Inhomogeneities in the spatial distribution of gamma-ray bursts

The distribution of pairwise distances f(l) for different dependences r(z) of the metric distance is used to reveal inhomogeneities in the spatial distribution of 201 long (T ₉₀>2^s) gamma-ray bursts with measured redshifts z. For a fractal set with dimensionality D, this function behaves asymptotically as f(l) ∼ l ^D−1 for small l. Signs of fractal behavior with dimensionality D = 2.2–2.5 show up in all the models considered for the spatial distribution of the gamma-ray bursts. Several spatially distinct groups of gamma-ray bursts are identified. The group with equatorial coordinates ranging from 23^h56^m to 0^h49^m and δ from +19° to +23° with redshifts of 0.81–0.94 is examined separately.     

Accelerated expansion from?a?modified-quadratic gravity

We investigate the late-time dynamics of a four-dimensional universe based on modified scalar field gravity in which the standard Einstein-Hilbert action R is replaced by f(φ)R+f(R) where f(φ)=φ ² and f(R)=AR ²+BR _μν R ^μν,(A,B)∈ℝ. We discussed two independent cases: in the first model, the scalar field potential is quartic and for this special form it was shown that the universe is dominated by dark energy with equation of state parameter w≈−0.2 and is accelerated in time with a scale factor evolving like a(t)∝t ^5/3 and B+3A≈0.036. When, B+3A→∞ which corresponds for the purely quadratic theory, the scale factor evolves like a(t)∝t ^1/2 whereas when B+3A→0 which corresponds for the purely scalar tensor theory we found when a(t)∝t ^1.98. In the second model, we choose an exponential potential and we conjecture that the scalar curvature and the Hubble parameter vary respectively like R=hH[(f)\dot]/f,h ? \mathbbRR=\eta H\dot{\phi}/\phi,\eta\in\mathbb{R} and H=g[(f)\dot]^c,(g,c) ? \mathbbRH=\gamma\dot{\phi}^{\chi},(\gamma,\chi)\in\mathbb{R}. It was shown that for some special values of  χ, the universe is free from the initial singularity, accelerated in time, dominated by dark or phantom energy whereas the model is independent of the quadratic gravity corrections. Additional consequences are discussed.     

Study of the dependence of the star formation rate in the nuclear regions of 39 Kazarian galaxies on their integral parameters

A statistical study of the dependence of the star formation rate in the nuclear regions of 39 Kazarian galaxies on the integral parameters of these galaxies is carried out on the basis of spectra from SDSS DR6. The value of SFR/kpc² for our sample lies in the range 0.013÷2.04M _⨀ year⁻¹kpc⁻² (with the maximum value of 2.04 corresponding to the Kaz 98 (merger)). It is found that the surface density of the rate of star formation correlates positively with the bar structure parameter and EW(Hα), and that, for spiral galaxies of early morphological types, SFR/kpc² is greater than for the later types. It is shown that the color B-R for the galaxies and the color (u − g) _nucl for the nuclear region correlate positively with the total absorption A(Hα) in the Ha line for the nuclear region. The average value of A(Hα) for our samples is found to be A(Hα)=1.3±0.09 magnitudes. Translated from Astrofizika, Vol. 52, No. 2, pp. 211–224 (May 2009).     

Collective plasma effects and the electron number problem in solar hard X-ray bursts

Due to the relatively high stream densities involved, collective interactions with the ambient plasma are likely to be important for the electrons producing solar hard X-ray bursts. In thick- and thin-target bremsstrahlung models the most relevant process is limitation of the invoked electron beams by ion sound wave generation in the neutralizing reverse current established in the atmosphere. For the thick target model it is shown that typical electron fluxes are near the maximum permitted by stability of the reverse current so that ion-sound wave generation may be the process which limits the electron injection rate. On the other hand the chromospheric reverse current is sufficient to supply the large total number of electrons which have to be accelerated in the corona. For the thin target the low density of the corona severely limits the possible reverse current so that the maximum upward flux of fast electrons is probably much too small to explain X-ray bursts but compatible with observations of interplanetary electrons.A distinct class of model postulates a small number of electrons confined by resonant scattering in a dense coronal slab surrounding a current sheet with continuous stochastic acceleration offsetting collisional losses. The energetic aspects of such a situation described by Hoyng (1975) are developed here by addition of equations describing the slab geometry in terms of electron diffusion by whistler scattering and of the collisional damping of the accelerating Langmuir waves. Solution of these equations results in values for the fieldB(70–350 G), densityn ₀(2–5 × 10¹² cm ^–3), slab dimensions (10¹⁸ km² × 0.3–3 km) and relative Langmuir energy density (10^–3 – 10^–2) required to produce the observed range of bursts. It is pointed out, however, that there may be no real gain in electron number requirements since the fast electrons in the emitting slab would be constantly swept out along with the frozen-in plasma as dissipation proceeds so that a large total number of electrons is still required. It could in fact be that just such a coronal region is the injection mechanism for the thick-target model.On leave from Department of Astronomy, University of Glasgow, Scotland.     

