Tidal dissipation in the solid cores of the major planets

If the orbital resonances in the Jovian and Saturnian satellite systems are the result of orbital evolution due to tidal dissipation then the present rates of energy dissipation ($\text{E}\text{dot}$) are >2 × 10²⁰ ergs sec^?1 (Jupiter) and ?2 × 10¹⁶ ergs sec^?1 (Saturn). These values of $\text{E}\text{dot}$ can be accounted for if the planets have rocky cores with volumes equal to those suggested by current models of the interiors and if the material of these cores is both solid and imperfectly elastic (Q_e ～ 34). The calculated values of Q_e are not strongly dependent on either the rigidity of the core or the densities of the core and the mantle. Thus, these quantities need not be known precisely. It may be significant that approximately the same value of Q_e is needed for all the major planets (Jupiter, Saturn, and Uranus) even though the values of $\text{E}\text{dot}$ for these planets differ by a factor greater than 10⁴.     

Dynamic fission instability of dissipative protoplanets

All theories of fission require a catastrophic, dynamic phase in order to produce two separate bodies. We have used nonlinear numerical and linear analytical calculations to show that the dynamic fission instability probably does not occur in dissipative protoplanets. The numerical calculations were performed with a three-spatial-dimension hydrodynamical code, with the proto-planet represented by a fluid with a Murnaghan equation of state. The kinetic energy in the protoplanet (other than rigid body rotation) is dissipated throughout the evolution in order to simulate the effects of viscous dissipation. Protoplanets rotating above the limit for dynamic instability were given initial asymmetric density perturbations; in each case the asymmetry did not grow during a time on the order of the rotational period. This dynamical stability has been verified by including the dissipative terms in the tensor-virial equation analysis for the stability of a Maclaurin spheroid: the dynamic instability vanishes when the dissipative terms are included, while the secular instability (with a growth time much larger than the rotational period) remains. The result applies to bodies of radius R with a kinematic viscosity ν? 4 × 10¹³ (R/6400 km)²cm²sec^?1, and hence may be applicable to any terrestrial protoplanet which is not totally molten. Current thermal histories for the Earth predict a partially molten mantle with a viscosity greater than this critical value. Depending on the detailed rheology of the early Earth, our results appear to rule out the possibility of forming the Earth-Moon system through a dynamic fission instability.     

On the exponential decay of western hemisphere solar particle events

Numerical solutions of the Fokker-Planck equation governing the transport of solar protons are obtained in three dimensions (time t, radial distance r, energy T) with the diffusion coefficient represented by κ = κ₀r^bT^a. The October 4, 1968, solar flare particle event is re-examined, and the rise and decay of the proton flux profiles for > 10, ;30 and > 60 MeV particles can be reasonably well reproduced with an instantaneous injection and a distant (10 AU) free escape boundary. The best fit is achieved with a diffusion coefficient $\text{κ = 1.4 × 10}{}^{20}\text{r}{}^{0.5}\text{T}{}^{0.75}\text{cm}{}^2\text{sec}$ where r is in AU and T in MeV.     

Stability of zonal flows on Jupiter

Jupiter's troposphere is bounded below by a deep layer of fluid which is probably extremely close to adiabatic. This paper explores the effect of this new boundary condition on the stability of atmospheric jets. The three parameters of the problem are the Rossby number Ro = U/fl, the ratio of the deformation radius l to the horizontal scale of jets y₀, and the nondimensional value of $\text{β,}\text{β}\text{= βl}{}^2\text{/U}$. The tropospheric deformation radius is unknown; all other quantities are constrained by observation. If the deformation radius is small, then nongeostrophic instabilities are of interest, and the regime is given by $\text{Ro = O(1), l/y}{}_0\text{? 1,}\text{β}\text{? 1}$. Using an Eady model, it is found for this case that the new boundary condition suppresses baroclinic instabilities but that if Ro > 1 (corresponding to a Richardson number less than unity) then inertial instabilities exist as usual. If the deformation radius is somewhat larger, the regime of interest if $\text{Ro ? 1, l/y}{}_0\text{? 1,}\text{β}\text{? 1}$. Horizontal shear can be neglected but β cannot. In this case, it is found that Eady-type baroclinic modes $\text{(}\text{β}\text{= 0)}$ again do not grow, but that the Charney modes $\text{(}\text{β}\text{≠ 0)}$ can exist. Finally, if l/y₀ = O(1) it is found that mixed barotropic-baroclinic instability can exist. Its stability boundaries and energetics approach those of pure barotropic instability when l/y₀ exceeds unity. Observations are discussed: the l/y₀ ? 1 regime appears most relevant. The mixed barotropic-baroclinic modes in this regime display upgradient momentum fluxes.     

