Vertical distribution of water vapor and mars model lower and middle atmosphere

Observations and model calculations of water vapor diffusion suggest that about half the amount of water vapor is distributed with constant mixing ratio in the Martian atmosphere, the other half is the excess water vapor in the lower troposphere. During 24 hr the total content of water vapor may vary by a factor of two. The eddy diffusion coefficient providing agreement between calculations and observations is K = (3–10) × 10⁶ cm² sec^?1 in the troposphere. An analytical expression is derived for condensate density in the stratosphere in terms of the temperature profile, the particle radius r, and K. The calculations agree with the Mars 5 measurements for r = 1.5 μm, condensate density 5 × 10^?12 g/cm³ in the layer maximum at 30 to 35 km, condensate column density 7 × 10^?6 cm^?2, K = (1?3) × 10⁶ cm² sec^?1, and the temperature profile T = 185 ? 0.05z ? 0.01z² at 20 to 40 km. Condensation conditions yield a temperature of 160°K at 60 km in the evening; the scale height for scattered radiation yields T = 110°k at 80 to 90 km. The Mars model atmosphere has been developed up to 125 km.     

The Galilean satellites as a source of CO in the Jovian upper atmosphere

Material from the Galilean satellites of Jupiter ejected by energetic particles in the Jovian magnetosphere may provide large sources of oxygen to the parent planet. Formation of a CO molecule is the ultimate fate of an oxygen atom in the upper Jovian atmosphere. This high altitude source of CO supports Beer and Taylor's (1978, Astrophys. J.221) observations and analysis, provided that the globally averaged O atom input flux is ～10⁷ cm^?2 sec^?1 and the eddy diffusion coefficient at the tropopause is ～10³ cm² sec^?1. Implications for the possible presence of other atoms and molecules derived from the satellites are discussed.     

The effect of interplanetary acceleration on the propagation of energetic solar particles in prompt events

Crank-Nicholson solutions are obtained to the time-dependent Fokker-Planck equation for propagation in the interplanetary medium following a point in time injection of energetic solar particles and including the acceleration terms $$\frac{\partial }{{\partial T}}\left( {D_{TT} \frac{{\partial U}}{{\partial T}}} \right) - \frac{\partial }{{\partial T}}\left( {\frac{{D_{TT} U}}{{2T}}} \right)$$ . The diffusion coefficient in kinetic energyD _TT is allowed to be either independent of radial distance,R(AU), or follow the lawD _TT=D₀T²R ₀ ² /(A²+R²) in either case with the 1 AU value ofD _TT at 10 MeV ranging between 10^?4 (MeV)² s^?1 and zero. The spatial diffusion mean free path at the Earth's orbit is fixed at λ_‖ AU at 10 MeV according to numerical estimates made by Moussas and Quenby. However, a variety ofR dependences are allowed. Reasonable agreement with experimental data out to 4 AU is obtained with the above values ofD _TT and the spatial diffusion coefficientK _r=K₀R^?2 forR«1 andK _r=K₀R^0.4 forR»1 AU. It is only in the decay phases of prompt events as seen at 2–4 AU that significant differences in the temporal behaviour of the events can be distinguished, depending on the value ofD _TT chosen within the above range. Experimental determination of the decay constant is difficult.     

Particle precipitation in the south atlantic geomagnetic anomaly

A simple model of the motion of charged particles in the closed field line magnetic field for L ? 4·5 is used together with Injun 3 measurements of 40 keV precipitated electrons made in the northern hemisphere to estimate theoretically the extent of electron precipitation, the energy input and the 3914 Å airglow in the South Atlantic geomagnetic anomaly. Using average values of the northern hemisphere precipitated electron flux, two regions of significantly enhanced electron precipitation are found in the southern hemisphere. One occurs in the region 10–20°E and 40–50°S, with L ≈ 2, and the second near 30°E and 65°S, with L ≈ 4.5. Approximately 0.04 erg cm^?2 sec^?1 are deposited by 40 keV electrons for 50 per cent of the time in the first region and half that amount in the second. This increases to ～0·1 and 0·02 erg cm^?2 sec^?1 respectively for 15 per cent of the time for near sunspot minimum conditions. The results show a gradual increase in precipitation on the western side of the anomaly followed by a rapid increase and sudden cut-off in precipitation within a few degrees west of minimum B. The flux on L = 2 reaches a “spike” in the southern hemisphere ～f35 times greater than the average flux precipitated on L = 2 in the northern hemisphere. This increase in precipitation arises from the loss of “trapped” particles to the atmosphere where the mirror heights are lowest.     

