Effects of variableC min on gamma-ray burstC max/C min distributions

Claims continue to be made that detector selection effects can explain the deviation of the gamma-ray burst brightness distributions from the -3/2 power law expected for homogeneous burst sources. However, these effects are insufficient to explain the BATSE observations. The BATSE sensitivity threshold does vary with time, independent of the burst brightness; however, a homogeneous distribution of standard candle sources would still produce a -3/2 power law. The variation in the threshold does affect inhomogeneous source models. As an example, the effect of a time-varyingC _min on theC _max/C _min distribution of an extended Galactic halo model is shown here. To fit the BATSEC _max/C _min distribution including a varyingC _min requires a larger observing distance (relative to the scale-height of the halo) than for a constantC _min; however, the observations can still be fit using the halo models.     

Threshold effects onV/V max for gamma-ray bursts

The interpretation of the observed-ray burstV/V _max statistic in terms of spatial distributions is model-dependent. Detection of-ray bursts requires the counting rate in one or more detectors to exceed a thresholdC _lim determined from a time-dependent background rateB(t). The sampling depth of the burst detector is thus time-dependent, and, if burst sources are non-uniform in space, the observedV/V _max distribution will be affected byB(t). We demonstrate this effect with a simple geometric distribution of standard candles and argue thatV/V _max statistic without information on threshold variations is insufficient for rigorous data analysis. Peak count rates and threshold values must be given separately for all events in order to facilitate a meaningful comparison of observations with theoretical distribution models.     

Limits for the Firehose Instability in Space Plasmas

Electromagnetic instabilities in high-β plasmas, where β is the ratio of the kinetic plasma energy to the magnetic energy, have a broad range of astrophysical applications. The presence of temperature anisotropies T _∥ /T _⊥ >1 (where ∥ and ⊥ denote directions relative to the background magnetic field) in solar flares and the solar wind is sustained by the observations and robust acceleration mechanisms that heat plasma particles in the parallel direction. The surplus of parallel kinetic energy can excite either the Weibel-like instability (WI) of the ordinary mode perpendicular to the magnetic field or the firehose instability (FHI) of the circularly polarized waves at parallel propagation. The interplay of these two instabilities is examined. The growth rates and the thresholds provided by the kinetic Vlasov – Maxwell theory are compared. The WI is the fastest growing one with a growth rate that is several orders of magnitude larger than that of the FHI. These instabilities are however inhibited by the ambient magnetic field by introducing a temperature anisotropy threshold. The WI admits a larger anisotropy threshold, so that, under this threshold, the FHI remains the principal mechanism of relaxation. The criteria provided here by describing the interplay of the WI and FHI are relevant for the existence of these two instabilities in any space plasma system characterized by an excess of parallel kinetic energy.     

Coronal Flux Rope Catastrophe in Octapole Magnetic Fields

As demonstrated by many previous studies, a system consisting of an isolated coronal flux rope and a surrounding background magnetic field exhibits a catastrophic behavior. In particular, if the magnetic field of the system is force-free and axisymmetric in spherical geometry, the magnetic energy at the catastrophic point, referred to as the catastrophic energy threshold, is found to be larger than the corresponding partly or fully open field energy. This paper takes an octapole field as the background and introduces a flux rope within the central arcade of the octapole field. A relaxation method based on time-dependent ideal magnetohydrodynamic (MHD) simulations is used to find axisymmetric force-free field solutions in spherical geometry associated with the flux rope system. With respect to an increase of either the annular flux Φ_p or the axial flux Φ_ϕ of the rope, the system exhibits a catastrophic behavior as expected, and the catastrophic energy threshold is larger than that of the corresponding partly open field, in which the central arcade is opened up, but the remainder remains closed. For a given octapole field, the energy threshold depends on either Φ_p or Φ_ϕ at the catastrophic point, and it increases with increasing Φ_p or decreasing Φ_ϕ. On the other hand, the extent to which the central bipolar component of the octapole field is open also affects the energy threshold. These results differ from those for the bipolar background field case, in which the catastrophic energy threshold is almost independent of the magnetic properties of the flux rope at the catastrophic points and the extent to which the background field is open. The reason for such a difference is briefly discussed.     

Numerical simulation of the electron capture process in a magnetar interior

In a superhigh magnetic field, direct Urca reactions can proceed for an arbitrary proton concentration. Since only the electrons with high energy E (E>Q, Q is the threshold energy of inverse β-decay) at large Landau levels can be captured, we introduce the Landau level effect coefficient q and the effective electron capture rate Γ _eff . By using Γ _eff , the values of L _X and L _ν are calculated, where L _X and L _ν are the average neutrino luminosity of AXPs and the average X-ray luminosity of AXPs L _X , respectively. The complete process of electron capture inside a magnetar is simulated numerically.     

Excitation of whistler waves driven by an electron temperature anisotropy

A 3-D particle simulation of excitation of whistler waves driven by an electron temperature anisotropy (T > T ) is presented. Results show that whistler waves can have appreciable growth driven by the anisotropy. The maximum intensity of the excited whistler waves increases as a quadratic function of the anisotropy. Due to the presence of a threshold, one needs a relatively large electron temperature anisotropy above threshold to generate large-amplitude whistler waves. The average amplitude of turbulence in the context of whistler waves is up to as large as about 1% of the ambient magnetic field when T /T . The total energy density of the whistler turbulence is adequate for production of relativistic electrons in solar flares through stochastic acceleration.     

