Saturn's rings: Particle composition and size distribution as constrained by microwave observations: I. Radar observations

We have calculated the radar backscattering characteristics of a variety of compositional and structural models of Saturn's rings and compared them with observations of the absolute value, wavelength dependence, and degree of depolarization of the rings' radar cross section (reflectivity). In the treatment of particles of size comparable to the wavelength of observation, allowance is made for the nonspherical shape of the particles by use of a new semiempirical theory based on laboratory experiments and simple physical principles to describe the particles' single scattering behavior. The doubling method is used to calculate reflectivities for systems that are many particles thick using optical depths derived from observations at visible wavelengths. If the rings are many particles thick, irregular centimeter- to meter-sized particles composed primarily of water ice attain sufficiently high albedos and scattering efficiencies to explain the radar observations. In that case, the wavelength independence of radar reflectivity implies the existence of a broad particle size distribution that is well characterized over the range 1 cm ? r ? m by n(r)dr = n₀r^?3dr. A narrower size distribution with $\text{a}\text{～ 6}\text{cm}$ is also a possibility. Particles of primarily silicate composition are ruled out by the radar observations. Purely metallic particles, either in the above size range and distributed within a many-particle-thick layer or very much larger in size and restricted to a monolayer, may not be ruled out on the basis of existing radar observations. A monolayer of very large ice “particle” that exhibit multiple internal scattering may not yet be ruled out. Observations of the variation of radar reflectivity with the opening angle of the rings will permit further discrimination between ring models that are many particles thick and ring models that are one “particle” thick.     

Airborne spectroscopy and spacecraft radiometry of Venus in the far infrared

In March 1979, the spectrum of Venus was recorded in the far infrared from the G.P. Kuiper Airborne Observatory when the planet subtended a phase angle of 62°. The brightness temperature was observed to be 275°K near 110 cm^?1, dropping to 230°K near 270 cm^?1. Radiance calculations, using temperature and cloud structure formation from the Pioneer Venus mission and including gaseous absorption by the collision-induced dipole of CO₂, yield results consistently brighter than the observations. Supplementing the spectral data, Pioneer Venus OIR data at similar phase angles provide the constraint that any additional infrared opacity must be contained in the upper cloud, H₂SO₄ to the Pioneer-measured upper cloud structure serves to reconcile the model spectrum and the observations, but cloud microphysics strongly indicates that such a high particle density haze $\text{(N ? 1.6 × 10}{}^7\text{cm}{}^{\mathrm{?3}}\text{)}$ is implausible. The atmospheric environment is reviewed with regard to the far infrared opacity and possible particle distribution modifications are discussed. We conclude that the most likely possibility for supplementing the far-infrared opacity is a population of large particles $\text{(}\text{r}\text{? 1 μm)}$ in the upper cloud with number densities less than 1 particle cm^?3 which has remained undetected by in situ measurements.     

Impact fragmentation experiments of basalts and pyrophyllites

Results of impact fragmentation experiments for basalts and pyrophyllites are reported. Aluminum cylindrical projectiles were impacted on cubic basalt and pyrophyllite targets at velocities of 70 to 990 m/sec. The targets and projectiles were 20 g to 3.3 kg and 2 to 20 g in weight respectively. Weights of the fragments produced by impacts were measured and the size distributions of fragments were examined. Data of the largest fragment mass (m_L) normalized to the original target mass (M_t), m_L/M_t, correlate better with the nondimensional impact stress, P_I, a new scaling parameter introduced by H. Mizutani, Y. Takagi, and S. Kawakami (1984, in preparation) than the conventional projectile's kinetic energy per unit target mass, E/M_t, used in the previous studies. All the m_L/M_t data for basalts obtained in the present study are summarized by m_L/M_t = 2.95 × 10^?2P_I^?1 where P_I = P₀L³/YR³, P₀ = peak shock pressure, L = projectile size, R = target size and Y = material strength of target. For aluminum targets, however, the m_L/M_t is 2.5 orders of magnitude larger than that for brittle targets at impacts with the same P_I. Size distributions of fragments expressed in a log N - log (m/M_t) diagram divided into three regimes bounded by two inflection points. In each regime the curve is expressed by $\text{N (>}\text{m}\text{M}{}_{\mathrm{t}}\text{) = A (}\text{m}\text{M}{}_{\mathrm{t}}\text{)}{}^{\mathrm{?a}}$. The slopes, a, of the log $\text{N -}\text{log}\text{(}\text{m}\text{M}{}_{\mathrm{t}}\text{)}$ curves in the regimes of a large and a medium size range are positively correlated with the nondimensional impact stress, P_I, and expressed as a = C₃ + a₃log P_I. The slopes, a, in the smallest size range are, on the other hand, nearly constant and have values of $\text{0.5}\text{to}\text{0.7 (}\text{1}\text{2}\text{?}\text{2}\text{3}\text{)}$. Present results indicate that the impact fragmentation is scaled well by the new scaling parameter, P_I, of Mizutani, Takagi, and Kawakami and that the present experimental data may shed new light on planetary impact processes.     

