We report on the measurements of the Cassini Ion Neutral Mass Spectrometer (INMS) of the density and structure of Enceladus' south polar plume during the E3 and E5 flybys on 12 March and 9 October 2008. Using a Monte Carlo simulation, we analyze the dependence of the INMS gas inlet transmittance on spacecraft pointing and the effect on the measurements at E3. We apply a finite element analysis to correct for water physisorption in the inlet and obtain a maximum plume density almost twice that suggested by the raw INMS data. The results indicate uniform spreading of the plume vapor from the source with a source rate of at least 100 kg/s. We also analyze the detection of ice grains by the INMS and find that, in contrast to the plume's vapor component, the grains are concentrated within the plume jets seen in Cassini imaging, supporting the suggestion that the jets are composed of fine-grained ice.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 One of the most remarkable findings of the Cassini spacecraft's mission to Saturn has been the detection of a cryovolcanic plume of gas and ice grains emanating from Saturn's icy satellite Enceladus [Dougherty et al., 2006; Hansen et al., 2006; Porco et al., 2006; Spahn et al., 2006; Waite et al., 2006]. The plume is located in the satellite's southern polar region and consists of several collimated jet-like sources [Spitale and Porco, 2007] emanating from hot spots [Spencer, 2006] located along several prominent elongated troughs or “tiger stripes” [Porco et al., 2006], which scar the surface. Water vapor is the dominant gaseous constituent of the plume (90% ± 1%), but other volatile constituents such as CO2 and possibly CO and N2 are present in significant abundance, in addition to trace amounts of hydrocarbons, nitriles, and a population of salt-bearing water ice grains [Waite et al., 2009; Postberg et al., 2008; Schneider et al., 2009]. The plume's discovery presents a unique opportunity to characterize the composition and active geological processes in Endeladus' interior and the supply of ice grains to Saturn's E ring [Kempf et al., 2008; Perry et al., 2010] and ultimately to gain insight into the formation of icy objects in the early solar system. Here we examine the measurements of the Cassini Ion Neutral Mass Spectrometer (INMS) of the neutral density and structure of the plume during the recent E3 and E5 encounters of Enceladus.
 The INMS consists of an open ion source for sampling ions, a closed electron impact source for analysis of the neutral gas (Figure 1), a quadrupole mass analyzer, focusing and switching lenses, and two secondary electron multiplier detectors [Waite et al., 2004]. The closed source is equipped with a titanium gas inlet system consisting of an antechamber to capture the neutral gas and a transfer tube to admit a portion of the captured gas into the electron impact ionizer. Molecules enter the antechamber at suprathermal velocities through an orifice faced in the direction of motion of the spacecraft, then thermally accommodate after a few collisions inside the inlet system. Once transmitted into the ionization region, the plume neutrals are ionized through electron impact. The electron impact ionization and fractionation efficiencies are based on laboratory calibration measurements and determine the sensitivity and mass spectra for a particular species.
 However, analyses of in-flight data show several phenomena occurring in the inlet system that were not measured during the laboratory calibrations. These phenomena include (1) wall adsorption, (2) enhanced transfer tube transmission at a particular spacecraft orientation, and (3) signal spikes caused by grain impacts in the closed source. In this work, we compare computer simulations to INMS measurements to investigate these processes. The results yield an improved characterization of the Enceladus plume gas-grain density and structure.
2. Transmission Versus Angle
 This paper reports on results from two Cassini flybys of Enceladus: E3 and E5, during which INMS pointing was optimal (Table 1). During each of these flybys, the spacecraft passed within sufficient proximity to the source of the south polar plume for INMS to obtain measurements of the plume's structure and composition. Both flybys occurred along an approximate north-to-south trajectory, and thus, both plume encounters took place outbound from Enceladus, with Cassini traveling roughly parallel to the plume. The spacecraft speed relative to Enceladus was more than an order of magnitude faster than the thermal velocity distribution of the molecules in the plume. As a result, the transverse velocity component of the incoming molecules is much less than their forward speed relative to the spacecraft and the sample molecules enter the antechamber as a tightly collimated beam.
Table 1. Parameters for the Enceladus Encounters Analyzed in This Work
Here we assume the temperature of the plume vapor to be 157 K: the maximum reported surface temperature in the hot spots [Spencer, 2006], which should be an upper limit.
