Energy changes of cosmic rays in the interplanetary region

A clarification and discussion of the energy changes experienced by cosmic rays in the interplanetary region is presented. It is shown that the mean time rate of change of momentum of cosmic rays reckoned for a fixed volume in a reference frame fixed in the solar system is 〈p〉 =p V·G/3 (p=momentum,V is the solar wind velocity andG=cosmic-ray density gradient). This result is obtained in three ways:

1. by a rearrangement and reinterpretation of the cosmic-ray continuity equation;
2. by using a scattering analysis based on that of Gleeson and Axford (1967);
3. by using a special scattering model in which cosmic-rays are trapped in ‘magnetic boxes’ moving with the solar wind.

The third method also gives the rate of change of momentum of particles within a moving ‘magnetic box’ as 〈p〉_ad = ?p ?·V/3, which is the adiabatic deceleration rate of Parker (1965). We conclude that ‘turnaround’ energy change effects previously considered separately are already included in the equation of transport for cosmic rays.     

Joule heating of Io's ionosphere by unipolar induction currents

The unexpectedly large scale height of Io's ionosphere (Kliore, A., et al., 1975, Icarus24, 407–410) together with the relatively large molecular weight of the likely principal constituent, SO₂ (Pearl, J., et al., 1979, Nature280, 755–758), suggest a high ionospheric temperature. Electrical induction in Io's ionosphere due to the corotating plasma bound to the Jovian magnetosphere is one possible source for attainment of such high temperatures. Accordingly, unipolar induction models were constructed to calculate ionospheric joule heating numerically. Heating rates produced by highly simplified models lie in the range 10^?9 to 10^?8 W/m³. These heating rates are lower than those determined from uv photodissociative heating models (Kumar, S., 1980, Geophys. Res. Lett.7, 9–12) at low levels in the ionosphere but are comparable in the upper ionosphere. The low electrical heating rate throughout most of the ionosphere is due to the power limitation imposed by the Alfvén wings which complete the electrical circuit (Neubauer, F.M., 1980, J. Geophys. Res.85, 1171–1178). Contrary to the pre-Voyager calculations of Cloutier, P. A., et al. (1978, Astrophys. Space Sci.55, 93–112), our numerical results show that the J × B force density due to unipolar induction currents in the ionosphere is much less than the gravitational force density when the combined mass of the neutral species is included. The binding and coupling of the ionosphere is principally due to the relatively dense (possibly localized) neutral SO₂ atmosphere. In regions where the ions and neutrals are collisionally coupled the ionosphere will not be stripped off by the J × B forces. However at a level above that (to which the ions move by diffusion only) the charged species would be removed. Thus there appears to be no need to postulate the existence of an intrinsic Ionian magnetic field as suggested by Kivelson, M. G., et al. (79, Science 205, 491–493) and Southwood, S. J., et al. (1980, J. Geophys. Res., in press) in order to retain the observed ionosphere.     

The angular momenta of solar system bodies: Implications for asteroid strengths

The angular momentum H is plotted versus mass M for the planets and for all asteroids with known rotation rates and shapes, primarily taken from D. C. McAdoo and J. A. Burns [Icarus18, 285–293 (1973)]. An asteroid's angular momentum is derived from its rotation rate as determined by the period of its lightcurve, its shape as indicated by the lightcurve amplitude, and where possible its size as given by polarimetry or radiometry. The asteroid is assumed to be rotating about its axis of maximum moment of inertia. As previously found by F. F. Fish [Icarus7, 251–256 (1967]) and W. K. Hartmann and S. M. Larson [Icarus7, 257–260 (1967)], H is approximately proportional to $\text{M}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$, which shows that the asteroids and most planets spin with nearly the same rate. The very smallest asteroids on the plot deviate from the above reaction, usually containing excess angular momentum. This suggests that collisions have transferred substantial angular momentum to the smallest asteroids, perhaps causing their internal stress states to be substantially modified by centrifugal effects.The forces produced by gravitation are then compared to centrifugal effects for a rotating, triaxial ellipsoid of density 3 g cm^?3. For all asteroids with known properties the gravitational attraction is shown to be larger than the centrifugal acceleration of a particle on the surface: thus the observed asteroid regoliths are gravitationally bound. Poisson's equation for the gravitational potential is investigated and it is shown by mathematical and physical arguments that any arbitrarily shaped ellipsoid with the attractive surface force boundary condition found above will have only attractive internal forces. Thus the internal stress states in asteroids are always compressive so that asteroids could be internally fractured without losing their integrity.     

