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1.
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2.
The aim of the present paper will be to give a mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum — an evolution activated by viscous friction of dynamical tides raised by the two components on each other. The first section contains a general outline of the problem; and in Section 2 we shall establish the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure. In Section 3 we shall investigate the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for given amount of total momentum; while in Section 4 we shall compare these results with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known to us from evidence furnished by the observed rates of apsidal advance.The results show that all such systems — be these of detached or semi-detached type — disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than a percent of the total — a situation characteristic of a state close to the minimum energy for given total momentum. This appears, moreover, to be true not only of the systems with both components on the Main Sequence, but also of those possessing evolved components in contact with their Roche limits.Under such conditions, a synchronism between rotation and revolution (characteristic of both extreme states of maximum and minimum energy) is not only possible, but appears to have been actually approached — if not attained — in the majority of cases. In other words, it would appear that — in at least a large majority of known cases — the existing close binaries have already attained orbits of maximum distension consistent with their momenta; and tidal evolution alone can no longer increase the present separations of the components to any appreciable extent.The virtual absence, in the sky, of binary systems intermediate between the stages of maximum and minimum energy for given momentum leads us to conjecture that the process of dynamical evolution activated by viscous tides may enroll on a time-scale which is relatively short in comparison with their total age — even for systems like Y Cygni or AG Persei, whose total age can scarcely exceed 107 yr. A secular increase of the semi-major axes of relative orbits is dynamically coupled with a corresponding variation in the velocity of axial rotation of both components through the tidal lag arising from the viscosity of stellar material. The differential equations of so coupled a system are given in Section 5; but their solution still constitutes a task for the future.The Lunar Science Institute Contribution No. 90. The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.  相似文献   

3.
Differential equations governing the dynamical tides in close binary systems consisting of centrally condensed components of viscous gas are split up (Section 2) in their real and imaginary parts, the ratio of which defines the tidal lag. In Sections 3 and 4 these equations will be particularized to a case in which the central mass-point of each star is surrounded by an evanescent envelope the density of which decreases as the inverse square of the central distance. It is shown that self-gravitating configurations built up in accordance with this model are incapable of performing free nonradial oscillations with a frequency comprised between 0 2 ; but explicit expressions for forced oscillations representing dynamical tides are given for an arbitrary form of the external field of force. Equations for the imaginary components of the displacement, constructed for the same model in Section 4, disclose that if the viscosity of stellar material is identified with that of hydrogen plasma, the tidal lag due to a viscous dissipation of kinetic energy may produce dynamical effects, the cumulative outcome of which becomes appreciable on the Kelvin time-scale, but over short intervals of time their stationary photometric effects should be negligible. The latter can become observationally significant only for stars in which turbulent viscosity under near-adiabatic conditions becomes and important factor.  相似文献   

4.
The aim of the present paper will be to develop from the fundamental equations of hydrodynamics a theory of dynamical tides in close binary systems, the components of which are regarded to consist of heterogeneous viscous fluid, and to revolve around their common centre of gravity in eccentric orbits; moreover, the equatorial planes of their axial rotation and the orbital plane need not be co-planar, but all may be inclined to the invariable plane of the system of arbitrary amounts. The changes in the pressure or density invoked by time-dependent deformation will be regarded as adiabatic; but, in the equilibrium state, both the density and viscosity of the material of our components may be arbitrary functions of the radial distance.Following a brief exposition in Section 2 of the fundamental equations linearized to small oscillations — be these free or forced — in Section 3 we shall particularize them to describe spheroidal deformations; with due regard to all terms arising from viscosity. Section 4 will contain a specification of the boundary conditions to be imposed upon such oscillations; and in Section 5 we shall solve the problem of non-radial oscillations of self-gravitating inviscid configurations in terms of hypergeometric series. The remaining Sections 6–8 will be devoted to a discussion of the phenomena arising from viscosity: in particular, we shall solve in a closed form the problem of non-radial oscillations of incompressible viscous globes in the terms of Bessel functions. It will be shown that the effect of viscosity — like those of compressibility — tend to de-stabilize all non-radial oscillations of homogeneous configurations.At the other extreme, a similar treatment of a mass-point model — as well as of one exhibiting high but finite degree of central condensation — is being postponed for a subsequent communication.  相似文献   