12 Mar 2008
9 Oct 2008
 Within a few minutes before and after closest approach at E3 and E5, the orientation of the spacecraft was adjusted to maintain a 0 (within ∼0.5°) ram angle θ, defined as the angle between the direction of the incoming molecular beam and the normal to the antechamber entrance orifice. Outside this time window, θ was allowed to drift away from zero as other Cassini instruments were given priority, in some cases while the spacecraft was still under the influence of the plume. The principal consequence of the change in θ is a reduction of the flux entering the antechamber, which varies in proportion to the projected area of the orifice, cosθ. However, a second effect is an enhancement of the transmittance when the ram direction causes the tightly collimated beam of incoming molecules to enter the transfer tube, which is off-axis to the entrance orifice (Figures 1 and 2). In this orientation, molecules arrive initially inside the tube and have much improved odds of reaching the ionizer.
 To quantify the transmittance versus ram direction, we performed a 3-D Monte-Carlo simulation of the molecular trajectories in the inlet system, with the aim of comparing against spacecraft orientation during each Enceladus encounter. We initialized the molecules as a collimated beam originating from the entrance orifice with a direction defined by θ and the azimuthal angle, then tracked their trajectories inside the inlet system until they escaped the orifice or reached the ionizer. Thermal spreading of the incident beam introduces only a small uncertainty (±1°) in the incoming molecule direction and did not significantly affect the results of our simulations. We do not consider reentry of transmitted molecules from the ionizer back into the transfer tube (however, we include the effects of return flux in the absolute calibration, discussed later). Upon striking the walls, the molecules exchange energy with the surface atoms and then desorb according to a cosϕ angular probability distribution, with ϕ the emission angle with respect to the surface normal. Molecules that reach the ionization chamber have, on average, ∼120 interactions with the instrument walls. We assume no intermolecular collisions, as appropriate for the mean free path, which is tens of kilometers at these densities.
 As shown in Figure 3, the transmittance is roughly constant near 8% at angles for which the incoming molecules strike the back surface of the antechamber, i.e., transmission is independent of the point of arrival of molecules in the antechamber. However, the transmission is enhanced by a factor of approximately 3, from roughly 8% to 25% when the incoming molecules arrive at the entrance of the transfer tube, which is at θ = 18° ± 8° within ±25° azimuth. In Figure 3 we trace the ram direction between 0 and 750 s after closest approach at E3 and find that the direction falls within this range of angle near 470 (±100) s. This causes a transient increase in the sensitivity of INMS which, as shown in Figure 4, enhances the H2O signal at 18 amu by a factor of 1.32 (±0.06) over the continuum baseline. This value is below the predicted threefold increase in transmission, since approximately 60–70% of the mass 18 signal at 470 s is due to outgassing of water adsorbed onto the inlet system walls earlier in the E3 encounter and is unaffected by the change in incident angle.
3. Water Adsorption
 Most volatile molecules are transmitted through the inlet system to the ionizer within a few milliseconds (Figure 5), and INMS therefore detects changes to the incoming molecule flux within one sample or integration period, which is 31 ms. By contrast, water molecules adsorb onto the titanium surfaces of the inlet system, a process that extends the transmission time, causing a significant time distortion in the measurements. The distortion is manifested at E3 and E5 as (1) a several-second delay in the appearance of water in INMS relative to other species on Cassini's arrival at the Enceladus plume; (2) a reduction in the peak count rate (apparent peak density); and (3) a widening of the time profile, including an hours long tail in the mass 18 signal due to gradual desorption of water from the inlet system. To determine accurately the flux of water entering the antechamber versus time requires a model of adsorption in the inlet system. Cui et al.  have modeled adsorption effects at Titan where N2, the dominant atmospheric constituent, drives the desorption of other species from the inlet through its bombardment of the walls. By contrast, water is itself the dominant constituent at Enceladus, and its adsorption/desorption on the walls is therefore determined by the competition between molecules for surface binding sites. It is therefore necessary to consider the positional dependence of the water surface coverage.
