Formation of trans-Neptunian satellite systems at the stage of condensations

The formation of trans-Neptunian satellite systems at the stage of rarefied preplanetesimals (i.e., condensations of dust and/or objects less than 1 m in diameter) is discussed. It is assumed that trans-Neptunian objects (including those with satellites) could form as a result of compression of parental rarefied preplanetesimals. The formulas for calculating the angular momentum of two colliding condensations with respect to their center of mass, which were applied earlier in (Ipatov, 2010) in the comparison of such momenta with the angular momenta of observed satellite systems, are used to estimate the angular momenta of condensations needed to form satellite systems. It is demonstrated that the angular velocities of condensations used in (Nesvorny et al., 2010) as the initial data in the computer simulation of compression of rarefied preplanetesimals and subsequent formation of trans-Neptunian satellite systems may be obtained in collisions of preplanetesimals with their radii comparable to the corresponding Hill radii. For example, these angular velocities are in the range of possible values of angular velocities of a parental rarefied preplanetesimal formed as a result of a merger of two colliding rarefied preplanetesimals that moved in circular heliocentric orbits before a collision. Some rarefied preplanetesimals formed as a result of collision of preplanetesimals in the region of formation of solid small bodies acquire such angular momenta that are sufficient to form satellite systems of small bodies. It is likely that the ratio of the number of rarefied preplanetesimals with such angular momenta to the total number of rarefied preplanetesimals producing classical trans-Neptunian objects with diameters larger than 100 km was 0.45 (the initial fraction of satellite systems among all classical trans-Neptunian objects).     

Eddy diffusion in the upper atmosphere by global deposition of meteoroids

A theory for the production of eddy diffusion in the upper atmosphere by the global deposition of meteoroids is presented. It is based on the assumption that meteoroids falling on the Earth carry, on the average, a greater amount of orbital angular momentum per unit mass than that corresponding to the Earth's orbit. This excess of orbital angular momentum of the meteoroids is deposited in some or the other form during their interaction with the Earth's atmosphere. The softer material deposits the excess of its orbital angular momentum in a region slightly higher than the harder material and is held responsible for the superrotation observed in the atmosphere. It is shown that the other population of meteoroids which is metallic in nature deposits the excess orbital angular momentum below 100 km altitude and produces eddies. The size and velocity of the eddies so formed give the value of the vertical eddy diffusion coefficient in agreement with the upper limit set by Johnson and Wilkins (1965) from the study of downward heat transport in the atmosphere.     

Superrotation of upper atmosphere by global deposition of meteoroids

A new theory of the superrotation of upper atmosphere is worked out on the basis of global deposition of meteoroids assuming that a certain constant influx of meteoroids is continually falling upon the Earth's atmosphere. On the average the meteoroids are shown to carry a greater amount of orbital angular momentum than that corresponding to the Earth's orbit about the Sun. It is argued that the excess of orbital angular momentum appears as extra spin angular momentum in the atmospheric layer in which the meteoroids are arrested and this is used to calculate the velocity difference which can be maintained across a certain layer of the atmosphere. It is found that a global deposition of 34 tons/day of meteoric material is required to account for the observed superrotation which agrees with the recent estimates on meteoric mass influx on the Earth.     

A merger tree with microsolar mass resolution: application to γ-ray emission from subhalo population

Observations of the southern Cepheid ℓ Car to yield the mean angular diameter and angular pulsation amplitude have been made with the Sydney University Stellar Interferometer at a wavelength of 696 nm. The resulting mean limb-darkened angular diameter is 2.990 ± 0.017 mas (i.e. ± 0.6 per cent) with a maximum-to-minimum amplitude of 0.560 ± 0.018 mas corresponding to 18.7 ± 0.6 per cent in the mean stellar diameter. Careful attention has been paid to uncertainties, including those in measurements, in the adopted calibrator angular diameters, in the projected values of visibility squared at zero baseline, and to systematic effects. No evidence was found for a circumstellar envelope at 696 nm. The interferometric results have been combined with radial displacements of the stellar atmosphere derived from selected radial velocity data taken from the literature to determine the distance and mean diameter of ℓ Car. The distance is determined to be 525 ± 26 pc and the mean radius  169 ± 8 R_⊙  . Comparison with published values for the distance and mean radius shows excellent agreement, particularly when a common scaling factor from observed radial velocity to pulsation velocity of the stellar atmosphere (the p -factor) is used.     

