Modeling of magnetic field vectors and plasma flow density contours in the X Z plane (after Ledvina &. Cravens , 1998). Several Titan flybys, confirming the basic.
The plasma-driven Schumann resonance on Titan revealed by Huygens enlightens new constraints on the characteristic scales of ocean depth and ionospheric conductivity by C.Béghin1, C. Sotin2 , M. Hamelin3 et al.
Presentation to 48th Cassini Project Science Group Meeting June 23, 2009, London, UK
a - LP2CE-CNRS-University of Orléans, Fr b - JPL & California Institute of Technology, Pasadena, CA, USA c - ATMOS-University Pierre & Marie Curie, Paris, Fr
Peculiarities of PWA- ELF data
MT 1930 s => Preprogrammed mode change MT 1884-1992 s => Maximum conductivity of the galactic cosmic rays layer (GCR) MT 900-903 s => Main chute jettison & stabilizer chute inflation 2
Peculiarities of the 36 Hz line Altitude (km)
conductivity
120
*+
100
*+ *+
36 Hz line
GCR layer
60
Average of 60 spectra (80 to 90 km)
Smoothed ELF power-density spectrum
20
0
**++
*+
*+
+
*
*+ + * *+ + +* +* + * *++* +* +* *+**++ *+++ + + **** ++
40
Large amplitude short term variations
*+
*+
80
0
1
2
3
4
5
6
Electric field (mVm -1 Hz -1/2)
• The altitude profile of signal strength depends on atmospheric conductivity • Three linear regression fits: •(i) h > 95 km •(ii) 60 < h < 90 km •(iii) h < 60 km • The signal strength is not zero at the surface
3
Electric Field Spin Modulation Selection of 360 ELF spectra, 19 min 10 s (45-30 km)
Probability within 12 azimuth classes for the 36 Hz signal amplitude being larger than the average level observed during 4 rotations at least (excerpt from Béghin et al, 2009)
Statistical analysis of antenna response versus Huygens attitude - none detectable modulation associated with the tilt of Huygens-probe vertical axis - the 36 Hz line amplitude is clearly modulated twice per rotation of the gondola
Conclusion : the signal is an EM wave with horizontal E field polarization The attitude data were obtained from DISR (Karkoschka et al, 2007)
4
Before HUYGENS Earth’s like Schumann TM mode expected Lightning: likely
Upper EM cutoff ? (h2~ 500 km ?)
Methane ocean ? Ice crust ? Conductive boundary ocean (H2O, NH3, + …) ?? Eigenmodes zero orderapproximation
η=2 (f ~ 30- 40 Hz)
2575 km
η =1
2 π nR η (η + 1) = λ
2
( f ~ 20 Hz) n = effective refractive index ~ 1.2 R = mean cavity radius ~ 2650 km ?
{
Referring to Earth conditions TM mode only
TM mode, with E field essentially vertical : expected TE mode, with E field only horizontal : ???? 5
After HUYGENS Earth’s like Schumann TM mode ? Lightning
Upper EM cutoff h2~ 200 km TBC
likely NO
Methane ocean NO Ice crust YES Conductive boundary ocean (H2O, NH3, likely YES Eigenmodes zero orderapproximation
η=2 (f ~ 36 Hz)
2575 km
η =1
2 π nR η (η + 1) = λ
2
( f ~ 20 Hz) n = effective refractive index ~ 1.2 R = mean cavity radius ~ 2650 km
{
Referring to Earth conditions TM mode only
TM mode, with E field essentially vertical : NO TE mode, with E field only horizontal : YES 56
Arguments against an Earth-like Schumann resonance Vertical Electric-field component
Horizontal Electric-field component h2 h1 h2/2
Earth’s usual TM mode (after Sentman, 1990)
World-wide lightning distribution 100 flashes/s, 500 Mega Joule each
Earth’s theoretical TE mode (Béghin, 2007)
•To account for the observed field strength (some mV m-1 Hz-1/2 ), a permanent power source of 20 Mega Watt might be converted into EM radiation in the ELF range (Béghin et al, 2007). • After tens of Titan’s fly-bys none lightning flash above a threshold of 10 k Joule was detected by RPWS (Fischer et al, 2007) • Then, what kind of source here ? 7
Power budget from Saturn’s magnetosphere
Pickup ions up to 5 keV after Hartle et al 2006
Sketch of Titan interaction through Saturn’s magnetosphere (after Béghin et al, 2007)
A rough estimate: v = 150-200 km s -1, B = 5-10 nT E ~ 1 mV m-1 ΔV = 5 kV through ~ 5000 km Tail current I = LB/μ0 , L ~ 10 Titan radii, B ~ 10 nT I = 2×105A Available power 1000
Mega Watt 8
Tail currents mapping from Cassini T5 flyby, April 16, 2005
ram
ram
Modeling of magnetic field vectors and plasma flow density contours in the X Z plane (after Ledvina & Cravens , 1998).