Titan: Far-infrared and microwave remote sensing of methane clouds and organic haze

It is shown that Titan's surface and plausible atmospheric thermal opacity sources—gaseous N₂, CH₄, and H₂, CH₄ cloud, and organic haze—are sufficient to match available Earth-based and Voyager observations of Titan's thermal emission spectrum. Dominant sources of thermal emission are the surface for wavelenghts λ ? 1 cm, atmospheric N₂ for 1 cm ? λ ? 200 μm,, condensed and gaseous CH₄ for 200 μm ? λ ? 20 μm, and molecular bands and organic haze for λ ? 20 μm. Matching computed spectra to the observed Voyager IRIS spectra at 7.3 and 52.7° emission angles yields the following abundances and locations of opacity sources: CH₄ clouds: 0.1 g cm^? at a planetocentric radius of 2610–2625 km, 0.3 g cm^?2 at 2590–2610 km, total 0.4 ± 0.1 g cm^–2 above 2590 km; organic haze: $\text{4 ± 2 × 10}{}^{\mathrm{?6}}\text{,}\text{g cm}\text{,}{}^{\mathrm{?2}}$ above 2750 km; tropospheric H₂: 0.3 ± 0.1 mol%. This is the first quantitative estimate of the column density of condensed methane (or CH₄/C₂H₆) on Titan. Maximum transparency in the middle to far IR occurs at 19 μm where the atmospheric vertical absorption optical depth is $\text{?0.6}$ A particle radius $\text{r}\text{? 2 μ}\text{m}$ in the upper portion of the CH₄ cloud is indicated by the apparent absence of scattering effects.     

Radiation forces on small particles in the solar system

We present a new and more accurate expression for the radiation pressure and Poynting-Robertson drag forces; it is more complete than previous ones, which considered only perfectly absorbing particles or artificial scattering laws. Using a simple heuristic derivation, the equation of motion for a particle of mass m and geometrical cross section A, moving with velocity v through a radiation field of energy flux density S, is found to be (to terms of order $\text{v}\text{c}$)

$\text{m}\text{v}\text{?}\text{= (}\text{SA}\text{c}\text{)Q}{}_{\mathrm{<mtext>pr</mtext>}}\text{[(1 ?}\text{r}\text{?}\text{c}\text{)}\text{S}\text{?}\text{?}\text{v}\text{c}\text{]}$

, where ? is a unit vector in the direction of the incident radiation, $\text{r}\text{?}$ is the particle's radial velocity, and c is the speed of light; the radiation pressure efficiency factor Q_pr ≡ Q_abs + Q_sca(1 ? 〈cos α〉), where Q_abs and Q_sca are the efficiency factors for absorption and scattering, and 〈cos α〉 accounts for the asymmetry of the scattered radiation. This result is confirmed by a new formal derivation applying special relativistic transformations for the incoming and outgoing energy and momentum as seen in the particle and solar frames of reference. Q_pr is evaluated from Mie theory for small spherical particles with measured optical properties, irradiated by the actual solar spectrum. Of the eight materials studied, only for iron, magnetite , and graphite grains does the radiation pressure force exceed gravity and then just for sizes around 0.1 μm; very small particles are not easily blown out of the solar system nor are they rapidly dragged into the Sun by the Poynting-Robertson effect. The solar wind counterpart of the Poynting-Robertson drag may be effective, however, for these particles. The orbital consequences of these radiation forces-including ejection from the solar system by relatively small radiation pressures-and of the Poynting-Robertson drag are considered both for heliocentric and planetocentric orbiting particles. We discuss the coupling between the dynamics of particles and their sizes (which diminish due to sputtering and sublimation). A qualitative derivation is given for the differential Doppler effect, which occurs because the light received by an orbiting particle is slightly red-shifted by the solar rotation velocity when coming from the eastern hemisphere of the Sun but blue-shifted when from the western hemisphere; the ratio of this force to the Poynting-Robertson force is $\text{(}\text{R}{}_{\mathrm{\odot }}\text{r}\text{)}{}^2\text{[(}\text{w}{}_{\mathrm{\odot }}\text{n}\text{) ? 1]}$, where R_⊙ and w_⊙ are the solar radius and spin rate, and n is the particle's mean motion. The Yarkovsky effect, caused by the asymmetry in the reradiated thermal emission of a rotating body, is also developed relying on new physical arguments. Throughout the paper, representative calculations use the physical and orbital properties of interplanetary dust, as known from various recent measurements.     