Neutral atmosphere near the icy surface of Jupiter’s moon Ganymede

The paper discusses the formation and dynamics of the rarefied gas envelope near the icy surface of Jupiter’s moon Ganymede. Being the most massive icy moon, Ganymede can form a rarefied exosphere with a relatively dense near-surface layer. The main parent component of the gas shell is water vapor, which enters the atmosphere due to thermal degassing, nonthermal radiolysis, and other active processes and phenomena on the moon’s icy surface. A numerical kinetic simulation is performed to investigate, at the molecular level, the formation, chemical evolution, and dynamics of the mainly H₂O- and O₂-dominant rarefied gas envelopes. The ionization processes in these rarefied gas envelopes are due to exposure to ultraviolet radiation from the Sun and the magnetospheric plasma. The chemical diversity of the icy moon’s gas envelope is attributed to the primary action of ultraviolet solar photons and plasma electrons on the rarefied gas in the H₂O- or O₂-dominant atmosphere. The model is used to calculate the formation and development of the chemical diversity in the relatively dense near-surface envelope of Ganymede, where an important contribution comes from collisions between parent molecules and the products of their photolysis and radiolysis.     

Further determinations of upper-atmosphere rotational speed from analysis of satellite orbits

The average angular velocity of the upper atmosphere, which we take as Λ times the Earth's angular velocity, can be evaluated by analysing the changes in the orbital inclinations of satellites. In this paper the nine most suitable orbits now available are analysed and values of Λ are found for heights between 200 and 260 km. The results, which are more accurate than in our previous studies, confirm that Λ 1, i.e. that the atmosphere rotates faster than the Earth at these heights, and show that Λ increases with height, from 1.1 at 210 km to 1.4 at 260 km. This corresponds to mean west-to-east winds of 30 m/s at 210 km, increasing to 130 m/s at 260 km height. Results from one satellite indicate that the wind is probably strongest at times near sunset, with Λ = 1.5 ± 0.1 at 200 km height in August 1966. Comparisons are made with previous observational results and some of the suggested theoretical explanations are outlined.     

The rotation of the solar atmosphere

A model of the solar atmosphere is presented in which we discuss the conservation of angular momentum for the two basic states in which the solar gas can be: namely, either confined by closed field lines or outflowing along open magnetic field lines. It can be shown that the boundary conditions are in general different for these two cases. From this we obtain the results that in the closed configuration the gas can corotate at the solar surface with the magnetic field lines and its angular velocity will then increase with height, whereas for a gas flowing along an open field line the angular velocity will decrease. An exception to the latter case can be found where the open magnetic field lines are strongly nonradial and where the density is a slowly varying function of radius. In such regions the angular velocity may initially increase with height, reach a maximum and then decrease.Kitt Peak National Observatory Contribution No. 439.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Spectroscopic investigation of the chromosphere

The cloud model employed in the analysis of chromospheric contrast profiles is subject to two criticisms. The source function in the cloud may not be varied independently of the Doppler width in the case of Hα and the radiative coupling between the cloud and the underlying atmosphere cannot be ignored. These criticisms are investigated quantitatively with two simple extreme models. It is found that by taking account of both effects the cloud model may be reinstated. Observed chromospheric features may be understood in terms of clouds of varying parameters embedded in the uppermost regions of a generally undisturbed homogeneous atmosphere. The variable cloud parameters are the optical thickness, the Doppler width, the bulk velocity and the angular size viewed from the line forming regions of the underlying atmosphere. Without multidimensional models the distribution of these parameters in chromospheric features observed at supergranulation boundaries for instance cannot be determined. General considerations however allow the interpretation of plagettes as simply low-lying mottles and allow the chromospheric velocity distribution derived by the original cloud model analysis to be upheld.     

