Non-similarity solutions for explosion waves in stellar interiors

Non-similarity solutions in closed-forms, for propagation of explosion (instantaneous or non-instantaneous) waves in stellar models, in which the density falls off inversely as a power of distance, has been obtained in this paper. The power index lies in the interval 1 < < 3. The similarity solutions for = 2 5, valid only for an instantaneous explosion, follows as a particular one. Unlike the case of similarity solutions, the total energy of the wave as well as the strength of the shock varies with time. Besides, the solutions are applicable for arbitrary values of time.The results are extensions of my previous work (1969).     

The blanketing in the rocket ultraviolet from 225.2 to 319.6 nm

The blanketing effect for the solar disc center and its value near the limb (cos = 0.23) are obtained for the rocket ultraviolet region using the Harvard center and limb spectra. The value of for the disc center appears to be 0.67 (on average) relative to the quasicontinuum. The essential decrease of towards the limb is also revealed.     

The solar wind and the temperature-density structure of the solar corona

The influence of the solar wind on large-scale temperature and density distributions in the lower corona is studied. This influence is most profoundly felt through its effect upon the geometry of coronal magnetic fields since the presence of expansion divides the corona into magnetically open and closed regions. Each of these regions is governed by entirely different energy transport processes. This results in significant temperature differences since only the open field regions suffer outward conductive heat losses. Because the temperature influences the density in an exponential manner, large density inhomogeneities are to be expected.An approximate method for calculating the temperature and density distribution in a known magnetic field geometry is outlined and numerical estimates are carried out for representative coronal conditions. These estimates show that temperature differences of a factor of about two and density differences of ten can be expected in the lower corona even for uniform base conditions. As a result, we do not regard the so-called coronal holes necessairly as locations of reduced mechanical heating. Alternatively, we suggest that they are regions of open magnetic field lines being continuously drained of energy contert by the solar wind expansion and outward thermal conduction.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Parametric relations of H II galaxies

The integrated H luminosities of giant H II regions and of H II galaxies can be predicted with accuracy comparable to the observational errors from the velocity widths of their emissionline profiles. In addition, giant H II regions also present a relation between linear size and their emission-line width. Based on the similarity of these relations with those expected for virialized systems, Terlevich and Melnick interpreted the observedsupersonic motions as due to the gravitational potential of a complex of gas and stars.We show that H II galaxies also present a relation between linear size and their emission-line width, which supports the gravitating model. We also show that the scatter in the luminosity-line width relation for H II galaxies seems to be correlated with linear size and compare the results with the fundamental plane for elliptical galaxies from Dressleret al. (1987).     

Early cosmological models in Lyra's geometry

A spatially homogeneous and isotropic Robertson-Walker model withzero-curvature of the universe is studied within the frame-work of Lyra'smanifold. The gauge-function in Lyra's manifold is taken to betime-dependent. Exact solutions of Einstein equations are obtained for twodifferent early phases of the universe viz. Inflationary phase andradiation-dominated phase by using `gamma-law' equation of statep = ( - 1) . The -index, describing the material content,varies continuously with cosmic time so that in the course of itsevolution, the universe goes through a transition from an inflationaryphase to a radiation-dominated phase. The physical properties of themodels are also discussed.     

Spatial development of X-ray emission during the impulsive phase of a solar flare

The flare of 11 November, 1980, 1725 UT occurred in a magnetically complex region. It was preceded by some ten minutes by a gradual flare originating over the magnetic inversion line, close to a small sunspot. This seems to have triggered the main flare (at 70 000 km distance) which originated between a large sunspot and the inversion line. The main flare started at 172320 UT with a slight enhancement of hard X-rays (E > 30 keV) accompanied by the formation of a dark loop between two H bright ribbons. In 3–8 keV X-rays a southward expansion started at the same time, with - 500 km s ^–1. At the same time a surge-like expansion started. It was observable slightly later in H, with southward velocities of 200 km s^–1. The dark H loop dissolved at 1724 UT at which time several impulsive phenomena started such as a complex of hard X-ray bursts localized in a small area. At the end of the impulsive phase at 172540 UT, a coronal explosion occurred directed southward with an initial expansion velocity of 1800 km s^–1, decreasing in 40 s to 500 km s^–1.Now at Fokker Aircraft Industries, Schiphol, The Netherlands.     

