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1.
A two-dimensional kinetic model calculation for the water group species (H2O, H2, O2, OH, O, H) in Europa's atmosphere is undertaken to determine its basic compositional structure, gas escape rates, and velocity distribution information to initialize neutral cloud model calculations for the most important gas tori. The dominant atmospheric species is O2 at low altitudes and H2 at higher altitudes with average day-night column densities of 4.5×1014 and 7.7×1013 cm−2, respectively. H2 forms the most important gas torus with an escape rate of ∼2×1027 s−1 followed by O with an escape rate of ∼5×1026 s−1, created primarily as exothermic O products from O2 dissociation by magnetospheric electrons. The circumplanetary distributions of H2 and O are highly peaked about the satellite location and asymmetrically distributed near Europa's orbit about Jupiter, have substantial forward clouds extending radially inward to Io's orbit, and have spatially integrated cloud populations of 4.2×1033 molecules for H2 and 4.0×1032 atoms for O that are larger than their corresponding populations in Europa's local atmosphere by a factor of ∼200 and ∼1000, respectively. The cloud population for H2 is a factor of ∼3 times larger than that for the combined cloud population of Io's O and S neutral clouds and provides the dominant neutral population beyond the so-called ramp region at 7.4-7.8 RJ in the plasma torus. The calculated brightness of Europa's O cloud on the sky plane is very dim at the sub-Rayleigh level. The H2 and O tori provide a new source of europagenic molecular and atomic pickup ions for the thermal plasma and introduce a neutral barrier in which new plasma sinks are created for the cooler iogenic plasma as it is transported radially outward and in which new sinks are created to alter the population and pitch angle distribution of the energetic plasma as it is transported radially inward. The europagenic instantaneous pickup ion rates are peaked at Europa's orbit, dominate the iogenic pickup ion rates beyond the ramp region, and introduce new secondary plasma source peaks in the solution of the plasma transport problem. The H2 torus is identified as the unknown Europa gas torus that creates both the observed loss of energetic H+ ions at Europa's orbit and the corresponding measured ENA production rate for H.  相似文献   

2.
Observations of the Europa environment using the Cassini UltraViolet Imaging Spectrograph (UVIS) show the presence of an extended atomic oxygen atmosphere in addition to the bound molecular oxygen atmosphere first detected by Hubble Space Telescope in 1994 [D.T. Hall, D.F. Strobel, P.D. Feldman, M.A. McGrath, H.A. Weaver, 1995, Detection of an oxygen atmosphere on Jupiter's moon Europa, Nature 373, 677-679]. The atomic oxygen measurement provides a direct constraint on the sputtering and loss of Europa's water ice surface and the interaction of Europa's atmosphere with Jupiter's magnetosphere. We derive a loss rate for O2 based on the emission rate of the OI 1356 Å multiplet. UVIS detected substantial variability in the oxygen emission from Europa's oxygen atmosphere that we attribute to the viewing geometry. B.H. Mauk, D.G. Mitchell, S.M. Krimigis, E.C. Roelof, C.P. Paranicas [2003, Energetic neutral atoms from a trans-Europa gas torus at Jupiter, Nature 421, 920-922] inferred the presence of a torus of neutral gas at Europa's orbit based on Cassini's energetic neutral atom (ENA) image of the Jupiter system acquired with the Magnetospheric Imaging Instrument (MIMI), with the most likely torus constituents being hydrogen and oxygen species sputtered from Europa. Cassini UVIS data rule out O and O2 as the possible torus species reported by Mauk et al. however, unless the torus density is so low that it is undetectable by UVIS (less than 8 atoms / cm3). The UVIS observations indicate the presence of atomic hydrogen and possibly other species, but a full analysis is deferred to a following paper. The hydrogen in the present observations shows a local-time asymmetry and complex spatial distribution.  相似文献   

3.
Ground based observations of sodium escaping from Europa suggest the presence of an extended cloud of neutrals orbiting Jupiter. Using a Monte Carlo model we show that the large scale morphology differs from the sodium cloud at Io. At Europa, the trailing cloud is brighter and more extended than the leading cloud. We then use our results to consider the morphology of Europa's oxygen cloud.  相似文献   