On the dispersal of artificially-injected gases in the night-time atmosphere

We have studied the extent to which various transport processes affect the dispersal of a gas artificially injected into the night-time atmosphere at F-region altitudes. In addition to diffusion, we have found that nonlinear acceleration, viscous stress, and thermospheric winds affect the dispersal of the injected gas. The magnitude of the effect depends on the atmospheric density, which is a function of solar activity. For an injected H₂ gas, non-linear acceleration and viscous stress rapidly become more important than diffusion above about 300 km for low solar activity (T_∞ = 750K), 340 km for moderate solar activity (T_∞ = 1000K), and 400 km for high solar activity (T_∞ = 1500K). For an injected H₂O gas, the corresponding altitudes are 350, 400, and 470 km for low, moderate and high solar activity, respectively. The effect of nonlinear acceleration and viscous stress is to retard the expansion of the injected gas. Thermospheric winds of 150–400 m s^?1 are important at altitudes near and below the F-region peak electron density. These winds act to transport the injected gas in the wind direction and this affects the shape and temporal development of the subsequent ionospheric hole. Because the H₂O diffusion coefficient is smaller than the H₂ diffusion coefficient, winds are more important for H₂O than for H₂.     

Evidence of energy dependent mechanisms for the precipitation of auroral electrons

This paper discusses the experimental results on electron precipitation in a diffuse aurora obtained by a sounding rocket launched from ANDENES (L ～ 6·2) on 3 November 1968. A considerable increase in the intensity of low energy electrons, E_e ? 5 keV, followed a large precipitation of more energetic electrons E_e ? 5 keV. From the observation of angular distributions and an estimate of the diffusion coefficient (D_α ? 10^?3 (sec)^?2), it is suggested that this higher energy precipitation is induced by gyroresonant interactions of magnetospheric electrons with radiation in the whistler mode. The lower energy precipitation separated in time and/or space, shows quasi-periodic modulations in the 5–15 sec range with periods close to the bounce period. It is suggested that this precipitation is the result of bounce-resonance interactions with electrostatic waves in the equatorial plane. Finally, from a comparison between the experimental energy spectra and plasma sheet spectra it can be concluded that these electrons are injected from the plasma sheet during a substorm and are then diffused and precipitated by energy dependent mechanisms.     

Eddy mixing coefficient on Saturn

Data on the composition and thermal structure, and the Lyman-alpha dayglow of Saturn when analyzed in conjunction with photochemical models of the hydrocarbons and the atomic hydrogen production yield the homopause value of the eddy diffusion coefficient to be approximately 10⁸ cm² s^?1. The equatorial value of the eddy diffusion coefficient at the homopause of Saturn is thus found to be approximately 100 times greater than on Jupiter. The mesosphere (and presumably, troposphere) of Saturn appears to be considerably more turbulent than the upper atmosphere of Jupiter.     

A Study of the Coefficient a in the Extended Nonlinear Guiding Center Theory

The diffusion mechanism of charged particles is one of the very im- portant problems in astrophysics. Recently, Matthaeus et al. (2003) developed a nonlinear guiding center theory (NLGC) of the perpendicular diffusion of en- ergetic charged particles with the parallel diffusion coefficient as an input. This theory agrees with the results of numerical simulations very well. In addition, Qin (2007) developed a nonlinear parallel diffusion theory (NLPA) following the idea of NLGC. Combining the NLGC with the NLPA, a new theory, NLGC-E was developed to solve the parallel and perpendicular diffusion coefficients simultaneously. In the NLGC theory, there is a coefficient a² which is selected to be 1/3 for the best agreement with the results of numerical simulations. In this work we tried the different values of a² for the NLGC-E theory to determine the optimal value which ?ts best the results of numerical simulations.     

