Cavitation by Nonlinear Interaction Between Inertial Alfvén Waves and Magnetosonic Waves in Low Beta Plasmas

This paper presents the model equations governing the nonlinear interaction between dispersive Alfvén wave (DAW) and magnetosonic wave in the low-β plasmas (β≪m _e/m _i; known as inertial Alfvén waves (IAWs); here \upbeta = 8pn₀T /B₀²\upbeta = 8\pi n_{0}T /B_{0}^{2} is thermal to magnetic pressure, n ₀ is unperturbed plasma number density, T(=T _e≈T _i) represents the plasma temperature, and m _e(m _i) is the mass of electron (ion)). This nonlinear dynamical system may be considered as the modified Zakharov system of equations (MZSE). These model equations are solved numerically by using a pseudo-spectral method to study the nonlinear evolution of density cavities driven by IAW. We observed the nonlinear evolution of IAW magnetic field structures having chaotic behavior accompanied by density cavities associated with the magnetosonic wave. The relevance of these investigations to low-β plasmas in solar corona and auroral ionospheric plasmas has been pointed out. For the auroral ionosphere, we observed the density fluctuations of ∼ 0.07n ₀, consistent with the FAST observation reported by Chaston et al. (Phys. Scr. T84, 64, 2000). The heating of the solar corona observed by Yohkoh and SOHO may be produced by the coupling of IAW and magnetosonic wave via filamentation process as discussed here.     

Exact solutions: classical electron model

Rahaman et al. (Astrophys. Space. Sci. 331:191–197, 2010) discussed some classical electron models (CEM) in general relativity. Bijalwan (Astrophys. Space. Sci. 334:139–143, 2011) present a general exact solution of the Einstein-Maxwell equations in terms of pressure. We showed that charged fluid solutions in terms of pressure are not reducible to a well behaved neutral counter part for a spatial component of metrice ^λ . Hence, these solutions represent an electron model in general relativity. We illustrated solutions in terms of pressure briefly with de-Sitter equation of state and charged analogues of Kohler Chao interior solution as a special cases.     

Relation between the Spatial Distribution and Spectral Index of Superthermal Electron Distribution in Solar cm-Radio Sources

A series of solar cm-radio bursts are analyzed by a new inverse method estimating spatial changes of the superthermal electron distribution in solar cm-radio burst sources. It is found that the measure of the spatial change of superthermal electrons in the radio source ν _n is always greater than that for the magnetic field ν _B and it is linearly dependent on the spectral index of the electrons δ as ν _n ≈0.5δ. This relation is explained in the simplified flare-loop model integrating the analytical solutions of the Fokker – Planck equation. The mean value of ν _B is found to be 0.36±0.04, which is very close to the value of ν _B =0.38±0.02 derived from the dependence of the magnetic field strength on the height in the active region measured by RATAN-600.     

Exact solution of perfect fluid massive string cosmology in Bianchi type?III space-time with decaying vacuum energy density?Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 20:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. The vacuum energy density Λ is found to be positive and a decreasing function of time which is supported by the results from recent supernovae Ia observations. It is also observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Some physical and geometric properties of the model are also discussed.     

Magnetic Turbulence and Ion Dynamics in the Magnetotail

The ion dynamics in the Earth's magnetotail is studied in the case when a cross tail electric field E ₀ and reconnection-driven magnetic turbulence are present in the current sheet. The magnetic turbulence observed by the Interball spacecraft is modeled numerically by a power law magnetic fluctuation spectrum. A test particle simulation is performed for the ions, and the distribution function moments are obtained as a function of the magnetic fluctuation level, δB/B ₀, and of the value of the normal component B _n. It appears that even in the presence of magnetic turbulence, the normal component has a marked influence on particle dynamics: the ion bulk velocity along E _y and ion temperature are almost inversely proportional to B _n. The magnetic turbulence causes the current to split in two layers, and the level of magnetic fluctuations needed to have splitting is roughly proportional to B _n. It appears that in the relevant range of parameters, B _n and δB/B ₀ have opposite effects on the current structure and on ion heating. This revised version was published online in July 2006 with corrections to the Cover Date.     

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).     