 We analyze this system in two steps. First, we infer the water density profile from the INMS data by assuming the plume molecular composition to be homogeneous since, except for water, the relative signals of other major volatile species are constant over the E3 and E5 encounters (Figure 6). Hence, we consider the true water density profile to have the same time dependence as that of other species and normalize the profile amplitude to the total amount of water detected by INMS within 24 h of the encounter.
 In the second step of our analysis, we simulate the propagation of water through the inlet system using a finite difference calculation and a model of the antechamber and transfer tube as a surface mesh (Figure A1), then adjust the sticking parameters to match the simulation results with the measured INMS water profile. The sticking is described in terms of two empirical parameters, β and γ that determine the average sticking time on each element according to equation (A6). The detailed description of the parameters and calculations are described in Appendix A, where we multiply the water density profile by spacecraft speed to obtain the incoming flux q and predict the resultant INMS counts using equation (A10).
Equation (A10) yields good agreement with the data obtained at E3 and E5 with b and γ set to 5.3 (±1) × 1017 s · m2γ and 1.1 ± 0.3 (see Figure 7 before 117 s). From equation (A6), these values give sticking times on the order of 0.1–1 s if one assumes σ ∼ 1016–1017 molecules/m2, as is typical during the plume encounter (Figure A1). This corresponds to transmission times of the order of 15–150 s if one considers an average of 120 wall interactions. We show the plume water density profile in Figure 8: the maximum densities, 7.6 (±0.1) and 34 (±0.2) × 1013 molecules/m3 at E3 and E5 (corresponding to mass densities of 2.3 (±0.03) and 10 (±0.06) × 10−12 kg/m3), are almost twice the values determined using a straight calibration from the peak INMS count rate. We have corrected the densities to account for conversion of water into H2 [Waite et al., 2009] by impact dissociation and/or chemical reactions in the antechamber by scaling q by 1/(1 − ɛ); with ɛ the conversion efficiency for H2O into H2. The efficiencies are 0.17 and 0.43 at E3 and E5, as determined from the ratio of the H2 mixing ratios seen by INMS over the encounters (0.17 and 0.39 at E3 and E5, respectively) to the total water mixing ratios (0.96 and 0.90 at E3 and E5, respectively) [Waite et al., 2009].
 Although the density profiles in Figure 8 provide information about the structure and overall source rate of the plume, in Figure 9 we investigate the expansion of the plume and its relationship to the sources reported by Spitale and Porco . The E3 trajectory passes almost directly over the VIII and II sources [Spitale and Porco, 2007], but the INMS does not measure significant density until approximately 50 s after closest approach, when it is within 20° of source II located in the Damascus vent. This observation is consistent with thermal analysis of CIRS data, which show that the Damascus sulcus is more active than the Cairo sulcus [Howett et al., 2009]. The indication that the plume half width is approximately 20° is similar to the results of the studies by Hansen et al.  and Smith et al. .
 To further investigate the source and its structure, we scale INMS data by the square of the distance to the planet's surface, z. The scaled density is nearly flat for 400 s after entering the plume. As Cassini was traveling close to the projected direction of source II (Damascus), a z−2 density dependence corresponds to uniform spreading within a cone, not the z−1 dependence sometimes seen in dust jets and comets [Boice et al., 2002]. Using a circular cone with a 20° half angle and the source velocity of 0.6 km/s recently found by Hansen et al. , the source rate is 100 kg/s or 3.5 × 1027 molecules/s. This result, which is slightly lower than those of Hansen (200 kg/s) [Hansen et al., 2008] and Smith (150 kg/s) [Smith, 2010], should be a low estimate because it does not account for emissions that do not intersect Cassini's trajectory. Estimates of the source rate are also subject to uncertainties, e.g., because current estimates of the source velocity are not well constrained [Tian et al., 2007; Hansen et al., 2008].