4.
T.A. Cassidy  R.E. Johnson  M.C. Wong 《Icarus》2007,191(2):755-764
Results from a three-dimensional ballistic model of Europa's O2 atmosphere are presented. Hubble Space Telescope (HST) ultraviolet observations show spatially non-uniform O2 airglow from Europa. One explanation for this is that the O2 atmosphere is spatially non-uniform. We show that non-uniform ejection of O2 alone cannot reproduce the required morphology, but that a non-uniform distribution of reactive species in Europa's porous regolith can result in a non-uniform O2 atmosphere. By allowing O2 molecules to react with Europa's visibly dark surface material, we produced a spatially non-uniform atmosphere which, assuming uniform electron excitation of O2 over the trailing hemisphere, compares favorably with the morphology suggested by the HST observations. This model, which requires a larger source of O2 than has previously been estimated, can in principal be tested by the New Horizons observations of Europa's O2 atmosphere.  相似文献   

5.
Strong experimental evidence is presented that the northern polar cloud observed in Titan's atmosphere by the Cassini orbiter (VIMS) was indeed composed of ethane aerosol as proposed by Griffith et al. [2006. Science 313, 1620-1622]. We report on the condensation and phase behavior of ethane aerosol under atmospheric conditions of Titan (145 hPa, 40 km altitude, 70-90 K, 10-30 ppm ethane in nitrogen). The results were obtained in an in-situ collisional cooling experiment combined with Fourier-transform infrared (FTIR) spectroscopy. Apart from the liquid phase, three crystalline phases (solid I, solid II, metastable) and the transitions into each other have been observed in the ethane aerosol. The phases were found to have a significant effect on the particles' IR spectra, their growth dynamics and the final size of the aerosols which varies between 0.5 and 4 μm (compared to 1-3 μm observed on Titan). This has strong implications on the ethane vapor pressure, precipitation and optical aerosol detection.  相似文献   

6.
Darrell F. Strobel 《Icarus》2006,182(1):251-258
Tidal waves driven by Titan's orbital eccentricity through the time-dependent component of Saturn's gravitational potential attain nonlinear, saturation amplitudes (|T|>10 K, , and ) in the upper atmosphere (?500 km) due to the approximate exponential growth as the inverse square root of pressure. The gravitational tides, with vertical wavelengths of ∼100-150 km above 500 km altitude, carry energy fluxes sufficient in magnitude to affect the energy balance of the upper atmosphere with heating rates in the altitude range of 500-900 km.  相似文献   

7.
《Icarus》2009,199(2):458-476
On September 8, 2001 around 2 h UT, the largest uranian moon, Titania, occulted Hipparcos star 106829 (alias SAO 164538, a V=7.2, K0 III star). This was the first-ever observed occultation by this satellite, a rare event as Titania subtends only 0.11 arcsec on the sky. The star's unusual brightness allowed many observers, both amateurs or professionals, to monitor this unique event, providing fifty-seven occultations chords over three continents, all reported here. Selecting the best 27 occultation chords, and assuming a circular limb, we derive Titania's radius: (1-σ error bar). This implies a density of using the value derived by Taylor [Taylor, D.B., 1998. Astron. Astrophys. 330, 362-374]. We do not detect any significant difference between equatorial and polar radii, in the limit , in agreement with Voyager limb image retrieval during the 1986 flyby. Titania's offset with respect to the DE405 + URA027 (based on GUST86 theory) ephemeris is derived: ΔαTcos(δT)=−108±13 mas and ΔδT=−62±7 mas (ICRF J2000.0 system). Most of this offset is attributable to a Uranus' barycentric offset with respect to DE405, that we estimate to be: and ΔδU=−85±25 mas at the moment of occultation. This offset is confirmed by another Titania stellar occultation observed on August 1st, 2003, which provides an offset of ΔαTcos(δT)=−127±20 mas and ΔδT=−97±13 mas for the satellite. The combined ingress and egress data do not show any significant hint for atmospheric refraction, allowing us to set surface pressure limits at the level of 10-20 nbar. More specifically, we find an upper limit of 13 nbar (1-σ level) at 70 K and 17 nbar at 80 K, for a putative isothermal CO2 atmosphere. We also provide an upper limit of 8 nbar for a possible CH4 atmosphere, and 22 nbar for pure N2, again at the 1-σ level. We finally constrain the stellar size using the time-resolved star disappearance and reappearance at ingress and egress. We find an angular diameter of 0.54±0.03 mas (corresponding to projected at Titania). With a distance of 170±25 parsecs, this corresponds to a radius of 9.8±0.2 solar radii for HIP 106829, typical of a K0 III giant.  相似文献   