Equilibrium models of differentially-rotating polytropic cylinders

The equilibrium structure of differentially rotating polytropic cylinders is determined numerically. We setn=3 and use a quadratic function for the law of differential rotation. We construct different models by varying the angular velocity at the axis and the ratio of the angular velocity at the surface to the angular velocity at the axis. By taking a decreasing function for the rotation law we are able to treat models with an angular velocity at the axis greater than the break-up velocity of uniformly rotating cylinders. We also determine whether a Richardson-like criterion for stability is violated in the models.     

Asymmetry of compton scattering by relativistic electrons with an isotropic velocity distribution: Astrophysical implications

The angular distribution of low-frequency radiation after a single scattering by relativistic electrons with an isotropic velocity distribution differs markedly from the Rayleigh angular function. In particular, the scattering by an ensemble of ultrarelativistic electrons is described by the law p=1?cosα, where α is the scattering angle. Thus, photons are mostly scattered backward. We discuss some consequences of this fact for astrophysical problems. We show that a hot atmosphere of scattering electrons is more reflective than a cold one: the fraction of incident photons reflected after a single scattering can be larger than that in the former case by up to 50%. This must affect the photon exchange between cold accretion disks and hot coronae (or advective flows) near relativistic compact objects, as well as the rate of cooling (through multiple inverse-Compton scattering of the photons supplied from outside) of optically thick clouds of relativistic electrons in compact radio sources. Scattering asymmetry also causes the spatial diffusion of photons to proceed more slowly in a hot plasma than in a cold one, which affects the shapes of Comptonization spectra and the time delay in the detection of soft and hard radiation from variable X-ray sources.     

Quasi-sinusoidal oscillations of the angular velocity of pulsars

We study the oscillations of the angular velocity of pulsars, obtaining an equation for the angular velocity and its derivative taking account of the curvature of vortices. We show that this equation has a quasisinusoidal solution and find the period of these oscillations. We show that the estimates for the value of the periods for various models of neutron stars give quantities of the order of tens of days, which is in agreement with the observations of the quasi-periodic oscillations and fluctuations of the angular velocity of pulsars.Translated fromAstrofizika, Vol. 38, No. 2, 1995.     

Stratification of optical emission from NGC 6888 as a trace of the interaction between Wolf-Rayet stellar wind and the shell of a red supergiant

We suggest a model that explains the stratification peculiarities of the [O III] and Hα line emission from some of the ring nebulae around Wolf-Rayet stars. These peculiarities lie in the fact that the [O III] line emission regions are farther from the central star than the Hα regions, with the distance between them reaching several tenths of a parsec. We show that the radiative shock produced by a Wolf-Rayet stellar wind and propagating with a velocity of ～100 km s^?1 cannot explain such large distances between these regions due to the low velocity of the gas outflow from the shock front. The suggested model takes into account the fact that the shock produced by a Wolf-Rayet stellar wind propagates in a two-phase medium: a rarefied medium and dense compact clouds. The gas downstream of a fast shock traveling in a rarefied gas compresses the clouds. Slow radiative shocks are generated in the clouds; these shocks heat the latter to temperatures at which ions of doubly ionized oxygen are formed. The clouds cool down, radiating in the lines of this ion, to temperatures at which Balmer line emission begins. The distance between the [O III] and Hα line emission regions is determined by the cooling time of the clouds downstream of the slow shock and by the velocity of the fast shock. Using the ring nebula NGC 6888 as an example, we show that the gas downstream of the fast shock must be at the phase of adiabatic expansion rather than deceleration with radiative cooling, as assumed previously.     

Angular velocity during the cycle deduced using the sunspot group age selection methodology

We have used the “age selection methodology” (ASM) (Zappalá and Zuccarello 1991) to study the variability of the sunspot groups angular velocity during the activity cycle. The ASM allows us to separate the contribution of Young Sunspot Groups (YSG) from that of Recurrent ones (RSG) in the Ω(θ) determination and therefore to evaluate whether the increase in angular velocity during minima (reported in literature using all sunspot groups as tracers), is due to a greater statistical weight of YSG on RSG or whether it reflects a global characteristic of the Sun. The results obtained from the analysis of sunspot groups data collected during the period 1874‐1981 (Greenwich Photoheliographic Results) indicate that during minima, besides the fact that the percentage of RSG drops to ≤ 5%, both YSG and RSG show the same increase in angular velocity, i.e. 0.16 degrees/day. Comparing our results with those reported in literature and taking into account the internal angular velocity as deduced by p‐mode oscillations, it is possible to conclude that the observed higher angular velocity of the Sun during minima concerns several layers of the Sun.     

