Stellar age and mass determinations from kinematic data

Assuming that some exchange of energy between stars in the galactic disk may be at work, I have generalized the formulae expressing the growth of the velocity variance with time by adding a mass term (M/M )^– with =0.35, which is a good fit to the kinematic data for young stars. The generalized formulae (5a) and (5b) and the evolutionary mass-age relation (Iben, 1967) were used jointly to derive mass and age values for different stellar species. The results, presented in Table IV, are followed by a discussion.     

Stability criteria in many-body systems

An expansion of the force function ofn-body dynamical systems, where the equations of motion are expressed in the Jacobian coordinate system, is shown to give rise naturally to a set of (n–1) (n–2) dimensionless parameters ^ki _li {i = 2,...,n;k = 2,...,i – 1 (i 3);l =i + 1,...,n (i n – 1)}, representative of the size of the disturbances on the Keplerian orbits of the various bodies. The expansion is particularized to the casen=3 which involves the consideration of only two parameters ²³ and ₃₂. Further, the work of Szebehely and Zare (1977) is reviewed briefly with reference to a sufficient condition for the stability of corotational coplanar three-body systems, in which two of the bodies form a binary system. This condition is sufficient in the sense that it precludes any possibility of an exchange of bodies, i.e. Hill type stability, however, it is not a necessary condition. These two approaches are then combined to yield regions of stability or instability in terms of the parameters ²³ and ₃₂ for any system of given masses and orbital characteristics (neglecting eccentricities and inclinations) with the following result: that there is a readily applicable rule to assess the likelihood of stability or instability of any given triple system in terms of ²³ and ₃₂.Treating a system ofn bodies as a set of disturbed three-body systems we use existing data from the solar system, known triple systems and numerical experiments in the many-body problem to plot a large number of triple systems in the ²³, ₃₂ plane and show the results agree well with the ²³, ₃₂ analysis above (eccentricities and inclinations as appropriate to most real systems being negligible). We further deal briefly with the extension of the criteria to many-body systems wheren>4, and discuss several interesting cases of dynamical systems.     

Expanding and superdense astrophysical systems in general relativistic hierarchical cosmology

A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( _i+1/ _i [r _i /r _i+1] is approximately equal to the exponentN in a continuous density law (=aR ^–N) provided (r _i /r _i+1)^3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c ² R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s^–1 Mpc^–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c ² R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R ^N ,N2); (j) for the Galaxy, theory predictsp _G7×10^–12 dyn cm^–2, observation givesp _G5×10^–12 dyn cm^–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 10¹² g s^–1, compared to 10¹¹ g s^–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×10⁹ years for the Sun and 10¹⁰ years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN _B of baryons; (o)N _B10⁵⁷N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L _max10⁵⁹ erg s^–1); (r) larger bodies have longer time-scales of energy radiation atL _max (10^–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR ^–N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.     

Nonradial oscillations of a neutron star in an inhomogeneous hydrodynamic model

An inhomogeneous model neutron star with a variable density profile of the type ₀(r)=_c[1–(2/3)r²/R²]exp(–r²/R²) is considered, where _c is the central density, R is the star's radius, and is the inhomogeneity parameter in the radial mass distribution. This parameterization adequately reproduces the results of numerical evolutionary calculations of the density profile and enables one to obtain in analytical form the parameters of hydrostatic equilibrium and the eigenmodes of nonradial oscillations of a nonrotating neutron star, modeled by a spherical mass of incompressible, inviscid liquid. It is shown that a characteristic manifestation of the star's inhomogeneity is the presence of a stable dipole f-mode, the lowest one in the spectrum of natural oscillations. The presence of this mode serves as a general and primary criterion that evidently distinguishes all inhomogeneous hydrodynamic models from the homogeneous Kelvin model, in which the quadrupole mode is the lowest stable mode. Estimates obtained for the periods of nonradial pulsations coincide with the periods of micropulses observed in the average pulse profiles of c-pulsars. This suggests that the detected variations in emission intensity in the range of micropulse duration (on the order of 10^–4 sec) are associated with nonradial stellar oscillations.Translated from Astrofizika, Vol. 39, No. 3, pp. 475–488, July–September, 1996.     