Impact cratering and spall failure of gabbro

Both hypervelocity impact and dynamic spall experiments were carried out on a series of well-indurated samples of gabbro to examine the relation between spall strength and maximum spall ejecta thickness. The impact experiments carried out with 0.04- to 0.2-g, 5- to 6-km/sec projectiles produced decimeter- to centimeter-sized craters and demonstrated crater efficiencies of 6 × 10^?9 g/erg, an order of magnitude greater than in metal and some two to three times that of previous experiments on less strong igneous rocks. Most of the crater volume (some 60 to 80%) is due to spall failure. Distribution of cumulative fragment number, as a function of mass of fragments with masses greater than 0.1 g yield values of b = d(log N_f)/d log(m) ?0.5 ?0.6, where N is the cumulative number of fragments and m is the mass of fragments. These values are in agreement or slightly higher than those obtained for less strong rocks and indicate that a large fraction of the ejecta resides in a few large fragments. The large fragments are plate-like with mean values of B/A and C/A 0.8 0.2, respectively (A = long, B = _termediate, and C = short fragment axes). The small equant-dimensioned fragments (with mass < 0.1 g and B ～ 0.1 mm) represent material which has been subjected to shear failure. The dynamic tensile strenght of San Marcos gabbro was determined at strain rates of 10⁴ to 10⁵ sec^?1 to be 147 ± 9 MPa. This is 3 to 10 times greater than inferred from quasi-static (strain rate 10⁰ sec^?1) loading experiments. Utilizing these parameters in a continuum fracture model predicts a tensile strenght of $\text{σ}{}_{\mathrm{<mtext>m</mtext>}}\text{∝}\text{ε}\text{?}{}^{\mathrm{[0.25–0.3]}}$, where ε is strain rate. It is suggested that the high spall strenght of basic igneous rocks gives rise to enhanced cratering efficiencies due to spall in the <10²-m crater diamter strength-dominated regime. Although the impact spall mechanism can enhance cratering efficiencies it is unclear that resulting spall fragments achieve sufficient velocities such that fragments of basic rocks can escape from the surfaces of planets such as the Moon or Mars.     

Gravitational Radiation of Relativistic <Emphasis Type="Italic">n</Emphasis> = 1 Polytropes

The gravitational radiation of n = 1 polytropes undergoing quasiradial pulsations is examined. The intensity of the gravitational radiation and the gravitational wave amplitudes are calculated for polytropic models of white dwarfs and neutron stars when the energy of rotation of the object serves as the source of the radiated energy. Calculations of h₀ show that objects with a polytropic equation of state can describe the expected gravitational radiation from white dwarfs and neutron stars. The gravitational radiation of polytropic models of galactic nuclei and quasars is also examined. These objects can create a high enough background of gravitational radiation at frequencies of 10^-8–10^-11 Hz for gravitational wave detectors operating in this frequency range. __________ Translated from Astrofizika, Vol. 48, No. 4, pp. 603–612 (November 2005).     

The structure of the tidally and rotationally distorted polytropes

A study of the structure of tidally and rotationally distorted polytropes has been carried out using Monaghan and Roxburgh (1965) method for rapidly rotating polytropes, at the new interfacial points (Singh and Singh, 1982), ξ_f = 3.025, 3.470, and 4.950 for the polytropic models with the indicesn=1.5, 2.0, and 3.0, respectively. The structure has been studied for various mass ratios too.     

Pole orientation of 16 psyche by two independent methods

Nineteen new lightcurves of 16 Psyche are presented along with a pole orientation derived using two independent methods, namely, photometric astrometry (PA) and magnitude-amplitude-shape-aspect (MASA). The pole orientations found using these two methods agree to within 4°. The results from applying photometric astrometry were prograde rotation, a sidereal period of $\text{0}\text{d}\text{dot}\text{1748143 ± 0}\text{d}\text{dot}\text{0000003}$, and a pole at longitude 223° and latitude +37°, with an uncertainty of 10°; and, from applying magnitude-amplitude-shape-aspect a pole at 220 ± 1°, +40 ± 4°, and a modeled triaxial ellipsoid shape (a > b > c) with a/b = 1.33 ± 0.02 and b/c = 1.33 ± 0.07. The discrepancy between the high pole latitude found here and the low latitudes reported by others is discussed.     

