Galactic models in the light of collision dynamics

A simple and flexible model of a spiral galaxy is developed in the light of the study of the dynamics of colliding galaxies. As such interactions are strongly characterised by the binding energy distributions of the systems involved; hence, the main criterion used in constructing the model is its compatibility with the observed shapes and intensity distribution of light of spirals. The model basically consists of thick exponential disk component and a spherical polytropic bulge component. The relevant quantities pertaining to the model, significant for dynamical studies, are computed and analysed.The study of the dynamics of colliding galaxies require galactic models with and without halos, depending upon the problem under study and the effects to be accessed. Consequently, we have preferred to tackle the problem of galactic models with massive halos separately in the next paper.     

Analytical formulation of thermal convection within a body of spherical shape

We modify Chandrasekhar's 1961 theory on convective motion by introducing an equation of state which depends both on pressure and temperature. We use this formulation to study the thermal convection within planetary masses of spherical shape. We proceed analytically to show that the flow field and the other geophysically relevant variables can be represented in terms of series of Bessel functions of the radial distance for those regimes which satisfy eigenvalue relations between the Rayleigh number and another nondimensional parameter. We provide numerical values for these eigenfunctions corresponding to the first six orders of harmonics.     

Thermodynamics of rare events and impulsive relaxation events in the magnetospheric substorm dynamics

The magnetosphere dynamics shows fast relaxation events following power-law distribution for many observable quantities during magnetic substorms. The emergence of such power-law distributions has been widely discussed in the framework of self-organized criticality and/or turbulence. Here, a different approach to the statistical features of these impulsive dynamical events is proposed in the framework of the thermodynamics of rare events [Lavenda, B.H., Florio, A., 1992. Thermodynamics of rare events, Int. J. Theor. Phys. 31, 1455–1475; Lavenda, B.H., 1995. Thermodynamics of Extremes. Albion]. In detail, an application of such a novel approach to the magnetospheric substorm avalanching dynamics as monitored by the auroral electroject index is discussed.     

On the possibility of studying the dynamics of astrophysical disks in a two-dimensional formulation

A closed system of two-dimensional equations describing the dynamics of rotating, gravitating gas disks is derived. It is an integrodifferential system for barotropic disks and a differential system for polytropic disks. For both barotropic and polytropic disks, these equations differ both from the dynamical equations used in the literature for astrophysical disks and from the traditional equations of two-dimensional hydrodynamics. The sufficient conditions under which the dynamics of a disk can be described in a two-dimensional formulation are obtained. The first condition reflects the thin-disk approximation. The second condition imposes a limit on the characteristic times of processes studied in a two-dimensional formulation. In most cases this condition limits the characteristic frequency of a process to the disk's rotational frequency.Translated from Astrofizika, Vol. 39, No. 3, pp. 441–466, July–September, 1996.     

Hard X-ray images of impulsive bursts

A morphological study is made for the hard X-ray images (25–50 keV) of nine impulsive bursts observed by Hinotori. Most of them revealed single sources, either extended or compact, during the whole duration of the bursts. The sources of all of four spike bursts in the present sample are compact. After the main phase of the impulsive bursts, generally the source size becomes smaller accompanying a shift of position. The X-ray source size is much greater than that of the Hα kernel in two events out of three. Four possible explanations for the X-ray source to be single are suggested. One of these is the strong electric field along the magnetic field as demonstrated to be produced at the decay of force-free current.     

Direct simulation of collision processes

The mass distribution of protoplanets is studied by a Monte Carlo technique. It is assumed that the bodies coalesce on collision and that their self-gravitation is important. It is found that over most of the mass range a distribution of the formn(m)αm ^?q develops, withq tending to ～1.8. However, there is an overabundance of large masses relative to the power law: in particular the simulations indicate the growth of a large nucleus which progressively dominates the growth process. It is also found that the axial inclinations of the planets are best explained if they grew out of a coagulating medium comprising planetesimals with random velocities ～5 km s^?1 and masses up to 10^?2 of the embryo masses. The inclinations of the giant planets are consistent with a floccule-type origin of these bodies.     

