Statefinder diagnostic for variable modified Chaplygin gas in Bianchi type-V universe

The Bianchi type-V cosmological model with variable modified Chaplygin gas having the equation of state p=Aρ−B/ρ ^α , where 0≤α≤1, A is a positive constant and B is a positive function of the average scale factor a(t) of the universe [i.e. B=B(a)] has been studied. While studying its role in accelerated phase of the universe, it is observed that the equation of state of the variable modified Chaplygin gas interpolates from radiation dominated era to quintessence dominated era. The statefinder diagnostic pair {r,s} is adopted to characterize different phases of the universe.     

Integrability of the Yang-Mills Hamiltonian system

This paper considers the integrability of generalized Yang-Mills system with the HamiltonianH _a (p, q)=1/2(p ₁ ² +p ₂ ² +a ₁ q ₁ ² +a ₂ q ₂ ² )+1/4q ₁ ⁴ +1/4a ₃ q ₂ ⁴ + 1/2a ₄ q ₁ ² q ₂ ² . We prove that the system is integrable for the cases: (A)a ₁=a ₂,a ₃=a ₄=1; (b)a ₁=a ₂,a ₃=1,a ₄=3; (C)a ₁=a ₂/4,a ₃=16,a ₄=6. Our main result is the presentation of these integrals. Only for cases A and B does the Yang-Mills Hamiltonian possess the Painlevé property. Therefore the Painlevé test does not take account of the integrability for the case C.     

A theoretical qualitatively-explained new-variant of Modified-Newtonian-Dynamics (MOND)

It is surprising that we hardly know only 4% of the universe. Rest of the universe is made up of 73% of dark-energy and 23% of dark-matter. Dark-energy is responsible for acceleration of the expanding universe; whereas dark-matter is said to be necessary as extra-mass of bizarre-properties to explain the anomalous rotational-velocity of galaxy. Though the existence of dark-energy has gradually been accepted in scientific community, but the candidates for dark-matter have not been found as yet and are too crazy to be accepted. Thus, it is obvious to look for an alternative theory in place of dark-matter. Milgrom (Astrophys. J. 270:365, 1983a; 270:371, 1983b) has suggested a ‘Modified Newtonian Dynamics (MOND)’ which appears to be highly successful for explaining the anomalous rotational-velocity. But unfortunately MOND lacks theoretical support. The MOND, in-fact, is (empirical) modification of Newtonian-Dynamics through modification in the kinematical acceleration term ‘a’ (which is normally taken as a=\fracv²ra=\frac{v^{2}}{r}) as effective kinematic acceleration a_effective = a m(\fracaa₀)a_{\mathit{effective}} = a \mu(\frac{a}{a_{0}}), wherein the μ-function is 1 for usual-values of accelerations but equals to \fracaa₀ ( << 1)\frac{a}{a_{0}} (\ll1) if the acceleration ‘a’ is extremely-low lower than a critical value a ₀(10⁻¹⁰ m/s²). In the present paper, a novel variant of MOND is proposed with theoretical backing; wherein with the consideration of universe’s acceleration a _d due to dark-energy, a new type of μ-function on theoretical-basis emerges out leading to a_effective = a(1 -K \fraca₀a)a_{\mathit{effective}} = a(1 -K \frac{a_{0}}{a}). The proposed theoretical-MOND model too is able to fairly explain ‘qualitatively’ the more-or-less ‘flat’ velocity-curve of galaxy-rotation, and is also able to predict a dip (minimum) on the curve.     

New exact solutions for power-law inflation Friedmann models

We consider the spatially flat Friedmann model For a ≈ t^p, especially, if p ≥ 1, this is called power-law inflation. For the Lagrangian L = R^m with p = − (m − 1) (2m − 1)/(m − 2) power-law inflation is an exact solution, as it is for Einstein gravity with a minimally coupled scalar field ϕ in an exponential potential V(ϕ) = exp (μϕ) and also for the higher-dimensional Einstein equation with a special Kaluza-Klein ansatz. The synchronized coordinates are not adapted to allow a closed-form solution, so we write The general solutions reads Q(a) = (a^b + C)^f/b with free integration constant C (C = 0 gives exact power-law inflation) and m-dependent values b and f: f = −2 + 1/p, b = (4m − 5)/(m − 1). Finally, special solutions for the closed and open Friedmann model are found.     