5.
The aim of the present paper will be to derive an equation of dissipation of energy for a rotating body of arbitrary viscosity distorted by tides, which arise from the gravitational field of its companion in a close pair of such bodies.By a transformation of the fundamental equation of energy dissipation in terms of velocity of tidal deformation (Section 2), the dissipation function is constructed for a tidally-distorted body (Section 3). From this equation, the rate of dissipation of tidal energy is formulated for a nearly-spherical rotating body distorted by second harmonic longitudinal tides (Section 4); the coefficients of viscosity (or the bulk modulus) are treated as arbitrary functions of spatial coordinates. Finally (Section 5), expressions for the total energy dissipation within the orbital cycle are given for axial rotation of the distorted body, provided its angular velocity is constant (for example, with the Keplerian angular velocity).Research financed in part by the Division of Scientific Research and Development of Ministry of Sciences and Culture of Greece.  相似文献   

6.
The aim of the present investigation will be to determine the explicit forms of differential equations which govern secular perturbations of the orbital elements of close binary systems in the plane of the orbit (i.e., of the semi-major axisA, eccentricitye, and longitude of the periastron ), arising from the lag of dynamical tides due to viscosity of stellar material. The results obtained are exact for any value of orbital eccentricity comprised between 0e<1; and include the effects produced by the second, third and fourth-harmonic dynamical tides, as well as by axial rotation with arbitrary inclination of the equator to the orbital plane.In Section 2 following brief introductory remarks the variational equations of the problem of plane motion will be set up in terms of the rectangular componentsR, S, W of disturbing accelerations with respect to a revolving system of coordinates. The explicit form of these coefficients will be established in Section 3 to the degree of accuracy to which squares and higher powers of quantities of the order of superficial distortion can be ignored. Section 4 will be devoted to a derivation of the explicit form of the variational equations for the case of a perturbing function arising from axial rotation; and in Section 5 we shall derive variational equations which govern the perturbation of orbital elements caused by lagging dynamical tides.Numerical integrations of these equations, which govern the tidal evolution of close binary systems prompted by viscous friction at constant mass, are being postponed for subsequent investigations.Prepared at the Lunar Science Institute, Houston, Texas, under the joint support of the Universities Space Research Association, Charlottesville, Virginia, and the National Aeronautics and Space Administration Manned Spacecraft Center, Houston, Texas, under Contract No. NSR 09-051-001. This paper constitutes Lunar Science Institute Contribution no. 100.Normally at the Department of Astronomy, University of Manchester, England.  相似文献   

7.
The current Cherenkov telescopes together with GLAST are opening up a new window into the physics at work close to black holes and rapidly rotating neutron stars with great breakthrough potential. Very high energy gamma-ray emission up to 10 TeV is now established in several binaries. The radiative output of gamma-ray binaries is in fact dominated by emission above 1–10 MeV. Most are likely powered by the rotational spindown of a young neutron star that generates a highly relativistic wind. The interaction of this pulsar wind with the companion’s stellar wind is responsible for the high energy gamma-ray emission. There are hints that microquasars, accretion-powered binaries emitting relativistic jets, also emit gamma-ray flares that may be linked to the accretion–ejection process. Studying high energy gamma-ray emission from binaries offers good prospects for the study of pulsar winds physics and may bring new insights into the link between accretion and ejection close to black holes.  相似文献   

8.
Skylab EUV observations of an active region near the solar limb were analyzed. Both cool (T < 106 K) and hot (T > 106 K) loops were observed in this region. For the hot loops the observed intensity variations were small, typically a few percent over a period of 30 min. The cool loops exhibited stronger variations, sometimes appearing and disappearing in 5 to 10 min. Most of the cool material observed in the loops appeared to be caused by the downward flow of coronal rain and by the upward ejection of chromospheric material in surges. The frequent EUV brightenings observed near the loop footpoints appear to have been produced by both in situ transient energy releases (e.g. subflares) and the infall/impact of coronal rain. The physical conditions in the loops (temperatures, densities, radiative and conducting cooling rates, cooling times) were determined. The mean energy required to balance the radiative and conductive cooling of the hot loops is approximately 3 × 10–3 erg cm–3 s–1. One coronal heating mechanism that can account for the observed behavior of the EUV emission from McMath region 12634 is heating by the dissipation of fast mode MHD waves.  相似文献   

