Quasi-stellar objects as rotating magnetic superstars

In this paper the magnetic superstar model is used to discuss QSO luminosity and density evolution. Our main hypotheses are that (i) mass loss from old stars in massive galaxies cools and then falls into the centre to form a nuclear disc (Bailey, 1980); and (ii) magnetic superstars in galactic nuclei condense out of gaseous material at the centre of a supermassive-magnetised disc (Kundt, 1979). On this generalised model we find that the non-thermal (synchrotron) optical luminosity scales asL _opt L ³ t ^–7/3, whereL is the total blue luminosity of old stars in the galaxy and t is cosmic time. In addition we show that QSO co-moving density follows the lawD(t)exp-(t/t _Evol)^16/15 with an evolution timescalet _Evol = 1.95 × 10⁹ yr. The model as a whole is in good agreement with observations.     

The mass-ratio distribution of spectroscopic binary stars

In order to determine the mass-ratio distribution of spectroscopic binary stars, the selection effects that govern the observations of this class of binary systems are investigated. The selection effects are modelled numerically and analytically. The results of the models are compared to the data inThe Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars (DAO8) compiled by Battenet al. (1989). The investigations involve binary systems with Main-Sequence primary components only, in order to avoid confusion of evolutionary and selection effects.For single-lined spectroscopic binaries (SBI) it is found that the mass ratios (q=M _sec/M _prim) in general adhere to a distribution _q q ^-2 forq>q ₀, withq ₀=0.3. The observations are consistent with a distribution that is flat forq<q ₀. The turn-over value varies fromq ₀=0.3 for systems with B-type primaries, toq ₀=0.55 for systems with K-type primaries. The semi-major axesa ₁ are distributed according to _a (a ₁)a ₁ ^-a with an average value of _a =1.3. The power varies from _a =1.7 for systems with B-type primaries to _a =0 for systems with K-type primaries. The eccentricitiese of the orbits of SBI systems are distributed according to _e (e)e ^-1.For double-lined spectroscopic binary stars (SBII) it is found that the shape of theq-distribution, as derived from observations, is almost entirely determined by selection effects. It is shown that the distribution is compatible with theq-distribution found for SBI systems. A sub-sample, consisting of the SBII systems from DAO8 with magnitudesm _V 5 ^m , is less hampered by selection effects, and shows the same shape of theq-distribution as the SBI systems, at theq-interval (0.67, 1).It is estimated that 19–45% of the stars in the solar neighbourhood are spectroscopic binary systems.     

Some applications of Jacobi dynamics to the stellar evolution

The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR _eff=R/ given by the stellar radii and the coefficients for the inner structure of the stars.As seen in a previous work (Paper I), during the lifetime in the Main SequenceR _eff(t) remains a near invariant when compared to the variation in the time ofR(t) and (t).With such an effectiveR _eff one obtains the amounts of actionA _c(M), the effective densities _eff(M)=(M)³(M), the densities of action and of energy (or mean presures in the stellar interior)a _c(M),e _c(M), and the potential energiesE _p(M).The amounts of action areA _cM ^k withk1.87 for the M stars,k5/3 for the KGF stars, andk1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek5/3 means a near invariant effective density _eff for the KGF stars, while for such stars the mean densities and coefficients present the strongest variations with masses (M)M ^–1.81, (M)M^0.6.The cases for the M stars (e _c(M)M ^–1) and for the A and earlier stars (betweena _c(M)=constant and _eff(M)M ^–1) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M M25M .With all this, one can build dynamical HR diagrams withA _c(M), E_p(M), _eff M ^–p , etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA _c(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs.The comparison of the potential energiesE _p(M)M ^–p according to the stellar models used here and the observed frequency function (MM _–q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE _p(M)(M) is a constant, but this must be confirmed with further studies of the function (M) and its fine structure.There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of actionA _c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.     

The Third Integral in a Self-consistent Galactic Model

We apply the theory of the third integral to a self-consistent galactic model, generated by the collapse of a N-body system. The final configuration after the collapse is a stationary triaxial system, that represents an almost prolate non-rotating elliptical galaxy with its longest axis in the z-direction. This system is represented by an axisymmetric potential V plus a small triaxial perturbation V ₁. The orbits in the potential V are of three types: box orbits, tube orbits (corresponding to various resonances), and chaotic orbits.The intersections of the box and tube orbits by a Poincaré surface of section z=0 are closed invariant curves. The main tube orbits are like ellipses and form an island of stability on the (R,R) plane.We calculated the third integral I in the potential V for the general non-resonant case and for various resonant cases. The agreement between the invariant curves of the orbits and the level curves of the third integral is good for the box and tube orbits, if we truncate the third integral at an appropriate level. As expected the third integral fails in the case of chaotic orbits. The most important result is the form of the number density F on the Poincaré surface of section. This function decreases exponentially outwards for the box orbits, like Fexp(–bI), while it is constant, as expected, for the chaotic orbits. In the case of the island of the main tube orbits it has a minimum at the center of the island. This can be explained by the form of the near elliptical orbits that are elongated along R, thus they fail to support a self-consistent galaxy, which is elongated along the z-axis.     

