1. Refining the analysis of the PWA-HASI / Huygens data to constrain Titan’s surface electrical properties
M. Hamelin(1), A. Lethuillier (1), A. Le Gall(1), C. Béghin(2), J.J. López-Moreno(3), R. Grard(4), K. Schwingenschuh(5), I. Jernej(5)
From the institutes
Sorbonne Universités, UPMC Univ. Paris 06; Université Versailles St-Quentin; CNRS/INSU, LATMOS-IPSL, UMR 8190, Paris.
LPC2E, CNRS, 3A Avenue de la Recherche Scientifique, F Orleans Cedex, France. (3) Instituto de Astrofisica de Andalucia (IAA), CSIC, P.O. Box 3004, E Granada, Spain. (4) European Space Agency, ESTEC, Noordwijk, The Netherlands (retired). (5) Space Research Institute, Austrian Acad. of Sciences (IWF), Schmiedlstrasse 6, 8042 Graz, Austria.
The CASSINI-HUYGENS is an ESA/NASA/ASI mission; the PWA-HASI was developped with the support of national space agencies of Austria, France, Italy, Spain and ESA-ESTEC; ISSI, Bern is thanked for working facilitiess.
EPSC
Photo JPL/NASA

2. Titan's surface electrical properties - Hamelin et al., EPSC 2014
Plan
The PWA-HASI MI experiment on Huygens
- principle
- the case of Huygens
- calibrations
2. Landing on Titan and MI data
- landing conditions
- overview of the data
3. Refined estimations of complex permittivity
- 45 Hz data
- estimations for higher frequencies
- the step change
4. Conclusions and enigmas
- bulk material characteristics
- the 9539 s event
Titan's surface electrical properties - Hamelin et al., EPSC 2014

3. Measurement principle
Mutual Impedance (MI):
Zm = V / I
In vacuum:
Zm0 = V0 / I0
Normalized MI, for the same transmitted current I0 = I :
ZN = Zm / Zm0
Presence of gondola and short booms: not a problem if:
Perfect current source and perfect voltmeter
Perfect calibration of the whole configuration in vacuum
Homogeneous, steady medium
Which is not applicable in this situation!
In PWA, the constant current is achieved with a small coupling capacitor in the transmitting circuit.
In an homogeneous medium:
ZN-1 = εr – i εi (εi =  / ω 0  )
Titan's surface electrical properties - Hamelin et al., EPSC 2014

4. Titan's surface electrical properties - Hamelin et al., EPSC 2014
MI receiver
RP disc
MI transmitter
The MI – PWA instrument
The MI electrodes consist of rings connected through small coupling capacitors
MI calibration in DASA
Titan's surface electrical properties - Hamelin et al., EPSC 2014

5. The MI real instrument Calibration issues
The natural medium under investigation is de facto limited by the Huygens body and attached items. The Titan surface morphology at the landing site is also an important feature
MIP operated during 32 mn at the surface of Titan at five emitting frequencies: 45, 90, 360, 1440 and 5760 Hz.
The laboratory ‘vacuum’ calibration, far from room ceiling and walls was disturbed by electromagnetic noise, but individual modules have been carefully calibrated in the laboratory.
The electronic current source and voltmeter are not perfect. The injected current and the measured voltage depend upon the medium complex permittivity.
The last measurements before landing were performed at 45 Hz in a neutral atmosphere that has a permittivity close to that of vacuum, and can therefore be used as a reference. A similar information is unfortunately not available at other frequencies.
The model
The electronic circuits are known, but may have aged (radiations)
The shape of Huygens can be simplified, as well as that of the electrodes (spheres or cylinders instead of rings). Assumptions will be made about the interface with the ground.
Lumped medium elements model computed with ComsolTM
(Laplace equation)
Electronic circuits
(components)
The vacuum reference at other frequencies is derived from an analytical modelling of the electronics that is validated against the 45 Hz in-flight reference.
During the descent the Relaxation Probe detects a layer without electrons, with two MIP measurements similar to those before touchdown. The two MIP 45 Hz measurements acquired simultaneously are very similar to those recorded immediately before landing, which confirms the above assumption.
Titan's surface electrical properties - Hamelin et al., EPSC 2014