Angular momentum drain: A mechanism for despinning asteroids

It is proposed that a new mechanism—angular momentum drain—helps account for the relatively slow rotation rates of intermediate-sized asteroids. Impact ejecta on a spinning body preferentially escape in the direction of rotation. This material systematically drains away spin angular momentum, leading to the counterintuitive result that collisions can reduce the spin of midsized objects. For an asteroid of mass M spinning at frequency ω, a mass loss δM correspond to an average decrease in rotation rate $\text{δω ≈}\text{ωδM}\text{M}$. A. W. Harris' (1979), Icarus40, 145–153) theory for the collisional evolution of asteroidal spins is significantly altered by inlusion of this effect. While the modified theory is still somewhat artificial, comparison of its predictions with the data of S. F. Dermott, A. W. Harris, and C. D. Murray (1984, Icarus57, 14–34) suggests that angular momentum drain is essential for understanding the statistics of asteroidal rotations.     

Anisotropic universe and observational constraint on the dark energy models with the cosmological redshift drift

This study set out to examine the effect of anisotropy on the various dark energy models by using the observational data, including the Sandage-Loeb test, Strongly gravitationally lensing, observational Hubble data, and Baryon Acoustic Oscillations data. In particular, we consider three cases of dark energy models: the cosmological constant model, which is most favored by current observations, the wCDM model where dark energy is introduced with constant w equation of state parameter and in Chevalier-Polarski-Linder parametrization where ω is allowed to evolve with redshift. With an anisotropy framework, a maximum likelihood method to constrain the cosmological parameters was implemented. With an anisotropic universe, we also study the behavior of different cosmological parameters such as Hubble parameter, EoS parameter, and deceleration parameter of dark energy models mentioned. The results indicate that the Bianchi type I model for the dark energy models are consistent with the combined observational data.     

On the Origin of Pulsations of Sub-THz Emission from Solar Flares

We propose a model to explain fast pulsations in sub-THz emission from solar flares. The model is based on the approach of a flaring loop as an equivalent electric circuit and explains the pulse-repetition rate, the high-quality factor, Q≥10³, low modulation depth, pulse synchronism at different frequencies, and the dependence of the pulse-repetition rate on the emission flux, observed by Kaufmann et al. (Astrophys. J. 697, 420, 2009). We solved the nonlinear equation for electric current oscillations using a Van der Pol method and found the steady-state value for the amplitude of the current oscillations. Using the pulse rate variation during the flare on 4 November 2003, we found a decrease of the electric current from 1.7×10¹² A in the flare maximum to 4×10¹⁰ A just after the burst. Our model is consistent with the plasma mechanism of sub-THz emission suggested recently by Zaitsev, Stepanov, and Melnikov (Astron. Lett. 39, 650, 2013).     

Long-Term Variations of Solar Differential Rotation and Sunspot Activity: Revisited

Long-term variations of solar differential rotation and sunspot activity are investigated through re-analyzing the data on parameters of the differential-rotation law obtained by Makarov, Tlatov, and Callebaut (Solar Phys. 170, 373, 1997), Javaraiah, Bertello, and Ulrich (Astrophys. J. 626, 579, 2005a; Solar Phys. 232, 25, 2005b), and Javaraiah et al. (Solar Phys. 257, 61, 2009). Our results indicate that the solar-surface-rotation rate at the Equator (indicated by the A-parameter of the standard solar-rotation law) shows a secular decrease since Cycle 12 onwards, given by about 1?–?1.5×10^?3 (deg?day^?1?year^?1). The B-parameter of the standard differential-rotation law seems to also show a secular decrease since Cycle 12 onwards, but of weak statistical significance. The rotation rate averaged over latitudes 0^°?–?40^° does not show a secular trend of statistical significance. Moreover, the average sunspot area shows a secular increase of statistical significance since Cycle 12 onwards, while a negative correlation is found between the level of sunspot activity (indicated by the average sunspot area) and the solar equatorial rotation on long-term scales.     