Non-integrability of Hénon-Heiles system

We show that the Hénon-Heiles system with Hamiltonian H=\frac12(y₁²+y₂²)+\frac12(ax₁²+bx₂²)+\frac13dx₂³+cx₁²x₂{H=\frac12(y_1^2+y_2^2)+\frac12(ax_1^2+bx_2^2)+\frac13dx_2^3+cx_1^2x_2} is integrable in Liouvillian sense (i.e., the existence of an additional first integral) if and only if c = 0; or \frac dc=1, a=b; or \frac dc=6, a, b{\frac dc=1, a=b; {\rm or}\, \frac dc=6, a, b} arbitrary; or \frac dc=16, b=16a{\frac dc=16, b=16a}. Therefore, we get a complete classification of the Hénon-Heiles system in sense of integrability and non-integrability.     

The relationship betweenG andh in a closed Universe

In a closed expanding-contracting Universe, matter will be subject to an inward acceleration large enough to prevent perpetual expansion. A closed Universe must also perform a simple harmonic motion, which might consist either of one single cycle or of an infinite series of oscillations about a central point. It is the purpose of this study to find the rate ofa ₀, the cosmic acceleration, from which the gravitational constantG can be determined. It will be shown from Ampère's equation and Planck's radiation law that it is possible to derivea ₀=7.623×10^–12 ms^–2, a value which also conforms with the uncertainty principle. The relationship betweena ₀ and electromagnetic radiation is based on the concept that charges (such as electrons) must emit radiation while accelerating. The rate ofa ₀ yields a universal gravitational constant ofG=6.645×10^–11 N m² kg^–2.     

Characteristics of DH type II bursts, CMEs and flares with respect to the acceleration of CMEs

A detailed investigation on DH-type-II radio bursts recorded in Deca-Hectometer (hereinafter DH-type-II) wavelength range and their associated CMEs observed during the year 1997–2008 is presented. The sample of 212 DH-type-II associated with CMEs are classified into three populations: (i) Group I (43 events): DH-type-II associated CMEs are accelerating in the LASCO field view (a>15 m s⁻²); (ii) Group II (99 events): approximately constant velocity CMEs (−15<a<15 m s⁻²) and (iii) Group III (70 events): represents decelerating CMEs (a<−15 m s⁻²). Our study consists of three steps: (i) statistical properties of DH-type-II bursts of Group I, II and III events; (ii) analysis of time lags between onsets of flares and CMEs associated with DH-type-II bursts and (iii) statistical properties of flares and CMEs of Group I, II and III events. We found statistically significant differences between the properties of DH-type-II bursts of Group I, II and III events. The significance (P _a ) is found using the one-way ANOVA-test to examine the differences between means of groups. For example, there is significant difference in the duration (P _a =5%), ending frequency (P _a =4%) and bandwidth (P _a =4%). The accelerating and decelerating CMEs have more kinetic energy than the constant speed CMEs. There is a significant difference between the nose height of CMEs at the end time of DH-type-IIs (P _a ≪1%). From the time delay analysis, we found: (i) there is no significant difference in the delay (flare start—DH-type-II start and flare peak—DH-type-II start); (ii) small differences in the time delay between the CME onset and DH-type-II start, delay between the flare start and CME onset times. However, there are high significant differences in: flare duration (P _a =1%), flare rise time (P _a =0.5%), flare decay time (P _a =5%) and CMEs speed (P _a ≪1%) of Group I, II and III events. The general LASCO CMEs have lower width and speeds when compared to the DH CMEs. It seems there is a strong relation between the kinetic energy of CMEs and DH-type-II properties.     

Das dynamische Verhalten interstellarer Staubteilchen beim Wolkenstoß Teil I. Ohne Berücksichtigung von Masseänderungen

During the collision of interstellar clouds a partial separation between gas and dust occurs. It can be expected that also a separation between heavier and lighter dust particles takes place. To determine the ratio of this dynamical effect the way of dust particles with different values of the product a · ϱ_p (a radius; ϱ_p density of the particles) during the three successive cooling periods is numerically calculated. It is shown that the heavier particles (a · ϱ_p ⪊ 5 · 10⁻⁵ g/cm²) at the end of the collision and the expansion period are gathered in a thin sheet in the inner parts of the new-built cloud whereas the lighter ones (a · ϱ_p 1 · 10⁻⁵ g/cm²) are distributed more or less uniformly among the gas of the cloud. The growth or destruction of the dust particles are not taken into account in this paper.     