A self-consistent model for the storm radio emission from the Sun

A self-consistent theoretical model for storm continuum and bursts is presented. We propose that the Langmuir waves are emitted spontaneously by an anisotropic loss-cone distribution of electrons trapped in the magnetic field above active regions. These high-frequency electrostatic waves are assumed to coalesce with lower-hybrid waves excited either by the trapped protons or by weak shocks, making the observed brightness temperature equal to the effective temperature of the Langmuir waves.It is shown that whenever the collisional damping ( _c ) is more than the negative damping (- _A ) due to the anisotropic distribution, there is a steady emission of Langmuir waves responsible for the storm continuum. The type I bursts are generated randomly whenever the collisional damping ( _c ) is balanced by the negative damping (- _A ) at the threshold density of the trapped particles, since it causes the effective temperature of Langmuir waves to rise steeply. The number density of the particles responsible for the storm radiation is estimated. The randomness of type I bursts, brightness temperature, bandwidth and transition from type I to type III storm are self-consistently explained.On leave from Indian Institute of Astrophysics, Bangalore 560034, India.     

RR Lyrae-Type Stars in the Sonneberg Fields in the Vicinity of the North Galactic Pole

For the derivation of distances and of the density distribution of the RR Lyrae stars in the Sonneberg fields near the north galactic pole (comprising 355 □°) we determined their photographic B-brightnesses. The density distribution of the RR Lyrae stars in each of the fields is almost identical with the density distribution given by KINMAN , WIRTANEN , and JANES (1966). Furthermore we derived the period-amplitude relations for RR Lyrae stars with 11^mg·<mpg < 16^m·7, which in the extended fields 92/93 Leo and 1 Boo turned out to be similar to those in the fields of KINMAN et al. near the pole. In the extended field 26 Com we found a slightly different period-amplitude relation pointing perhaps to a less homogeneous population.     

Expansion Speed of Coronal Mass Ejections

A large set of limb coronal mass ejections (CMEs) are used to determine the accurate relationship between radial (V _rad) and expansion (V _exp) speeds of CMEs. It is demonstrated that this relation is exceptionally well described by the function f(w)=1/2(1+cot w), representing a full cone model for the CME with a half-width, w. We also demonstrate that for extremely fast CMEs (V _exp>3000 km s⁻¹), it is better to use the approximation V _rad≈V _LE. This implies that such CMEs expand spherically above the solar surface.     

Statistics of magnetic fields for OB stars

Based on an analysis of the catalog of magnetic fields, we have investigated the statistical properties of the mean magnetic fields for OB stars. We show that the mean effective magnetic field B of a star can be used as a statistically significant characteristic of its magnetic field. No correlation has been found between the mean magnetic field strength B and projected rotational velocity of OB stars, which is consistent with the hypothesis about a fossil origin of the magnetic field. We have constructed the magnetic field distribution function for B stars, F(B), that has a power-law dependence on B with an exponent of ≈−1.82. We have found a sharp decrease in the function F(B) for B ⩽ 400 G that may be related to rapid dissipation of weak stellar surface magnetic fields.     

On the adelphic potentials compatible with a set of planar orbits

Given a planar potentialB=B(x, y), compatible with a monoparametric family of planar orbitsf(x, y)=c, we face the problem of producing potentialsA=A(x, y), adelphic toB(x, y), i.e. nontrivial potentials which have in common withB(x, y) the given set of orbits. We establish a linear, second order partial differential equation for a functionP(x, y) and we prove that, to any definite positive solution of this equation, there corresponds a potentialA(x, y) adelphic toB(x, y).     