The distinctive feature of relativistic stellar systems

In this paper we adopt the method of relativistic fluid dynamics to examine the number density distribution of stars around a massive black hole in the core of stellar clusters. We obtain extensive results,n(r) r ^–a, 3/2a9/2, which include, respectively, then(r) r ^–7/4 power law obtained by Bahcall and Wolf and then(r) r ^–9/4 power law by Peebles. Sincen(r) is not an observable quantity for star clusters, we also consider general relativity effects, i.e., the consequence of the bending of light, in calculating the projected density of stars in such a system. As an example we employ a massive black hole 10³ M inlaid in the center of a globular cluster and calculate various projected densities of stars. The results show that cusp construction occurs in all cases unless the central black hole massM=0, and the polytropic index does not affect at all the position of the capture radiusr _a. The obvious differences in the surface density is only embodied in the interior of the capture radius. At the outer regions of the core, the surface density of stars declines rapidly with ar ^–5 power law in all cases. These results can be applied to cases of unequal-mass and non-steady state.     

Relativistic hierarchical cosmology

While Euclidean models with uniform matter density have a number of radio sources of flux density greater thanF at frequencyv that varies asN(>F, v)¹ F ^–3/2, hierarchical models with = ₀ r ^–2 haveN(>F,)F ^–1/2 (Section 1). Since the observed dependency isN(>F,)F ^–1.8, severe density and/or luminosity evolution must be present in a workable hierarchical cosmology (Section 2). The same argument applies (Section 3) to the number of sources of apparent luminosity greater thanl,N(>l) and (Section 4) to the number of sources within redshift distancez from the local origin. To give agreement with empirical data demandsq _o=+1 and large first and second derivatives with respect to time of the number source density (Section 5). The adoption ofq _o=+1 allows one to show (Section 6) that a Lemaitre-type hierarchical Universe with a long coasting or waiting time can give agreement with observations of the numbers of QSO's etc. if the age of the Universe is more than 10¹³ yr. The dependence of the effective Hubble parameter onk(t), (t) andR (Section 7) leads one to suggest that ak=0, =0 hierarchy with 0 might be the simplest acceptable form of model Universe. Section 8 (Conclusion) points out that further data on source count anisotropies should allow the component levels of the hierarchy to be delineated.     

Spectrum of the galactic magnetic fields

The magnetic fields observed in the galactic disc are generated by the differential rotation and the helical turbulent motions of interstellar gas. On the scalesl=2k ^–1 which lie in the intervall ₀<l<l _e (l ₀100 pc is the energy-range scale of the galactic turbulence), the spectral density of the kinetic energy of turbulence (k ^–5/3) exceeds the magnetic energy spectral density (k ^–1). The equipartition between magnetic and kinetic energies is reached atl=l _e 6 pc in the intercloud medium and is maintained down to the scalel=l _d 0.03 pc. In dense interstellar cloudsl _e is determined by the individual cloud size andl _d 0.1 pc.The internal turbulent velocities in Hi clouds (cloud size is assumed to be 10 pc) lie in the range from 1.8 to 5.6km s^–1, fitting well within the observed range of internal rms velocities. Dissipation of the interstellar MHD turbulence leads to creation of temperature fluctuations with amplitudes of 150 K and 65 K in dense clouds and intercloud medium, respectively. The small-scale fluctuations observed in the interstellar medium may arise from such perturbations due to the thermal instability, for instance. Dissipation of the MHD turbulence energy provides nearly half of the energy supply needed to maintain the thermal balance of the interstellar medium.     

Excitation class of nebulae—An evolution criterion?

A principally new, quantitative system of the classification of the spectra of planetary nebulae is proposed. Spectral class of excitation class of the nebulap is determined according to the relative intensities of emission lines (N ₁+N ₂) [OIII]/4686 HeII and (N ₁+N ₂) [OIII]/H (Table I, Figure 1). The excitation classes are obtained for 142 planetary nebulae of all classes—low (p=1–3), middle (p=4–8), and high (p=9–12⁺) (Tables II, III, and IV). An empirical relationship between excitation classp and mean radius of nebulae is discovered (Figure 2). This relationship as well as excitation classp, as an independend parameter, admit an evolutionary interpretation. It is shown that after reaching the highest class of excitationp=12⁺ the nebulae decrease their class of excitation with the further increases of sizes. The diagram of this relationship has two nearly-symmetric branches — rising and descending with the apogee onp=12⁺ (Figure 2).     