On the structure of Mars' atmosphere at 120–220 km

Altitude dependences of [CO₂] and [CO₂⁺] are deduced from Mariner 6 and 7 CO₂⁺ airglow measurements. CO₂ densities are also obtained from n_e radio occultation measurements. Both [CO₂] profiles are similar and correspond to the model atmosphere of Barth et al. (1972) at 120 km, but at higher altitudes they diverge and at 200–220 km the obtained [CO₂] values are three times less the model. Both the airglow and radio occultation observations show that a correction factor of 2.5 should be included into the values for solar ionization flux given by Hinteregger (1970). The ratio of [CO₂⁺]/n_e is 0.15–0.2 and, hence, [O]/[CO₂] is ～3% at 135 km. An atmospheric and ionospheric model is developed for 120–220 km. The calculated temperature profile is characterized by a value of T ≈ 370°K at h ? 220 km, a steep gradient (～2°/km) at 200-160 km, a bend in the profile at 160 km, a small gradient (～0.7°/km) below and a value of T ≈ 250°K at 120 km. The upper point agrees well with the results of the Lyman-α measurements; the steep gradient may be explained by molecular viscosity dissipation of gravity and acoustical waves (the corresponding energy flux is 4 × 10^?2 erg cm^?2sec^?1 at 180 km). The bend at 160 km may be caused by a sharp decrease of the eddy diffusion coefficient and defines K ≈ 2 × 10⁸cm²sec^?1; and the low gradient gives an estimate of the efficiency of the atmosphere heating by the solar radiation as ? ≈ 0.1.     

Dragfree spaceprobe

Dragfree missions are needed for very accurate planetary sounding, and for testing of Einstein's theory of gravity. With the state-of-the-art technology, drag compensation in the approximate plane of a spaceprobe orbit is feasible down to 10^?13 g (g=10³ cm s^?2); for the out-of-plane component, the achievable dragfree level is only 10^?12 g. However, future technology (larger launchers, electric propulsion) can decrease these limits.     

Ion-ion recombination rates in the earth's atmosphere

The temperature dependence of the binary recombination coefficient, α₂, for the reaction NO⁺+NO₂^? → products has been obtained over the range 185–530 K. It is found that the corresponding mean cross section $\text{σ}$ is described by the power law $\text{σ}\text{? A · T}{}^{\mathrm{?0.9}}$, and that α₂ ? B · T^?0.4. Data has also been obtained for two cluster ion recombination reactions which indicate that their recombination cross sections are only about 40% larger than for the parent ions at a given temperature, the cross sections for these reactions also apparently increasing with decreasing temperature. In the light of this data and by considering the most probable positive and negative ions existing at various altitudes up to 90km in the atmosphere, the most appropriate ionic recombination coefficients in various altitude ranges are deduced. Thus, between 30 and 90 km, where the recombination process is two-body, the coefficient varies over the narrow range 5–9 × 10^?8 cm³s^?1, while below 30 km the process is predominantly three-body with an effective two-body rate increasing rapidly to a maximum value ≈3 × 10^?6 cm³s^?1 in the troposphere, these deductions being based on published laboratory determinations of three-body recombination coefficients.     

Cosmic ray anisotropies observed late in the decay phase of solar flare events

Concurrent interplanetary magnetic field and 0.7–7.6 MeV proton cosmic-ray anisotropy data obtained from instrumentation on Explorers 34 and 41 are examined for five cosmic-ray events in which we observe a persistent eastern-anisotropy phase late in the event (t ? 4 days). The direction of the anisotropy at such times shows remarkable invariance with respect to the direction of the magnetic field (which generally varies throughout the event) and it is also independent of particle species (electrons and protons) and particle speed over the range 0.06 ? β ? 0.56. The anisotropy is from the direction 38.3° ± 2.4° E of the solar radius vector, and is inferred to be orthogonal to the long term, mean interplanetary field direction. Both the amplitude of the anisotropy and the decay time constant show a strong dependence on the magnetic field azimuth. Detailed comparison of the anisotropy and the magnetic field data shows that the simple model of convection plus diffusion parallel to the magnetic field is applicable for this phase of the flare effect. It is demonstrated that contemporary theories do not predict the invariance of the direction as observed, even when the magnetic field is steady; these theories need extension to take into account the magnetic field direction ψ varying from its mean direction ψ _o. It is shown that the late phase anisotropy vector is not expected to be everywhere perpendicular to the mean magnetic field. The suggestion that we are observing kinks in the magnetic field moving radially outwards from the Sun leads to the conclusion that the parallel diffusion coefficient varies as 1/cos² (ψ ? ψ _o). Density gradients in the late decay phase are estimated to be ≈ 700%∣AU for 0.7–7.6 MeV protons. A simple theory reproduces the dependence of the decay time constant on anisotropy; it also leads to a radial density gradient of about 1000%∣AU and diffusion coefficient of 1.3 × 10²⁰ cm² s^?1.     