Hydromagnetic waves driven by velocity shear instability in the magnetospheric boundary layer

The bulk flow of the solar wind plasma in the flank-side of the magnetospheric boundary layer, where the magnetic field lines are closed, has a component transverse to the ambient field. There is quite a strong velocity shear. The theoretical model ignores inhomogeneities in the ambient field and the mass density which occur at the magnetopause on about the same length scale as that of the velocity shear.Consideration is restricted to hydromagnetic waves which have a k-vector nearly normal to the B_o-V_o plane, i.e., approximately the magnetopause surface (k_x >k_z ～ k_y′k_xL_B > 1 and L_B = 0.1 ～ 1.0 R_E where L_B is a characteristic length of the boundary layer). It is found that a long-period (T ? 40 sec) hydromagnetic wave [the Alfvén-like wave ($\text{Ω}{}_{\mathrm{<mtext>A</mtext>}}$)] driven by velocity shear instability can be excited in the shear plasma. It is also found that the group velocity of the HM-wave is directed almost along the magnetic field line and that the magnetic variance in the shear plasma tends to be parallel to the B_o-V_o plane. The velocity shear instability in the magnetospheric boundary layer is judged to be a likely source of long-period magnetic pulsations.     

Phase curves of materials of Io: Interpretation in terms of Hapke's function

The photometric function developed by B. Hapke (1981,J. Geophys. Res.86, 3039–3054; 1984, Icarus59, 41–59) has been applied to near-opposition (α = 2–8°) disk-resolved phase curves for three color classes on Io, and the disk-integrated phase curve (α = 2–159°) of the satellite as a whole. Derived values of the Hapke compaction parameter h suggest that (1) a large percentage of the material on Io's surface has a porosity significantly greater significantly greater than 60%, supporting the estimate of high porosity made by D.L. Matson and D.B. Nash (1983,J. Geophys. Res.88, 4771–4783) and Nelson et al. (1984, Bull. Amer. Astron. Soc.16, 683–685; 1984,EOS65, 982–983); and (2) Average (“orange”) and Polar (“brown”) materials are significantly more porous than Bright (“white”) materials, a cottrast consistent with the Matson and Nash (1983) SO₂ cold trap model. The best-fit single particle phase function becomes more backscattering on moving from Polar to Average to Bright materials, with the surface of Io on average exhibiting significant backscattering comparable in magnitude to that of the lunar surface. For the color classes, and for Io as a whole, the degree of backscattering tends to increase toward longer wavelengths. The average macroscopic roughness of the Ionian surface, characterized by a mean slope angle of Ø ≃ 25°, is similar to that of other solid surface in the solar system. Consistency between observed limb darkening and that predicted by the Hapke model requires the presence of significant macroscopic roughness (Ø ≥ 20°) for the Average regions, but not necessarily for the Bright and Polar materials.     

Infrared limb darkening of the Venus atmosphere

An analysis of the limb darkening component obtained by Ingersoll and Orton [Icarus21 (1974), 121–128] from the thermal infrared maps of Venus published by Murray, Wildey, and Westphal [J. Geophys. Res.68 (1963), 4813–4818] and Westphal, Wildey, and Murray [Astrophys. J.142 (1965), 799–802] shows that the Cytherean cloud tops were close to radiative equilibrium in 1962. A method for obtaining the optical depth, the extinction coefficient, and the extinction scale height from such data is derived and values are extracted from Marov's [Icarus16 (1972), 415–461] standard model of the Venus atmosphere.     

Fabry-Perot determinations of midlatitude F-region neutral winds and temperatures from 1975 to 1979

Fabry-Perot interferometer measurements of the Doppler shifts and widths of the nightglow 630.0 nm line at Laurel Ridge Observatory, Pennsylvania are presented for the period 1975 to 1979, covering both solar minimum and solar maximum conditions. The F-region neutral wind vectors v_n and temperatures T_n deduced from these measurements show both day-to-day changes and overall seasonal patterns in the nocturnal variations during geomagnetically quiet conditions. Divergence in both the meridional and zonal horizontal flow is noted on occasion. The v_n results are compared with models including only solar EUV heating and those with EUV plus a high latitude heat source. The aggregate v_n data for solar cycle minimum conditions agree best with model predictions for winter zonal and equinoctal meridional winds and worst for winter meridional and summer zonal winds. At solar cycle maximum the predicted, rapid transition at equinox from summer to winter wind patterns and vice-versa is observed. The T_n data are in reasonable agreement with the MSIS model predictions.     