Photometric observations of Cepheids from the ASAS-3 catalog: Photoelectric <Emphasis Type="Italic">BV I</Emphasis><Subscript>c</Subscript> observations of 46 low-amplitude Cepheids

From December 2006 to January 2008, we performed 1699 BV I _c observations for 46 low-amplitude Cepheids discovered in the course of the ASAS project using the 76-cm telescope of the South-African Astronomical Observatory (SAAO). We provide the tables of observations and V light and B-V and V-I _c color curves. These new observations, along with data from the ASAS-3 catalog, have been used to improve the elements of the light variations. Our data allow the number of known Galactic low-amplitude Cepheids to be almost doubled. This makes it possible to increase the number of distance indicators suitable for studying the structure of the inner Galactic arms by almost 15%.     

Spin parameter and scale-free density perturbations in hierarchical clustering

The present attempt aims to predict the dependence of the spin parameter, , the angular momentum,J, and the typical radius,a _vir, on the mass,M, which have been found inN-body simulations of expanding density perturbations in hierarchical clustering, when virialization is attained. We show that M ⁰ for systems with same adimensional density distribution and velocity distribution, and in particular for scale-free density perturbations in hierarchical clustering. In the special case of ellipsoidal perturbations, it is also found:J M ^7/4,a _vir M ^1/2. All these results turn out to be in close agreement withN-body simulations, despite the simple model adopted. Expanding and virialized perturbations are modelled, respectively, by homogeneous and heterogeneous, similar ellipsoids which allow flat rotation curves far from the centre. Both energy and angular momentum maintain from a given time on, lying between the beginning of strong decoupling from the Hubble flow and the occurrence of maximum volume. Then the whole set of virialized ellipsoidal configurations with same energy and angular momentum are derived, and the dependence of the spin parameter on the anisotropy parameter, _pec is investigated. Turning our attention to the formation of galaxies, we derive the total mass as a function of the collapse factor, using the empirical anticorrelation between dark to visible mass ratio within the optical radius of disk galaxies and their luminous masses. Observational data related to a sample of elliptical galaxies provide evidence that the contraction in these bodies occurred in proportion to the square root of the ratio of total to luminous mass. On the contrary, it is deduced that dissipation of angular momentum in elliptical galaxies occurred more or less at the same rate. If both shape and anisotropy parameter are preserved during the collapse, typical axis rations ₂₁ = 0.98, ₃₁ = 0.69, are found to correspond to a moderate anisotropy, _pec 0.27, with a small dependence on the spin parameter in the range allowed.     

RevisedV/V max test with incompleteness-compensated factors and its application to X-ray quasar sample

Both density- and luminosity-evolution of quasars proceed sumultaneously. If only one of them is considered, the value of V/V _max would be too high. Here we present an idea that the quasar luminosity-redshift relationship curve can be obtained by statistics, from which the incompleteness-compensated factorK(Z|l _min) for each source will be given, and then theV/V _max test for density law can be carried out. We use this revisedV/V _max test in investigating 3CR and 4C samples including the 3CR sources detected in X-ray. The result is that the space density distribution of quasars is relative toq _o.     

Turbulent motions in molecular clouds

We have studied the behavior of the inner motions of OH, H₂CO, and CO molecular clouds. This study shows the existence of two main components of these clouds: the narrow one, associated to dense small clouds and a wide one representing the large diffuse clouds seen in neutral hydrogen, the large clouds are the vortex and intermediate state between turbulent and hydrodynamic motions in the Galaxy.For the dense clouds with sizesd<10 pc we have found a relationship d ^0.38 consistent with the Kolmogorov law of turbulence; the densities and sizes of these clouds behave asnd ^–1. This last relation for these molecular clouds is compared with theHII one. Also, we discuss the effects of the inner magnetic field in these clouds.     