The aeronomy of the upper atmosphere of Venus

Density profiles for CO, O, and O₂ in the Cytherean atmosphere above 90 km are plotted with eddy diffusion coefficient (K) as a parameter, subject to the constraint that the mixing ratios of CO and O₂ approach their observed value or values under the observed upper limit at the lower boundary. It is then shown that the value of K puts upper limits on the amount of hydrogen (in the form of H₂O, HCl, and H₂) the atmosphere near 90km can contain. This value is a function of the density and temperature of hydrogen at the critical level and the magnitude of the total escape flux, where unspecified flux mechanisms other than thermal are postulated ad hoc. In general these constraints call for large values of K to accomodate the atomic hydrogen produced by measured mixing ratios of HCl and H₂O. Hence they constrain thee amount of O in the upper atmosphere to values well under 1% at 130 km unless there are very large hydrogen escape fluxes, 10⁷ cm^?2sec^?1 or larger. The freedom to assume arbitrary amounts of H₂ in the atmosphere is also restricted. We suggest either very effective escape mechanisms—despite low exospheric hydrogen densities—or novel excitation mechanisms for O(3³S) and O(3⁵S) in the upper atmosphere.     

Kinematic control of the inertiality of the system of Tycho-2 and UCAC2 stellar proper motions

Based on the Ogorodnikov-Milne model, we analyze the proper motions of Tycho-2 and UCAC2 stars. We have established that the model component that describes the rotation of all stars under consideration around the Galactic y axis differs significantly from zero at various magnitudes. We interpret this rotation found using the most distant stars as a residual rotation of the ICRS/Tycho-2 system relative to the inertial reference frame. For the most distant (d≈900 pc) Tycho-2 and UCAC2 stars, the mean rotation around the Galactic y axis has been found to be M ₁₃ ^? =?0.37±0.04 mas yr^?1. The proper motions of UCAC2 stars with magnitudes in the range 12–15^m are shown to be distorted appreciably by the magnitude equation in μ_α cos δ, which has the strongest effect for northern-sky stars with a coefficient of ?0.60±0.05 mas yr^?1 mag^?1. We have detected no significant effect of the magnitude equation in the proper motions of UCAC2 stars brighter than ≈11^m.     

Small-scale turbulence in the atmosphere of Venus

Previous studies based on radio scintillation measurements of the atmosphere of Venus have identified two regions of small-scale temperature fluctuations located in the vicinity of 45 and 60 km. A global study of the fluctuations near 60 km, which are consistent with wind-shear-generated turbulence, was conducted using the Pioneer Venus measurements. The structure constants of refractive index fluctuations c_n² and temperature fluctuations c_T² increase poleward, peak near 70° latitude, and decrease over the pole; c_n² varies from 2 × 10^?15 to 1.5 × 10^?14m^{$\text{2}\text{3}$} and c_T² from 4 × 10^?3 to 7 × 10^?2°K²m^{$\text{?2}\text{3}$}. These results indicate greater turbulent activity at the higher latitudes. In the region near 45 km the refractive index fluctuations and the corresponding temperature fluctuations are substantially lower. Based on the analysis of one representative occultation measurement, $\text{c}{}_{\mathrm{<mtext>n</mtext>}}{}^2\text{= 2 × 10}{}^{\mathrm{?16}}\text{m}{}^{\mathrm{<mtext>?2</mtext><mtext>3</mtext>}}\text{and}\text{c}{}_{\mathrm{<mtext>T</mtext>}}{}^2\text{= 7.3 × 10}{}^{\mathrm{?4}}\text{°}\text{K}{}^2\text{m}{}^{\mathrm{<mtext>?2</mtext><mtext>3</mtext>}}$ in the 45-km region. The fluctuations in this region also appear to be consistent with wind-shear-generated turbulence. The turbulence level is considerably weaker than that at 60 km; the energy dissipation rate ε is 4.9 × 10^?5m²sec^?3 and the small-scale eddy diffusion coefficient K is 2 × 10³ cm² sec^?1.     

