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1.
A dust disc within a planetary magnetosphere constitutes a novel type of dust-ring current. Such an azimuthal current carrying dust disc is subject to the dusty plasma analog of the well known finite-resistivity ‘tearing’ mode instability in regular plasma current sheets, at long wavelengths. It is proposed that the presently observed fine ringlet structure of the Saturnian ring system is a relic of this process operating at cosmogonic times and breaking up the initial proto-ring (which may be regarded as an admixture of fine dust and plasma) into an ensemble of thin ringlets. It is shown that this instability developes at a rate that is many orders of magnitude faster than any other known instability, when the disc thickness reaches a value that is comparable to its present observed value.  相似文献   

2.
Photometric observations of the short-period (RS CVn-type) eclipsing binary system CG Cyg have been presented. Two sets of results, obtained from an analysis of theB, V andR light curves, represent ‘occultation’ and ‘transit’ solutions. The occultation solution is preferred as it gives a better fit to the colour curve. This hypothesis may also offer a more promising explanation of the observed peculiarities such as period changes and the light variation outside eclipses.  相似文献   

3.
The principal dynamical properties of the planetary and satellite systems listed in Section 2 require these bodies to have condensed in highly-flattened nebulae which provided the dissipation forces that produced the common directions of orbital motion, and the lowe andi values. Minimum masses of these nebulae can be estimated on the assumption that the initial solar abundances apply, starting from the empirical data on present planetary and satellite compositions and masses. The asteroids and comets are assumed to be direct condensations and accretion products in their respective zones (2–4 AU and 20–50 AU), without the benefit of gravitational instability in the solar nebula, owing to the comparatively low density there; with gravitational instability accelerating and ultimately dominating the accretion of the planets and major satellites, in zones approaching and exceeding the local Roche density. Only in the case of Jupiter, gravitational instability appears to have dominated from the outset; the other planets are regarded as hybrid structures, having started from limited accretions. In Section 3 the empirical information on protostars is reviewed. ‘Globules’ are described, found to have the typical range of stellar masses and with gaseous compositions now well known thanks largely to radio astronomy. They contain also particulate matter identified as silicates, ice, and probably graphite and other carbon compounds. The measured internal velocities would predict a spread of total angular momenta compatible with the known distribution of semi-major axes in double stars. The planetary system is regarded as an ‘unsuccessful’ binary star, in which the secondary mass formed a nebula instead of a single stellar companion, with 1–2% of the solar mass. This mass fraction gives a basis for an estimate of thefrequency of planetary systems. The later phases of the globules are not well known empirically for the smaller masses of solar type; while available theoretical predictions are mostly made for non-rotating pre-stellar masses. Section 5 reviews current knowledge of the degree of stability of the planetary orbits over the past 4.5×109 yr, preparatory to estimates of their original locations and modes of origin. The results of the Brouwer and Van Woerkom theory and of recent numerical integrations by Cohenet al. indicate no drastic changes in Δa/a over the entire post-formation history of the planets. Unpublished numerical integrations by Dr P. E. Nacozy show the remarkable stability of the Jupiter-Saturn system as long as the planetary masses are well below 29 times their actual values. Numerical values of Δa/a are collected for all planets. The near resonances found for both pairs of planets and of satellites are briefly reviewed. Section 6 cites the statistics on the frequency and masses of asteroids and information on the Kirkwood gaps, both empirical and theoretical. An analogous discussion is made for the Rings of Saturn, including its extension observed in 1966 to the fourth Saturn satellite, Dione. The reality, or lack of it, of the divisions in the Rings are considered. The numbers of Trojan asteroids are reviewed, as is the curious, yet unexplained, bimodal distribution of their orbital inclinations. Important information comes from the periods of rotation of the asteroids and the orientation of their rotational axes. The major Hirayama families are considered as remnants of original asteroid clusterings whose membership has suffered decreases through planetary perturbations. Other families with fewer large members may be due to collisions. The three main classes of meteorites, irons, stones, and carbonaceous chondrites all appear to be of asteroidal origin and they yield the most direct evidence on the early thermal history of the solar system. While opinion on this subject is still divided, the author sees in the evidence definite confirmation of thecold origin of the planetary system, followed by ahot phase due to the evolving sun that caused the dissolution of the solar nebula. This massive outward ejection, that included the smaller planetesimals, appears to have caused the surface melting of the asteroids by intense impact, with the splashing responsible for the formation of the chondrules. The deep interiors of the asteroids are presumably similar to the C1 meteorites which have recently been found to be more numerous in space by two orders of magnitude than previously supposed.  相似文献   