The effects of intense magnetic fields on Landau levels in a neutron star

In this paper, an approximate method of calculating the Fermi energy of electrons (E _F (e)) in a high-intensity magnetic field, based on the analysis of the distribution of a neutron star magnetic field, has been proposed. In the interior of a neutron star, different forms of intense magnetic field could exist simultaneously and a high electron Fermi energy could be generated by the release of magnetic field energy. The calculation results show that: E _F (e) is related to density ρ, the mean electron number per baryon Y _e and magnetic field strength B.     

The Variation of Solar Wind Correlation Lengths Over Three Solar Cycles

We present the results of a study of solar wind velocity and magnetic field correlation lengths over the last 35 years. The correlation length of the magnetic field magnitude λ _|B| increases on average by a factor of two at solar maxima compared to solar minima. The correlation lengths of the components of the magnetic field l_BXYZ\lambda_{B_{XYZ}} and of the velocity l_VYZ\lambda_{V_{YZ}} do not show this change and have similar values, indicating a continual turbulent correlation length of around 1.4×10⁶ km. We conclude that a linear relation between λ _|B|, VB ², and Kp suggests that the former is related to the total magnetic energy in the solar wind and an estimate of the average size of geoeffective structures, which is, in turn, proportional to VB ². By looking at the distribution of daily correlation lengths we show that the solar minimum values of λ _|B| correspond to the turbulent outer scale. A tail of larger λ _|B| values is present at solar maximum causing the increase in mean value.     

Neutrino radiation of the AGN black holes

In the framework of ‘microscopic’ theory of black holes (J. Phys. Soc. Jpn. Suppl. B 70, 84, 2001; Astrophys. USSR 4, 659, 1996; 35, 335, 1991, 33, 143, 1990, 31, 345, 1989a; Astrophys. Space Sci. 1, 1992; Dokl. Akad. Nauk USSR 309, 97, 1989b), and references therein, we address the ‘pre-radiation time’ (PRT) of neutrinos from black holes, which implies the lapse of time from black hole’s birth till radiation of an extremely high energy neutrinos. For post-PRT lifetime, the black hole no longer holds as a region of spacetime that cannot communicate with the external universe. We study main features of spherical accretion onto central BH and infer a mass accretion rate onto it, and, further, calculate the resulting PRT versus bolometric luminosity due to accretion onto black hole. We estimate the PRTs of AGN black holes, with the well-determined masses and bolometric luminosities, collected from the literature by Woo Jong-Hak and Urry (Astrophys. J. 579, 530, 2002) on which this paper is partially based. The simulations for the black holes of masses M _BH ≃(1.1⋅10⁶ ÷4.2⋅10⁹) M _⊙ give the values of PRTs varying in the range of about T _BH ≃(4.3⋅10⁵ ÷5.6⋅10¹¹) yr. The derived PRTs for the 60 AGN black holes are longer than the age of the universe (∼13.7 Gyr) favored today. At present, some of remaining 174 BHs may radiate neutrinos. However, these results would be underestimated if the reservoir of gas for accretion in the galaxy center is quite modest, and no obvious way to feed the BHs with substantial accretion.     

Comparison of the Characteristics of Magnetic Clouds and Magnetic Cloud-Like Structures for the Events of 1995 – 2003

Using nine years of solar wind plasma and magnetic field data from the Wind mission, we investigated the characteristics of both magnetic clouds (MCs) and magnetic cloud-like structures (MCLs) during 1995 – 2003. A MCL structure is an event that is identified by an automatic scheme (Lepping, Wu, and Berdichevsky, Ann. Geophys. 23, 2687, 2005) with the same criteria as for a MC, but it is not usually identifiable as a flux rope by using the MC (Burlaga et al., J. Geophys. Res. 86, 6673, 1981) fitting model developed by Lepping, Jones, and Burlaga (Geophys. Res. Lett. 95(11), 957, 1990). The average occurrence rate is 9.5 for MCs and 13.6 for MCLs per year for the overall period of interest, and there were 82 MCs and 122 MCLs identified during this period. The characteristics of MCs and MCL structures are as follows: (1) The average duration, Δt, of MCs is 21.1 h, which is 40% longer than that for MCLs (Δt=15 h); (2) the average (minimum B _z found in MC/MCL measured in geocentric solar ecliptic coordinates) is −10.2 nT for MCs and −6 nT for MCLs; (3) the average Dst_min (minimum Dst caused by MCs/MCLs) is −82 nT for MCs and −37 nT for MCLs; (4) the average solar wind velocity is 453 km s⁻¹ for MCs and 413 km s⁻¹ for MCLs; (5) the average thermal speed is 24.6 km s⁻¹ for MCs and 27.7 km s⁻¹ for MCLs; (6) the average magnetic field intensity is 12.7 nT for MCs and 9.8 nT for MCLs; (7) the average solar wind density is 9.4 cm⁻³ for MCs and 6.3 cm⁻³ for MCLs; and (8) a MC is one of the most important interplanetary structures capable of causing severe geomagnetic storms. The longer duration, more intense magnetic field and higher solar wind speed of MCs, compared to those properties of the MCLs, are very likely the major reasons for MCs generally causing more severe geomagnetic storms than MCLs. But the fact that a MC is an important interplanetary structure with respect to geomagnetic storms is not new (e.g., Zhang and Burlaga, J. Geophys. Res. 93, 2511, 1988; Bothmer, ESA SP-535, 419, 2003).     