Solar flare neutrons and their capture gamma ray emission

Solar Physics - We briefly describe our recent Monte Carlo calculations of the energy and angular distributions of neutrons escaping from the solar atmosphere. Comparing the calculation results...     

Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

We explore the evolution of the angular velocity of an elastic Earth model, within the Hamiltonian formalism. The evolution of the rotation state of the Earth is caused by the tidal deformation exerted by the Moon and the Sun. It can be demonstrated that the tidal perturbation to spin depends not only upon the instantaneous orientation of the Earth, but also upon its instantaneous angular velocity. Parameterizing the orientation of the Earth figure axis with the three Euler angles, and introducing the canonical momenta conjugated to these, one can then show that the tidal perturbation depends both upon the angles and the momenta. This circumstance complicates the integration of the rotational motion. Specifically, when the integration is carried out in terms of the canonical Andoyer variables (which are the rotational analogues to the orbital Delaunay variables), one should keep in mind the following subtlety: under the said kind of perturbations, the functional dependence of the angular velocity upon the Andoyer elements differs from the unperturbed dependence (Efroimsky in Proceedings of Journées 2004: Systèmes de référence spatio-temporels. l’Observatoire de Paris, pp 74–81, 2005; Efroimsky and Escapa in Celest. Mech. Dyn. Astron. 98:251–283, 2007). This happens because, under angular velocity dependent perturbations, the requirement for the Andoyer elements to be canonical comes into a contradiction with the requirement for these elements to be osculating, a situation that parallels a similar antinomy in orbital dynamics. Under the said perturbations, the expression for the angular velocity acquires an additional contribution, the so called convective term. Hence, the time variation induced on the angular velocity by the tidal deformation contains two parts. The first one comes from the direct terms, caused by the action of the elastic perturbation on the torque-free expressions of the angular velocity. The second one arises from the convective terms. We compute the variations of the angular velocity through the approach developed in Getino and Ferrándiz (Celest. Mech. Dyn. Astron. 61:117–180, 1995), but considering the contribution of the convective terms. Specifically, we derive analytical formulas that determine the elastic perturbations of the directional angles of the angular velocity with respect to a non-rotating reference system, and also of its Cartesian components relative to the Tisserand reference system of the Earth. The perturbation of the directional angles of the angular velocity turns out to be different from the evolution law found in Kubo (Celest. Mech. Dyn. Astron. 105:261–274, 2009), where it was stated that the evolution of the angular velocity vector mimics that of the figure axis. We investigate comprehensively the source of this discrepancy, concluding that the difference between our results and those obtained in Ibid. stems from an oversimplification made by Kubo when computing the direct terms. Namely, in his computations Kubo disregarded the motion of the tide raising bodies with respect to a non-rotating reference system when compared with the Earth rotational motion. We demonstrate that, from a numerical perspective, the convective part provides the principal contribution to the variation of the directional angles and of length of day. In the case of the x and y components in the Tisserand system, the convective contribution is of the same order of magnitude as the direct one. Finally, we show that the approximation employed in Kubo (Ibid.) leads to significant numerical differences at the level of a hundred micro-arcsecond.     

Co-accretion of the Earth-Moon system after the giant impact: reduction of the total angular momentum by lunar impact ejecta

Though the Moon is considered to have been formed by the so-called giant impact, the mass of the Earth immediately after the impact is still controversial. If the Moon was formed during the Earth's accretion, a subsequent accretion of residual heliocentric planetesimals onto the protoearth and the protomoon must have occurred. In this co-accretion stage, a significant amount of lunar-impact-ejecta would be ejected to circumterrestrial orbits, since the mean impact velocity of the planetesimals with the protomoon is much larger than the escape velocity of the protomoon. Orbital calculations of test particles ejected from the protomoon, whose semimajor axis is smaller than that of the present Moon, reveal that most of the particles escaping from the protomoon also escape from the Hill sphere of the protoearth and reduce the planetocentric angular momentum of the primordial Earth-Moon system. Using the results of the ejecta simulations, we investigate the evolution of the mass ratio and the total angular momentum (Earth's spin angular momentum + Moon's orbital angular momentum) of the Earth-Moon system during the co-accretion. We find that the mass of the protomoon is almost constant or rather decreases and the total angular momentum decreases significantly, if the random velocity of planetesimals is as large as the escape velocity of the protoearth. On the other hand, if the random velocity is the half of the escape velocity of the protoearth, the mass ratio is kept to be almost as large as the present value and the decrease of the total angular momentum is not so significant. Comparing with the results of giant impact simulations, we find that the mass of the protoearth immediately after the Moon-forming impact was 0.7-0.8 times the present value if the impactor-to-target mass ratio was 3:7, whereas the giant impact occurred almost in the end of the Earth's accretion if the impactor-to-target mass ratio was 1:9.     