A relation in families of periodic solutions

We show the existence of a general relation between the parameters of periodic solutions in dynamical systems with ignorable coordinates. In particular, for time-independent systems with an axis of symmetry, the relation takes the form T/A=–/E, whereT is the period,A is the angular momentum, is the angle through which the system has rotated after one period, andE is the energy.     

X-radiation (E > 10keV), Hα and microwave emission during the impulsive phase of solar flares

A study has been made of the variation in hard (E 10 keV) X-radiation, H and microwave emission during the impulsive phase of solar flares. Analysis shows that the rise-time in the 20–30-keV X-ray spike depends on the electron hardness, i.e., t _rise exp (0.87 ). The impulsive phase is also marked by an abrupt, very intense increase in H emission in one or more knots of the flare. Properties of these H kernels include: (1) a luminosity several times greater than the surrounding flare, (2) an intensity rise starting about 20–30 s before, peaking about 20–25 s after, and lasting about twice as long as the hard spike, (3) an effective diameter of 3000–6000 km for class 1 flares, representing less than 1/8-1/2 of the main flare, (4) a location lower in the chromosphere than the remaining flare, (5) essentially no expansion prior to the hard spike, (6) a position within 6000 km of the boundary separating polarities, usually forming on both sides of the neutral line near both feet of the same tube of force, (7) a shape often resembling isogauss contours of the photospheric field indicated on magnetograms and (8) total radiated energy less than l/50 that of the hard electrons. Correspondingly, impulsive microwave events are characterized by: (1) the detection of a burst at 8800 MHz for every X-ray spike ifthe number of electrons above 100 keV is greater than 10³³, (2) great similarity in burst structure with 20–32 keV X-rays but only at f > 5000 MHz, (3) typical low frequency burst cutoff between 1400–3800 MHz, and (4) maximum emission at f > 7500 MHz. Finally the H, X-ray and microwave data are combined to present a picture of the impulsive phase consistent with the above observations.     

Size of the hard X-ray source in the Crab Nebula

The size of the hard X-ray source in the Crab Nebula was observed with scintillation counters on board two balloons at a lunar occulatation on 24 January, 1975. The Gaussian width of the source is 34 (+17, –14) and the center thereof is offset from the pulsar by 6±4 at position angle 102°. The observed time profile can also be fitted to an alternative model of two line sources whose intensities are 48% at 11 and 25.5% at 7 on both sides of the pulsar.Paper presented at the COSPAR Symposium on Fast Transients in X- and Gamma-Rays, held at Varna, Bulgaria, 29–31 May, 1975.     

Linearly expanding universes in JBD-theory

The assumption of a linearly expanding universe for the JBD-cosmological equations generates a set of solutions for the barotropic equations of statep= (=const.). These solutions turn out to be valid for closed space-except in the casep= which is for open space. The gravitational constant which is inversely proportional to the scalar field increases with time if >–1/3 and decreases for <–1/3. No solution exists for =1/3. The Brans-Dicke parameter is negative if <–1/3.     

Isothermal self-similar blast wave theory of supernova remnants driven by relativistic gas pressure