9.
Wegener concluded that the Earth's surface has suffered regionally variable westward displacement. Modern data support Wegener's conclusion, but a causative mechanism has not been evident. The retarding torque is too small to distort the viscous Earth. At the same time difficulty has been experienced in explaining the large value of the astronomically detected tidal dissipation. We have examined the effect of the secular rotational strain imposed by tidal bulge formation on convection in the mantle of arbitrary origin. The dissipation as measured by the lag in the bodily tides appears adequate to explain the missing part of the dissipation, some 8.5 × 1026 erg yr–1, without recourse to an unidentified mechanism in the seas. The convection must itself be influenced by the external force system. The effect to be expected is that circulation resulting in westward displacement at surface must be fostered at the expense of circulation in other directions. The history of the tidal couple, if this is based on dissipation in the mantle, is likely to differ greatly from that of a couple based on dissipation in the seas.  相似文献   

10.
The aim of this paper is to study the dynamical problem of tidal friction in a binary system consisting of deformable components, with the restriction that the angle of lag or advance of the tidal distortion with respect to the direction of the disturbing companion is small. The fractional distortion of the bodies due to rotation and tidal interaction is also treated as a first-order small quantity, and terms up to the fourth harmonic in the tidal potential are retained. In this linear approximation, the time-dependent tidal potential can be Fourier decomposed into a spectrum of simple harmonic terms, each of which is responsible for raising a partial wave in the body; each such partial wave can then be treated independently of the others. This is the method first employed by Darwin.In Section 2, it is assumed that the phase lag in the response of the body (due to dissipation of kinetic energy of deformation) is proportional to the forcing frequency, which is justified for small amplitude oscillations of a viscous fluid or visco-elastic body. A simple expression is then obtained for the potential function for the distortion in terms of the disturbing potential and the structure of the body.In Section 3, the distortion potential function is employed in deriving the componentsR, S andW of the disturbing force which are then substituted in the Gaussian form of the equations for variation of the elements. In Section 4, the Eulerian equations for motion of deformable bodies are derived, using the so-called mean axes of the body as the rotating axes of reference. In Section 5, it is shown that the dynamical effects of rotational distortion occur on a much shorter time scale than those arising from tidal friction, which allows one to consider the two phenomena as acting independently of one another. The collected set of Gaussian (orbital) and Eulerian (body) equations is re-written in terms of dimensionless variables for the tidal friction case, and the stability of the system is examined on the basis of these equations.In Section 6, the tidal friction equations are integrated numerically for the close binary system AG Persei and for the Earth-Moon system. In the former, the integrations were started from a highly elliptical orbit and the system was found to relax into a circular orbit, with synchronous rotation perpendicular to the orbit. In the latter, the integrations were performed backwards in time from the present day, and it was found that the lunar orbit rapidly becomes highly elliptical at the time of closest approach, thus indicating a probable capture of the Moon by the Earth. This result is in agreement with that obtained by other investigators; however, it is shown that the detailed behaviour of the system at the time of capture, in particular the inclination of the lunar orbit to the ecliptic, depends critically on the chosen rate of dissipation in the Moon's interior. A simple argument is presented which allows an estimation for the mean viscosity of a fluid body from the known age of the system: for the components of AG per, the result is 2×1011 g cm–1 s–1, indicating that the stars must have possessed turbulent convective outer regions during some part of their tidal evolution, while for the Earth, the result, is 1.4×1012 g cm–1 s–1. It is shown that the angle of tidal lag in nonsynchronous close binary systems in general is expected to be extremely small, and not observationally detectable.  相似文献   