4.
Loukas Vlahos 《Solar physics》1987,111(1):155-166
Energetic electrons, with energies 10–100 keV, accelerated during the impulsive phase of solar flares, sometimes encounter increasing magnetic fields as they stream towards the chromosphere. A consequence of the conservation of their magnetic moment is that the electrons with large initial pitch angle will be reflected at different heights from the atmosphere. Energetic electrons reflected below the transition zone will lose most of their energy to collisions and will never return to the corona. Thus, electrons reflected above the transition zone form a loss-cone velocity distribution which can be unstable to Electron Cyclotron Maser (ECM). The interaction of quasi-perpendicular shocks with the ambient coronal plasma will form a ‘ring’ or ‘hollow beam’ velocity distribution upstream of the shock. ‘Ring’ velocity distributions are also unstable to the ECM instability. A review of the recent results on the theory of ECM will be presented. We will focus our discussion on the questions: (a) What are the characteristics of the linear growth rate of the ECM during solar flares? (b) How does the ECM saturate and what is its efficiency? (c) How does the ECM generated radiation modify the flare environment? Finally we will review the outstanding questions in the theory of ECM and we will relate the theoretical predictions to current observations.  相似文献   

5.
Monochromatic photographs of the Orion Nebula taken through narrow bandpass interference filters (Δλ=10 Å) centred on Hα, Hβ and [NII] lines are presented. Ratio contours of Hα/[NII] and Hα/Hβ are derived. They enable a detailed study of the point-to-point variation in ionization structure and temperature throughout the nebula. Dust located within the ionized gas is studied from the Hα/Hβ ratio which varies from point to point over the nebula. Its strongest concentration, apart in the obvious ‘dark bay’, occurs in a shell surrounding the exciting stars, with about 2′ of diameter. Close to Θ1 Ori the Hα/Hβ ratio, corrected for interstellar reddening, is about 3.0 in good agreement with the predicted value (Brocklehurst, 1971). To account for these measures, the following arguments are proposed:
  1. Dust grains are completely or partially destroyed in region close to the exciting stars.
  2. Radiation pressure and stellar wind push the remaining dust up to some equilibrium distance outwards. The consequence of this action is obviously the formation of a ‘dust mantle’ which is seen as a ring in projection.
  相似文献   

6.
We examine the non-radial modes of oscillation, belonging to spherical harmonics of ordersl=1 andl=3, of a gaseous polytrope with a toroidal magnetic field. We find that a toroidal magnetic field increases the growth rate of convective instability for deformations belonging to the spherical harmonicl=1 whereas it decreases the growth rate of convective instability for deformations belonging to the harmonicsl=2 andl=3. The frequencies of the ‘acoustic’ mode and the ‘Kelvin’ mode are decreased by the presence of the toroidal magnetic field.  相似文献   

7.
Structural patterns of ion and electron currents observed on the wake axes of the Ariel J and the Gemini 10 space vehicles are re-examined, together with relevant theoretical and laboratory ‘simulation’, studies. Some insight into existingin-situ data is provided. The possibility that ‘converging-stream’ models describe structural features of current enhancements in the wake region of large spacecraft is discussed.  相似文献   