8.
William H. Smyth  M.C. Wong 《Icarus》2004,171(1):171-182
Two-dimensional model calculations (altitude and solar zenith angle) are performed to investigate the impact of electron chemistry on the composition and structure of Io's atmosphere. The calculations are based upon the model of Wong and Smyth (2000, Icarus 146, 60-74) for Io's SO2 sublimation atmosphere with the addition of new electron chemistry, where the interactions of the electrons and neutrals are treated in a simple fashion. The model calculations are presented for Io's atmosphere at western elongation (dusk ansa) for both a low-density case (subsolar temperature of 113 K) and a high-density case (subsolar temperature of 120 K). The impact of electron-neutral chemistry on the composition and structure of Io's atmosphere is confined primarily to an interaction layer. The penetration depth of the interaction layer is limited to high altitudes in the thicker dayside atmosphere but reaches the surface in the thinner dayside and/or nightside atmosphere at larger solar zenith angles. Within most of the thicker dayside atmosphere, the column density of SO2 is not significantly altered by electrons, but in the interaction layer all number densities are significantly altered: SO2 is reduced, O, SO, S, and O2 are greatly enhanced, and O, SO, and S become comparable to SO2 at high altitudes. For the thinner nightside atmosphere, the species number densities are dramatically altered: SO2 is drastically reduced to the least abundant species of the SO2 family, SO and O2 are significantly reduced at all altitudes, and O and S are dramatically enhanced and become the dominant species at all altitudes except near the surface. The interaction layer also defines the location of the emission layer for neutrals excited by electron impact and hence determines the fraction of the total neutral column density that is visible in remote observation. Electron chemistry may also impact the ratio of the equatorial to polar SO2 column density deduced from Lyman-α images and the north-south alternating and System III longitude-dependent asymmetry observed in polar O and S emissions.  相似文献   

9.
Ran Qin  W. Roger Buck 《Icarus》2007,189(2):595-597
We show Lee, Pappalardo, and Makris' [2005. Icarus 177, 367-379] argument that surface cracks in Europa's icy shell penetrate 3-10 times deeper in the presence of subsurface ocean is not correct. We use numerical calculations to demonstrate that there is at most 50% increase in penetration depth for a crack opening in a shell of finite thickness compared to a half-space. We also propose a simple equation based on force balances to estimate the maximum thickness of an ice shell that can be opened under tensile stress. Our calculations show that a crack can only penetrate 330-m-thick ice shell under 200 kPa far-field tensile stress and half of that if the stress is 100 kPa. But the presence of water would allow crack penetrate ∼4.0 km into the ice shell with zero porosity.  相似文献   

10.
We use data from the VIMS instrument on board the Cassini spacecraft to construct high sensitivity and high spatial-resolution maps of the locations of tropospheric clouds on Titan in the late northern winter season during which the Cassini prime mission took place. These observations show that, in this season, clouds on Titan are strongly hemispherically asymmetric. Mid-latitude clouds, in particular, occur only in the southern hemisphere and have not ever been observed in the north. Such an asymmetry is in general agreement with circulation models where sub-solar surface heating controls the locations of clouds and appears in conflict with models where perennial polar hazes prevent significant summertime polar heating from affecting the circulation. The southern mid-latitude clouds appear to be distributed uniformly in longitude, in contrast to some previous observations. Southern high-latitude clouds exhibit a significant concentration, however, between about 180° and 270°E longitude. A spatially and temporally uniform cloud always appears northward of ∼50°N latitude. This cloud appears unchanged over the course of the observations, consistent with the interpretation that it is caused by continuous ethane condensation as air subsides and radiatively cools through the tropopause. The location of this cloud likely provides a direct tracer of elements of north polar atmospheric circulation, potentially allowing continuous monitoring of circulation changes as Titan passes through equinox into north polar spring and summer. We show that a similar analysis of this dataset by Rodriguez et al. (2009) contains substantial errors and should not be used.  相似文献   