6. HUYGENS on Titan: Landing attitude
Study configuration models
HUYGENS on Titan: Landing attitude
Our goal is to explore the variability of the derived complex permittivity with the depth of penetration or height above the ground (gondola sitting on a peeble), and the possible partial penetration of the receiving electrodes into the ground.
With a structural strength of kPa, the theoretical penetration depth is very small (< mm), but it defines the contact surface area between the gondola and the soil and the associated electrical impedance.
The 4 selected models (vs. height and gondola tilt in the vertical-receiving dipole plane):
Shröder et al., Planet. Space Sci., 2012*
The landing scenario has been clarified as a first impact digging a 12 cm depth hole, followed by a rebound outside the hole and a glide of ~10 seconds.
At rest Huygens would be tilted in the direction of DISR (perpendicularly to the HASI booms direction)
*doi: /j.pss
Titan's surface electrical properties - Hamelin et al., EPSC 2014

7. HUYGENS on Titan: the MIP raw data
The most intriguing fact:
A discontinuity of phase and amplitude at around 9539 s already mentionned in Grard et al.,2006*.
From 360 Hz data, the transition time is estimated to ~4 s
A rather small amplitude at 5760 Hz.
time (s)
time (s)
*doi: /j.pss
Titan's surface electrical properties - Hamelin et al., EPSC 2014

8. 45 Hz vacuum calibration and analysis procedure
The MIP measurement loop model consists of 3 sections:
The emitting circuit (capacitors)
The medium (a network of capacitors estimated with COMSOLTM models)
The receiving circuit model (a very accurate transfer function derived from laboratory calibrations and experimental corrections for coupling circuits at cryogenic temperature )
The comparison between the Titan vacuum data and the modelling reveals discrepancies:
~0.7 dB in amplitude
~3° in phase (not really understood as parts A and B involve only capacitors; this phase-shift might due to a stray resistance of ~1OO G Ω in the transmitting coupling circuits).
Corrections are added to the model to obtain exactly the mean experimental values of the case of a vacuum.
Normalized experimental V in complex plan
εr and εi results
Abacus of theoretical values for any pair εr and εi
Titan's surface electrical properties - Hamelin et al., EPSC 2014

9. 45 Hz relative permittivity results
Complex permittivity results for the 4 configurations. Huygens in levitation: symbols ^ (bold if horizontal [A], normal if tilted [B]), or Huygens slightly inside the ground: symbols v (bold if horizontal [C], normal if tilted [D]). Dashed rectangles represent 2σ contours of data.
The fact that a receiving electrode is inserted or not in the medium has little influence. On the contrary the depth of penetration of Huygens is a more important factor.
The surprising fact is that the data collected after 9539 s lead to a zero mean value of εi and a zero conductivity at 45 Hz. Is it be the same at higher frequencies?
Titan's surface electrical properties - Hamelin et al., EPSC 2014

10. Vacuum reference at higher frequencies and instrument status
Unfortunately only 45 Hz was used during the descent and there are no in-situ vacuum calibrations at higher frequencies. Our approach is to use tentatively the analytical model of the transfer functions to derive vacuum calibrations at any frequency from the 45 Hz value.
However, the low amplitude observed at 5760 Hz raises a new problem. The model shows that there should be a 6.1 dB difference between the 1440 and 5760 Hz amplitudes, whereas 9.5 dB are measured. There is a significant difference of 3.4 dB.
This might prove that the instrument performance has evolved after its calibration in the laboratory.
Possible cause: aging, due in particular, to radiations? Still, the internal electronics was better protected than the cables and coupling capacitors that remained outside Huygens, under the heat shield during the transit.
However, if we exclude the 5760 Hz frequency, and if we assume that εi is zero for t > 9539 s at 90, 360, and 1440 Hz, as it is at 45 Hz, we obtain a vacuum reference for the phase, which is the most critical parameter.
Titan's surface electrical properties - Hamelin et al., EPSC 2014