We investigate the spherically symmetric, self-similar flow behind a blast wave from a point explosion in a medium whose density varies with distance asr ^– with the assumption that the flow is both isothermal and contains a relativistic component of pressure. A self-similar solution is shown to exist only if both the blast wave speed,u _s ,and the local sound speed,w, are constant. If [(1–w ²/c ²)] lies in 1>>0, there exists a critical point in the radial distance-flow velocity plane. To be physically acceptable, the solution must pass through the origin and through the critical point and then through to the blast front; solution branches between these points exist, although a proper connection at the critical point has not been demonstrated. If <0, a continuous single-valued solution does not exist. If 2>>1, the critical point is beyond the blast curve and the flow is subsonic everywhere. For 2<<3, the critical point disappears, but a new one arises. To be physically acceptable, the flow must by-pass this new critical point. It is shown that it does. The dependence of the solutions of is non-analytic for <1, so that interpolation between neighboring values of is not permitted. We investigate the stability of these isothermal blast waves to spherically symmetric but non-self-similar perturbations. If 3>>3/2 or 0<<1, the solutions are shown to be definitively linearly unstable against short wavelength disturbances near the blast front, they are also unstable there in 3/2>>1 unless the flow meets the blast front atprecisely the velocity (normalized) of (2–1)^1/2/(3–2)^1/2. The solutions are also unstable for all in 1>>0 near the critical point. Since there is no characteristic time scale in the system, all the instabilities grow as a power law in time rather than exponentially. The existence of these instabilities implies that initial deviations do not decay and the system does not tend to a self-similar form. We conclude that isothermal self-similar blast waves do not provide a valid model for a supernova remnant driven by a relativistic gas pressure. Since the validity of the adiabatic blast wave models has elsewhere been shown to be questionable, it is doubtful whether the self-similar property can be involved at all in the case of supernova remnants. This raises serious questions of interpretation of quantities deduced for supernova remnants on the basis of the use of self-similar models.     

Гидромагнитное Излучение Межпланетной Плазмы

0–2 ( ). . . .     

Containment of an adiabatic plasma on magnetic lines of force by a self-generated electrostatic field

One component of a three-fluid adiabatic plasma is under certain conditions contained in a restricted region of space by a large-scale electrostatic field generated within the plasma. The containment is discussed here for plasma consisting of ions and two populations of electrons characterized by different pitch angle distribution functions.The bouncing motion of electrons along open fieldlines between a magnetic mirror and an electrostatic mirror produces a velocity distribution function similar to that generated by bouncing particles on closed fieldlines.     

Dynamical fine structure of a quiescent prominence

A quiescent prominence has been observed with the MSDP spectrograph at the Pic du Midi Observatory. H profiles are obtained simultaneously in a 2D field, allowing a statistical analysis. The standard deviations of Doppler shifts and line widths are investigated as functions of the line intensity. The observations are compared with numerical simulations assuming that the prominence is made of identical threads, the velocity of which is distributed according to gaussian functions. The processing of simulations is very close to the processing of observations. The mixing by seeing effects and the transfer of radiation across several threads along the line of sight are considered. The results are consistent with the values derived by Engvold et al. (1989) and Zirker and Koutchmy (1989, 1990, 1991).The best fits are obtained with the following conditions. The temperature is 8500 K. In the middle range of intensities, each pixel results typically from the mixing of 6 velocity threads, the optical thickness of which is roughly 0.2 at H center, and the geometrical thickness larger than 1000 km. It is likely that the velocity threads have larger sizes than the density threads. The fit of the results is improved by taking into account a slight scatter of source functions throughout the prominence.In the central parts of the prominence, the fit is obtained by assuming that the line-of-sight velocities of the threads have a gaussian probability function (standard deviation 7 km s^–1).In the edges, we suggest larger scatter of velocities, and two combined dispersions. The velocity threads observed along a given line of sight are supposed to have neighbouring velocities (dispersion 7 km s^–1) around a mean value taken at random inside another distribution function (dispersion 7 km s^–1).     

Models of clusters of point masses with large central redshifts

Conclusions In the Newtonian case we have obtained an isotropic self-consistent distribution of gravitationally interacting point masses which satisfies the transport equation without collisions, and the gravitational equation for an arbitrary powerfunction density distribution =r^–s, s<3.For =r^–2 the analogous self-consistent solution was obtained for the anisotropic distribution function both in Newtonian and GTR cases.The GTR solutions with =r^–2 have central redshifts which increase without limit in accordance with the law 1+zr^–1/ as we approach the center. In the isotropic case, they appear to be stable when the mean velocities are much less than the velocity of light u<0.2c, >21.The hydrodynamic GTR solution was found for a perfect gas at constant temperature (but variable T=T(g₀₀)^1/2) which also has z for r0.We should like to thank K. Thorne, L. Hazin, and M. Podurets for valuable discussions. K. Thorne was particularly helpful in supplying unpublished results on circular orbits obtained by American authors.Astrofizika, Vol. 5, No. 2, pp. 223–234, 1969     

