the conduction boundary 
h1 is nearly the region of maximum signal strength 
(Fig. 1), i.e. between 90-100 km here, so that we may 
keep only four unknown parameters (zc , εc, δ and ζ) 
to be cross-constrained by the measured quantities ωl 
and Q. The most likely cross-constraint area for the 
three parameters of the crust is shown in Fig. 2. The 
value of the ice thickness determined by the present 
study strongly suggests that the ice crust lies over an 
ammonia-rich ocean, which is consistent with either 
convection or conduction processes. We find indeed 
that a crust thicker than 80 km would be unstable to 
convection processes unless the viscosity at the base 
of the crust would be larger than 2.1016 Pa.s, which 
suggests a temperature less than 220 K. On the other 
hand, a convective 40-km thick crust cannot be in 
equilibrium with the internal heating, which suggests 
a crust growing at the expense of the ocean.   
EPSC Abstracts
Vol. 6, EPSC-DPS2011-194, 2011
EPSC-DPS Joint Meeting 2011
c© Author(s) 2011
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  f = 36 Hz 
 Q = f/Δf = 6
 
 
 
 
 
 
 
Figure 1. Experimental data. ELF Electric Field and Electron Conductivity were measured with sensors mounted on two 
deployable booms.  A 36 Hz resonance with a level of few mVm-1Hz-1/2 and a high Quality Factor (Q = 6) was clearly 
identified throughout the descent. A peak of conductivity, attributed to Galactic Cosmic Rays, was observed at around 60 km.  
 
 
 
 
 
 
 
 
 
 
Figure 2. Cross-constrained shadowed area for the ocean 
depth versus the crust permittivity (2 < Re εc < 3) and the 
ionospheric scale height of conductivity (3.2 < ζ  < 5). 
 
3. Summary 
Our interpretation of the Titan’s Schumann 
resonance complies with a conduction ionospheric 
boundary lying at ~ 100 km, and a 60 km thermally 
conductive crust with an ocean temperature of 200 
K (Fig.3) or an 80 km convective crust with a 
minimum viscosity of 5x1015 Pa.s.  
Figure 3. Heat power in equilibrium with the crust 
thickness (60 < zc < 80 km) for a temperature of the 
crust-ocean interface < 260 K. 
 
References 
[1] Béghin, C., et al.: New insights on Titan’s plasma-
driven Schumann resonance inferred from Huygens and 
Cassini data, Planet. Space Sci., 57, 1872-1888, 2009. 
 
[2] Fischer, G. and Gurnett, D.A.:The search for Titan 
lightning radio emissions, Geophys. Res. Lett., 38, 
L08206,. doi:10.1029/2011GL047316, 2011. 
3 4 5 6
Crust thickness (km)
Heat power (GW)
0
1
2
3
4
gr
Tan
Scale height . of ionospheric conductivity (km)
*
l = 2


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Constraints on Titan's atmospheric conductivity and buried ocean depth, disclosed by the Schumann resonance

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