Direct simulation of collision processes

A Monte Carlo technique for examining the mass distribution of mutually colliding bodies is described. The technique is simple to program and can handle a wide variety of physical circumstances. Some illustrative cases are given.     

Imaging of impulsive solar flare phenomena

We review some recent advances in our understanding of impulsive solar flare phenomena obtained through new hard X-ray and radio imaging instruments (the Solar Maximum Mission and Hinotori satellites, the VLA and VLBI).     

Fragmentation model dependence of collision cascades

Mass depletion of bodies through successive collisional disruptions (i.e., collision cascade) is one of the most important processes in the studies of the asteroids belt, the Edgeworth-Kuiper belt, debris disks, and planetary formation. The collisional disruption is divided into two types, i.e., catastrophic disruption and cratering. Although some studies of the collision cascades neglected the effect of cratering, it is unclear which type of disruption makes a dominant contribution to the collision cascades. In the present study, we construct a simple outcome model describing both catastrophic disruption and cratering, which has some parameters characterizing the total ejecta mass, the mass of the largest fragment, and the power-law exponent of the size distribution of fragments. Using this simple outcome model with parameters, we examine the model dependence of the mass depletion time in collision cascades for neglect of coalescence of colliding bodies due to high collisional velocities. We find the cratering collisions are much more effective in collision cascades than collisions with catastrophic disruption in a wide region of the model parameters. It is also found that the mass depletion time in collision cascades is mainly governed by the total ejecta mass and almost insensitive to the mass of the largest fragment and the power-law exponent of fragments for a realistic parameter region. The total ejecta mass is usually determined by the ratio of the impact energy divided by the target mass (i.e. Q-value) to its threshold value for catastrophic disruption, as well as in our simple model. We derive a mass depletion time in collision cascades, which is determined by of the high-mass end of collision cascades. The mass depletion time derived with our model would be applicable to debris disks and planetary formation.     

A model of impulsive loop flares revisited

A critical examination of the components of the recent impulsive loop flare model of Takakura is made. It is found that his analysis of the stability of the electron distribution resulting from anomalous heat conduction is in error and electron plasma waves would not be excited. Rather, in the regions where the electron/proton temperature ratioT _e/T _i 10, electrostatic ion-cyclotron waves would be excited and in the regions whereT _e 10, ion-acoustic waves would be excited. Ratios ofT _e/T _i 10 occur only in the late time development behind the conduction fronts. Since the anomalous resistivity due to electrostatic ion-cyclotron waves is fortuitously about 70% of the one used by Takakura, the general development will follow closely the one calculated by him. Because the anomalous resistivity due to ion-acoustic waves is about 95 times the one used by Takakura, the development in the parts of the loop whereT _e/T _i 10 for late times would be altered considerably.Also Guest Worker at NOAA Space Environment Laboratory, Boulder, Colorado, U.S.A.     

The characteristics of impulsive solar EUV bursts

We examine a number of high time resolution intensity-time profiles of EUV impulsive bursts as observed by the Harvard College Observatory EUV Spectroheliometer carried aboard the Skylab Apollo Telescope Mount. These bursts are found to be synchronous (to within the instrumental time resolution of 5.5 s) in all wavelengths observed, corresponding to emissions from temperatures ranging from upper chromospheric to coronal. The distribution with temperature of a suitably defined emission measure parameter is also examined as a function of time throughout the bursts and a marked similarity in the shape of this distribution, both between different events and throughout the time history of any particular event, is noted. The significance of these observations for physical processes associated with EUV bursts is briefly discussed.On leave from Dept. of Astronomy, University of Glasgow, Glasgow G12 8QQ, Scotland, U.K.     

Behavior of transition-region lines during impulsive solar flares

We describe briefly the Ultraviolet Spectrometer and Polarimeter on the Solar Maximum Mission and discuss data pertaining to the emissions observed in lines originating in the transition-region plasma, particularly during impulsive flares. The data pertain to lines from the following ions: SiII, CIV, OIV, SiIV, OV, and FeXXI.     