4. Ice Grains
 INMS detects the signatures of ice grains entering the gas inlet as spikes in several mass channels: 1, 2, 15, 16, 17, 25, 26, 27, 28, and 44 amu, as shown in Figure 10 for H2 at E3. The grains generate bursts of volatile species when vaporized on impact in the antechamber, with the volatiles either (1) present originally as grain constituents or (2) produced in the antechamber through chemical reactions between grain constituents or with titanium atoms ejected during grain impact [Waite et al., 2009]. The transmission time for volatile constituents (Figure 5) is much shorter than the INMS integration period at each mass (0.031 s), and the INMS captures the arrival of a grain within one period as a single spike. The frequency of spikes varies with the number density of the ice grains in the vicinity of Cassini. The number of detected spikes (33 and 41 at E3 and E5, respectively, as shown in Figure 11) is sufficient to allow us to estimate through statistical analysis the density of grains in the Enceladus plume versus time during each encounter. To perform the analysis we group the total number of spikes in all of the volatile mass channels into time bins, then multiply by tcyc/Δt, which is the instrument cycle time (∼6.3 s at E3 and E5) divided by the time spent on the required mass channels (the ratios were ∼9.0 and ∼8.1 at E3 and E5, respectively). Here tcyc is the interval between complete mass scans (measured repeatedly according to a pre-set table of mass channels), and Δt = y × 0.031 s, with y as the number of volatile mass channel measurements per scan. Dividing by the time bin size, the entrance orifice area, and the spacecraft speed, we obtain a grain density versus time for the E3 and E5 encounter, as shown in Figure 12, where we have used an adaptive time-binning algorithm to maximize resolution near sharp density features while maintaining reasonable counting statistics in each bin. We point out that the densities are likely underestimates, since trace species [1, 8] in the plume vapor and molecules such as H2 and CO produced in the antechamber [Waite et al., 2009] can overwhelm the signatures of small grains during the plume encounter. However, the densities exceed those indicated by the Cassini Cosmic Dust Analyzer (CDA), which may indicate a greater sensitivity of INMS to small grains (less than 1 μm size) (J. Schmidt, Universität Potsdam, unpublished data, 2009). Unfortunately, an estimation of grain size from the spike amplitudes is currently not possible due to uncertainty regarding the degree to which the amplitude reflects the grain composition and/or chemistry in the antechamber and questions about the nature of the chemistry. An example is the H2 spikes appearing in mass 2, which are generated by the reaction of H2O (vaporized during grain impact) with the ejected titanium [Waite et al., 2009]. Although the amount of hydrogen produced in the antechamber is given by equation (B4b) in Appendix B (with Y in equation (B4b) as the spike amplitude), the grain size required to produce this amount depends on several unknowns, e.g., the fraction of H2O in the grains that reacts to form H2, and the amount of H2 that then binds to unreacted titanium deposited onto the antechamber walls [Waite et al., 2009].
 As shown in Figure 12, a sharp peak of grain density at E3 and several at E5 are consistent with the optical measurements indicating that the Enceladus jets consist of fine-grained ice [Porco et al., 2006]. In Figure 13 we color the E5 ground track according to the grain density and compare with the grain jet locations and directions observed by Spitale and Porco [Spitale and Porco, 2007]. The E5 peak 27 s after closest approach shows good correspondence with Cassini's passage 24 km from the Baghdad VI jet (see Figure 13). By comparison, the sources of the peak (or possibly two peaks) seen at 17 s (or of the E3 peak at 118 s) are less obvious, but other jet sources cannot be ruled out in light of recent imaging data indicating that the actual number of jets far exceeds the eight analyzed by Spitale and Porco [CICLOPS Press Release, 2010]. Even for the sources analyzed by these authors, knowledge of the jet directions are subject to uncertainty due to angular spreading (roughly 10°) and, in some cases, poorly constrained azimuthal angles [Spitale and Porco, 2007]. The confinement of the grains to discrete collimated jets suggests acceleration by a unidirectional gas flow emanating, e.g., from fissures terminating at Enceladus' surface [13, 14]. By contrast, the relatively smooth water vapor distribution (Figure 8) is consistent with simulations [Tian et al., 2007; Tenishev et al., 2010] and observations [Hansen et al., 2008] indicating that the thermal velocity distribution of the plume's gaseous component is of a similar order of magnitude as its forward-directed motion (300–700 m/s: [Tian et al., 2007; Hansen et al., 2008; Tenishev et al., 2010]). We also note the significant density of grains on the inbound portion of the encounters (Figures 11 and 12), several Re to the north of Enceladus and well before the encounter with the south polar plume. This may be indicative of grains ejected from the plume close to the Enceladus escape speed (239 m/s) that remain in the satellite's vicinity, e.g., due to orthogonal oscillations of the grains about Enceladus' orbital plane [Kempf et al., 2008].