11.
M.L Marconi 《Icarus》2003,166(2):410-424
Quite generally, the atmosphere of a planet has an escaping component that forms a gas cloud in its circumplanetary space. This gas cloud is frequently detectable and its observation provides important information about both the source and the circumplanetary environment. As a result, there is a strong motivation to investigate the nature of such gas clouds. Up to now, attention has been directed almost exclusively to the case of collisionless clouds, i.e., the collision time is much longer than the lifetime of the cloud constituents. In this study, we consider the relatively unexplored case of a quasi-collisional cloud, i.e., the self-collision time is much longer than the orbital period and much shorter than the lifetime of the cloud constituents. A slightly modified version of the traditional DSMC approach is applied to the case of the hydrogen torus of Triton, which is an example of a spatially axisymmetric quasi-collisional cloud that is generated from a source orbiting a central planet. A large number of calculations were performed for different models, primarily with different source velocity distributions. The results for two models that bracket the full span of these calculations are presented in detail and compared. The spatial structure and temporal evolution is discussed for these systems. The effect of lifetime processes and radiation pressure is also discussed.  相似文献   

12.
A 1-D collisional Monte Carlo model of Europa's atmosphere is described in which the sublimation and sputtering sources of H2O molecules and their molecular fragments are accounted for as well as the radiolytically produced O2. Dissociation and ionization of H2O and O2 by magnetospheric electron, solar UV-photon and photo-electron impact, and collisional ejection from the atmosphere by the low-energy plasma are taken into account. Reactions with the surface are discussed, but only adsorption and atomic oxygen recombination are included in this model. The size of the surface-bounded oxygen atmosphere of Europa is primarily determined by a balance between atmospheric sources from irradiation of the satellite's icy surface by the high-energy magnetospheric charged particles and atmospheric losses from collisional ejection by the low-energy plasma, photo- and electron-impact dissociation, and ionization and pick-up from the surface-bounded atmosphere. A range of sources rates for O2 to H2O are used with a larger oxygen-to-water ratio than suggested by laboratory measurements in order to account for differences in adsorption onto grains in the regolith. These calculations show that the atmospheric composition is determined by both the water and oxygen photochemistry in the near-surface region, escape of suprathermal oxygen and water into the jovian system, and the exchange of radiolytic water products with the porous regolith. For the electron impact ionization rates used, pick-up ionization is the dominant oxygen loss process, whereas photo-dissociation and atmospheric sputtering are the dominant sources of neutral oxygen for Europa's neutral torus. Including desorption and loss of water enhances the supply of oxygen species to the neutral torus, but hydrogen produced by radiolysis is the dominant source of neutrals for Europa's torus in these models.  相似文献   

13.
A one-dimensional Direct Simulation Monte Carlo (DSMC) model is used to examine the effects of a non-condensable species on Io's sulfur dioxide sublimation atmosphere during eclipse and just after egress. Since the vapor pressure of SO2 is extremely sensitive to temperature, the frost-supported dayside sublimation atmosphere had generally been expected to collapse during eclipse as the surface temperature dropped. For a pure SO2 atmosphere, however, it was found that during the first 10 min of eclipse, essentially no change in the atmospheric properties occurs at altitudes above ∼100 km due to the finite ballistic/acoustic time. Hence immediately after ingress the auroral emission morphology above 100 km should resemble that of the immediate pre-eclipse state. Furthermore, the collapse dynamics are found to be greatly altered by the presence of even a small amount of a non-condensable species which forms a diffusion layer near the surface that prevents rapid collapse. It is found that after 10 min essentially no collapse has occurred at altitudes above ∼20 km when a nominal mole fraction of non-condensable gas is present. Collapse near the surface occurs relatively quickly until a static diffusion layer many mean free paths thick of the non-condensable gas builds up which then retards further collapse of the SO2 atmosphere. For example, for an initial surface temperature of 110 K and 35% non-condensable mole-fraction, the ratio of the SO2 column density to the initial column density was found to be 0.73 after 10 min, 0.50 after 30 min, and 0.18 at the end of eclipse. However, real gas species (SO, O2) may not be perfectly non-condensable at Io's surface temperatures. If the gas species was even weakly condensable (non-zero sticking/reaction coefficient) then the effect of the diffusion layer on the dynamics was dramatically reduced. In fact, if the sticking coefficient of the non-condensable exceeds ∼0.25, the collapse dynamics are effectively the same as if there were no non-condensable present. This sensitivity results because the loss of non-condensable to the surface reduces the effective diffusion layer size, and the formation of an effective diffusion layer requires that the layer be stationary; this does not occur if the surface is a sink. Upon egress, vertical stratification of the condensable and non-condensable species occurs, with the non-condensable species being lifted (or pushed) to higher altitudes by the sublimating SO2 after the sublimating atmosphere becomes collisional. Stratification should affect the morphology and intensity of auroral glows shortly after egress.  相似文献   