Luminosity evolution of quasars

Based on four previous studies with standard-candle quasars and using the correct formula for the luminosity distance, we obtain an improved determination of the deceleration parameter, q₀ = +2.07. From the new catalog of quasars, we find the statistical $\text{m}\text{?}\text{(z) - z}$ relation and hence the mean quasar luminosity $\text{M}\text{?}\text{(z)}$ or $\text{M}\text{?}\text{(t)}$ and its rates of change $\text{d}\text{M}\text{?}\text{(z)}\text{dz}$ and $\text{d}\text{M}\text{?}\text{(t)}\text{dt}$. Finally, we discuss the question whether there is a Malmquist effect in our sample and the question of the dichotomy of published q₀-values.     

The microwave opacity of Saturn's rings at wavelengths of 3.6 and 13 cm from Voyager 1 radio occultation

Radio occultation observations of Saturn's rings with Voyager 1 provided independent measurements of complex (amplitude and phase) microwave extinction and near-forward scattering cross section of the rings at wavelengths (λ) of 3.6 and 13 cm. The ring opening was 5.9°. The normal microwave opacities, τ[3.6] and τ[13], provide a measure of the total cross-sectional area of particles larger than about 1 and 4 cm radius, respectively. Ring C exhibits gently undulating (～ 1000 km) structure of normal opacity τ[3.6] ? 0.25 except for several narrow imbedded ringlets of less than about 100 km width and τ[3.6] ～ 0.5 to 1.0. The normalized differential opacity Δτ/τ[3.6], where Δτ = τ[3.6] ? τ[13], is about 0.3 over most of ring C, indicating a substantial fraction of centimeter-size particles. Some narrow imbedded ringlets show marked increases in Δτ/τ[3.6] near their edges, implying an enhancement in the relative population of centimeter-size and smaller particles at those locations. In the Cassini division, several sharply defined gaps separate regions of opacity τ ～ 0.08 and τ ～ 0.25; the opacity in the Cassini Division appears to be nearly independent of λ. The boundary features at the outer edges of ring C and the Cassini Division are remarkably similar in width and opacity profile, suggesting a similar dynamical control. Ring A appears to be nearly homogeneous over much of its width with 0.6 < τ[3.6] < 0.8 but with considerable thickening, to τ[3.6] ～ 1.0, near its inner boundary with the Cassini division. Normalized differential opacity decreases from ～0.3 at the inner and outer edges of ring A to Δτ/τ[3.6] ～ 0 at a point about one-third of the distance from the inner edge to the outer. The inner one-fourth of ring B has τ[3.6] ～ 1.0, except very near the boundary with ring C, where it is greater. The outer three-fourths of ring B has $\text{τ[3.6] ? 1.2}$. The differential opacity for the inner one-fourth of ring B is Δτ/τ[3.6] ～ 0.15. There are no gaps in ring B exceeding about 2 km in width. Ring F was observed at 3.6 cm as a single ringlet of radial width $\text{? 2}\text{km}$, but was not detected in 13 cm data.     