Mgix emission lines in an active region spectrum obtained with the Solar EUV Rocket Telescope and Spectrograph (SERTS)

Theoretical electron-temperature-sensitive Mgix emission line ratios are presented forR _I =I(443.96 )/I(368.06 ),R ₂ =I(439.17 )/I(368.06 ),R ₃ =I(443.37 )/I(368.06 ),R ₄ =I(441.22 )/I(368.06 ), andR ₅ =I(448.28 )/I(368.06 ). A comparison of these with observational data for a solar active region, obtained during a rocket flight by the Solar EUV Rocket Telescope and Spectrograph (SERTS), reveals excellent agreement between theory and observation forR ₁ throughR ₄, with discrepancies that average only 9%. This provides experimental support for the accuracy of the atomic data adopted in the line ratio calculations, and also resolves discrepancies found previously when the theoretical results were compared with solar data from the S082A instrument on boardSkylab. However in the case ofR ₅, the theoretical and observed ratios differ by almost a factor of 2. This may be due to the measured intensity of the 448.28 line being seriously affected by instrumental effects, as it lies very close to the long wavelength edge of the SERTS spectral coverage (235.46–448.76 ).     

Unsteady hydromagnetic free convection flow past an accelerated infinite vertical porous plate

Unsteady laminar free convection flow of a viscous incompressible and electrically conducting fluid past an accelerated vertical infinite porous plate subjected to a suction velocity proportional to (time)^–1/2 is studied in presence of a uniform horizontal magnetic field. Results are discussed with the effects of the Grashof number Gr, and the magnetic field parameterM for Pr (the Prandtl number)=0.71 and 7.0 representing air and water respectively at 20 °C.Nomenclature a suction/injection parameter - C _p specific heat at constant pressure - B ₀ magnetic induction - g acceleration due to gravity - Gr Grashof number (vg(T'_w-T')/U ₀ ³ ) - K thermal conductivity - M magnetic field parameter (B ₀ ² _e ² /U ₀ ² ) - Pr Prandtl number (C _p/K) - T' temperature of the fluid near the plate - T' _w temperature of the plate - T' temperature of the fluid at infinity - t' time variable - t dimensionless time (t' U ₀ ² /v) - u non-dimensional velocity (u'/U ₀) - U' velocity of the plate - U dimensionless velocity of the plate (U'/U _o) - U ₀ reference velocity - v' ₀ suction velocity - v ₀ nondimensional suction velocity (v' ₀/U ₀)=at^–1/2 - v' normal velocity component - v dimensionless normal velocity - Ec Eckert number ((vU ₀)^2/3/C _p(T' _w -T' )) - T dimensionless temperature of the fluid near the plate ((T'-T' )/T' _w –T' )) - x',y' coordinates along and normal to the plate - y dimensionless ordinate (=y' U _o/v) - v kinematic viscosity - coefficient of volume expansion - electric conductivity of the fluid - similarity variable (y/2t) - _w density of the fluid at the plate - density of the fluid at infinity - ' skin-friction - dimensionless skin-friction - coefficient of viscosity - _e magnetic permeability     

Effects of metal abundances on the evolutionary period changes of classical Cepheids

Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values _i = _i + _i ,v _i = _i + v _i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,² =v ² = 10^–8) grow many times in marginally-stable state.     

Космическое черенковское излучение

, . N/E, E _r, (E _r)=1. , (, ) . .     

Numerical determination of families of three-dimensional double-symmetric periodic orbits in the restricted three-body problem,II

New families of three-dimensional double-symmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the vertical-critical orbits ( _v = – 1, b _v – 0) of the basic plane familiesi, g ₁, g₂, c andI. Further, the predictor-corrector procedure employed to reveal these families has been described and interesting numerical results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections.     