14.
Io’s sublimation-driven atmosphere is modeled using the direct simulation Monte Carlo (DSMC) method. These rarefied gas dynamics simulations improve upon earlier models by using a three-dimensional domain encompassing the entire planet computed in parallel. The effects of plasma heating, planetary rotation, inhomogeneous surface frost, molecular residence time of SO2 on the exposed (non-volatile) rocky surface, and surface temperature distribution are investigated. Circumplanetary flow is predicted to develop from the warm dayside toward the cooler nightside. Io’s rotation leads to a highly asymmetric frost surface temperature distribution (due to the frost’s high thermal inertia) which results in circumplanetary flow that is not axi-symmetric about the subsolar point. The non-equilibrium thermal structure of the atmosphere, specifically vibrational and rotational temperatures, is also examined. Plasma heating is found to significantly inflate the atmosphere on both the dayside and nightside. The plasma energy flux causes high temperatures at high altitudes but plasma energy depletion through the dense gas column above the warmest frost permits gas temperatures cooler than the surface at low altitudes. A frost map (Douté, S., Schmitt, B., Lopes-Gautier, R., Carlson, R., Soderblom, L., Shirley, J., and the Galileo NIMS Team [2001]. Icarus 149, 107-132) is used to control the sublimated flux of SO2 which can result in inhomogeneous column densities that vary by nearly a factor of four for the same surface temperature. A short residence time for SO2 molecules on the “rock” component is found to smooth lateral atmospheric inhomogeneities caused by variations in the surface frost distribution, creating an atmosphere that looks nearly identical to one with uniform frost coverage. A longer residence time is found to agree better with mid-infrared observations (Spencer, J.R., Lellouch, E., Richter, M.J., López-Valverde, M.A., Jessup, K.L, Greathouse, T.K., Flaud, J. [2005]. Icarus 176, 283-304) and reproduce the observed anti-jovian/sub-jovian column density asymmetry. The computed peak dayside column density for Io assuming a surface frost temperature of 115 K agrees with those suggested by Lyman-α observations (Feaga, L.M., McGrath, M., Feldman, P.D. [2009]. Icarus 201, 570-584). On the other hand, the peak dayside column density at 120 K is a factor of five larger and is higher than the upper range of observations (Jessup, K.L., Spencer, J.R., Ballester, G.E., Howell, R.R., Roesler, F., Vigel, M., Yelle, R. [2004]. Icarus 169, 197-215; Spencer et al., 2005).  相似文献   

15.
M.L. Marconi 《Icarus》2007,190(1):155-174
A multispecies, 2-D axisymmetric, kinetic model that accounts for all kinetic regimes is applied to the neutral atmosphere of Ganymede. Using reasonable interpretations of the limited observations, it is found that Ganymede has a two-part atmosphere, with H2O being dominant between the subsolar point and a subsolar latitude of about 45 degrees, and O2 dominating elsewhere at the lower altitudes. H2 is dominant everywhere above a few hundred kilometers. Except for a small region near the subsolar point, the atmosphere is quasicollisional or collisionless. The resulting nonequilibrium is manifest in the atmospheric constituents having generally different temperatures and bulk velocities. Escape rates are similar to those of Europa, but a less visible torus is expected. The escape rates are also highly latitude and species dependent. The effect on the atmosphere by a fast ion plasma is investigated and found to primarily affect the O2 scale height above a few hundred kilometers. It is also found that Lyman α emission from collision of electrons with H2 may be significant near the surface.  相似文献   