A physical model of Titan's clouds

We have constructed a model of the physical processes controlling Titan's clouds. Our model produces clouds that qualitatively match the present observational constraints in a wide variety of model atmospheres, including those with low atmospheric pressures (25 mbar) and high atmospheric pressures. We find the following: (1) high atmospheric temperatures (160°K) are important so that there is a large scale height in the first few optical depths of cloud; (2) the aerosol mass production occurs at very low aerosol optical depth so that the cloud particles do not directly affect the photochemistry producing them; (3) the production rate of aerosol mass by chemical processes is probably greater than 3.5 × 10^?14 g cm^?2 sec^?1; (4) and the eddy diffusion coefficient is less than 5 × 10⁶ cm² sec^?1 except perhaps in the top optical depth of the cloud. Our model is not extremely sensitive to particle shape, but it is sensitive to particle density. Higher particle densities require larger aerosol mass production rates to produce satisfactory clouds. Particle densities of unity require a mass production rate on the order of 3.5 × 10^?13 g cm^?2 sec^?1. We also show that an increase in mass input causes a decrease in the mean particle size, as required by J. B. Pollack et al. (1980, Geophys. Res. Lett. 7, 829–832), to explain the observed correlation between the solar cycle and Titan's albedo; that coagulation need not be extremely inefficient in order to obtain realistic clouds as proposed by M. Podolak and E. Podolak (1980, Icarus43, 73–83); that coagulation could be inefficient due to photoelectric charging of the particles; and, that the lifetime of particles near the altitude of unit optical depth is a few months, as required to explain the temporal variability observed by S. T. Suess and G. W. Lockwood and D. P. Cruikshank and J. S. Morgan (1979, Bull. Amer. Astron. Soc.11, 564). Although Titan's aerosols are ottically thick in the vertical direction, the atmosphere is so extended that the horizontal visibility is greater than that found anywhere at Earth's surface.     

Quenching of O+(2D) by electrons in the thermosphere

A major loss process for the metastable species, O⁺(²D), in the thermosphere is quenching by electrons

$\text{O}{}^{\mathrm{+}}\text{(}{}^2\text{D) + e → O}{}^{\mathrm{+}}\text{(}{}^4\text{S) + e}$

.To date no laboratory measurement exists for the rate coefficient of this reaction. Thermospheric models involving this process have thus depended on a theoretically calculated value for the rate coefficient and its variation with electron temperature. Earlier studies of the O⁺(²D) ion based on the Atmosphere Explorer data gathered near solar minimum, could not quantify this process. However, Atmosphere Explorer measurements made during 1978 exhibit electron densities that are significantly enhanced over those occurring in 1974, due to the large increases that have occurred in the solar extreme ultraviolet flux. Under such conditions, for altitudes ? 280 km, the electron quenching process becomes the major loss mechanism for O⁺(²D), and the chemistry of the N⁺₂ ion, from which the O⁺(²D) density is deduced, simplifies to well determined processes. We are thus able to use the in situ satellite measurements made during 1978 to derive the electron quenching rate coefficient. The results confirm the absolute magnitude of the theoretical calculation of the rate coefficient, given by the analytical expression k(T_e) = 7.8 × 10^?8 (T_e/300)^?0.5cm³s^?1. There is an indication of a stronger temperature dependence, but the agreement is within the error of measurement.     

Ozone and photochemistry of the Martian lower atmosphere

The calculation of number densities of CO₂, H₂O and N₂ photolysis products was carried out for the Martian atmosphere at heights up to 60 km. The ozone distributed in the atmosphere as a layer of 10 km width with [O₃] max = 2.5 × 10⁹ cm³ at height of 35 km which agree well with the results of u.v. observations on the evening terminator from the Mars-5 satellite. The calculated densities of O₂, CO and H₂O are also in good agreement with the measured data. The eddy diffusion coefficient is equal to 3 × 10⁶ in the troposphere (h ? 30 km) and 10⁸ cm² s^?1 above 40 km. The dependence of the total ozone content on water vapour amount in the atmosphere is considered; the hypothesis about the influence of water ice aerosol on the ozone formation is proposed to explain the high concentrations of ozone in the morning.     

Generalized elliptic anomalies

A two-parameter time transformationdt=r ^3/2(α₀+α₁ r)^?1/2 dτ is proposed, where τ is the radial distance while α₀ and α₁ are, if not constants, at least conservative functions of positions and velocities. In Keplerian systems, the quadrature implied by the transformation may by carried out by elliptic functions. When α₀=0, τ is the eccentric anomaly; if α₁=0, then τ is the intermediate or elliptic anomaly. Considering several values of α₀ and α₁, numerical examples of the relation of thegeneralized elliptic anomaly τ with the classical and elliptic anomalies are given. Application of this transformation to some perturbed Kepler problems is briefly outlined.