Heat flow of the Earth and resonant capture of solar <Superscript>57</Superscript>Fe axions

In a very conservative approach, supposing that all heat flow of the Earth is exclusively due to resonant capture inside the Earth of axions emitted by ⁵⁷Fe nuclei on Sun, we obtain limit on the mass of hadronic axion: m _a < 1.8 keV. Taking into account release of heat from decays of ⁴⁰K, ²³²Th, ²³⁸U inside the Earth, this estimation could be improved to the value: m _a < 1.6 keV. Both the values are less restrictive than limits set in devoted experiments to search for ⁵⁷Fe axions (m _a < 216–745 eV), but are much better than limits obtained in experiments with ⁸³Kr (m _a < 5.5 keV) and ⁷Li (m _a < 13.9–32 keV). Published in Ukrainian in Kinematika i Fizika Nebesnykh Tel, 2009, Vol. 25, No. 2, pp. 143–149. The article was translated by the authors.     

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).     

Model atmosphere parameters of the binary systems COU1289 and COU1291

The spectral energy distributions between λ 3700 Å and λ 8100 Å of the binary systems COU1289 and COU1291 have been measured with the Carl‐Zeiss‐Jena 1 m telescope of the Special Astrophysical Observatory. Their B, V, R magnitudes and B – V colour indices were computed and compared with earlier investigations. Model atmospheres of both systems were constructed using a grid of Kurucz blanketed models, their spectral energy distributions in the continuous spectrum were computed and compared with the observational ones. The model atmosphere parameters for the components of COU1289 were derived as: T ^a_eff = 7100 K, T ^b_eff = 6300 K, log g _a = 4.22, log g _b = 4.22, R _a = 1.50 R_⊙, R _b = 1.40 R_⊙, and for the components of COU1291 as: T ^a_eff = 6400 K, T ^b_eff = 6100 K, log g _a = 4.20, log g _b = 4.35, R _a = 1.47 R_⊙, R _b = 1.12 R_⊙. The spectral types of both components of the system COU1289 were concluded as F1 and F7, and of the system COU1291 as F6 and F9. Finally the formation and evolution of the systems were discussed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of variations of parallel angular velocity and vorticity on the oscillations of compressible homogeneous rotating ellipsoids

Earlier work on the oscillations of an ellipsoid is extended to investigate the behaviour of a nonequilibrium compressible homogeneous rotating gaseous ellipsoid, with the components of the velocity field as linear functions of the coordinates, and with parallel angular velocity and uniform vorticity. The dynamical behaviour of the ellipsoid is obtained by numerically integrating the relevant differential equations for different values of the initial angular velocity and vorticity. This behaviour is displayed by the (a ₁,a ₂) and (a ₁,a ₃) phase plots, where thea _i's (i = 1, 2, 3) are the semi-diameters, and by the graphs ofa ₁,a ₂,a ₃, the volume, and the angular velocity as functions of time.The dynamical behaviour of the nonequilibrium ellipsoid depends on the deviation of the angular momentum from its equilibrium value; for larger deviations, the oscillations are more nonperiodic with larger amplitudes.An initially ellipsoidal configuration always remains ellipsoidal, but it cannot become spheroidal about its rotation axis, though it may become spheroidal instantaneously about either one of the other two principal axes.For an ellipsoid approaching axisymmetry about its axis of rotation, the angular velocity can suddenly increase by a large amount. Thus if an astrophysical object can be modelled by a nonequilibrium ellipsoid, it may occasionally undergo sudden large increases of angular velocity.     

The velocity sensitivity of resonant scattering spectrometers employing a piezoelastic modulator

The resonant scattering spectrometers of the IRIS ground-based network for measuring whole-disc solar velocity oscillations make use of a piezoelastic modulator. The velocity noise generated by this optical component is analysed with particular emphasis on the required stability of the amplitude of oscillation, a. The product of the absolute stability ¦ a – a _m ¦/a _m and the relative stability a _r.m.s./a _m may not be larger than 10 ^–4 to 10 ^–5 (depending on specific wishes), where a _m is the optimum amplitude. The velocity noise due to photon statistics is slightly enhanced, but other instrumental sources of velocity noise remain unaffected.     