Chemical Evolution of Gas-Rich Galaxy Mergers

We investigate numerically the chemodynamical evolution of major disc–disc galaxy mergers in order to explore the origin of the mass-dependent chemical, photometric and spectroscopic properties observed in elliptical galaxies. We investigate especially the dependence of the fundamental properties on merger progenitor disc mass (M _d). Three main results are obtained in this study:– More massive (luminous) ellipticals formed by galaxy mergers between more massive spirals have higher metallicity (Z) and thus show redder colours; the typical metallicity ranges from ∼ 1.0 solar abundance (Z∼ 0.02) for ellipticals formed by mergers with M _d = 10¹⁰ M _⊙to ∼ 2.0 solar (Z∼ 0.04) for those with M _d= 10¹² M _⊙.– Both the Mg₂ line index in the central part of ellipticals (R ≤ 0.1 R _e) and the radial gradient of Mg₂ (δ Mg₂ / δ log R) are more likely to be larger for massive ellipticals. δ Mg₂ / δ log R correlates reasonably well with the central Mg₂ in ellipticals. For most of the present merger models, ellipticals show a positive radial gradient of the H_β line index. – Both M/L _B and M/L _K (where M, L _B, and L _K are the total stellar mass of galaxy mergers, the B-band and the K-band luminosities, respectively) depend on galactic mass in such a way that more massive ellipticals have larger M/L _B and smaller M/L _K. This revised version was published online in July 2006 with corrections to the Cover Date.     

Interstellar electron density

We impose the requirement that the spatial distribution of pulsars deduced from their dispersion measures using a model of the galactic electron density (n _e ) should be consistent with cylindrical symmetry around the galactic centre (assumed to be 10 kpc from the Sun). Using a carefully selected subsample of the pulsars detected by the II Molonglo Survey (II MS), we test a number of simple models and conclude that (i) the effective mean 〈n_e〉) for the whole galaxy is 0.037_-0.012 ^+0.020 cm^-3, (ii) the scale height of electrons is greater than 300 pc and probably about 1 kpc or more, and (iii) there is little evidence for variation of n_e with galactic radius R_GC for R_Gc ≳ 5 kpc. Further, we make a detailed analysis of the contribution to n_e from H II regions. Combining the results of a number of relatively independent calculations, we propose a model for the galactic electron density of the formn _e (z) = 0.030 + 0.020 exp (- |z|/70) cm^-3 where z(pc) is the height above the galactic plane and the second term describes the contribution from H II regions. We believe the statistical uncertainties in the parameters of this model are quite small.     

Magnetic fields and quasi-periodic oscillations of black hole radiation

Various relations are found between the key parameters of black holes and active galactic nuclei. Some have a statistical property, others follow from the theoretical consideration of the evolution of these objects. In this paper we use a recently discovered empirical relation between the characteristic frequency of quasi-periodic oscillations of radiation ν _br of black holes, their masses and matter accretion rates to determine the magnetic field strength B _H at the black hole event horizon. Since the characteristic frequency can be determined from observations, the use of a new relation for the estimations of magnetic field B _H can yield more definite results, since we are decreasing the number of the unknown or poorly-determined parameters of objects (it especially concerns the accretion rate Ṁ). The typical values which we have found are B _H ≃ 10⁸G for the stellar mass black holes, and B _H ≃ 10⁴G for the supermassive black holes. Besides, we demonstrate that if the linear polarization of an object is caused by the radiation of a magnetized accretion disk, then the degree of observable polarization is p ∼ ν _br ^−1/2.     