A note on the asymptotic density-potential relation of a spiral galaxy with a finite thickness

It is shown that the asymptotic σ₁(r) and ψ₁(r) relations can be derived very simply by using the method of double series expansion, where σ₁, ψ₁(r,0) and ψ₁ are the surface density perturbation, the gravitational potential perturbation at the symmetric plane Z=0 and the average potential perturbation respectively. The results are accurate to the order of both m²(kr)^?2 and k〈∣z∣〉, where m is the number of spiral arms, k is the radial wave number, r is the distance from the centre of the galaxy, and 〈∣z∣〉 is the average vertical distance of a star from the Symmetrie plane Z=0. Such an accuracy is usually sufficient for the discussion of spiral modes in a spiral galaxy of small but finite disk thickness. It is pointed out that ψ₁(r,0)～(σ₁(r) relation can be expressed in a unified form for different vertical density profiles if 〈∣z∣〉 is adopted as the thickness scale, and that ψ₁(r,0)～(σ₁(r) can be expressed in a unified form for different vertical density profiles if 〈∣z?z∣〉 the average vertical separation between two stars, is adopted as the thickness scale. Only the value of the ratio $\text{〈|z?z′|〉z}\text{〈|z|〉}$ is a functional of the vertical density profile. However, for the usual physically meaningful profiles, these values are very close to each other: It is $\text{2}$ for the Gaussian profile, $\text{1}\text{Ln}\text{2}\text{= 1.443}$ for the $\text{rmsech}{}^2\text{(}\text{z}\text{z}{}_1\text{(r)}\text{)}$ profile, and 1.5 for the $\text{exp}\text{[}\text{?|z|}\text{z}{}_1\text{(r)}\text{]}$ profile.     

Substorm energy

It is shown that the area A_k(× 10⁶km²) covered by brightest auroras and the area A_q bounded by the auroral oval have a simple relation given by

$\text{A}{}_{\mathrm{k}}\text{= 0.05(A}{}_{\mathrm{q}}\text{? A}{}_0\text{)}{}^2$

, where A₀ denotes the area of the minimum size oval and the quantity (A_q ? A₀)² is proportional to the energy ε_q which is stored in the magnetotail and is available for substorms. Following the definition of the intensity of solar flares, A_k may be chosen as a measure of the intensity of substorms. It is also found that the joule heat energy produced by the auroral electrojet is also proportional to (A_q ? A₀)². Thus, it may be concluded that the intensity of substorms is proportional to the energy ε_q stored in the magnetotail.     

The locating of hydromagnetic whistler sources and determination of their generating proton spectra

Results are given of the calculations of the group delay time propagating τ(ω, φ₀) of hydromagnetic whistlers, using outer ionospheric models closely resembling actual conditions. The τ(ω, φ₀) dependencies were compared with the experimental data of τ_exp(ω, φ₀) obtained from sonagrams. The sonagrams were recorded in the frequency range $\text{? ? (0.5?2.5) Hz}$ at observation points located at geomagnetic latitudes φ₀ = (53?66)° and in the vicinity of the geomagnetic poles. This investigation has led us to new and important conclusions.The wave packets (W.P.) forming hydromagnetic whistlers (H.W.) are mainly generated in the plasma regions at L = 3.5?4.0. This is not consistent with ideas already expressed in the literature that their generation region is $\text{L ? 3?10}$. The overwhelming majority of the τ_exp values differ considerably from the times at which wave packets would, in theory, propagate along the magnetic field lines corresponding to those of the geomagnetic latitudes φ₀ of the observation points. The second important fact is that the W.P. frequency ω is less than $\text{Ω}{}_{\mathrm{H}}$ everywhere along its propagation trajectory, including the apogee of the magnetic force line ($\text{Ω}{}_{\mathrm{H}}$ is the proton gyrofrequency). Proton flux spectra $\text{E ? (30?120)}$ keV, responsible for H.W. generation, were determined. Comparison of the Explorer-45 and OGO-3 measurements published in the literature, with our data, showed that the proton flux density energy responsible for the H.W. excitation $\text{N}{}_{\mathrm{p}}\text{(}\text{MV}{}_6{}^2\text{2}\text{) ? (5 × 10}{}^{\mathrm{?3}}\text{?10}{}^{\mathrm{?1}}\text{)}\text{H}{}_{\mathrm{a}}{}^2\text{8π}$ where H_a is the magnetic field force in the generation region of these W.P. The electron concentration is $\text{N}{}_{\mathrm{a}}\text{? (10}{}^2\text{?10}{}^3\text{) cm}{}^{\mathrm{?3}}$. The values given in the literature are $\text{N}{}_{\mathrm{a}}\text{? (10}{}^{\mathrm{?10}}\text{?10}{}^3\text{) cm}{}^{\mathrm{?3}}$. The e data considered also leads to the conclusion that the generating mechanism of the W.P. studied probably always co-exists with the mechanism of their amplification.     