A photometric study of faint galaxies in the field of GRB 000926

We present our B, V, R_c, and I_c observations of a \(3'.6 \times 3'\) field centered on the host galaxy of GRB 000926 (α_2000.0=17^h04^m11^s, \(\delta _{2000.0} = + 51^ \circ 47'9\mathop .\limits^{''} 8\)). The observations were carried out on the 6-m Special Astrophysical Observatory telescope using the SCORPIO instrument. The catalog of galaxies detected in this field includes 264 objects for which the signal-to-noise ratio is larger than 5 in each photometric band. The following limiting magnitudes in the catalog correspond to this limitation: 26.6 (B), 25.7 (V), 25.8 (R), and 24.5 (I). The differential galaxy counts are in good agreement with previously published CCD observations of deep fields. We estimated the photometric redshifts for all of the cataloged objects and studied the color variations of the galaxies with z. For luminous spiral galaxies with M(B)z～1.     

Physically realizable relativistic stellar structures

Relativistic stellar structures can be obtained both analytically and by computation, but all these models do not stand the tests of physical reality. It is shown that for a physically reasonable solution d/dr -r and d(e ^v /dr r near the centre, d(P/)/dr<-0 and (dP/d)>-(P/). If we change the variabler tox=Cr ², whereC is a constant, the field equations are reduced to a form which is easier to solve. A new set of exact solutions is obtained by consideringe ^v (1-x) ⁿ . Also, a method has been given to obtain generalized solution.It is shown that the solution discussed by Durgapal and Rawat (1980) is the only exact solution which in its most generalized form for a given density distribution stands all the tests of physical reality and for which both (P/) and (dP/d) decrase with increasing value ofr.Neutron star model is proposed by assuming >-2×10¹⁴g cm^–3. Two specific cases are considered, viz.,P<-1/3 and dP/d<-1, respectively. The structures are found to be bound and stable under radial perturbations. The models have been studied for slow rotation and the mass of the Crab pulsar has been estimated for different mechanisms.     

Annihilation radiation from a power-law distributed electron-positron plasma on the ground Landau level: the case of low magnetic fields

Intensity, polarization, and cooling rate of the two-photon annihilation radiation are studied in detail in the case of one-dimensional power-law distributions of electrons and positrons, assuming that they occupy the ground Landau level in a strong magnetic fieldB10¹⁰–10¹² G. Simple analytical expressions for limiting cases are obtained and results of numerical calculations of radiation characteristics are presented. Power-lawe ^± distributions _{± ±} ^–k are shown to generate power-law spectra of the annihilation radiation atEmc ² andEmc ², with indices depending on the direction of radiation. The annihilation spectra at =0 show the largest blue-shifts of their maxima and the hardest high-energy tailsI(Emc ², =0)E ^–(k–1). The blue-shifts reduce, and the hard tials steepen, with increasing . At >(2mc ²/E)^1/2 the slopes of the high-energy tails rapidly transform to that at =2,I(Emc ², =/2)E ^–(2k+3). The direction-integrated spectraS(E) also display the power-law tials at low and high energies,S(Emc ²)E ^–(k+1). The total annihilation rate and energy losses decrease with decreasingk, being higher than for the isotropice ^± power-law distributions at the samek. The radiation is linearly polarized in the plane formed by the magnetic field and wave-vector. The polarization degreeP is maximum atEmc ²:P _max0.6 for =/2. Annihilation features and power-law-like hard tails observed in many gamma-ray burst spectra may be associated with the annihilation radiation of the magnetized power-law distributed plasma near neutron stars. Comparison of the observed and theoretical spectra allows one to estimate the power-law index of thee ^– e ⁺-distribution and the gravitational redshift factor in the radiating region.     

Facular structures derived from precise two-color contrast observations

A precise solar surface photometric observing system was developed and intensity observations of the whole Sun were carried out at a fairly quiet period from December 1987 to April 1988, attaining the photometric accuracy of 10^–3. Using 28 days observation of 4 hours duration each and 0.3 s time interval, we obtained the center-to-limb variation of the ratio of the facular intensity contrast (I _f÷I_o) between two colors of 545 nm (G) and 770 nm (R): (I _f÷I₀)_G÷(I_f÷I₀)_R = 2.20 – 1.16, where is the direction cosine between the line of sight and the surface normal. While this relationship was obtained mostly for active regions from the whole Sun data, we also found an almost identical relation for the quiet Sun network by excluding active regions. This suggests the similarity of faculae at both places.Using the above relation and the difference of optical depth, , in two colors, we found that the facular temperature gradient, dT/d _G, is smaller than that of the quiet photosphere if the gradient is measured more or less vertically (i.e., seen at > 0.7) in accord with Foukal and Duvall (1985), while it is larger than that of the quiet photosphere if the temperature gradient is measured more obliquely (i.e., seen at > 0.7). These findings are free from the low spatial resolution of the present observations because the contrast ratio was used, and also independent of a specific model of hot-wall or hillock. In particular, if the true contrast of facular bright points of 0'2 size is taken as 40% in the green from high-resolution observations, the facular point temperature may even be increasing towards higher geometrical levels ar _G 1. We found also that the area filling factor in active regions is on the order of a few percent or so in accordance with the previous studies.     