Emden-Chandrasekhar axisymmetric,rigid-body rotating polytropes

In connection with the basic theory reported in a previous paper (Paper I) for EC1 (rigidly rotating) polytropes, we define exact configurations as configurations for which the equilibrium equation has solutions which are infinitely close to some analytical function and the related gravitational potential coincides, in fact, with the gravitational potential due to mass distribution, at any point not outside the system. Then we restrict to the special casen=5 and divide the related polytropes into two components, a massive body where each mass element has a finite (polytropic) distance from the centre, and a massless atmosphere where each mass element has an infinite (polytropic) distance from te centre. It is found a single exact configuration exists, which under some assumptions may be related to Roche systems. In the special casen=0 it is shown a particular configuration, the spheroidal one, is an exact configuration and evidence is given that spheroidal configurations are the stablest among all the allowed (axisymmetric) configurations. It is also pointed out that EC1 polytropes withn=0 and incompressible MacLaurin spheroids belong to different sequences, even if they exhibit some common features. In the special casen=1 it is shown each allowed configuration is expressible by a convenient series development, which reduces to the relatedn=0 configuration by maintaining only the first two or the first one terms of the sum. It is also deduced, by analogy with the casen=0, that pseudospheroidal configurations are exact and the stablest among all the allowed (axisymmetric) configurations.     

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.     

The influence of a flow field on the stability of the force-free magnetic field

In order to analyse the convective instability of the force-free magnetic field, an exact solution of the MHD equation for the magnetic field (1) together with the flow field (2) of constant speed V₀ making an angle θ with the magnetic field, was chosen as the unperturbed state. The stability of the fields between two parallel conducting walls of seperation d was studied by a linear perturbation method, which led to the eigenvalue problem (12), X being given by (13). It was shown by an approximate variational method that instability will set in by the flow field if V₀ is greater than 1/ $\text{3}$ times Alfven velocity V_A. For , the stability of the force-free field (1) is not influenced by the flow field, which may still be significant in other respects. Perturbations transverse to the magnetic field were found to be the most unstable modes.     

The role of protons of the radiation belts in the generation of Pc 3–5

A new theory of the Alfvén wave generation in inhomogeneous finite β two component plasma is developed ($\text{β =}\text{8πρ}\text{β}{}_0{}^2$, ρ and B₀ are plasma pressure and unperturbed magnetic field, respectively). The analysis was carried out for these waves both for long wave approximation kρ_i ? 1 as well as for $\text{kρ}{}_{\mathrm{i}}\text{? 1}$ (k and ρ_i are wave vector and larmor radius of protons). The influence of the loss-cone on the development of the instability is considered. The theory is applied to explain the generation mechanism of Pc 3–5.     

Equilibrium structure of differentially rotating polytropic models of the stars

In this paper we propose a method for computing the equilibrium structure of differentially rotating polytropic models of the stars. A general law of differential rotation of the type ²=b ₀+b ₁ s ²+b ₂ s ⁴, which can account for a reasonably large variety of possible differential rotations in the stars has been used. The distortional effects have been incorporated in the structure equations up to second order of smallness in distortion parametersb ₀,b ₁, andb ₂ using Kippenhahn and Thomas' averaging approach in conjunction with Kopal's results on Roche equipotentials in manner similar to the one earlier used by Mohan and Saxena for computing the equilibrium structure of polytropes having solid body rotation. Numerical results have been obtained for various types of differentially rotating polytropic models of stars of polytropic indices 1.5, 3, and 4. Certain differentially rotating models of the Sun which are possible with such a type of law of differential rotation, have also been computed.     

Secular resonance,solar spin down,and the orbit of Mercury

A mechanism capable of accounting for the large mean eccentricity (0.175) and inclination (7°.2) of Mercury is discussed. Provided the gravitational field of the rapidly rotating primordial Sun had a sufficiently large second degree harmonic (i.e., J₂ ? order 10^?3), subsequent solar spin down would drive the orbit of Mercury through two secular resonances with Venus, one involving the precession of the line of apsides, the other one involving the regression of the nodal line. Resonance passage generates contributions to the eccentricity and inclination that are proportional to the square root of the characteristic solar spin down time. We find that an initial solar rotation l period of $\text{P ? 5}\text{1}\text{2}\text{hr}$ guarantees passage through resonance and that a spin down time of $\text{τ = Ω|dΩ/dt|}{}^{\mathrm{?1}}$ of order 10⁶ years could have produced the observed eccentricity and inclination. Such a primordial rotation rate is comparable to the measured rotations of very young stars and the spin down time appears consistent with the time scale derived for magnetic braking of the Sun's rotation by an intense solar wind during a T-Tauri stage of solar evolution.     

