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Figure 2. Ganymede, Jupiter’s largest satellite, is one of several moons in the Solar System thought to contain liquid water. Source: NASA [NASA, 2014], Image credit: NASA/JPL-Caltech
noted in the following by NEPWI,f , with corresponding level LN,f = 10 log10[NEPWI,f /(I0/f0)] dB, where f0 is a suitable refer- ence frequency. Although the quantity LN,f , defined in this way, has a reference value of I0 / f0 (i.e., 0.65 aW/(m2 Hz) on Earth, with f0 = 1 Hz), its value is widely reported in units of “dB re 1 μPa2/Hz”, consistent with the reference values of sound pressure and frequency from Table 1, but raising questions about the appropriate choice of Z, Z0 in Equation 2. The definition of LN,f leads to several different interpreta- tions of the stated noise value (LN,f = 40 dB re 1 μPa2/Hz), depending on this choice. For a receiver in Ligeia, Z must be the impedance of the local medium (e.g., Z ≈ 1.2 MPa s/m for a measurement in liquid ethane, or Z ≈ 0.67 MPa s/m for liquid methane), but what is Z0? On Titan there is no estab- lished convention, but one possible
interpretation is that the reference intensity is a universal constant, i.e., that the value for seawater (I0 = 0.65 aW/m2) is used as a uni- versal standard reference intensity. In this interpretation, the 40 dB corresponds to EPWI = 6500 aW/ (m2Hz), leading to an MSP spec- tral density of precisely 7800 μPa2/ Hz for a receiver in ethane or 4355 μPa2/Hz in methane. Four further values are obtained if the reference intensity is based instead on the impedance of either liquid ethane (I0 = 0.83 aW/m2) or liquid meth- ane (I0 = 1.49 aW/m2), making six combinations in all. These six pos-
sibilities are summarized in Table 2, illustrating a maximum difference in MSP exceeding a factor of four.
It is not the hydrocarbon nature of Ligeia Mare that results in the ambiguity illustrated by Table 2, but the contrast between the impedance of Ligeia's (liquid) hydrocarbons and that of seawater under standard conditions on Earth. Pointed out originally by (Horton, 1959) (Horton’s proposed solution at the time was the adoption of a standard reference intensity of 1 W/cm2), it is also not a new problem, but Horton’s warn- ing has gone unheeded for more than half a century.
The ambiguity exists in any medium whose impedance dif- fers from Z0 ≈ 1.5 MPa s/m, including water subject to high pressure. The impedance of liquid water increases with in- creasing pressure, up to about 1.7 MPa s/m in a deep ocean trench on Earth (Leroy et al., 2008). Even higher pressures are to be found at the bottom of the oceans thought to exist in the Jovian moons Europa and Ganymede and other ocean planets (Hussmann et al., 2006), with sound speeds in liq- uid water of up to 1750 m/s estimated for Europa (Leighton et al., 2008) and 2500 m/s measured for conditions similar to those expected on Ganymede (Vance and Brown, 2010), compared to 1500 m/s in seawater at atmospheric tempera- ture and pressure. Taking into account expected variations in density with pressure (Vance, 2007), the estimated imped- ance values corresponding to these sound speeds are Z ≈ 1.7 MPa s/m (ocean trench), 1.9 MPa s/m (Europa) and 2.9 MPa s/m (Ganymede). The resulting uncertainty in any reported noise level, estimated as 10 log10(Z/Z0) dB, is between 0.5 dB (ocean trench) and 2.8 dB (Ganymede).
Table 2: Possible values ofthesspeeccttrraallddeennssitiytyooffEEPPWIIaannddMMSPS,Pa,lal cllocnosnistiestnetnwtiwthitthethneoise
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level in Ligeia Mare of 40 dB re 1 μPa /Hz, depending only on the choice of Z and Z .
noise level in Ligeia Mare of 40 dB re 1 μPa /Hz, depending only on the choice o0f Z and Z0.
EPWI spectral
density MSP
/ aW m-2 Hz-1
Spectral Density / μPa2 Hz-1
case
𝑍𝑍!!d𝑝𝑝!/d𝑓𝑓
receiver in liquid ethane
(Z = 1.2 MPa s/m)
d𝑝𝑝!/d𝑓𝑓
receiver in liquid methane
(Z = 0.67 MPa s/m)
d𝑝𝑝!/d𝑓𝑓
universal standard (seawater: I0 = 0.65 aW/ m2)
6500 7800.00 4355.00
local Ligeia standard
(liquid ethane: I0 = 0.83 8300 9960.00 5561.00
aW/ m2)
alternative local Ligeia standard
(liquid methane: I0 = 1.49 aW/ m2)
14900
17880.00
9983.00
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