 Although water ice is the primary grain constituent [Kempf et al., 2008; Postberg et al., 2008], vaporized H2O generated by the arrival of a grain has a distribution of transmission times through the inlet on the order of seconds due to wall adsorption (as indicated by equation (A6) for σ ∼ 1016–1017 m−2), and water reaches the ionizer gradually only over many integration periods. This explains the absence of sharp spikes in the mass 18 channel and, in almost all cases, renders H2O from the grains indistinguishable from ambient water vapor in the plume. However, a notable exception occurs during E3, with a sudden increase in the H2O signal 117 s after closest approach (Figure 7). Since adsorption precludes the transmission of such fast changes in ambient water vapor density through the entire inlet, this anomaly can be explained only by the sudden arrival of H2O inside the transfer tube, i.e., due to the arrival of a grain with a sufficient transverse velocity component to impact inside the tube. We have confirmed this with our surface-dependent adsorption model by initializing at t = 117 s from closest approach a sudden increase in water coverage on different individual surface elements to simulate the arrival of a grain at different locations in the inlet. Through optimization of (1) the impact location and (2) the grains' water content, we find that the height and shape of the observed anomaly (Figure 7) can be approximated only by the impact of an ice grain ∼0.5 cm from the exit of the transfer tube containing ∼4.5 × 1012 H2O molecules. We note that the optimization somewhat overestimates the signal decay after 117 s, a discrepancy that might result from desorption of water deposited inside the ionizer due to the grain's close proximity to the tube exit. The assumption of spherical grains yields a diameter of 6.6 μm. This is larger than the expected size range based on the measured grain densities (as discussed above) and the CDA measurements (J. Schmidt, Universitat Potsdam, unpublished data, 2009) but within the range suggested by the Cassini Visual and Infrared Mapping Spectrometer (VIMS) [Hedman et al., 2009]. The grain impact point requires an entry angle of θ = 4.5°–9.0° into the antechamber. This corresponds to a transverse velocity component of 1134–2282 m/s with respect to Enceladus, which is significantly greater than the speeds of a few hundred meters per second suggested by Cassini imaging [2, 6, 13], VIMS [Hedman et al., 2009], and CDA measurements [Kempf et al., 2008]. A possible explanation is the deflection of the grain (or fragmentation of a grain >6.6 μm diameter) after a collision with the edge of the antechamber entrance orifice or other spacecraft surface.
 We have applied detailed computer simulations of the Cassini INMS closed source gas inlet to elucidate the distribution of gas and grains at Enceladus by addressing several poorly characterized anomalies in the results of the Cassini INMS during the E3 and E5 encounters. These are (1) a transiently enhanced transmission of gas through the inlet at E3 due to spacecraft pointing, (2) delayed detection of water vapor due to water adsorption on the inlet walls, (3) spikes observed in multiple mass channels due to the release of volatile species by ice grains impacting the inlet, and (4) a sudden jump in the mass 18 signal at E3 117 s after closest approach due to the arrival of an ice grain inside the inlet transfer tube. Our results provide an interpretation of the in situ, measured density profiles of the Enceladus plumes for the E3 and E5 encounters. The profiles indicate that the density of water vapor, comprising more than 90% of the plume composition [1, 8], is more sharply peaked than indicated by the raw INMS data. The proportionality of the density profile to the inverse square of the distance from the surface of Enceladus indicates uniform spreading of the plume vapor from the source, with a source rate of at least 100 kg/s. Compared to the relatively isotropic emission of water vapor from the plume sources, INMS measurements of the grain density indicate that the grains are ejected into collimated jets that coincide with those seen in Cassini imaging results [Porco et al., 2006; Spitale and Porco, 2007]. Our findings constitute one of the most detailed descriptions of the gas grain structure of the Enceladus plume to date and will provide valuable constraints for future studies that require quantitative estimates of the plume density profile and magnitude.