Production and condensation of organic gases in the atmosphere of Titan

The rates and altitudes for the dissociation of atmospheric constituents of Titan are calculated for solar UV, solar wind protons, interplanetary electrons, Saturn magnetospheric particles, and cosmic rays. The resulting integrated synthesis rates of organic products range from 10²–10³ g cm^?2 over 4.5 × 10⁹ years for high-energy particle sources to 1.3 × 10⁴ g cm^?2 for UV at $\text{λ < 1550}\text{A}\text{?}$, and to 5.0 × 10⁵ g cm^?2 if $\text{λ > 1550}\text{A}\text{?}$ (acting primarily on C₂H₂, C₂H₄, and C₄H₂) is included. The production rate curves show no localized maxima corresponding to observed altitudes of Titan's hazes and clouds. For simple to moderately complex organic gases in the Titanian atmosphere, condensation occurs below the top of the main cloud deck at 2825 km. Such condensates comprise the principal cloud mass, with molecules of greater complexity condensing at higher altitudes. The scattering optical depths of the condensates of molecules produced in the Titanian mesosphere are as great as ～ 10²/(particulate radius, μm) if column densities of condensed and gas phases are comparable. Visible condensation hazes of more complex organic compounds may occur at altitudes up to ～ 3060 km provided only that the abundance of organic products declines with molecular mass no faster than laboratory experiments indicate. Typical organics condensing at 2900 km have molecular masses = 100–150 Da. At current rates of production the integrated depth of precipitated organic liquids, ices, and tholins produced over 4.5 × 10⁹ years ranges from a minimum ～ 100 m to kilometers if UV at $\text{λ > 1550}\text{A}\text{?}$ is important. The organic nitrogen content of this layer is expected to be ～ 10^?1?10^?3 by mass.     

Excitation of magnetosonic waves with discrete spectrum in the equatorial vicinity of the plasmapause

There is a magnetosonic waveguide under the arch of the plasmasphere. This channel, in the form of a ring with radius L～4, surrounds the Earth. It is shown that in this region of the magnetosphere the flute-like electromagnetic disturbances (k6 = 0) with frequencies ω = sω_p can be excited by energetic protons, with non-monotonic dependence on transverse energy ($\text{??/?ε}{}_{\mathrm{\perp }}\text{> 0}$). The interpretation of magnetic pulsations which have been observed in the equatorial vicinity of the plasmapause on the satellite OGO-3 in the frequency range ～10² cps (Russell et al., 1970) is given. In particular the origin of discrete structure of the observed spectra (narrow band spikes for a rather broad range of frequency) is discussed.     

Emden-chandrasekhar axisymmetric,rigidly rotating polytropes

We determine equilibrium configuration of Emden-Chandrasekhar axisymmetric, solid-body rotating polytropes, defined as EC polytropes, for polytropic indices ranging from 0 (homogeneous bodies) to 5 (Roche-type bodies). To this aim, we improve Chandrasekhar's method to determine equilibrium configurations on two respects: namely, (a) no distinction exists between undistorted and distorted terms in the expression of the potential, and (b) the comparison between the expressions of gravitational potential and its first derivatives inside and outside the body has to be made on the boundary of a sphere of radius Ξ_E, which does not necessarily coincide with the undistorted Emden's sphere of radius \(\bar \xi _0 \geqslant \Xi _{\text{E}} \) . We also allow different values of \(\bar \xi _0 \) for different physical parameters, and choose a special set which best fits more refined results (involving more complicated and more expensive computer codes) by James (1964). We find an increasing agreement with increasing values of polytropic indexn and vice-versa, while a large discrepancy arises for 0≤n<1, which makes the approximations used here too much rough tobe accepted in this range. A real slight non-monotonic trend is exhibited by axial rations and masses related to rotational equilibrium configurations — i.e., when gravity at the equator is balanced by centrifugal force-with extremum points for 4.8<n<4.85 in both cases. The same holds for masses related to spherical configurations, as already pointed out by Seidov and Kuzakhmedov (1978). Finally, it is shown that isotrophic, one-component models of this paper might provide the required correlation between the ratio of a typical rotation velocity to a typical peculiar velocity and the ellipticity, for about \(\tfrac{3}{4}\) of elliptical systems for which observations are available.     

10 μm polarimetry of ceres

Linear polarimetry of Ceres at 10 μm is presented. These data represent the first published polarization measurements of an asteroid in the thermal infrared. It is found that Ceres is polarized at the 0.2-0.6% level. This data set is compared with theoretical models of the linear polarization of emitted radiation from a spherical plane. These models are used to derive the pole position and thermal inertia of Ceres. Ceres is best fit with a thermal inertia of $\text{0.0010±0.0003}\text{cal}\text{cm}{}^{\mathrm{?2}}\text{°}\text{K}{}^{\mathrm{?1}}\text{sec}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and a pole orientation of β_p = 36° ± 5°, λ_p = 270° ± 3°. It is concluded that 10μm polarimetry is a potentially powerful technique for remotely sensing the pole orientation and thermal inertia of asteroids.