Cryogenic Dielectric Property Measurements Applied to Constraining the Composition of Titan’s Seas: Implications for the hydrocarbon cycle

Abstract:

To model quantitatively the response of Titan’s lakes and seas to Cassini’s RADAR instrument, and thus determine surface reflectivity, attenuation and penetration depth, it is necessary to constrain the dielectric properties of their liquids at ~14 GHz. Pre-Cassini estimates of methane loss tangents ranged from ~1.6 to 1.7 (real component) and ~10^-5 to 10^-3(imaginary components).

We present a new technique for measuring dielectric properties, used to measure the complex dielectric constant of relevant materials. A cylindrical cavity containing a cylindrical quartz tube, filled with pure methane or ethane situated along the cavity axis, was excited in TM_0n0 modes, where the n= 2 mode had a resonant frequency of ~14 GHz at 90K. Calibration required measurement of cavity resonant frequency and quality factor for the empty cavity, the inserted empty tube, and the tube filled with a hydrocarbon liquid. These quantities were determined by fitting the measured amplitude versus frequency curve with a Lorentzian line shape.

Several sets of measurements have been performed, giving complex dielectric constants (ε’ + ε” i) of 1.72 + 0.000049i for methane (tan δ = 2.8 x 10^-5) and 2.00 + 0.000246i for ethane (tan δ = 1.23 x 10^-4). Assuming that the dielectric properties of Ligeia Mare, as calculated by Mastrogiuseppe et al., are dominated by a nitrogen-saturated, binary methane-ethane mixture that obeys simple mixture modeling, our results are most consistent with pure methane-nitrogen. We can accommodate up to 13 vol% ethane, based on statistical uncertainties, or 19 vol% ethane, based on more conservative analytical uncertainties (incorporating uncertainties in measured quality factors, Lorentzian line shape fits, cavity radius, and quartz tube dimensions and calculated dielectric constant). All alternative compositions exhibit greater loss tangents, and so it is difficult to avoid the conclusion that methane is the dominant constituent of Ligeia Mare. We infer that ethane is either lost from or concentrated within Titan’s hydrocarbon cycle.