8.
Several authors (Basano and Hughes, 1979; ter Haar and Cameron, 1963, Dermott, 1968; Prentice, 1976) give the revised Titius-Bode law in the form $$r_n = r_o C^n ,$$ wherer n stands for the distance of thenth planet from the Sun;r o andC are constant. They pointed out, in addition, that regular satellites systems around major planets obey also that law. It is now generally thought that the Kant-laplace primeval nebula accounts for the origin and evolution of the solar system (Reeves, 1976). Furthermore, it is shown (Prentice, 1976) that rings, which obey the Titius-Bode law, are formed through successive contractions of the solar nebula. Among difficulties encountered by Prentice's theory, the formation of regular satellites similar to the planatery system is the most important one. Indeed, the starting point of the planetary system is a rotating flattened circular solar nebula, whereas a gaseous ring must be the starting point of satellites systems. As far as the Titius-Bode law is concerned, we have the feeling that orbits of planets around the Sun and of satellites around their primaries do not depend on starting conditions. That law must be inherent to gravitation, in the same manner that electron orbits depend only on the atomic law instead of the starting conditions under which an electron is captured. If it is correct, then one may expect to formulate similarity between the T-B law and the Bohr law in the early quantum theory. Such a similarity is found (Louise, 1982) by using a postulate similar to the Bohr-Sommerfeld one — i.e., $$\int_{r_o }^{r_n } {U(r) dr = nk,}$$ whereU(r)=GM /r is the potential created by the Sun,k is a constant, andn a positive integer. This similarity suggests the existence of an unknown were process in the solar system. The aim of the present paper is to investigate the possibility of such a process. The first approach is to study a steady wave encountered in special membrane, showing node rings similar to the Prentice's rings (1976) which obey the T-B law. In the second part, we try to apply the now classical Lindblad-Lin density wave theory of spiral galaxies to the solar nebula case. This theory was developed since 1940 (Lindblad, 1974) in order to account for the persistence of spiral structure of galaxies (Lin and Shu, 1964; Lin, 1966; Linet al., 1969; Contopoulos, 1973). Its basic assumption concerns the potential functionU expressed in the form $$U = U_0 + \tilde U,$$ whereU o stands for the background axisymmetric potential due to the disc population, and ?«U o is responsible of spiral density wave. Then, the corresponding mass-density distribution is \(\rho = \rho _o + \tilde \rho\) , with \(\tilde \rho \ll \rho _o\) . Both quantities ? and \(\tilde \rho\) must satisfy the Poisson's equation $$\nabla ^2 \tilde U + 4\pi G\tilde \rho = 0.$$ It is shown by direct observations that most spiral arms fit well with a logarithmic spiral curve (Danver, 1942; Considère, 1980; Mulliard mand Marcelin, 1981). From the physical point of view, they are represented by maxima of ? (or \(\tilde \rho\) ) which is of the form $$\tilde U = cte cos (q log_e r - m\theta ),$$ wherem is an integer (number of arms),q=cte, andr and θ are polar coordinates. The distancer is expressed in an arbitrary unit (r=d/do). In the case of an axisymmetric solar nebula (m=0), successive maxima of \(\tilde U\) are rings showing similar T-B law $$d = d_o C^n ,$$ withC=e 2 π/q constant, andn is a positive integer. It is noted, in addition, that the steady wave equation within the special membrane quoted above and the new expression of the Poisson's equation derived from (5) are quite similar and expressed in the form $$\nabla ^2 \tilde U + cte\tilde U/r^2 = 0.$$ This suggests that both spiral structure of galaxies and Prentice's rings system result from a wave process which is investigated in the last section. From Equation (2) it is possible to derive the wavelength of the assumed wave ‘χ’, by using a procedure similar to the one by L. De Broglie (1923). The velocity of the wave ‘χ’ process is discussed in two cases. Both cases lead to a similar Planck's relation (E=hv).  相似文献   

9.
Observed W-shaped occultation signatures of certain narrow ringlets in the ring systems of Saturn and Uranus imply a concentration of material near their inner and outer radial edges. A model is proposed where edge bunching is a natural consequence of particles in entwined elliptical orbits, with the same particles alternately defining both edges. While such orbits cross over in radius, collisions would not occur if they have small inclinations, the same fixed argument of periapse ω, and other parameters whereby the particles would “fly in formation” along compressed helical paths relative to the core of the ringlet, which is taken to be a circle in the equatorial plane. For this model to match the observed ring thickness and ringlet widths, orbit inclinations i must be much smaller than their eccentricities e, which themselves would be very small compared to unity. Thus, the meridional cross section of the resultant torus would be a very thin ellipse of thickness proportional to i∣cos ω∣, tilted slightly from the equatorial plane by (i/e)∣sin ω∣ radians. However, gravitational perturbations due to the oblateness of the planet would cause a secular change in ω so that this cross section would collapse periodically to a tilted line, and collisions would then occur. If this collapse could be prevented, the torus could remain in a continuous state of nearly zero viscosity. Stabilization against collapse appears possible due to several remarkable characteristics that are added to the model when the particles are electrically charged. First, because of inherent features of the torus structure, a weak electric force could counter the key effect of the vastly larger oblateness force. Second, because the electric perturbation also affects i, there is a large region in ω,i space where stability against cross-sectional collapse is automatic. For this region, the thickness of the elliptical cross section would expand and contract in concert with the way that the major axis of the ellipse rocks back and forth relative to the equatorial plane. The period of these “rocking and breathing” changes would be from 1 to 3 weeks for a torus in the C ring of Saturn, for example. The electric effects could change considerably without driving the parameters of the torus from the stable domain where cross-sectional collapse does not occur. While specialized and in several important ways still incomplete, the proposed model could account for the W-shaped patterns and explain how very dense ringlets might endure without energy loss due to collisions. It also appears to be capable of explaining the observed sorting of particles by size within a ringlet. Several characteristics of the model suggest definitive tests of its applicability, including its prediction that a nonsymmetrical W-shaped occultation signature could be reversed a half orbit away, and that grazing solar illumination of tilted ringlets might cast shadows that change with time in a prescribed way.  相似文献   