An electrodynamic model of the solar wind interaction with the ionospheres of Mars and Venus

The electrodynamic model for the solar wind interaction with non-magnetic planets. (Cloutier and Daniell, Planet. Space Sci.21, 463, 1973; Daniell and Cloutier, Planet. Space Sci.25, 621, 1977) is modified to include the effects of non-ohmic currents in the upper ionosphere. The model is then used to calculate convection patterns induced by the solar wind in the ionospheres of Mars and Venus. For Mars the observations of the neutral mass spectrometer or Vikings 1 and 2 provided the neutral atmosphere. Model calculations reproduced the retarding potential analyzer data and indicate that the ionosphere above about 200 km is probably controlled by convection rather than chemistry or diffusion. For Venus a model atmosphere based on Dickenson and Ridley, J. Atmos. Sci.32, 1219 (1975) and Mayr et al., J. geophys. Res.83, 4411 (1978) was used. The resulting model calculations were compared to radio occultation data from Mariners 5 and 10 and Venera 9 which represent extremes in the variability of the upper Cytherean ionosphere. The model calculations are shown to fall within this variation. These results represent the state of the theory immediately prior to the Pioneer-Venus encounter.     

Bending waves in Saturn's rings

We investigate certain brightness variations seen in Saturn's A ring and find them to be due to vertical corrugations of the local ring plane caused by a spiral bending wave. This wave is resonantly excited by Mimas and propagates inward via the collective gravity of the ring particles. B. A. Smith et al. [Science212, 163–191 (1981)] had previously associated vertical relief with this feature due to its observed azimuthal variations and its proximity to an inclination resonance with Mimas. We develop the theory of forced bending waves, some aspects of which have been treated in the galactic context by C. Hunter and A. Toomre [Astrophys. J.155, 747–776 (1969)] and by G. Bertin and J.W.-K. Mark [Astron. Astrophys.88, 289–297 (1980)]. Our theory is in good agreement with the observations. In particular, the presence of these bending waves may resolve the conflict between ground-based estimates of 1–2 km for the global ring thickness [e.g., A. Brahic and B. Sicardy, Nature289, 447–450 (1981)] and Voyager stellar occultation measurements of <200 m for the local ring thickness [A. L. Lane et al., Science215, 537–543 (1982); E. A. Marouf and G. L. Tyler, Science217, 243–245 (1982)].     

Dynamics of artificial plasma clouds in “Spolokh” experiments: Movement pattern

The data on space location and movement of the high-density (n_c? n_b) barium clouds injected at midlatitudes during the “Spolokh-1” and “Spolokh-2” shaped-charge experiments in the ionosphere are presented. At the initial stage, the neutral and ionized components move together at a speed of the neutral wind. An outflow of ions in the form of a stratified tail was also observed. Its movement is interpreted as a drift in [E₀ × B] fields. The evolution pattern of artificial plasma clouds agrees with the qualitative scheme described in the paper.     

A perturbative treatment of motion near the 3/1 commensurability

A semianalytic perturbation theory for motion near the 3/1 commensurability in the planar elliptic restricted three-body problem is presented. The predictions of the theory are in good agreement with the features found on numerically generated surfaces of section; a global understanding of the phase space is achieved. The unusual features of the motion discovered by J. Wisdom (1982, Astron. J.87, 577–593; 1983a, Icarus56, 51–74) are explained. The principal cause of the large chaotic zone near the 3/1 commensurability is identified, and a new criterion for the existence of large-scale chaotic behavior is presented.     

Some properties of finite energy constant-α force-free magnetic fields in a half-space

Some useful properties of a finite energy, constant-α, force-free magnetic field B _α occupying a half-space D are presented. In particular:

1. Fourier and Green representations of B _α are obtained and used to derive conditions for the existence and uniqueness of a B _α having a given normal component B _z on the boundary ?D.
2. The asymptotic behaviour of B _α at infinity as well as stability results against changes in the boundary condition on ?D and in the value of α are established.
3. The energy of B _α is shown to be smaller than the energy of the open field having the same B _z on ?D, thus confirming an earlier conjecture (Aly, 1984).
4. B _α is proved to not be a Taylor-Heyvaerts-Priest state, in spite of the fact that its relative helicity H is finite and that it is the only solution of the Lagrange-Euler equation associated with the problem of minimizing the energy among all the fields having the same value of H and the same B _z on ?D.