Chaos and secondary resonances in the mimas–tethys system

We have investigated the role of the 200yr period discovered by Vienne and Duriez (1992) on the tidal evolution of the Mimas–Tethys system through the 2:4 ii present resonance. Three terms are found to generate this period. We present a perturbedpendulum model in which these terms bring about a perturbation to the ideal ii resonance pendulum, which is in a direct ratio to the eccentricity e of Tethys. Although e is now very small, it is shown that this quantity could have been much greater in the past. We also show, thanks to this model, that these terms may have brought about a stochastic layer of noticeable width at the time of capture in the ii resonance, with the consequence that the possible values of the inclination i of Mimas before capture range from 0.4° to 0.6° (these uncertainties arise from the present uncertainties on e). The role of each one of the three terms is examined in the appearance of chaos. A capture into the 1/1 secondary resonance (between the libration period of the primary ii resonance and the period of about 200yr) is found possible. It means that the system could have experienced several captures in the primary resonance, instead of a single one, and that i could have been, with this assumption, much lower than 0.4°. A probability of capture into this secondary resonance as a function of the eccentricity of Tethys on encounter is derived, using Malhotra's method (Malhotra, 1990). Allan's values of i = 0.42° and e 0 (Allan, 1969) are therefore called into question, and taking e 0 is shown to be absolutely necessary if we want to understand the phenomena at work in the Mimas–Tethys system.     

On the stability of equilibria of Hamiltonian systems near the main resonances

The equilibrium point O of an autonomous Hamiltonian system of two degrees of freedom is considered for small-oscillation frequencies related as ₂=2₁+. If under the precise resonance (=0) the equilibrium is unstable, the inner diameter () of the domain of stability containing the point O is estimated. It is shown that for the normalized variables ()/b where b is the corresponding resonance coefficient. The estimates () for other main resonances are reported.     

Magnetic reconnection in high-temperature plasma of solar flares

Quasi-steady high-temperature current sheets are an energy source during the main or hot phase of solar flares. Such sheets are shown to be stabilized with respect to the tearing instability by a small transverse component of magnetic field existing in the sheets.     

Radio evidence for a delayed acceleration process in solar flares

Evidence for a delayed acceleration process in solar flares is presented in the form of an analysis of simultaneous observations in microwaves, decimetre and metrewaves, and hard X-rays of six delayed gradual bursts which appear 0.5–1 hr after the strong main bursts have faded. The observed characteristics of the delayed bursts are: (a) similarity of flux time profiles at all the wavelengths, (b) low turn-over frequency (4 GHz) of the microwave spectrum, (c) moderately strong circular polarization (30–40%) and low altitude of the microwave source (which is displaced toward the disk centre by a projected distance of 10–20 from that of the preceding main burst), and (d) low spectral index of the energy spectrum of hard X-rays.From these observations it is suggested that (i) electrons are accelerated up to MeV even some tens of minutes after the impulsive phase acceleration has almost ceased, (ii) the delayed acceleration occurs in a large magnetic structure extending to a height of at least 2 × 10⁵ km, and (iii) the radio source has columnar structure with the microwave source predominantly near a leg or legs and the metrewave source near the top of the magnetic structure. The present observations of the delayed bursts do not seem to be consistent with the classical second-phase acceleration mechanism proposed in the past for normal hard X-ray gradual (extended) bursts.Minamimaki-mura, Minamisaku-gun, Nagano-ken 384-13, Japan.Greenbelt, MD 20771, U.S.A., NASA/NRC Research Associate, on leave from Tokyo Astronomical Observatory.P.O. Box 76, Epping, N.S.W. 2121, Australia.Berkeley, CA 94720, U.S.A.