10.
If an electrically conducting medium (e.g. a dusty plasma) rotates around a gravitating central body, which possesses an axisymmetric dipole field, the medium is supported to two-thirds by the centrifugal force and to one-third by electromagnetic forces under the condition that the magnetic field is strong enough to controll the motion. If the electromagnetic forces disappear — e.g. by a de-ionisation of the dusty plasma — the medium will fall down to two-thirds of its original central distance. The result of this process will be a cosmogonic shadow effect which is described in some detail.The Voyager 1/Saturn results demonstrate that the macro-structure of the Saturnian ring system can be explained as a result of this effect working at the formation of the system. The agreement between the theoretical results and the observations is better than a few percent.A similar analysis of the asteroidal belt shows that its macro-structure can also be explained by the cosmogonic shadow effect. The agreement between theory and observations is perhaps even better than in the Saturnian ring system.The observational results demonstrate that during their formation both the Saturnian ring and the asteroidal belt passed a plasma state dominated by electromagnetic effects.  相似文献   

11.
Fixed points and eigencurves have been studied for the Hénon-Heiles mapping:x′=x+a (y?y 3),y′=y(x′?x′ 3). Eigencurves of order 21 proceed rapidly to infinity fora=1.78, but as ‘a’ decreases, they spiral around the origin repeatedly before escaping to infinity. Fixed pointsx f on thex-axis have been located for the range 1≤a≤2.4, for ordersn up to 100. Their locations vary continuously witha, as do the eigencurves, and hyperbolic points remain hyperbolic. Forn=3 and 2.4≥a≥2.37, a very detailed study has been made of how escape occurs, with segments of an eigencurve mapping to infinity through various escape channels. Further calculations with ‘a’ decreasing to 2.275 show that this instability is preserved and that the eigencurve will spiral many times around the origin before reaching an escape channel, there being more than 34 turns fora=2.28. The rapid increase of this number is associated with the rapid decrease of the intersection angle between forward and backward eigencurves (at the middle homoclinic point), with decreasing ‘a’, this angle governing the outward motion. By a semi-topological argument, it is shown that escape must occur if the above intersection angle is nonzero. In the absence of a theoretical expression for this angle, one is forced to rely on the numerical evidence. If the angle should attain zero for a valuea=a c>am,wherea m .is the minimum value for which the fixed points exist, then no escape would be possible fora c However, on the basis of calculations by Jenkins and Bartlett (1972) forn=6, and the results of the present article forn=3, it appears highly probable thata c=am,and that escape from the neighborhood of a hyperbolic point is always possible. If there is escape from the hyperbolic fixed point forn=4,a=1.6, located atx f=0.268, then the eigencurve must cross the apparently closed invariant curve of Hénon-Heiles which intersects thex-axis atx?±0.4, so that this curve cannot in fact be closed.  相似文献   

12.
Parts I and II of our analysis of the evolution of the solar system were devoted mainly to the mechanical processes. The present part (Part III) deals primarily with the plasma processes and the hydromagnetic aspects.Much confusion in the cosmogonic field is due to the treatment of the early phases of the evolution of a circumstellar medium by pre-hydromagnetic methods, or by erroneous application of magnetohydrodynamics. In order to reduce the speculative element as far as possible the present analysis tries to connect the cosmogonic processes as directly as possible to laboratory plasma physics and to space phenomena actually observed today (Section 10).Models of the Laplacian type have been made obsolete by magnetohydrodynamics. Furthermore they are in conflict with observations. A new model is suggested (Section 11).A plasma surrounding a rotating central body may attain a state of partial corotation which is determined by the balance between gravitation and the centrifugal force acting on a plasma in a dipole field. Condensation from a partially corotating plasma results in grains orbiting in ellipses withe=1/3 and finally accreting to bodies at 2/3 of the central distance of the point of condensation (Section 12).An application of the theory to the Saturnian rings and to the asteroidal belt shows that the falldown ratio 2/3 (derived from the geometry of a dipole field) is essential for the understanding of their structure. The structure of the groups of planets and satellites is also discussed but only in a preliminary way. The behavior of volatile substances is a major problem which still awaits an appropriate treatment (Section 13).  相似文献   