     

A regularization of the three-body problem

Letr ₁,r ₂,r ₃ be arbitrary coordinates of the non-zero interacting mass-pointsm ₁,m ₂,m ₃ and define the distancesR ₁=|r ₁?r ₃|,R ₂=|r ₂?r ₃|,R=|r ₁?r ₂|. An eight-dimensional regularization of the general three-body problem is given which is based on Kustaanheimo-Stiefel regularization of a single binary and possesses the properties:

1. The equations of motion are regular for the two-body collisionsR ₁→0 orR ₂→0.
2. Provided thatR?R ₁ orR?R ₂, the equations of motion are numerically well behaved for close triple encounters.

Although the requirementR? min (R ₁,R ₂) may involve occasional transformations to physical variables in order to re-label the particles, all integrations are performed in regularized variables. Numerical comparisons with the standard Kustaanheimo-Stiefel regularization show that the new method gives improved accuracy per integration step at no extra computing time for a variety of examples. In addition, time reversal tests indicate that critical triple encounters may now be studied with confidence. The Hamiltonian formulation has been generalized to include the case of perturbed three-body motions and it is anticipated that this procedure will lead to further improvements ofN-body calculations.     

Ion momentum and energy transfer rates for charge exchange collisions

The rates of momentum and energy transfer have been obtained for charge exchange collisions between ion and neutral gases having arbitrary Maxwellian temperatures T_i and T_n and bulk transport velocities c_i and c_n. The results are directly applicable to the F-region of the ionosphere where O⁺ - O charge is the dominant mechanism affecting ion momentum and energy transfer.     

Some problems of Venus' atmospheric dynamics

A brief survey is given of the observational data on wind speeds in the atmosphere of Venus, as well as results of the theory of similitude and of a scale analysis for estimation of the wind speeds and temperature contrasts. It is shown that, in the lower portion of the atmosphere, containing roughly half of the mass, the first method produces results which are in somewhat better agreement with the measurements. Measurements of the wind distribution in the atmosphere are discussed. It is shown that, in the slowly rotating atmosphere of Venus, we should expect the Solberg mechanism of inertial instability of the circulation to be effective with respect to axisymmetrical perturbations. The numerical experiments of G.P. Williams (1968, J. Atmos. Sci., 25, 34–1045; 1970, Geophys. Fluid Dyn., 1, 357–369) indicate that in this case the circulation in the meridional plane can be broken down into a series of forward and reverse cells. The existence of such cells can serve to preserve the angular momentum of the planet with its atmosphere—the total momentum of the atmospheric frictional forces against the surface should on the average equal zero. This supports the hypothesis of G. Schubert et al. (1980, J. Geophys. Res., 85, 8007–8025) concerning the multicellular structure of the meridional circulation. Data are analyzed with regard to the time variability of the circulation. If the angular momentum of Venus′ atmosphere can change by 30% (which is not excluded by the presently available data; in Earth's atmosphere seasonal variations of the momentum reach 50%), then the relative variations in the length of a Venusian day will attain 10^?3, i.e., several hours. The surface boundary layer is considered. It is shown that, due to the small transparency of the atmosphere to thermal radiation, heat transfer between the surface and the atmosphere should basically take place by turbulent heat exchange. The basic parameters of the dynamic and thermal regimes of this layer are estimated. Questions of light refraction in the boundary layer are discussed. A strict theory of refraction, developed for these conditions, confirms the preliminary rough estimates of V.I. Moroz (1976, Cosmic Res., 14, No. 5, 691–692; Space Sci. Rev., 25, 3–127), viz, that the horizon is visible on the panorama at a distance of order 100m, due to a relatively sharp negative gradient near the surface.     

Martian occultation of ϵ Gem as observed from the C. E. Kenneth Mees observatory

Ground-based observations of the occultation of ? Gem by Mars on April 8, 1976 have been reduced in the manner of French et al. [Icarus 33, 186–202 (1978)] to yield the scale height and temperature profiles of the Martian atmosphere for number densities between 10¹³ and 10¹⁵ cm^?3. The deduced variations in temperature are remarkably similar to those obtained by Elliot et al. [Astrophys. J.217, 661–679 (1977)] and to the in situ measurements from the Viking landers.