The angular momentum-vs-mass relation and the distribution of mass ratios for visual binary systems

The investigation of the angular momentum vs mass relation for binary stars is completed with a study of the 847 systems contained in theFourth Catalog of Orbits of Visual Binary Stars. Because bothJ andM of a visual binary depend steeply on the distance to the system (5th and 3rd powers, respectively), and many of the distances are not well known, the study makes use of an auxiliary parameterR which is independent of distance and proportional toJM ^–5/3.R appears to be uncorrelated withM for the 789 systems for which both can be determined. The non-correlation implies thatJ M ^5/3, expected from Kepler's third law, provides a better fit to the visual binaries than doesJ M ², predicted by some more complex considerations.The distribution functionf(q=M ₂/M₁) of mass ratios for the visual binaries results as a byproduct of the investigation. It peaks extremely sharply towardq=1.0 (much more so than for spectroscopic binaries). Because most visual binaries are wide enough to consist of stars that condensed independently (and so that can be thought of as chosen at random from an initial mass function), one expects the realf(q) to rise toward low ratios. Observational selection against the discovery and study of systems with large magnitude differences between the components must be very large indeed to account for the discrepancy between expectation and observation. The alternative is a mechanism for formation of wide binaries that favours equal components. The distribution of mass ratios for eclipsing binaries is given in an appendix. It peaks strongly atq=0.6–0.75 and largely reflects processes of angular momentum, mass, and energy exchange between the stars in contact systems.     

Some characteristic magnetic properties of lunar materials

One of the typical magnetic characteristics of lunar materials is the composition of their ferromagnetic constituent. Lunar breccias often contain kamacite (less than 7 weight per cent of Ni content) as well as almost pure metallic iron. Metallic ferromagnetics in most igneous rocks are almost pure iron, but the kamacite phase also has been found in some Apollo 15 igneous rocks. It seems likely therefore the metallic ferromagnetics in the lunar crust are more or less similar to those in chondrites.Another typical magnetic characteristic of lunar materials is the presence of a considerable amount of superparamagnetically fine particles of metallic iron. A higher relative content of such fine iron particles results in a higher value of the ratio of magnetic susceptibility (o) to saturation magnetization (I _s), a smaller ratio of the coercive force (H _c) to remanence coercive force (H _RC), and an extremely higher ratio of the viscous component (I _v) to the stable one (I _s) of the remanent magnetization.Communication presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

Metallicity of Young and Old Stars in Irregular Galaxies

Based on archived images obtained with the Hubble Space Telescope, stellar photometry for 105 irregular galaxies has been conducted. We have shown the red supergiant and giant branches in the obtained Hertzsprung-Russel diagrams. Using the TRGB method, distances to galaxies and metallicity of red giants have been determined. The color index (V ? I) of the supergiant branch at the luminosity level M_I = ?7 was chosen as the metallicity index of red supergiants. For the galaxies under study, the diagrams have been built, in which the correlation can be seen between the luminosity of galaxies (M_B) and metallicity of red giants and supergiants. The main source of variance of the results in the obtained diagrams is, in our opinion, uncertainty inmeasurements of galaxy luminosities and star-forming outburst. The relation between metallicity of young and old stars shows that main enrichment of galaxies with metals has taken place in the remote past. Deviations of some galaxies in the obtained relation can possibly be explained with the fall of the intergalactic gas on them, although, this inconsiderably affects metallicities of the stellar content.     

Flare-associated high-speed solar plasma streams

Characteristics of flare-associated high-speed solar plasma streams are investigated using measurements from space probes and Earth-orbiting spacecraft for the period 1964–1982. The maximum observed velocity (V _m) of these streams range from 400 to 850 km s^–1} with peak probability for 600 km s^–1}. These remain for the period of 1–10 days with the peak occurrence 3 days. The difference between the pre-stream velocity (V ₀) and the maximum velocity (V _m) of any high-speed stream serves as the measure of its intensity. For about 60% of the flare associated streams, (V _m-V ₀) is well in excess of 200 km s^–1} and in some cases becomes as large as 450 km s^–1}. The yearly percentage occurrence, total duration and the product of mean (V _m - V ₀) with total duration of the high-speed streams during the year correlates well with solar activity, e.g., maximum during high solar activity period and minimum during low solar activity. The study suggests that presence of sunspots plays a significant role in the generation of flare associated high-speed solar streams.