11.
The classical picture of the transition region is that of a thin spherically symmetric shell maintained in a steady average thermodynamical state by a balance between conductive heating from the hot overlying corona and radiative losses. The further analysis of existing extreme ultraviolet flux data casts doubt on the correctness of this simple model. It is shown that the downward heat flux between the chromosphere and corona cannot be nearly as large as the value 6 × 105 erg cm–)= 13.46 - 2.99 sin2 s–1 derived in previous studies by assuming a planar atmosphere, and in fact is insufficient to balance transition-region radiative losses. An alternative picture is developed, consisting of a transition region network covering only a small fraction of the solar disk. The dissipation of mechanical energy, previously neglected in many calculations of theoretical transition region models, appears to play a dominant role in the local energy balance of the network.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

12.
The characteristics of gravitational bursts from active galactic nuclei, and globular clusters are obtained for three astrophysical situations:(i) scattering of stars by massive black holes residued at the centers of galaxies and globular clusters; (ii) the close encounters of stars in the nuclear regions of these objects; (iii) scattering of stars by black holes of stellar mass containing in the stellar population of galactic nuclei and clusters. The most effective source of gravitational bursts appears to be a scattering of stars by the massive central black holes which produces the bursts with dimensionless amplitudeh10–19–10–21 and frequencies from 10–1 to 10–5 Hz. The characteristics obtained correspond to the possiblities of a future gravitational-wave experiment with use of laser Doppler tracking of interplanetary spacecrafts.  相似文献   

13.
We discuss the formation and evolution of interacting low-mass close binaries with a He-1CO- or ONe-dwarf neutron star or a black hole as a compact component. Mass exchange leads to cataclysmic events in such systems. The rate of semidetached low-mass close binary formation is 5×10–3 yr–1 if the accreting component is a He degenerate dwarf, 5×10–3 yr–1 if it is a CO-dwarf and 3×10–8 yr–1 if it is a neutron star. Systems with compact accretors arise as the result of the common envelope phase of close binary evolution or due to collisions of single neutron stars or dwarfs with low-mass single stars in dense stellar clusters. Evolution of LMCB to the contact phase in semi-detached stages is determined mainly by the angular momentum losses by a magnetic stellar wind and radiation of gravitational waves. Numerical computations of evolution with momentum loss explain observed mass exchange rates in such systems, the absence of cataclysmic variables with orbital periods 2h–3h, the low number and the evolutionary status of systems with orbital periods shorter than 80m. In conclusion we list unsolved problems related to magnetic stellar wind, the distribution of young close binaries over main initial parameters, stability of mass exchange.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.  相似文献   

14.
Campos  L.M.B.C.  Mendes  P.M.V.M. 《Solar physics》2000,191(2):257-280
The present paper concerns Alfvén waves, in a resistive and viscous atmosphere, under a steep temperature gradient (Section 1). The dissipative Alfvén wave equation is deduced assuming uniform vertical background magnetic field, and allowing for arbitrary profiles of Alfvén speed, and viscous and resistive diffusivities as functions of altitude (Section 2). A three-parameter family of temperature profiles, allowing for independent choice of initial and asymptotic temperature, and of initial temperature gradient, is used to re-write the wave equation, with the temperature as the independent variable, instead of altitude (Section 3). It is shown that, for the conditions prevailing in the solar transition region between the chromosphere and corona, two approximations of the dissipative wave equations may be considered, the simplest leading to solution in terms of Gaussian hypergeometric functions (Section 4). The exact analytical solution allows calculation of the (i) velocity and (ii) magnetic field perturbations, (iii) kinetic, (iv) magnetic and (v) total energy density, (vi) energy flux, (vii) rate-of-strain and (viii) electric current, and (ix) viscous, (x) resistive and (xi) total rate of dissipation (Section 5). These are plotted versus temperature, across the transition region from the chromosphere to the corona, for the quiet and active Sun (Section 6). The feasibility of heating of the transition region by dissipation of Alfvén waves is discussed (Section 7), by comparing empirical heating rates, with theoretical values for a range of physical conditions, including initial velocity perturbations 5 to 15 km s –1, background magnetic field 12 to 120 G, wave periods 60 to 300 s, thickness of the transition region 100 to 300 km, resistive and anomalous diffusivities to 100 and viscous and turbulent diffusivities to 100 . The conclusion is that dissipation of Alfvén waves is not an effective heating mechanism for the transition region and corona, although it may be for the chromosphere (see Campos and Mendes, 1995, and references therein).  相似文献   