Several Titan flybys, confirming the basic scheme of draped field lines around the ram hemisphere, are still under scrutiny to mapping the contact region known as Induced Magnetospheric Boundary (IMB) Excerpt from Béghin et al (2009)
8
Candidates sources of ELF wave emissions Quasi-Electrostatic emissions associated with IMB
Different generation mechanisms are potential candidates • MHD emission by pick-up energetic ions (Gurnett et al, 1982) . Rejected because of too weak Doppler shift. • Whistler-mode instability, routinely observed on Earth. The most likely mechanism invoked for Voyager 1 observations (Gurnett et al, 1992) and repeatedly confirmed when Cassini is crossing the far tail-lobes. • Ion-acoustic instability (electrostatic turbulence) and subsequent coupling with EM mode (Béghin et al, 2009).
A 36 Hz wave frequency may propagate in the whistler-mode as long as the steady B field strength is above 1.4 nT and the electron-neutral collision frequency is smaller than ~ 100 s-1. Thus, an EM wave generated above ~ 800 km cannot propagate deeply downwards (Béghin et al, 2009).
T5 flyby Excerpt from Béghin et al (2009)
Recent model shows that conditions are favorable for ion-acoustic instability to develop within a wide region extending down to 200 km. This would be the most likely source of the 36 Hz emission observed by Huygens. 9
An exotic conductivity profile EM cutoff boundary
Conduction boundary
Borucki & Whitten model (2008)
MI measurements
Several scenarios & models (e.g. Tobie et al, 2004) - Ice 1 dielectric crust, thickness 70 to 300 km - Experimental presumption for presence of ocean (Lorenz, 2008)
Such a slab-loaded conductivity profile cavity leads to consider a Longitudinal Section Electric (LSE) mode instead of the usual TE mode (Collin, 1991)
• Black stars, MI measurements (Hamelin et al, 2007), 90 to 30 km and at the surface • Scale-height and (h1- h2) values derived from the TE-like model (Béghin et al, 2009) • Dashed red line, model from Borucki and Whitten (2008) for photoemission 10 threshold of aerosols = 7.2 eV and particle density = 420 kg m-3 .
Model of Titan’s LSE2,0 mode For LSE modes, the electric field lies within the longitudinal plane parallel to the layers, and it is proportional to the Curl of the magnetic Hertzian vector potential πH (Collin, 1991). In spherical geometry, the E-field polarization is azimuthal at the antinodes of even modes, and its amplitude obeys the Helmoltz’s scalar radial equation ∂ 2 EL ∂E L r + 2 r + [k02 r 2 nr2 − l (l + 1)] EL = 0 2 ∂r ∂r 2
where nr2 = ε - iσ /(ε0 ω)
The second zonal spherical-harmonic LSE2,0 presumed to have been observed The ionospheric current-sources are assumed to be connected North/South symmetrically to the ionosphere through the IMB. Blue and red surfaces (positive and negative phases respectively) are antinodes for the horizontal electric field at ~ 36 Hz, and white zone shows the Northern middlelatitude node. The Huygens landing site lies nearly at the antinode. 11
Altitude profiles of the mode LSE2,0 Electron conductivity
36 Hz E-field amplitude
? linear extrapolation for σ ≤ 1 nS m-1 The exact solution of the Helmoltz equation which satisfies the boundary conditions on each portion of the conductivity profile is in progress for the mode LSE2,0. Neglecting the second order effect due to the GCR layer, the eigen-frequency is again given by the usual relation (Sentman,1990), in which the altitudes h1 and h2 are referred to the estimated altitude of a perfectly conducting surface ( - 45 km, assuming pure Ice crust).