A sky-noise measurement and its implication for ground-based infrared astronomy in the 10μm atmospheric window

A spectral analysis of the fluctuations of the infrared sky radiance at 10m was made at the ESO-site of La Silla in Northern Chile. The data are compared to literature. The consequences of the results on infrared observing for future large telescopes are discussed: our data suggest that in order to achieve background noise limited performance in the 10m atmospheric window chopping with frequencies of 8 Hz and amplitudes of 10 arcsec is mandatory.based on observations obtained at the European Southern Observatory, La Silla, Chile     

Radio source orientation and the cosmological interpretation of the angular size-redshift relation for double-lobed quasars

The angular size-redshift test for quasars was compared with various cosmological models including non standard models. The possible effects of radio source orientation and relativistic beaming were taken into account in the analysis.It was found that orientation effects alone were not sufficient to explain the observed-z relation in terms of Friedmann models. In addition, linear size evolution of the formD ~ (1 +z)^–n , with 0.75 n 1.2 would be required for 0 1.0, or possibly an inverse correlation between luminosity and linear size. The non-standard cosmological models all gave better fits to the deprojected data than the Friedmann models in the absence of evolutionary effects, with the tired light effect providing the best fit.     

Динамические равновесные плазменные конфигуации и физика магнитосферы

, 1-, 2- 3- . , .     

The variation of solar proton energy spectra and size distribution with heliolongitude

A statistical study of the initial phases of 185 solar particle events has been carried out using the data from the Goddard cosmic ray experiments on IMPs IV and V. Special emphasis is placed on the identification of the associated solar flare. The parent flare can be determined for 68 % of the events. It appears probable that most of the unidentified increases occur on the non-visible disc of the Sun. The existence of a preferred-connection longitude between 20°W and 80° W is established by examining the heliolongitude of all the flare associated events. While power law in differential kinetic energy appears to give the best representation it cannot be distinguished from exponential in rigidity over the limited range of 20–80 MeV. It is argued that for heliolongitudes = 20–80°W, _p ,the spectral index determined at the time of maximum particle intensity is representative of the source spectra. For these heliolongitudes _p displays a surprisingly small range with magnitudes varying mainly between 2.0 and 3.1. At lower energies _p is smaller. Previous electron measurements provide almost identical average values of the source spectra over similar energy ranges. These results are discussed briefly in terms of Fermi acceleration models.For flare events located further away from the nominal field line connecting the Earth and the Sun, _p becomes progressively steeper. The lower energies (4–20 MeV) do not exhibit this behavior. It is argued that this spectral steepening at the higher energies is the result of energy-dependent escape during the coronal diffusion process. The size distribution can be represented by a power law of the form dN/dI=I ^- where N is the number of events per unit intensity and I is the maximum particle intensity at a given energy (usually taken at 40 MeV) with 1.15 ±0.1. The same value of a applies to both eastern and western hemisphere events. The event size, on the average, appears to decrease approximately two orders of magnitude for each 60° away from the preferred connection region.Also: Dept. of Physics and Astronomy, University of Maryland, College Park, Md., U.S.A.     

The effect of chemical abundance oscillations on the pulsational properties of A 5M ⊙ hydrogen-helium star

A model of a first generation intermediate star of 5M , with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell. =(log/log) _T and _T =(log/logT) were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including =(log/log) _T and =(log/logT) of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode.     

Bidimensional spectroscopy of network bright points

We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec² at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C _min the H- 1.5 Å image (C _m 0.1 type I, C _m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C _m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C _m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C _min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C _m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C _m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C _m- A scatter diagram, in H and H wings, indicates a wide range of variability for C _m in correspondence with very narrow range of variability for A.     

In situ acceleration and gradients of charged particles in the outer solar system observed by the voyager spacecraft

The probable connection between cosmic rays and the electromagnetic state of the interplanetary medium was recognized by Hannes Alfvén as early as 1949 (Alfvén, 1949, 1950); he pointed out that the properties of cosmic rays necessitate a mechanism, external to Earth but within the solar system, capable of accelerating particles to extremely high energies. In advocating the view of local origin for part of the cosmic-ray spectrum, Alfvén and his colleagues developed a very general type of acceleration mechanism called magnetic pumping. The unique data set of the two Voyagers extends over an entire decade (1977–1987) and is most suitable to explore the problem of acceleration of charged particles in the heliosphere. The energy coverage of the Low Energy Charged Particle (LECP) experiment covers the range 30 keV to several hundred MeV for ions and 22 keV to several MeV for electrons. Selected observations of interplanetary acceleration events from 1 to 25 AU are presented and reviewed. These show frequent acceleration of ions to several tens of MeV in association with shocks; highest energies (220 MeV oxygen) were measured in the near-perpendicular ( _Bn 87.5°) shock of January 5, 1978 at 1.9 AU, where electron acceleration was also observed. Examples of ion acceleration in association with corotating interaction regions are presented and discussed. It is shown that shock structures have profound effects on high-energy (70 MeV) cosmic rays, especially during solar minimum, when a negative latitudinal gradient was observed after early 1985 at all energies from 70 MeV down to 30 keV. By early 1987, most shock acceleration activity in the outer heliosphere (25 to 30 AU) had ceased both in the ecliptic (Voyager-2) and at higher (30°) ecliptic latitudes (Voyager-1). The totality of observations demonstrate that local acceleration to a few hundred MeV, and as high as a few GeV is continually present throughout the heliosphere. It should be noted that in 1954 when Alfvén suggested local acceleration and containment of cosmic rays within the solar system, no one treated his suggestion seriously, at any energy. The observations reviewed in this paper illustrate once more Alfvén's remarkable prescience and demonstrate how unwise it is to dismiss his ideas.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Galactic4He and heavy elements enrichment by stellar nucleosynthesis