 Here we give a detailed description of our model of water adsorption in the inlet system and its propagation to the ionizer during the Enceladus encounters. Our approach is to model the inlet system as a surface mesh consisting of 1293 elements and to evaluate the propagation of water through the inlet via a finite difference calculation, taking into consideration adsorption and desorption at each surface element during each time step (Figure A1). The parameters used in the model are shown in Table A1. The model can be described in six parts, as follows:
Table A1. Parameters Used in the Simulation of the INMS Inlet System
Surface element index
Source: number of molecules hitting surface element i
Area of surface element i
Density of molecules adsorbed onto surface element i
Rate that molecules desorb from surface element i
Rate that molecules transfer from surface element j to surface element i
Gas temperature in the ionizer
Flux entering the ionizer from the transfer tube
Sticking time per molecule (function of σi)
Probability that a molecule entering the ionizer will reenter the transfer tube
Angle from the surface normal of surface element i to surface element j
Angular distribution function for molecules leaving the surface
Distance between surface elements i and j
Sticking parameter; linear coefficient
Sticking parameter: exponent coefficient
Delay to adjust rise time of simulated water counts
Conductance to escape the ionization chamber
INMS sensitivity for a particular molecule
Probability that a molecule entering the antechamber will reach the ionizer
INMS count rate
Average molecular velocity at temperature T
 1. The surface density (coverage) of water σi adsorbed onto a surface element i is controlled by the water input flux and the desorption and adsorption rates:
where t is time. qi, Fi, and Fji, are the source, desorption rate, and transfer rate between elements, respectively, and are described below. Because the entrance orifice and tube exit planes do not constitute real physical surfaces, we set σi = 0 at all times for elements on these planes. We also assume a clean inlet system, i.e., σ = 0 everywhere, as our initial condition; we investigated using a nonzero surface coverage as indicated by the nonzero background count rates, but this low coverage did not affect the simulation of E3 and E5.
 2. The desorption rate Fi from element i is given by
where the average sticking time τ is in general a function of coverage (see below). For elements that comprise the plane of the exit of the transfer tube into the ionization chamber, we define Fi as the rate of return of molecules from the ionizer back into the transfer tube (i.e., after collisions inside the ionizer). For these elements,
with β denoting the return probability for a molecule entering the ionizer (see calculations in part 6 of the model description) and Φ the average flux per unit area exiting the transfer tube into the ionizer. Φ is given by
where Fji denotes the transfer rate from element j to i (as explained below), and we have summed i only over elements on the plane of the transfer tube exit. Equation (A3) ignores the time delay for a molecule to enter the ionization chamber and then find its way back to the transfer tube, but this time is short, as described in the section on ice grains.
 3. The transfer rate Fji from element j to i (i.e., molecules desorbing from j that adsorb on i) is given in terms of the distance rij between the elements, the angle θij between the normal to surface element i and the vector connecting i and j, the opposing angle θji, the area Aj of j, and the angular distribution f(θji) of desorption from j evaluated at angle θji, as follows:
where we assume a cosine desorption distribution f(θji) = cos θji. As an exception to equation (A5), we set Fji = 0 when no line of site exists between i and j.
 4. For the average sticking time we use
which yields a power law dependence of the desorption rate on time, as is typical for metals in a vacuum system [Dylla et al., 1993; Toth, 2002]. The σ dependence of sticking time results from the distribution of adsorption binding energies on the inlet system surface, with water molecules migrating by surface diffusion to the strongest available adsorption sites. With increasing coverage, adsorbed molecules have no option but to occupy weaker sites, thus lowering the average sticking time. Although the parameters b and γ are empirical, the magnitude of γ can be considered a qualitative measure of the width of the binding energy distribution, with the limit γ → 0 corresponding to the existence of only one binding energy [Toth, 2002].