Charged analogues of Schwarzschild interior solution in terms of pressure

Recently, Bijalwan (Astrophys. Space Sci., doi:, 2011a) discussed charged fluid spheres with pressure while Bijalwan and Gupta (Astrophys. Space Sci. 317, 251–260, 2008) suggested using a monotonically decreasing function f to generate all possible physically viable charged analogues of Schwarzschild interior solutions analytically. They discussed some previously known and new solutions for Schwarzschild parameter u( = \fracGMc²a ) ￡ 0.142u( =\frac{GM}{c^{2}a} ) \le 0.142, a being radius of star. In this paper we investigate wide range of u by generating a class of solutions that are well behaved and suitable for modeling Neutron star charge matter. We have exploited the range u≤0.142 by considering pressure p=p(ω) and f = ( f₀(1 - \fracR²(1 - w)a²) +f_a\fracR²(1 - w)a² )f = ( f_{0}(1 - \frac{R^{2}(1 - \omega )}{a^{2}}) +f_{a}\frac{R^{2}(1 - \omega )}{a^{2}} ), where w = 1 -\fracr²R²\omega = 1 -\frac{r^{2}}{R^{2}} to explore new class of solutions. Hence, class of charged analogues of Schwarzschild interior is found for barotropic equation of state relating the radial pressure to the energy density. The analytical models thus found are well behaved with surface red shift z _s ≤0.181, central red shift z _c ≤0.282, mass to radius ratio M/a≤0.149, total charge to total mass ratio e/M≤0.807 and satisfy Andreasson’s (Commun. Math. Phys. 288, 715–730, 2009) stability condition. Red-shift, velocity of sound and p/c ² ρ are monotonically decreasing towards the surface while adiabatic index is monotonically increasing. The maximum mass found to be 1.512 M _Θ with linear dimension 14.964 km. Class of charged analogues of Schwarzschild interior discussed in this paper doesn’t have neutral counter part. These solutions completely describe interior of a stable Neutron star charge matter since at centre the charge distribution is zero, e/M≤0.807 and a typical neutral Neutron star has mass between 1.35 and about 2.1 solar mass, with a corresponding radius of about 12 km (Kiziltan et al., [astro-ph.GA], 2010).     

Surface Density of Bright, Active Extragalactic Objects

A new sample of local, active extragalactic objects has been compiled: a combined sample that is the sum of two samples, of Sy1 galaxies and of quasars from Markarian's survey and quasars from the Bright Quasar Survey. A log N(<B)-B relation is constructed for the new sample of active galaxies, limited to the apparent stellar magnitude B = 15 ^m .5. It can be represented by a straight line with a slope = 0.60 ± 0.06. It is a good extension, without a noticeable jog, of the analogous relationship for the Hamburg—ESO survey, which has a slope = 0.59 ± 0.04. The combined surface density of bright active galaxies and quasars down to B = 15 ^m .5 is 0.01 per square degree.     

Effect of overtaking disturbances on the propagation of spherical shock wave through self-gravitating gas

Effect of overtaking disturbances on the propagation of a spherical shock wave in self gravitating gas has been studied by the technique developed by the first author [Mod. Meas. Cont. B,46(4), 1 (1992)]. The analytical expressions for modified shock velocity and shock strength have been obtained for an initial density distribution0 =r ^–w, where is the density at the axis of symmetry andw is a constant; simultaneously, for the two cases viz.; (i) when the shock is strong and ii) when it is weak. The results accomplished here have been compared with those for freely propagation of shock.It is observed that the conclusions arrived at here agree with experimental observations. Finally, the modified expressions for the pressure, the density and the particle velocity immediately behind the shock have also been derived from, for both cases.     

Evaluation of a Selected Case of the Minimum Dissipative Rate Method for Non-Force-Free Solar Magnetic Field Extrapolations

The minimum dissipative rate (MDR) method for deriving a coronal non-force-free magnetic field solution is partially evaluated. These magnetic field solutions employ a combination of three linear (constant-α) force-free-field solutions with one being a potential field (i.e., α=0). The particular case of the solutions where the other two α’s are of equal magnitude but of opposite sign is examined. This is motivated by studying the SOLIS (Synoptic Optical Long-term Investigation of the Sun (SOLIS), a National Solar Observatory facility) vector magnetograms of AR 10987, which show a global α value consistent with an α=0 value as evaluated by (∇×B) _z /B _z over the region. Typical of the current state of the observing technology, there is no definitive twist for input into the general MDR method. This suggests that the special α case, of two α’s with equal magnitudes and opposite signs, is appropriate given the data. Only for an extensively twisted active region does a dominant, nonzero α normally emerge from a distribution of local values. For a special set of conditions, is it found that (i) the resulting magnetic field is a vertically inflated magnetic field resulting from the electric currents being parallel to the photosphere, similar to the results of Gary and Alexander (Solar Phys. 186:123, 1999), and (ii) for α≈(α _max/2), the Lorentz force per unit volume normalized by the square of the magnetic field is on the order of 1.4×10⁻¹⁰ cm⁻¹. The Lorentz force (F _L) is a factor of ten higher than that of the magnetic force d(B ²/8π)/dz, a component of F _L. The calculated photospheric electric current densities are an order of magnitude smaller than the maximum observed in all active regions. Hence both the Lorentz force density and the generated electric current density seem to be physically consistent with possible solar dynamics. The results imply that the field could be inflated with an overpressure along the neutral line. However, the implementation of this or any other extrapolation method using the electric current density as a lower boundary condition must be done cautiously, with the current magnetography.     