Titan aerosols: Optical properties and vertical distribution

An analysis of Titan's solar phase variation as a function of wavelength together with the continuum geometric albedo makes it possible to set limits on the real part of the refractive index and on the average particle size of the aerosol component of Titan's atmosphere: $\text{1.5 ?n}{}_{\mathrm{r}}\text{< 2.0}\text{and}\text{0.20 μm <}\text{r}\text{?0.35 μm}$. If n_ris known $\text{r}$ can be determined to within a few percent, and varies inversely with n_r. Using this information in a two-layer model of a methane-aerosol atmosphere and comparing the result with Titan's visible and near-infrared methane spectrum leads to the conclusion that the top layer of Titan's atmosphere contains 0.01 km atm of methane and 2.5 extinction optical depths of aerosol, while the data are consistent with a bottom layer containing 2.2 km atm of methane and about 7.5 aerosol optical depths for $\text{n}{}_{\mathrm{<mtext>r</mtext>}}\text{= 1.7,}\text{r}\text{= 0.25 μ}\text{m}$.     

The vertical structure and thickness of Saturn's rings

We have considered the steady state vertical structure of Saturn's rings with regard to whether collapse to a monolayer due to collisions between particles, the end state predicted by Jeffreys (1947a), may be prevented by any of a variety of mechanisms. Given a broad distribution of particle sizes such as a typical power law n(R) = n₀R^?3, it is found that gravitational scattering of small particles by large particles maintains a true ring thickness of several times the radius of the largest particles, or many times the radius of the smallest particles. Thus the “many-particle-thick” condition which best satisfies optical observations, such as the opposition effect, may be reconciled with ongoing particle collisions. If we consider the obvious sources of energy available for such a process, we find that a ring thickness of only tens of meters may be sustained over the lifetime of the solar system. This implies a maximum particle size on the order of a few meters.     

Laboratory measurements of the microwave opacity of sulfur dioxide and other cloud-related gases under simulated conditions for the middle atmosphere of Venus

Recent papers attributing the observed microwave opacity of the middle atmosphere of Venus to gaseous sulfur dioxide (SO₂) and other cloud-related gases have motivated laboratory measurements of their microwave absorbing properties under simulated conditions for this region. In the pressure range from 1 to 5 atmospheres and in the temperature range from 297 to 355°K, the absorption of SO₂ in a carbon dioxide (CO₂) atmosphere, at 2.257 and 8.342 GHz, has been found to be approximately 50% larger than that calculated from Van Vleck-Weisskopf theory. The measured absorption is about $\text{25 × 10}{}^6\text{q?}{}^2\text{p}{}^{1.20}\text{T}{}^{\mathrm{?3.1}}\text{(}\text{dB km}{}^{\mathrm{?1}}\text{)}$, where q is the sulfur dioxide number mixing ratio, ? is frequency in gigahertz, p is pressure in atmospheres, and T is temperature in degrees Kelvin. This represents the best-fit expression to the observed pressure dependence, while theoretical values of frequency and temperature dependence are accepted as being consistent with the measurements. Another cloud-related gas, sulfur trioxide (SO₃), was also tested in a CO₂ atmosphere and found to be relatively transparent. These results reduce the amount of SO₂ in the Venus middle atmosphere required to explain the opacity measured by radio occulatation, but this amount still exceeds the abundance measured in situ by atmospheric probes, suggesting that there must be another important source of opacity. Preliminary measurements of the 13-cm absorptivity of gaseous sulfuric acid (H₂SO₄) show it to be a strong microwave absorber, and thus likely to be responsible for a significant and possibly major part of the observed opacity.     