15.
Inelastic molecular collisions are incorporated into the statistical model for turbulent circumstellar discs (Hämeen-Anttila, 1991; Verronenet al., 1993), and are found to provide a more effective cooling mechanism than molecule-grain impacts. Examination of the viscous evolution of the disc shows that the chemical composition and the coefficient of viscosity are crucial for determining the existence and properties of a state of equilibrium. A detailed study is carried out for carbon monoxide and hydroxyl. Abundances as small as 10–5 for CO and 10–8 for OH are sufficient to balance the disc against the viscous production of heat. The disc is usually non-convective. Near the equilibrium state the dust layer becomes thin enough to be gravitationally unstable. Infall of interstellar material is not expected to change the occurrence of instability, since the disc was not found to be convective even in the homogeneous circumstances. The results also remain unaltered even if the abundances of coolants are reduced by several orders of magnitude.  相似文献   

16.
The aim of this paper is to present the results of a construction of five models of composite stellar configurations, consisting of an energy-generating convective core surrounded by source-free envelope in radiative equilibrium, and of sufficient density for the coefficient of absorption to vary approximately as inverse square of the local temperature. The principal characteristic of such models proved to be their very high degree of central condensation; their central densities being 103–104 times as large as the mean density of the composite configuration. The relevance of such models to the internal structure of subdwarf components of close binary systems with periods less than a day is briefly pointed out.Investigation supported in part by Contract N5 ori-07843 with the Office of Naval Research of the U.S. Navy Department.  相似文献   

17.
Tsap  Y.T. 《Solar physics》2000,194(1):131-136
A model of the cascading acceleration of quasi-thermal electrons by MHD turbulence in solar flares is considered. Analysis shows that fast magnetoacoustic wave modes with large wavenumbers (>3×10–8 cm–1) strongly damp due to ion viscosity for both preflare and flare conditions. The viscous damping of fast magnetoacoustic wave modes is 10–100 times more efficient than Fermi or transit-time electron acceleration.  相似文献   

18.
The detailed evolution of low-mass main-sequence stars (M < 1M ) with a compact companion is studied. For angular momentum loss associated with magnetic braking it is found that about 10–11–10–12 M yr–1 in stellar wind loss would be required. This wind is 102–103 times stronger than the solar wind, so we believe here magnetic stellar wind is insufficient. It is well known that there is mass outflow in low-mass close binary systems. We believe here that these outflows are centrifugal driven winds from the outer parts of the accretion disks. The winds extract angular momentum from these systems and therefore drive secular evolution. Disk winds are preferred to winds from the secondary, because of the lower disk surface gravity.  相似文献   

19.
In Sections 1–6, we determine an approximate analytical model for the density and temperature distribution in the protoplanetary could. The rotation of the planets is discussed in Section 7 and we conclude that it cannot be determined from simple energy conservation laws.The velocity of the gas of the protoplanetary cloud is found to be smaller by about 5×103 cm s–1 in comparison to the Keplerian circular velocity. If the radius of the planetesimals is smaller than a certain limitr 1, they move together with the gas. Their vertical and horizontal motion for this case is studied in Sections 8 and 9.As the planetesimals grow by accretion their radius becomes larger thanr 1 and they move in Keplerian orbits. As long as their radius is betweenr 1 and a certain limitr 2 their gravitational interaction is negligible. In Section 10, we study the accretion for this case.In Section 11, we determine the change of the relative velocities due to close gravitational encounters. The principal equations governing the late stages of accretion are deduced in Section 12, In Section 13 there are obtained approximate analytical solutions.The effect of gas drag and of collisions is studied in Sections 14 and 15, respectively. Numerical results and conclusions concerning the last and principal stage of accretion are drawn in Section 16.  相似文献   

20.
It is shown that during contact eclipsing binaries evolution under the influence of stellar wind, magnetic stellar wind and with matter transfer by gas flow, in binary stellar systems there may take place a process of star merger (low mass stars) within 105–107 yr and a fast increase of distance between stars of massive binaries. W UMa-type stars are a finite evolutionary stage of very close and low mass binary pairs. As for contact systems of early spectral types (CE-systems), they are more varied in evolution.  相似文献   

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