Ion-Acoustic Wave Generation by Two Kinetic Alfvén Waves and Particle Heating

In this paper we have investigated the beat wave excitation of an ion-acoustic wave at the difference frequency of two kinetic (or shear) Alfvén waves propagating in a magnetized plasma with β<1 (β=8π n _e0 T _e/B ₀ ² , where n _e0 is the unperturbed electron number density, T _e is the electron temperature, and B ₀ is the external magnetic field). On account of the interaction between two kinetic Alfvén waves of frequencies ω ₁ and ω ₂, the ponderomotive force at the difference frequency ω ₁−ω ₂ leads to the generation of an ion-acoustic wave. Also because of the filamentation of the Alfvén waves, magnetic-field-aligned density dips are observed. In this paper we propose that the ion-acoustic wave generated by this mechanism may be one of the possible mechanisms for the heating and acceleration of solar wind particles.     

Nonlinear Evolution of Kinetic Alfvén Waves and Filament Formation

The transfer of wave energy to plasma energy is a very crucial issue in coronal holes and helmet streamer regions. Mixed mode Alfvén waves, also known as kinetic Alfvén wave (KAW) can play an important role in the energization of the plasma particles because of their potential ability to heat and accelerate the plasma particles via Landau damping. This paper presents an investigation of the growth of a Gaussian perturbation on a non-uniform kinetic Alfvén wave having Gaussian wave front. The effect of the nonlinear coupling between the main KAW and the perturbation has been studied. The dynamical equations for the field of the main KAW and the perturbation have been established and their semi-analytical solution has been obtained in the low (β≪ m_e/m_i≪ 1) and the high (β≫ m_e/m_i≪ 1) β cases. The critical field of the main KAW and the perturbation has been evaluated. Nonlinear evolution of the main KAW and the perturbation into the filamentary structures and its dependence on various parameters of the solar wind and the solar corona have been investigated in detail. These filamentary structures can act as a source for the particle acceleration by wave particle interaction because the KAWs are mixed modes and Landau damping is possible. Especially, in the solar corona, the low β and the high β cases could correspond to the coronal holes and the helmet streamer. The presence of the primary and the secondary filaments of the perturbation may change the spectrum of the Alfvénic turbulence in the solar wind.     

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.     

Monte Carlo Simulation of Solar Active-Region Energy

A Monte Carlo approach to solving a stochastic-jump transition model for active-region energy (Wheatland and Glukhov: Astrophys. J. 494, 858, 1998; Wheatland: Astrophys. J. 679, 1621, 2008) is described. The new method numerically solves the stochastic differential equation describing the model, rather than the equivalent master equation. This has the advantages of allowing more efficient numerical solution, the modeling of time-dependent situations, and investigation of details of event statistics. The Monte Carlo approach is illustrated by application to a Gaussian test case and to the class of flare-like models presented in Wheatland (Astrophys. J. 679, 1621, 2008), which are steady-state models with constant rates of energy supply, and power-law distributed jump transition rates. These models have two free parameters: an index (δ), which defines the dependence of the jump transition rates on active-region energy, and a nondimensional ratio ( ) of total flaring rate to rate of energy supply. For the nondimensional mean energy of the active-region satisfies , resulting in a power-law distribution of flare events over many decades of energy. The Monte Carlo method is used to explore the behavior of the waiting-time distributions for the flare-like models. The models with δ≠0 are found to have waiting times that depart significantly from simple Poisson behavior when . The original model from Wheatland and Glukhov (Astrophys. J. 494, 858, 1998), with δ=0 (i.e., no dependence of transition rates on active-region energy), is identified as being most consistent with observed flare statistics.     

Molecular systems in a strong magnetic field

Brief overview of one-two electron molecular systems made out of protons and/or α-particles in a strong magnetic field B≤4.414×10¹³ G is presented. A particular emphasis is given to the one-electron exotic ions H₃⁺⁺(pppe), He₂³⁺(α α e) and to two-electron ionsH₃⁺(pppee), He₂⁺⁺(α α ee). Quantitative studies in a strong magnetic field are very complicated technically. Novel approach to the few-electron Coulomb systems in magnetic field, which provides accurate results, based on variational calculus with physically relevant trial functions is briefly described.      

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.