Effects of crossed magnetic and (spatially dependent) electric fields on charged particle motion

The motion of charged particles is examined in the case of a homogeneous magnetic field B together with an orthogonal electric field E, which has a gradient ▽E parallel to E. If

$\text{B}{}^2\text{q}{}^2\text{m}{}^2\text{?}\text{q▽E}\text{m}\text{> 0}$

, the particles drift at right angles to E and B with a modified gyrofrequency and produce a current in that direction. If

$\text{B}{}^2\text{q}{}^2\text{m}{}^2\text{?}\text{q▽E}\text{m}\text{< 0}$

, the particles not only drift in the direction of E × B but are also accelerated in the direction of E, in which direction they also produce a current.     

Pitch angle dependence of the charge-exchange lifetime of ring current ions

Previous work has parameterized the pitch angle dependence of the charge-exchange lifetime τ of ring current ions in terms of γ, the power of the cosine of the mirror latitude λ_m of the particles, such that $\text{τ(λ}{}_{\mathrm{m}}\text{)}\text{τ(0) ≌}\text{cos}{}^{\mathrm{\gamma }}\text{λ}{}_{\mathrm{m}}$ at given L. Using the atomic hydrogen density model of Johnson and Fish, previous authors have suggested values of γ = 5 or 6. We here evaluate γ as a function of λ_m and L using the more recent Chamberlain density models, and show that γ = 3?4 is more appropriate over most of the pitch angle and L range. Consequently, ion distributions in the ring current decay phase are expected to become rather less anisotropic in pitch angle due to chargeexchange than previously believed. We have also investigated the use of several other simple approximate analytic forms for $\text{τ(λ}{}_{\mathrm{m}}\text{)}\text{τ(0)}$, one of which gives far better agreement with the numerical results than the cos^γ λ_m, variation, and should hence be used in future studies.     

Calculating Method and Characteristics of the Distribution of Neutron Exposures in the Radiative S-process Nucleosynthesis Model for AGB Stars

A study on the distribution of neutron exposures in a low-mass asymptotic giant branch (AGB) star is presented, according to the s-process nucleosynthesis model with the ¹²C(α, n)¹⁶O reaction occurred under radiative conditions in the interpulse phases. The model parameters, such as the over- lap factor r of two successive convective thermal pulses, the mass ratio q of the ¹³C shell with respect to the He intershell, and the effective mass of ¹³C in the ¹³C shell, vary with the pulse number. Considering these factors, a calculating method for the distribution of neutron exposures in the He intershell has been presented. This method has the features of simplicity and universality. Using this method, the exposure distribution for the stellar model of a star with the mass of 3 M_? and the solar metallicity has been calculated. The results suggest that under the reasonable assumption that the number density of neutrons is uniform in the ¹³C shell, the ?nal exposure distribution approaches to an exponential distribution. For a stellar model with the de?nite initial mass and metallicity, there is a de?nite relation between the mean neutron exposure τ₀ and the neutron exposure Δτ of each pulse, namely τ₀ = 0.434λ(q1, q2, …, qm_max +1, …, r₁, r₂, …, rm_max +1)Δτ, where m_max is the total number of thermal pulses with the third dredge-up episode, and the proportional coeffcient λ(q₁, q₂, …, qm_max +1, …, r₁, r₂, …, rm_max +1) can be determined by an exponential curve ?tting to the ?nal exposure distribution. This new formula quantitatively uni?es the classical model with the s-process nu- cleosynthesis model by means of neutron exposure distribution, and makes the classical model continue to offer guidance and constraints to the s-process nu- merical calculations of stellar models.     