Solar radio burst and in situ determination of interplanetary electron density

We review and discuss a few interplanetary electron density scales which have been derived from the analysis of interplanetary solar radio bursts, and we compare them to a model derived from 1974–1980 Helios 1 and 2 in situ density observations made in the 0.3–1.0 AU range. The Helios densities were normalized to 1976 with the aid of IMP and ISEE data at 1 AU, and were then sorted into 0.1 AU bins and logarithmically averaged within each bin. The best fit to these 1976-normalized, bin averages is N(R _AU) = 6.1R ^-2.10 cm^-3. This model is in rather good agreement with the solar burst determination if the radiation is assumed to be on the second harmonic of the plasma frequency. This analysis also suggests that the radio emissions tend to be produced in regions denser than the average where the density gradient decreases faster with distance than the observed R ^-2.10.NAS/NRC Postdoctoral Research Associate on leave from Laboratory Associated with CNRS No. 264, Paris Observatory, France.     

On the UV-excesses of cepheid variables

On the basis of the intrinsic (U – B)₀ colours of the cepheid variables, found by the authors, the UV-excesses in the maximum and minimum light δ(U – B)^max and δ(U – B)^min are defined. It is found out that the UV-excesses in the maximum light δ(U – B)^min increase with the period P (Fig. 2), but there is no correlation between δ(U – B)^min and log P. A correlation between δ(U – B)^max and the “amplitude defects” f_B is also determined. These results in connection with some other considerations, as well as the possible causes of the UV-excesses, are discussed.     

Steady models for the hard X-ray loops in the solar corona

In some gradual hard X-ray bursts with high intensity, hard X-ray source (15–40 keV) is steadily located in the corona along with softer X-ray source (5–10 keV).Two stationary models, high density and high temperature models, are proposed to solve the difficult problem of confinement of hot (or nonthermal) plasma in the direction of the magnetic field along the loops in the corona. In both models, an essential point is that the effective X-ray source is composed of fine dense filamentary loops imbeded in a larger rarefied coronal loop, and the electron number density in the filaments is so high as 10¹¹–10¹² cm^-3. If the density is so high heat conduction can be as reasonably small as of the order of 10²⁷ erg s ^-1 for the given emission measures of observed X-rays, since the required cross-sectional area is small and also classical conduction is valid. Collisional confinement of thermal tail, and nonthermal electrons if any, up to 50–60 keV in the filaments is also possible, so that the hard X-ray images can be loop like structure instead of double source (foot points).High density model is applicable to the coronal filamentary loops with temperature T _m < 5 × 10⁷ K at the loop summit. The heat flow from the summit downwards is lost almost completely by the radiation from the loop during the conduction to the foot points. A continuous energy release is assumed near the summit to maintain the stationary temperature T _m, and pressure balance is maintained along the loop. In this model, the number density at the summit is given by n _m - 10⁶ T _m ² /s_m, where s _m is the length of the loop from the summit to the foot point, and the distribution of temperature and density along the loop are given by T = T _m(s/s_m)^1/3 and n = n _m(s/s_m)^-1/3, respectively.High temperature model is applicable to the filamentary loops with higher temperature up to about 10^8.5 K and comparatively lower number density as 10¹¹ cm^-3 for the requirement of magnetic confinement of the hot plasma in radial direction. The radiation from the loop is negligibly small in this model so that the heat flux is nearly conserved down to the foot points. In this case, temperature gradient is smaller than that of the high density model, depending on the tapering of the magnetic bottle.In both models, the differential emission measure is maximum at the highest temperature T _m and the brightness distribution along the loop shows a maximum around the summit of the loop if some magnetic tapering is taken into account.     