13.
Evidence is discussed showing that a representative solar flare event comprises three or more separate but related phenomena requiring separate mechanisms. In particular it is possible to separate the most energetic effect (the interplanetary blast) from the thermal flare and from the rapid acceleration of particles to high energies. The phenomena are related through the magnetic structure characteristic of a composite flare event, being a bipolar surface field with most of its field lines ‘closed’. Of primary importance are helical twists on all scales, starting with the ‘flux rope’ of the spot pair which was fully twisted before it emerged. Subsequent untwisting by the upward propagation of an Alfvén twist wave provides the main flare energy.
  1. The interplanetary blast model is based on subsurface, helically twisted flux ropes which erupt to form spots and then transfer their twists and energy by Alfvén-twist waves into the atmospheric magnetic fields. The blast is triggered by the prior-commencing flash phase or by a coronal wave.
  2. The thermal flare is explained in terms of Alfvén waves travelling up numerous ‘flux strands’ (Figure 3) which have frayed away from the two flux ropes. The waves originate in interaction (collisions, bending, twisting, rubbing) between subsurface flux strands; the sudden flash is caused by a collision. The classical twin-ribbon flare results from the collision of a flux rope with a tight bunch of S-shaped flux strands.
  3. The impulsive acceleration of electrons (hard X-ray, EUV, Hα and radio bursts) is tentatively attributed to magnetic reconnection between fields in two parallel, helically twisted flux strands in the low corona.
  4. Flare (Moreton) waves in the corona have the same origin as the interplanetary blast. Sympathetic flares represent only the start of enhanced activity in a flare event already in the slow phase. Filament activation also occurs during the slow phase as twist Alfvén waves store their energy in the atmosphere.
  5. Flare ejecta are caused by Alfvén waves moving up flux strands. Surges are attributed to packets of twist Alfvén waves released into bundles of flux strands; the waves become non-linear and drive plasma upwards. Spray-type prominences result from accumulations of Alfvén wave energy in dome-shaped fields; excessive energy density eventually explodes the field.
  相似文献   

14.
15.
LetH=T(p)?U(q) the Hamiltonian of theN-body problem in cartesian coordinates. In his ‘Nouvelles Méthodes de la Mécanique Céleste’ (tome 1, p. 172) Poincaré observes that the equations leave invariant the differential form $$\alpha = \Sigma (q \delta p + \tfrac{1}{2}p \delta q) - \tfrac{3}{2}t \delta H.$$ This property was rediscovered by Elie Cartan in the framework of his ‘Leçons sur les Invariants Intégraux’ (p. 89, last line). We propose to study some applications of this fact from the point of view of Poincaré, that is: the point of view of the equations of variation.  相似文献   

16.
We build a simple dissipative analytical model considering an averaged restricted 3-body problem taking into account the effect of the oblateness of a planet on a small satellite and on its perturber. We apply this model to the inner Uranian system and we follow the dynamical evolution of the satellites Cressida or Desdemona, these latter being close to a 3:1 commensurability with the large satellite Miranda. Our analysis shows that the positions of the two inner satellites, on both sides of the exact resonance, are temporary, Cressida having already crossed the resonance, and Desdemona approaching the commensurability to jump over later on.  相似文献   

17.
It was recognized over a year ago that a requirement to improve the ephemerides of the natural satellites existed and that it might be satisfied by a coordinated effort. Both the national ephemeris offices, which publish the satellite ephemerides, and NASA, which plans to send spacecraft to observe the satellites, require improved ephemerides of the natural satellites, but individually none of the organizations has the personnel or finances to undertake the task alone. At that time a few people and institutions had become interested in or were beginning to work on the theories and to make observations of the satellites. It was apparent that if the efforts of the various people and institutions were coordinated and others were encouraged to contribute, it might be possible in the next five years to satisfy the requirement for improved ephemerides. The coordinated effort includes personnel from the University of Texas, Smithsonian Astrophysical Center, University of Cincinnati, Bureau des Longitudes, Jet Propulsion Laboratory, University of Virginia, Vanderbilt University, Lowell Observatory, NASA Headquarters, and the U.S. Naval Observatory, with the latter institution serving as the coordinator.  相似文献   