A multiwavelength study of a double impulsive flare

Extensive data from the Solar Maximum Mission (SMM) and ground-based observatories are presented for two flares; the first occurred at 12:48 UT on 31 August, 1980 and the second just 3 min later. They were both compact events located in the same part of the active region. The first flare appeared as a typical X-ray flare: the Caxix X-ray lines were broadened ( 190±40 km s^-1) and blue shifted ( 60±20 km s^-1) during the impulsive phase, and there was a delay of about 30 s between the hard and soft X-ray maxima. The relative brightness of the two flares was different depending on the spectral region being used to observe them, the first being the brighter at microwave and hard X-ray wavelengths but fainter in soft X-rays. The second flare showed no significant mass motions, and the impulsive and gradual phases were almost simultaneous. The physical characteristics of the two flares are derived and compared. The main difference between them was in the pre-flare state of the coronal plasma at the flare site: before the first flare it was relatively cool (3 × 10⁶ K) and tenuous (4 × 10⁹ cm^-3), but owing to the residual effects of the first flare the coronal plasma was hotter (5 × 10⁶ K) and more dense (3 × 10¹¹ cm^-3) at the onset of the second flare. We are led to believe from these data that the plasma filling the flaring loops absorbed most of the energy released during the impulsive phase of the second flare, so that only a fraction of the energy could reach the chromosphere to produce mass motions and turbulence.A simple study of the brightest flares observed by the SMM shows that at least 43% of them are multiple. Thus, the situation studied here may be quite common, and the difference in initial plasma conditions could explain at least some of the large variations in observed flare parameters. We draw a number of conclusions from this study. First, the evolution of the second flare is substantially affected by the presence of the first flare. Secondly, the primary energy release in the second event is in the corona. Thirdly, the flares occur in a decaying magnetic region, probably as a result of the interaction of existing sheared loops; there is no evidence of emerging magnetic flux. Also, magnetic structures of greatly varying size participate in the flare processes. Lastly, there is some indication that the loops are not symmetrical or stable throughout the flares, i.e. the magnetic field does not act as a uniform passive bottle for the plasma, as is often assumed in flare models.NOAA/Space Environment Laboratory, currently at NASA/MSFC, Ala., U.S.A.Now at Sacramento Peak Observatory, Tucson, Ariz., U.S.A.     

Energetics and morphology of powerful impulsive solar flares

We have studied the energetics of two impulsive solar flares of X-ray class X1.7 by assuming the electrons accelerated in several episodes of energy release to be the main source of plasma heating and reached conclusions about their morphology. The time profiles of the flare plasma temperature, emission measure, and their derivatives, and the intensity of nonthermal X-ray emission are compared; images of the X-ray sources and magnetograms of the flare region at key instants of time have been constructed. Based on a spectral analysis of the hard X-ray emission from RHESSI data and GOES observations of the soft X-ray emission, we have estimated the spatially integrated kinetic power of nonthermal electrons and the change in flare-plasma internal energy by taking into account the heat losses through thermal conduction and radiation and determined the parameters needed for thermal balance. We have established that the electrons accelerated at the beginning of the events with a relatively soft spectrum directly heat up the coronal part of the flare loops, with the increase in emission measure and hard X-ray emission from the chromosphere being negligible. The succeeding episodes of electron acceleration with a harder spectrum have virtually no effect on the temperature rise, but they lead to an increase in emission measure and hard X-ray emission from the footpoints of the flare loops.     

Observation of the impulsive phase of a simple flare

We present a broad range of complementary observations of the onset and impulsive phase of a fairly large (1B, M1.2) but simple two-ribbon flare. The observations consist of hard X-ray flux measured by the SMM HXRBS, high-sensitivity measurements of microwave flux at 22 GHz from Itapetinga Radio Observatory, sequences of spectroheliograms in UV emission lines from Ov (T ≈ 2 × 10⁵ K) and Fexxi (T ≈ 1 × 10⁷ K) from the SMM UVSP, Hα and Hei D₃ cine-filtergrams from Big Bear Solar Observatory, and a magnetogram of the flare region from the MSFC Solar Observatory. From these data we conclude:

1. The overall magnetic field configuration in which the flare occurred was a fairly simple, closed arch containing nonpotential substructure.
2. The flare occurred spontaneously within the arch; it was not triggered by emerging magnetic flux.
3. The impulsive energy release occurred in two major spikes. The second spike took place within the flare arch heated in the first spike, but was concentrated on a different subset of field lines. The ratio of Ov emission to hard X-ray emission decreased by at least a factor of 2 from the first spike to the second, probably because the plasma density in the flare arch had increased by chromospheric evaporation.
4. The impulsive energy release most likely occurred in the upper part of the arch; it had three immediate products:

1. An increase in the plasma pressure throughout the flare arch of at least a factor of 10. This is required because the Fexxi emission was confined to the feet of the flare arch for at least the first minute of the impulsive phase.
2. Nonthermal energetic (～ 25 keV) electrons which impacted the feet of the arch to produce the hard X-ray burst and impulsive brightening in Ov and D₃. The evidence for this is the simultaneity, within ± 2 s, of the peak Ov and hard X-ray emissions.
3. Another population of high-energy (～100keV) electrons (decoupled from the population that produced the hard X-rays) that produced the impulsive microwave emission at 22 GHz. This conclusion is drawn because the microwave peak was 6 ± 3 s later than the hard X-ray peak.

     

Numerical investigation of collision orbits of lunar satellites

In the present study an investigation of the collision orbits of natural satellites of the Moon (considered to be of finite dimensions) is developed, and the tendency of natural satellites of the Moon to collide on the visible or the far side of the Moon is studied. The collision course of the satellite is studied up to its impact on the lunar surface for perturbations of its initial orbit arbitrarily induced, for example, by the explosion of a meteorite. Several initial conditions regarding the position of the satellite to collide with the Moon on its near (visible) or far (invisible) side is examined in connection to the initial conditions and the direction of the motion of the satellite. The distribution of the lunar craters-originating impact of lunar satellites or celestial bodies which followed a course around the Moon and lost their stability - is examined. First, we consider the planar motion of the natural satellite and its collision on the Moon's surface without the presence of the Earth and Sun. The initial velocities of the satellite are determined in such a way so its impact on the lunar surface takes place on the visible side of the Moon. Then, we continue imparting these velocities to the satellite, but now in the presence of the Earth and Sun; and study the forementioned impacts of the satellites but now in the Earth-Moon-Satellite system influenced also by the Sun. The initial distances of the satellite are taken as the distances which have been used to compute periodic orbits in the planar restricted three-body problem (cf. Gousidou-Koutita, 1980) and its direction takes different angles with the x-axis (Earth-Moon axis). Finally, we summarise the tendency of the satellite's impact on the visible or invisible side of the Moon.     

Shock versus stochastic acceleration of impulsive solar flare protons

The two major candidates for proton acceleration in impulsive -ray producing flares, shock and stochastic acceleration, are considered in light of recent observations of mass motions and turbulence in flares. Starting with the basic problem of energies required, energy storage and the currents which must be involved, it is concluded that the primary energy release must occur close to the temperature minimum region. It is shown that energy can propagate upwards in the form of fast magnetosonic waves which become evanescent in the transition region, converting a large fraction of their energy to mass motions and turbulence. Present observations are mostly of rather coarse (7000 km) spatial resolution and it is quite possible that significantly higher velocities than those observed were present. Using the results of recent simulations of parallel shocks and the well tested theory of Lee (1983) for parallel shock acceleration in the interplanetary medium, it is shown that shock acceleration is a viable candidate at velocities slightly higher than present observations. It is also shown that shocks must be driven by a mass of material which would be visible in coronal lines such as Caxix for them to be energetically important in proton acceleration.Stochastic acceleration is examined using the hypothesis that there is an equipartition of energy between observed turbulence and magnetic field fluctuations. It is shown that this is a viable acceleration mechanism within a large range of presently observed turbulence provided that the above equipartition hypothesis is valid and the turbulent elements are of small scale (1–200 km). Since turbulence is observed in many flares without any evidence of -rays, one of the above conditions must not be satisfied in general. It is concluded that although present observations favor stochastic acceleration, no definitive conclusion can be made without higher spatial resolution observations and additional theoretical work.