Deuteron whistler and trans-equatorial propagation of the ion cyclotron whistler

New ion cyclotron whistlers which have the asymptotic frequency of one half the local proton gyrofrequency, $\text{G}{}_{\mathrm{p}}\text{2}$, and the minimum (or equatorial) proton gyrofrequency, G_pm, along the geomagnetic field line passing through the satellite have been found in the low-latitude topside ionosphere from the spectrum analysis of ISIS VLF electric field data received at Kashima, Japan. Ion cyclotron whistlers with asymptotic frequency of G_pm or $\text{G}{}_{\mathrm{pm}}\text{2}$ are observed only in the region of $\text{B}{}_{\mathrm{m}}\text{>}\text{B}\text{2}$ or rarely $\text{B}{}_{\mathrm{m}}\text{>}\text{B}\text{4}$, where B is the local magnetic field and B_m is the mini magnetic field along the geomagnetic field line passing through the satellite.The particles with one half the proton gyrofrequency may be the deuteron or alpha particle. Theoretical spectrograms of the electron whistlers (R-mode) and the ion cyclotron whistlers (L-mode) propagating along the geomagnetic field lines are computed for the appropriate distributions of the electron density and the ionic composition, and compared with the observed spectrograms.The result shows that the ion cyclotron whistler with the asymptotic frequency of $\text{G}{}_{\mathrm{p}}\text{2}$ is the deuteron whistler, and that the ion cyclotron whistlers with the asymptotic frequency of G_pm or $\text{G}{}_{\mathrm{pm}}\text{2}$ are caused by the trans-equatorial propagation of the proton or deuteron whistler from the other hemisphere.     

Application of methane band-model parameters to the visible and near-infrared spectrum of Uranus

Laboratory band-model absorption coefficients of CH₄ are used to calculate the Uranus spectrum from 5400 to 10,400 Å. A good fit of both strong and weak bands for the Uranus spectrum over the entire wavelength interval is achieved for the first time. Three different atmospheric models are employed: a reflecting layer model, a homogeneous scattering layer model, and a clear atmosphere sandwiched between two scattering layers. The spectrum for the reflecting layer model exhibits serious discrepancies but shows that large amounts of CH₄ (5–10 km-am) are necessary to reproduce the Uranus spectrum. Both scattering models give reasonably good fits. The homogeneous model requires a particle scattering albedo $\text{(}\text{g}\text{?}\text{w}{}_{\mathrm{<mtext>p</mtext>}}\text{) ? 0.998}$ and an abundance per scattering mean free path $\text{(}\text{a}\text{?}\text{)}\text{of}\text{a}\text{?}\text{1}\text{km-am}$. The parameters derived from the sandwich layer model are: forsb the upper scattering layer a continuum single scattering albedo ($\text{g}\text{?}\text{w}{}_0$) of 0.995 and a scattering optical depth variable with wavelength consistent with Rayleigh scattering; for the clear layer they are a CH₄ abundance (a) of 2.2 km-am and an effective pressure (p) ? 0.1 atm; for the lower cloud deck a Lambert reflectivity (L) of 0.9 resulted. A severe depletion of CH₄ in the upper scattering layer is required. An enrichment of CH₄/H₂ over the solar ratio by a factor of 4–14 in the lower atmosphere is, however, indicated.     

Global color variations on the Martian surface

Surface materials exposed throughout the equatorial region of Mars have been classified and mapped on the basis of spectral reflectance properties determined by the Viking II Orbiter vidicon cameras. Frames acquired at each of three wavelengths (0.45 ± 0.03 μm, 0.53 ± 0.05 μm, and 0.59 ± 0.05 μm) during the approach of Viking Orbiter II in Martian summer (L_s = 105°) were mosaicked by computer. The mosaics cover latitudes 30°N to 63°S for 360° of longitude and have resolutions between 10 and 20 km per line pair. Image processing included Mercator transformation and removal of an average Martian photometric function to produce albedo maps at three wavelengths. The classical dark region between the equator and ～30°S in the Martian highlands is composed of two units: (i) and ancient unit consisting of topographic highs (ridges, crater rims, and rugged plateaus riddled with small dendritic channels) which is among the reddest on the planet $\text{(0.59/0.45 μ}\text{m}\text{? 3)}$; and (ii) intermediate age, smooth, intercrater volcanic plains displaying numerous mare ridges which are among the least red on Mars $\text{(0.59/0.45 μ}\text{m}\text{? 2)}$. The relatively young shield volcanoes are, like the oldest unit, dark and very red. Two probable eolian deposits are recognized in the intermediate and high albedo regions. The stratigraphically lower unit is intermediate in both color $\text{(0.59/ 0.45 μ}\text{m}\text{? 2.5)}$ and albedo. The upper unit has the highest albedo, is very red $\text{(0.59/0.45 μ}\text{m}\text{? 3)}$, and is apparently the major constituent of the annual dust storms as its areal extent changes from year to year. The south polar ice cap and condensate clouds dominate the southernmost part of the mosaics.