1/ 2
c h l (l + 1) 1 f ≈ 2πR h2
≈ 36.5 Hz (l = 2), with h1 = 100 + 45 km h2 = 180 + 45 km 12
CONCLUSION • The 36 Hz signal presents all characteristics of an EM wave (a) Its amplitude is modulated at twice the gondola spin period (b) Such feature indicates a quasi-linear horizontal polarization plane (c) The field-strength altitude profile fits ideally that of the conductivity (d) The GCR conductivity layer bends the E-field profile as expected
• It resembles the expected 2d harmonic of a Schumann resonance (a) Earth-like TM mode doesn’t comply with a major horizontal E-field (b) Earth-like lightning have no experimental evidence on Titan (c) The power budget complies with the available energy from the wake (d) Cassini-Titan flybys confirm entry regions of currents through IMB
• Constraints induced by the plasma-driven Schumann resonance (a) Expected strong ion-acoustic turbulence below the ionopause (b) A global conductivity scale-height ~ 10 km from 100 to 200 km (c) Necessary presence of a subsurface conductive ocean (d) Maximum and probable thickness of the dielectric ice crust. 13
References •
Béghin, C. 2007. Théorie analytique du mode TE (in French), report LPCE-CNRS Univ. Orléans, ftp://lpce.cnrs-orleans.fr/users/Christian_BEGHIN/pub/Titan_papers/Mode%20TE%20.pdf
•
Béghin, C. and 11 colleagues, 2007. A Schumann-like resonance on Titan driven by Saturn’s magnetosphere possibly revealed by the Huygens Probe. Icarus, 191, 251-266.
•
Béghin, C. and 10 colleagues, 2009. New insights on Titan’s plasma-driven Schumann resonance inferred from Huygens and Cassini data. Planet. Space Sci., doi:10.1016/j.pss.2009.04.006. Collin, R.E., 1991. Field Theory of Guided Waves. Second Edition, IEEE Inc., New York, pp 1-852.
• •
Fischer, G., Kurth, W.S., Dyudina, U.A., Kaiser, M.L., Zarka, P., Lecacheux, A., Ingersoll, A.P., Gurnett, D.A., 2007. Analysis of a giant lightning storm on Saturn. Icarus, 190, 528-544.
•
Hamelin, M., and 17 colleagues, 2007. Electron conductivity and density profiles derived from the Mutual Impedance Probe measurements performed during the descent of Huygens through the atmosphere of Titan. Planet. Space Sci., 55, 1964-1977.
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Hartle, R.E., et al., 2006. Initial interpretation of Titan plasma interaction as observed by the Cassini plasma spectrometer. Comparison with Voyager 1. Planet. Space Sci., 54, 1211-1224.
•
Karkoschka, E., Tomasko, M.G., Doose, L.R., See, C., McFarlane, E.A., Schröder, S.E., and Rizk, B., 2007. DISR imaging and the geometry of the descent of the Huygens probe within Titan’s atmosphere. Planet. Space Sci., 55, 1896-1935.
•
Ledvina, S.A. and Cravens, T.E., 1998. A three-dimensional MHD model of plasma flow around Titan. Planet. Space Sci., 45, 1175-1191.
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Lorenz, R.D., and 8 colleagues, 2008. Titan’s Rotation Reveals an Internal Ocean and Changing Zonal Winds. Science, 319, 1649-1651.
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Sentman, D.D., 1990. Approximate Schumann resonance parameters for a two-scale height ionosphere. J. Atmos. Terr. Phys., 52, 35-46.
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Tobie, G., Grasset, O., Lunine, J., Mocquet, A., Sotin, C., 2005. Titan’s internal structure inferred from a coupled thermal-orbital model. Icarus, 175, 496-502.
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