The contribution to the galactic abundance of He and heavy elements by stellar nucleosynthesis is calculated as a function of time, keeping account of present knowledge about stellar and galactic evolution. A model is used which distinguishes the phase of the contracting halo from the subsequent history of the disc. Various uncertainties involved both in stellar and in galactic evolutionary theory are discussed. The amount of⁴He produced by stars of different masses and ejected in interstellar medium is fairly well known from stellar theory, while we have assumed its primordial abundance as a free parameter, ranging from 0 up to 0.4. We find that stellar activity provides a significant contribution to the cosmic⁴He, though not sufficient to explain the observed abundance. The best agreement with observational data (Y 0.26 andY _now0.28) is obtained starting with a primordial abundanceY =(0.20–0.23), which is consisten with the Big-Bang theory predictions and with recent observational estimates. The contribution to the abundance of heavy elements depends on the last stellar stages and on the final explosion mechanism, which are only now beginning to be understood. Nevertheless, in the framework of present theories, we individuate a stellar evolutionary scheme reproducing the observedZ abundances for Populationi and Populationii stars, with the correctly estimated Y/Z value. In this scheme, only stars belonging to two narrow mass ranges (10m/m 15 andm/m 80) are allowed to eject metal-enriched matter, possibly with the solar (C+O)/(Si+Fe) ratio.     

A systematic method for the analysis of high-resolution fraunhofer line profiles

A fraunhofer line profile depends on various parameters, partly related to the photospheric structure (T, P _g, P _e, v _conv, v _turb), partly to the atom or ion involved (such as oscillator strength, energy levels), partly also resulting from the interaction of the relevant kind of particles with the photosphere, and the photospheric radiation field. In this paper we shall mainly pay attention to the determination of: the macroturbulent (convective) velocities, v _conv (); the damping constant (); the abundance, A _el; the distribution function (v _conv, ) of the convective velocities at each depth ; the source function, S (); the microturbulent velocities, v _turb ().The particular difficulty with these unknowns is that they are, as a rule, coupled in the resulting line profiles, that is: the shapes and intensities in these profiles are determined by the combined influence of these unknowns (together with the other above-given parameters).In this paper we describe a method to determine these six unknowns empirically by separating them, in analysing accurate high-resolution observations of line profiles of a multiplet. The unknown functions and quantities are consecutively determined in the above given succession. For each determination another, appropriate part of the line profile is used. In some cases the influence of the mutual coupling of the various parameters cannot be completely eliminated, and an iterative method has to be used.The method is summarized in Table II and section 2, and is further explained in sections 3 to 8. It is applied to an infrared Ci multiplet. The main results are the following:     

Redshift cutoff and evolution of QSOs

In this paper I present a new evolution model of QSOs luminosity. The model is based on edges distribution of apparent magnitude-redshift of QSOs. After the quasars were formed, the luminosities were increasing until they attained their maximum value atz=2+a, where –0.1a0.6, then the luminosities were decreasing. If the QSOs originate from superconducting cosmic string of same initial massM _i 10¹² M , the formation epochs are different, most of the quasars start atz _cutoff5.6. The most luminous QSOs start at later epochz _cutoff5.15. The present sky survey echniques may give us the possibility to see the formation of QSOs at apparent magnitudem _V 22.5 by chance of 0.3%.