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 requirements of a colliding comet source of gamma ray bursts

Colliding comets in the Solar System may be an important source of gamma ray bursts. The spherical gamma ray comet cloud required by the results of the Venera Satellites (Mazets and Golenetskii, 1987) and the BATSE detector on the Compton Satellite (Meeganet al., 1992a, b) is neither the Oort Cloud nor the Kuiper Belt. To satisfy observations ofN(>P _max) vsP _max for the maximum gamma ray fluxes,P _max > 10^–5 erg cm^–2 s^–1 (about 30 bursts yr^–1), the comet density,n, should increase asn a ¹ from about 40 to 100 AU wherea is the comet heliocentric distance. The turnover above 100 AU requiresn a ^–1/2 to 200 AU to fit the Venera results andn a ^1/4 to 400 AU to fit the BATSE data. Then the masses of comets in the 3 regions are from: 40–100 AU, about 9 earth masses,m _E; 100–200 AU about 25m _E; and 100–400 AU, about 900m _E. The flux of 10^–5 erg cm^–2 s^–1 corresponds to a luminosity at 100 AU of 3 × 10²⁶ erg s^–1. Two colliding spherical comets at a distance of 100 AU, each with nucleus of radiusR of 5 km, density of 0.5 g cm^–3 and Keplerian velocity 3 km s^–1 have a combined kinetic energy of 3 × 10²⁸ erg, a factor of about 100 greater than required by the burst maximum fluxes that last for one second. Betatron acceleration in the compressed magnetic fields between the colliding comets could accelerate electrons to energies sufficient to produce the observed high energy gamma rays. Many of the additional observed features of gamma ray bursts can be explained by the solar comet collision source.     

Contraction of the solar nebula

The concept of Roche limit is applied to the Laplacian theory of the origin of the solar system to study the contraction of a spherical gas cloud (solar nebula). In the process of contraction of the solar nebula, it is assumed that the phenomenon of supersonic turbulent convection described by Prentice (1978) is operative and brings about the halt at various stages of contraction. It is found that the radius of the contracting solar nebula follows Titius-Bode law R _p = Ra^p, where R is the radius of the present Sun and a = 1.442. We call a the Roche's constant. The consequences of the relation are also discussed. The aim, here, is an attempt to explain, on the basis of the concept of Roche limit, the distribution of planets in the solar system and try to understand the physics underlying it.     

Astrophysical observations exclude the hypothesis on the universe expansion

It is known that the correlation between the observed visible luminositym(z), angular dimension (z) of galaxies on the red shiftz and theoretical relations of the standard cosmology is possible only under the assumption that the luminosity and object dimension evolution are equal toL(z) =L ₀(z + 1)^3.2 andl(z) =l ₀(z + 1)^–2, respectively. This evolution is hypothetical, since it is defined by a theory which is not confirmed by experience. In order to solve the problem on the reality of the Universe expansion, it is sufficient to prove or disprove these conclusions using methods of measurement independent of the theory. One of these methods consists of defining the dependence of the radiation spectra of galaxies and quasars onz which evidently is proportional to the spectrum of absolute luminosityL(, z). It has subsequently been shown that the spectrum form is practically independent of the red shift - i.e., it remains constant during the lifetime of galaxies and quasars. Consequently, to explain the luminosity increase required by the standard cosmology, it is necessary to admit a completely unreal entity (at all wavelengths of the optical spectrum increase) of the radiation spectral density of (z + 1)^3.2 times. We can conclude that in reality the luminosity evolution is either absent or its power index is smaller at least by an order of magnitude. It is likely, therefore, that the established is the result of an inadequate standard in cosmology.Another method is the use of the observed relations between the parameters ofL andl galaxies. A number of measurements made by different authors gives the relationlL ^a , where 0.33a1.6. It then follows thatl(z)(z + 1)^3.2a . This dependence of the galaxy dimension is inverse to the dependence predicted by the standard cosmology. Besides, in order to make a correlation between thel(z)(z + 1)^3.2a and measurements of (z), it is necessary that indices of the degree of luminosity evolution should be smaller by an order of magnitude.Thus, the luminosity increase and simultaneous decrease of galaxy and quasar dimensions predicted by the standard cosmolog are not confirmed by the direct astrophysical measurements. This discrepancy is the consequence of an incorrect hypothesis of Universe expansion and the relativistic cosmology based on it.     