The dependence of solar hard X-ray burst intensity on magnetic field strength

The measurements of peak intensities of hard X-ray bursts from hot flare plasma electrons as a function of peak frequency of associated microwave radio bursts are discussed. The latter is proportional to the magnetic field strength. The results suggest that the flare hard X-rays are emitted when the electron plasma frequency is comparable to the electron gyrofrequency. Thus, the hard X-ray peak intensity varies as B ^4.2, where B is the magnetic field strength.On leave from the Geophysical Institute, Slovak Academy of Sciences, 947 01 Hurbanovo, Czechoslovakia.Deceased 22 July, 1986.     

Some results of the cooperative photometric observations of the UV Cet-type flare stars in the years 1967–71

The list of the cooperative photometric observations of the UV Cet-type flare stars that have been organized during the years 1967 to 1971 by the Working Group on Flare Stars of the IAU Commission 27 is given. The completeness and reliability of the data obtained are evaluated by comparing simultaneous observations at different observatories. the statistical analysis of the UV Cet, YZ CMi, EV Lac and AD Leo flares observed in the B-band is carried out. The flare energy spectrum in the energy range where observational selection effects are small is found to be d lnv/d lnE _B=–1.4 to –1.9,v is an occurrence of flares with radiation energy ofE _B. The total flares' radiation is equal to 1.7%, 1.2%, 0.3% and 0.4% of the quiet radiation in the B-band of the stars listed, and the main part of this total radiation is due to the strongest flares. Distributions of flare rise times (t _r) and of rates of flare absolute luminosity increase (d² E _B/dt _r ²Ë _r) are considered; these parameters of flare are independent statistically for all stars studied. Correlation coefficientsr (E _B,t _r) andr (E _B,r(E _B,Ë _r)) are rather small except r (E _B,t _r)=0.86 for the AD Leo flares. Contradictory conclusions on temporal distribution of flares infered by different investigators are noted.     

Scalar field as dark energy accelerating expansion of the Universe

The features of a homogeneous scalar field ϕ with classical Lagrangian L = ϕ_;i ϕ^;i /2 − V(ϕ) and tachyon field Lagrangian L = −V(ϕ)√1 − ϕ_;i ϕ^;i causing the observable accelerated expansion of the Universe are analyzed. The models with constant equation-of-state parameter w _de = p _de/ρ_de < −1/3 are studied. For both cases the fields ϕ(a) and potentials V(a) are reconstructed for the parameters of cosmological model of the Universe derived from the observations. The effect of rolling down of the potential V(ϕ) to minimum is shown. Published in Ukrainian in Kinematika i Fizika Nebesnykh Tel, 2008, Vol. 24, No. 5, pp. 345–359. The article was translated by the authors.     

Is the Entropy S q Extensive or Nonextensive?

The cornerstones of Boltzmann-Gibbs and nonextensive statistical mechanics respectively are the entropies S _BG ≡ −k ∑ _{i = 1} ^W p _i ln p _i and S _q ≡ k (1−∑ _{i = 1} ^W p _i ^q )/(q−1) (q∊ℜ S ₁ = S _BG ). Through them we revisit the concept of additivity, and illustrate the (not always clearly perceived) fact that (thermodynamical) extensivity has a well defined sense only if we specify the composition law that is being assumed for the subsystems (say A and B). If the composition law is not explicitly indicated, it is tacitly assumed that A and B are statistically independent. In this case, it immediately follows that S _BG (A+B) = S _BG (A)+S _BG (B), hence extensive, whereas S _q (A+B)/k = [S _q (A)/k]+[S _q (B)/k]+(1−q)[S _q (A)/k][S _q (B)/k], hence nonextensive for q ≠ 1. In the present paper we illustrate the remarkable changes that occur when A and B are specially correlated. Indeed, we show that, in such case, S _q (A+B) = S _q (A)+S _q (B) for the appropriate value of q (hence extensive), whereas S _BG (A+B) ≠ S _BG (A)+S _BG (B) (hence nonextensive). We believe that these facts substantially improve the understanding of the mathematical need and physical origin of nonextensive statistical mechanics, and its interpretation in terms of effective occupation of the W a priori available microstates of the full phase space. In particular, we can appreciate the origin of the following important fact. In order to have entropic extensivity (i.e., lim _N→∞ S(N)/N < ∞, where N≡ numberof elements of the system), we must use (i) S _BG , if the number W ^eff of effectively occupied microstates increases with N like W ^{{eff}}∼ W ∼ μ ^N (μ ≥ 1); (ii) S _q with q = 1−1/ρ, if W ^{{eff}}∼ N^ρ < W (ρ ≥ 0). We had previously conjectured the existence of these two markedly different classes. The contribution of the present paper is to illustrate, for the first time as far as we can tell, the derivation of these facts directly from the set of probabilities of the W microstates.