 5. The source function qi is equal to the ambient water density times the spacecraft speed. It is zero except on elements located within the circular patch of the antechamber surface directly in the path of the incoming molecular beam. As explained earlier, we assume qi(t + Δ) to have the same shape versus time as the signals of other volatile species and set the amplitude of q (times the entrance orifice area A0 = 2.173 × 10−5 m2) so that its time integral yields C/αS times the total number of water molecules detected by INMS. C is the conductance for gas to escape the ionizer (4.1 × 10−4 m3/s for H2O at room temperature [Kasperzak, 2009]), α = 0.08 is the transmittance to the ionizer, and S is the species-dependent INMS calibration sensitivity factor (∼1.48 × 10−10 m3/s for water [Gell et al., 2009]). The derivation of the factor C/αS is given in Appendix B. After mass 18 the strongest signals are seen in mass channels 2, 26, 28, and 44 (corresponding to H2, C2H2, CO and/or N2, and CO2 [Waite et al., 2009], as shown in Figure 6. Accordingly, we use these three channels to determine the shape of the source profile by normalizing (after background subtraction and removal of ice grain spikes) and then averaging the signals. The simulation best matches the data with an offset Δ = −12 s. The requirement of an offset suggests either (1) that INMS encounters the water 12 s earlier than the other volatile species (unlikely) or (2) that there is a phenomenon not accounted for in the sticking model such as surface diffusion of adsorbed H2O, which would reduce the water transmission time through the inlet. Further refinement of the model in future work will include additional effects such as diffusion.
 6. The INMS signal χ (i.e., the count rate) is proportional to the density ρ of molecules inside the ionizer times the sensitivity:
where S is the calibration sensitivity factor for water and Ti and T0 are the ionizer temperature and room temperature, respectively. The correction for temperature is needed since S was measured in the laboratory with respect to an equilibrium room temperature gas density surrounding the instrument [Gell et al., 2009], which is different by a factor (Ti/T0)1/2 from the density inside the ionizer. The flux per unit area Fi reentering the transfer tube (with i now denoting only elements on the tube exit plane) is v/4 times the density [Gombosi, 1994], and therefore,
where v, the average speed of gas molecules in the ionizer, is given by
with m the molecule mass and k the Boltzmann's constant. Using equations (A3), (A4), (A7), (A8), and (A9), one can express the count rate in terms of Fji:
Here we note that knowledge of Ti is not required for the model because it cancels from equation (A10).
 For S we use 1.48 × 10−10 m3/s for water. This sensitivity is one third the value based on laboratory measurement: analyses show that the total densities derived by INMS in-flight data are consistently lower by a factor of around 3 than those determined by the navigation and attitude-control teams assessing the drag on the spacecraft at Titan (H. Niemann et al., personal communication, 2009). Although the cause of this difference is not certain, the requirement for an adjustment to the INMS sensitivities is clear. β is given by Ce/(Ce + C′) = 0.97, where Ce = vAe/4 is the gas conductance through the transfer tube exit and C′ is the conductance through all other ionizer escape paths (7.97 × 10−5 m3/s for H2O at room temperature [Kasperzak, 2009]).
 In the discussion of the source function we multiply by the factor C/αS to convert the integrated counts into the total number of molecules detected by the INMS, where C is the conductance for gas to escape the ionizer (4.1 × 10−4 m3/s for H2O [Kasperzak, 2009]), α = 0.08 is the transmittance to the ionizer, and S is the species-dependent INMS calibration sensitivity factor [Gell et al., 2009]. Although we applied the factor for the case of H2O, the relationship is valid for any species, provided that the correct S is used, and that C is corrected for the molecular mass. To derive the conversion factor we first note that the rate of change of gas density in the ionizer is given by
where Q denotes the arrival rate of molecules into the ionizer and V is the ionizer volume (0.512 cm3) (P. Mahaffy, Goddard Space Flight Center, unpublished data, 2009). We now integrate equation (B1) between times t0 and t1
Setting t0 and t1 such that ρ(t0) and ρ(t1) are zero, as would be the case before and after an event of interest (e.g., an Enceladus encounter), we can write
where we have canceled V and substituted the count rate χ = Sρ as given in equation (A7). The integral over Q is equal to αn, with n as the total number of molecules arriving in the antechamber, and the integral over X is just the integrated counts Y. Therefore,
Finally, because the ionizer time constant V/C is very short (of the order 10−3 s), one can for volatile species approximate equation (B1) as
Again, substituting χ = Sρ and Q = α(dn/dt), and writing dn/dt ≈ v0A0ρ0, with v0 the spacecraft speed (assumed here to be much greater than the ambient thermal velocity), one obtains an expression (valid for volatile species) for the ambient molecule density ρ0 in terms of the count rate, which does not require explicit knowledge of the antechamber's ram enhancement factor:
 This research was supported by the NASA Jet Propulsion Laboratory through contract 1228303.
 Masaki Fujimoto thanks the reviewers for their assistance in evaluating this paper.