Evolution of collapse nonuniformity for rotating magnetic interstellar clouds

We investigate the formation and evolution of isothermal collapse nonuniformity for rotating magnetic interstellar clouds. The initial and boundary conditions correspond to the statement of the problem of homogeneous cloud contraction from a pressure equilibrium with the external medium. The initial uniform magnetic field is collinear with the angular velocity. Fast and slow magnetosonic rarefaction waves are shown to be formed and propagate from the boundary of the cloud toward its center in the early collapse stages. The front of the fast rarefaction wave divides the gas mass into two parts. The density, angular velocity, and magnetic field remain uniform in the inner region and have nonuniform profiles in the outer region. The rarefaction wave front surface can take both prolate and oblate shapes along the rotation axis, depending on the relationship between the initial angular velocity and magnetic field. We derive a criterion that separates the two regimes of rarefaction wave dynamics with the dominant role of electromagnetic and centrifugal forces. Based on analytical estimations and numerical calculations, we discuss possible scenarios for the evolution of collapse nonuniformity for rotating magnetic interstellar clouds.     

Exchange of global mean angular momentum between an atmosphere and its underlying planet

This paper investigates the exchange of global mean angular momentum between an atmosphere and its underlying planet by a simple model. The model parameterizes four processes that are responsible for zonal mean momentum budget in the atmospheric boundary layer for a rotating planet: (i) meridional circulation that redistributes the relative angular momentum, (ii) horizontal diffusion that smoothes the prograde and retrograde winds, (iii) frictional drag that exchanges atmospheric angular momentum with the underlying planet, and (iv) internal redistribution of the zonal mean momentum by wave drag. It is shown that under a steady-state or a long-term average condition, the global relative angular momentum in the boundary layer vanishes unless there exists a preferred frictional drag for either the prograde or the retrograde zonal wind. We further show quantitatively that one cannot have either a predominant steady prograde or retrograde wind in the boundary layer of a planetary atmosphere. The parameter dependencies of the global relative angular momentum and the strength of the atmospheric circulation in the boundary layer are derived explicitly and used to explain the observational differences between the atmospheres of Earth and Venus.     

Rotation of the elastic Earth: the role of the angular-velocity-dependence of the elasticity-caused perturbation

We calculate the so-called convective term, which shows up in the expression for the angular velocity of the elastic Earth, within the Andoyer formalism. The term emerges due to the fact that the elasticity-caused perturbation depends not only on the instantaneous orientation of the Earth but also on its instantaneous angular velocity. We demonstrate that this term makes a considerable contribution into the overall angular velocity. At the same time the convective term turns out to be automatically included into the correction to the nutation series due to the elasticity, if the series is defined by the perturbation of the figure axis (and not of the rotational axis) in accordance with the current IAU resolution. Hence it is not necessary to take the effect of the convective term into consideration in the perturbation of the elastic Earth as far as the nutation is related to the motion of the figure axis.     

On a probable mechanism of superrotation of the atmosphere of venus

It is shown in the paper that the mechanism of superrotation of the atmosphere of Venus consists of several interrelated processes, including the transport of angular momentum from the solid planet to the atmosphere at a wind flow over the planet’s surface relief, the upward transport of momentum by threedimensional turbulent vortices, the inverse energy cascade in a large-scale quasi-two-dimensional flow, and the horizontal transfer of angular momentum in the Hadley cell. These processes make different contributions to the superrotation at different altitudes.