11. Titan's surface electrical properties - Hamelin et al., EPSC 2014
90 Hz relative permittivity results (assuming zero conductivity for t > 9539 s)
t < 9539 s
t > 9539 s εi εi εr εr
Complex permittivity results for the 4 configurations. Huygens in levitation: symbols ^ (bold if horizontal [A], normal if tilted [B]), or Huygens slightly inside the ground: symbols v (bold if horizontal [C], normal if tilted [D]). Dashed rectangles represent 2σ contours of data.
Titan's surface electrical properties - Hamelin et al., EPSC 2014

12. Titan's surface electrical properties - Hamelin et al., EPSC 2014
Summary of permittivity results (assuming zero conductivity for t > 9539 s for 90, 360 and 1440 Hz)
Blue line: t < 9539 s
Black line: t > 9535 s
Dielectric constant and conductivity of Titan as measured at the landing site.. Height of bars shows 2σ for the whole set of geometrical models A, B, C, D.
The dielectric constant is well constrained around 2.2. A slightly higher value is obtained for 1440 Hz, but this may be due to the increasing bias of the measurement at higher frequencies. The measured permittivity is clearly higher than that of methane and ethane (<2.0), of the order of that of solid thiolins, and less than that of water at low temperature (3.15), but possibilities of porous ice or heterogeneous sub-surface are open. Conductivity remains at around 0.9 nS/m for t < 9539 (the well calibrated value being that for 45 Hz).
Titan's surface electrical properties - Hamelin et al., EPSC 2014

13. Titan's surface electrical properties - Hamelin et al., EPSC 2014
The intriguing 9539 s event
The MIP instrument provides an estimation of the apparent permittivity of the material around the electrode array down to a depth of a few tens of cm (~ the inter-electrodes distances). The subsurface is assumed to be homogeneous. A MIP instrument with several geometrical configurations (as for the MIP instrument on Philae) could resolve a multi-layered model of the subsurface, but not on Huygens.
Passive measurements do not show any change (Béghin et al., 2009*). The sudden change of the apparent conductivity at 9535 s cannot result from a global change within a large volume at the landing site but might be explained by the rapid evolution of a surface layer. It could be due to some sudden evolution of a superficial layer. This is also supported by the conclusions of Atkinson et al., 2010 suggesting the presence of an upper fluffy layer on the surface. Two possible scenarii are:
the upper –conductive- layer is wiped out suddenly by melting or by flooding,
an outburst of condensed gases from a subsurface reservoir (Niemann et al., 2010 suggest the presence of such a reservoir under Huygens)
The intriguing 9539 s event
The MIP istrument provides no more than an estimation of the apparent permittivity, that is not enough to characterize the subsurface. But, if some model is proposed (multi-layer for instance), the MIP analysis can be performed with our approach, allowing to approve or disprove this model.
For that reason the HASI-MIP data and simulation technique can be useful in further studies.
Titan's surface electrical properties - Hamelin et al., EPSC 2014

14. Summary and main conclusions
Effects of hardware changes during flight assessed
Calibrations at higher frequencies restored under condition
Constraints on apparent permittivity measurements => values and error bars on dielectric constant (~2.20±0.15) and conductivity (~0.9±0.3 nS/m)
Lookup of the 9539 s event and further possibilities to investigate it with other data and models
We acknowledge particularly the former contribution of Dr. Fernando Simões who moved for another field of science. Also, thanks to CNES for support of joint permittivity HUYGENS and ROSETTA-PHILAE activities
Titan's surface electrical properties - Hamelin et al., EPSC 2014

15. Additionnal slides for discussion
Titan's surface electrical properties - Hamelin et al., EPSC 2014

16. Titan's surface electrical properties - Hamelin et al., EPSC 2014

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19. Titan's surface electrical properties - Hamelin et al., EPSC 2014