On the intercomponent emission in close binary systems

An empirical relationship is discovered for RS CVn type close binary systems between their absolute luminosity, L(MgII), of the ultraviolet magnesium doublet 2800 MgII, and the intercomponent distancea of the system. It has the following form: L(MgII) a ⁿ(Figure 1). It is shown that for the overwhelming majority of binary systemsn = 1 (Figure 4). This correlation presents itself as a direct confirmation of the intercomponent origin of the observed emission, particularly, in the magnesium doublet in close binary systems. The basic relationship of intercomponent emission is derived in the form: L(MgII) = 1.0 × 10³² a ergs s^–1. At the same time, accidental statistical divergences from this correlation are possible on both sides: asn > 1 as welln < 1 (Figure 4). The correlationn = 1 determines also the character, - i.e. cylindric for a stream - of the transfer of gaseous matter from one component of the system to the other, and in the general gas dynamics of the intercomponent medium.The existence of a new category of stellar atmosphere, - which we callroundchrom, is predicted, representing the common chromosphere of a superclose binary system, surrounding or blending both components of the system (Figure 3). The boundaries between the three most important divisions of magnesium doublet emission - chromosphere of single stars, roundchrom of superclose binary systems and intercomponent space - are established for RS CVn type systems. Finally, a number of new problems, both observational and theoretical, are brought forward.     

MGS electron density profiles: Analysis of the peak magnitudes

We analyze here the behavior of the magnitudes of the F₁ and E peaks of the electron density profiles measured by the Radio Science Subsystem of the Mars Global Surveyor spacecraft, as a function of solar zenith angle χ and solar flux. For each of the 658 days of data in the six occultation seasons in the northern hemisphere, we choose one profile to analyze, which is that for which the F₁ peak is the median value. We assume that the variations of the measured peak densities can be represented as Aa(cosχ) and as Bb(F_10.7), where F_10.7 is the usual solar flux proxy, appropriately shifted to the orbital position of Mars. To minimize the effect of solar activity, we divide the data into 6 F_10.7 bins, fit the data in each bin, and derive the values of the exponent a and the coefficient AF10.7 for each bin. The median values that we derive for the exponent a is 0.46 for the F₁ peak, and 0.395 for the E peak. To minimize the effect of SZA, we divide the data into eight SZA bins, and derive the exponent b and the coefficient Bχ for each SZA bin. We argue that the last three SZA bins should be excluded because the fits were poor, due partly to the small number of data points in each of these bins. If we do so, the median values of b that we derive are 0.27 and 0.40 for the F₁ and E peaks, respectively. Finally we derive a 3-parameter fit to all the data, which expresses the variability of the peak densities as a function of a^′(cosχ) and b^′(F_10.7) simultaneously. The fitted values of the exponents a^′ and b^′ for the F₁ peak are 0.45 and 0.26, respectively; for the E peak, the values are 0.39 and 0.46, respectively. We compare our results to Chapman theory, and to those of other investigators.     

Estimates of the physical parameters of supernova remnants (SNR)

The various physical parameters of a SNR can easily be worked out from graphs established on the basis of the recalibrated relation between the radio surface brightness , and the linear diameterD of a SNR (Ilovaisky and Lequeux, 1972). These graphs lead to the estimation of the distancer (kpc), linear diameterD (pc), monochromatic power at 1 GHz,P ₁ GHz (W Hz^–1); and total powerP _tot (a) (erg. s^–1) of a SNR, given its mean angular diameter <> (arc min), flux density at 1 GHz, S₁ GHz (f.u.) and spectral indexa. Three SNR (W28A₁, Monoceros SNR, W49B) are used to illustrate the case. The radio spectrum of one of these (W49B), curved at low frequencies, is explained in terms of absorption by the diffuse interstellar medium. Various cases are discussed and some physical parameters of the absorbing matter are established.