16.
Europa's interior structure may be determined by relatively simple and robust seismo-acoustic echo sounding techniques. The strategy is to use ice cracking events or impacts that are hypothesized to occur regularly on Europa's surface as sources of opportunity. A single passive geophone on Europa's surface may then be used to estimate the thickness of its ice shell and the depth of its ocean by measuring the travel time of seismo-acoustic reflections from the corresponding internal strata. Quantitative analysis is presented with full-field seismo-acoustic modeling of the Europan environment. This includes models for Europan ambient noise and conditions on signal-to-noise ratio necessary for the proposed technique to be feasible. The possibility of determining Europa's ice layer thickness by surface wave and modal analysis with a single geophone is also investigated.  相似文献   

17.
Our knowledge about the lunar environment is based on a large volume of ground-based, remote, and in situ observations. These observations have been conducted at different times and sampled different pieces of such a complex system as the surface-bound exosphere of the Moon. Numerical modeling is the tool that can link results of these separate observations into a single picture. Being validated against previous measurements, models can be used for predictions and interpretation of future observations results.  相似文献   

18.
A fracture mechanics model is developed for the initiation and propagation of a crack through a porous ice layer of finite thickness under gravitational overburden. It is found that surface cracks generated in response to a tidally induced stress field may penetrate through the entire outer brittle layer if a subsurface ocean is present on Europa. Such penetration is found to be very unlikely in the absence of an ocean. A cycloidal crack would then form as a sequence of near instantaneous discrete failures, each extending roughly the brittle layer thickness in range, linked with a much lower apparent propagation speed set by the moving tidal stress field. The implications of this porous ice fracture model for ice-penetrating radar scattering loss and seismic activity are quantified.  相似文献   

19.
Lijie Han  Adam P. Showman 《Icarus》2010,207(2):834-505
We performed 2D numerical simulations of oscillatory tidal flexing to study the interrelationship between tidal dissipation (calculated using the Maxwell model) and a heterogeneous temperature structure in Europa’s ice shell. Our 2D simulations show that, if the temperature is spatially uniform, the tidal dissipation rate peaks when the Maxwell time is close to the tidal period, consistent with previous studies. The tidal dissipation rate in a convective plume encased in a different background temperature depends on both the plume and background temperature. At a fixed background temperature, the dissipation increases strongly with plume temperature at low temperatures, peaks, and then decreases with temperature near the melting point when a melting-temperature viscosity of 1013 Pa s is used; however, the peak occurs at significantly higher temperature in this heterogeneous case than in a homogeneous medium for equivalent rheology. For constant plume temperature, the dissipation rate in a plume decreases as the surrounding temperature increases; plumes that are warmer than their surroundings can exhibit enhanced heating not only relative to their surroundings but relative to the Maxwell-model prediction for a homogeneous medium at the plume temperature. These results have important implications for thermal feedbacks in Europa’s ice shell.To self-consistently determine how convection interacts with tidal heating that is correctly calculated from the time-evolving heterogeneous temperature field, we coupled viscoelastic simulations of oscillatory tidal flexing (using Tekton) to long-term simulations of the convective evolution (using ConMan). Our simulations show that the tidal dissipation rate resulting from heterogeneous temperature can have a strong impact on thermal convection in Europa’s ice shell. Temperatures within upwelling plumes are greatly enhanced and can reach the melting temperature under plausible tidal-flexing amplitude for Europa. A pre-existing fracture zone (at least 6 km deep) promotes the concentration of tidal dissipation (up to ∼20 times more than that in the surroundings), leading to lithospheric thinning. This supports the idea that spatially variable tidal dissipation could lead locally to high temperatures, partial melting, and play an important role in the formation of ridges, chaos, or other features.  相似文献   

20.
This paper reports on the results from an extensive study of all nadir-looking spectra acquired by Cassini/CIRS during the 44 flybys performed in the course of the nominal mission (2004-2008). With respect to the previous study (Coustenis, A., and 24 colleagues [2007]. Icarus 189, 35-62, on flybys TB-T10) we present here a significantly richer dataset with, in particular, more data at high northern and southern latitudes so that the abundances inferred here at these regions are more reliable. Our enhanced high-resolution dataset allows us to infer more precisely the chemical composition of Titan all over the disk. We also include improved spectroscopic data for some molecules and updated temperature profiles. The latitudinal distributions of all of the gaseous species are inferred. We furthermore test vertical distributions essentially for acetylene (C2H2) from CIRS limb-inferred data and from current General Circulation Models for Titan and compare our results on all the gaseous abundances with predictions from 1-D photochemical-radiative models to check the reliability of the chemical reactions and pathways.  相似文献   

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