18.
Mid-infrared extinction coefficients of five natural amorphous silicates and seven synthetic glasses were measured. Three bands at about 10, 12, and 20 μm were seen for all the measured samples. The quantities of these bands are found to have good correlations with the SiO2 content of the samples. The correlations are the most remarkable for the 10 μm band. As the SiO2 content decreases, the peak wavelengthλ m shifts to longer side, the peak heightK m decreases and the full width of half maximumW increases. A quantityλ m K m W is constant within 15%. Empirical formula $$\lambda_m (\mu m) = {11.10-2.30 x 10^-2} {[SiO_2 wt.\%]} \pm 0.15$$ and $$W(\mu m) = {5.14-4.68 x 10^- 2} {[SiO_2 wt.\%]} \pm 0.30$$ are obtained for the measured samples. Therefore, the correlation is present between the 10 μm peak wavelengthλ m and peak widthW for amorphous silicates. The change in peak widthW is remarkable compared the change in peak wavelengthλ m as the SiO2 content varies. For the 12 μm band the correlations with the SiO2 content are not so good. A tendency that theλ m shifts to the red and theK m lowers as the decreasing SiO2 content are found. For the samples with SiO2 content less than 50% the 12 μm band cannot recognized as the peak. For the 20 μm band, theλ m is almost independent on SiO2 content and theK m lowers with decreasing SiO2 content. The results are compared with the observed 10 μm band of the astronomical objects. A method to estimate the SiO2 content of astronomical grain materials is proposed and 48±8% SiO2 wt.% is found corresponding to the peak wavelength of 9.7 μm and the peak width of 2.5–3.0 μm of typical celestial objects.  相似文献   

19.
Terrestrial ring dike structures are features consisting of one or more series of concentric fracture systems along which the central block often subsided and up through which lavas intruded and extruded and other volcanic features formed. Before the lunar probe satellites, a search for lunar features that showed characteristics of terrestrial ring dikes was conducted using the LAC charts andKuiper Atlas photographs. More recently the search was extended on the nearside features and to the farside features using the Lunar Orbiter series of photographs resulting in a catalog of 559 nearside candidates and 82 farside. Features exhibiting one or more of the following four criteria were included as lunar analogs to terrestrial ring dikes: (1) inner ridge(s) approximately concentric with the crater wall, (2) inner rill(s) approximately concentric with the crater wall, (3) outer ridge(s) and/or rill(s) approximately concentric with the crater wall, and (4) interior and exterior slopes of the crater wall approximately equal (implying extrusion of lava along a ring fracture). Equal slopes are in contradistinction to a central source eruptive feature or an impact feature both of which usually produce craters with walls whose inner slopes are about twice as steep as their outer flanks, which characterize the vast majority of lunar craters. Features exhibiting each of the four criteria were found and some had combinations of two or more including rills merging into ridges, e.g., in Taruntius and Posidonius. Gambart is an example of equal inner and outer slopes, while Hesiodus A and Marth are two of the best examples of complete inner rings concentric with the outer rings. Ten percent of the candidates were probable impact craters but had subsequent volvanic activity of a ring dike nature. The initial search showed a distribution of the possible lunar ring dikes that was non-random and strongly associated with the margins of the maria, further implying that they are volcanic features. This relation was upheld when extended by the recent survey. The anticipated dearth of farside ring dikes was corroborated in our study and their distribution is restricted to those few mare-like areas on the farside, further supporting the volcanic nature of these features  相似文献   

20.
The solution of the partial differential equation describing the ‘non-isentropic’ oscillations of a star in thermal imbalance has been obtained in terms of asymptotic expansions up to the first order in the parameterII/t s, whereII is the adiabatic pulsation period for the fundamental mode andt s , a secular time scale of the order of the Kelvin-Helmholtz time. Use has been made of the zeroth order ‘isentopic’ solution derived in I. The solution obtained allows one to derive unambiguously a general integral expression for the coefficient of vibrational stability for arbitrary stellar models in thermal imbalance. The physical interpretation of this stability coefficient is discussed and its generality and its simplicity are stressed. Application to some simple analytic stellar models in homologous and nonhomologous contraction enables one to recover, in a more straightforward manner, results obtained by Coxet al. (1973). Aizenman and Cox (1974) and Davey (1974). Finally, we emphasize that the inclusion of the effects of thermal imbalance in the stability calculations of realistic evolutionary sequences of stellar models, not considered up to now by the other authors, is quite easy and straightforward with the simple formula derived here.  相似文献   

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