On the threshold effect of proton acceleraton in solar flares

Based on the reconnection theory of a flare and on recent observational and statistical findings, the problem of the initial acceleration of solar cosmic rays (SCR) is discussed. Simple estimates of the electric fields required to start the electron acceleration are obtained and the problem of proton ionization losses for overcoming the Coulomb barrier is considered. We take into account also the possible differences between proton and electron spectra from the very beginning of the acceleration process. Special attention is paid to the distribution functions of solar flare events in various parameters (peak fluxes and/or energy fluences in X-ray and radio wave bursts, in proton and electron emissions, etc.). It is shown that the distribution functions allow the interpretation of some scale and time flare parameters in terms of expected threshold effects. However, these functions are still insufficient to evaluate the relative share of different emissions in the global energy budget of a flare. In this context, a more promising approach is to derive the direct ratio between the number of accelerated protons,N _p, and total flare energy,W _f, within the frame of a certain acceleration model. It is argued that an absolute threshold for proton production (in Hudson's formulation) does not exist. Meanwhile, the flux and threshold energy of accelerated protons overcoming the Coulomb loss maximum, in fact, may depend heavily on the global output of flare energy.     

Separation of meteor streams from the sporadic background

A cluster analysis procedure has been used to estimate the fraction of the sporadic interlopers (sporadis bias) identified as stream members among the observed meteor orbits. Using the artificial meteor orbits with the same distribution as the observed one, the sporadic bias is estimated for the given threshold value of the orbital similarityD _c. It has been shown that in case of the radio meteor catalogues theD _c values given by the formula proposed in Southworth and Hawkins (1963)and in Lindblad (1971) correspond to the sporadic bias of 8–21%. For the five radio meteor catalogues the values ofD _c corresponding to the fixed bias equal to 10% and 15% are given.     

Nonpotential waves in the auroral electrojet

An ionospheric plasma instability in the auroral electrojet region believed to be responsible for electromagnetic waves with angular frequency smaller thanv _i is discussed. The threshold current velocityU _t and oscillation growth rate are found for the realistic physical situation when a nonuniform plasma density and an ionization function are considered. It is found that the gradient of plasma density n may be neglected in the expressions forU _t and and that the spectral density of fluctuations in the density of the plasma agrees well with the experimental data.     

Searching for curvature pion radiation from protons in strongly magnetized pulsars

By using rather conservative estimates based on the simplest polar cap model, we search the ATNF Pulsar Catalogue for strongly magnetized stars that could accelerate relativistic protons up to the curvature pion production threshold. The best candidate turns out to be the 16 ms pulsar J0537-6910, but the corresponding characteristic parameter χ=a/m _p is yet too small to give origin to observable signals. We show that, for pulsars with period P≈1 ms, a surface polar magnetic field B≈10¹² G is required in order to induce detectable curvature pion radiation from accelerated protons in the magnetosphere. Some other emission processes are also considered.     

Electromagnetic lower hybrid instability driven by solar wind heat flux

Under a fully electromagnetic treatment, the threshold for excitation of the lower hybrid instability driven by solar wind electron heat flux is found to be much higher than that predicted by electrostatic approximation. For average solar wind conditions at 1 AU, the fully electromagnetic lower hybrid instability is excited when the core electron drift speed is about 8V _A, whereV _A is the Alfvén speed. The region between the Sun and 1 AU is expected to be more favourable than 1 AU for this instability.     

Solar Flare Phenomena as Phase Transition Caused by Frustration of Current Percolation

We present analysis of flare process as "phase transition" phenomena caused by frustration of current percolation in turbulent current sheet. We show that numerous plasma instabilities in the sheet will form random resistors network with "bad resistors"-turbulent domains and "good resistors"-normal plasma domains. We show that current percolation in random inhomogeneous turbulent current sheet like to another percolated systems is able to produce phase transition with drastic change of global properties of system as whole (conductivity, heat-conductivity, elasticity,) on the threshold value of critical density of "bad" elements (p= p _c ). Another property of solar flares, what may be understood on the base of percolation approach is observed universal power dependence of frequency of flares and microflares (elementary events-spikes) on their amplitude: N _W ∝ W ^−k . It may be explained as natural sequence of universal power dependence of clusters' masses in percolated systems on their sizes. The slope of resulted spectra is determined by the fractal dimension of clusters and depends on feedback between current propagation and turbulence generation. We show that percolation approach allow to explain phenomena of preflare bursts-precursors observed in radio and hard X-ray. It may be understood as results of pre-catastrophic lose of elasticity of system to small disturbance on the percolation threshold, with formation of short life nuclear of "new phase". This revised version was published online in July 2006 with corrections to the Cover Date.     

The Landau level-superfluid modified factor and the overal soft X/<Emphasis Type="Italic">γ</Emphasis>-ray efficiency coefficient of a magnetar

As soon as the energies of electrons near the Fermi surface exceed Q, the threshold energy of inverse β-decay, electron capture (EC) dominates inside a neutron star. The high-energy neutrons released by EC will destroy anisotropic ³ P ₂ neutron Cooper pairs in the degenerate superfluid. By colliding with the neutrons produced in the process n+(n↑n↓)→n+n+n, the kinetic energies of the neutrons released by EC will be transformed into thermal energy. A portion of this thermal energy will be transported from the star interior to the star surface by conduction, then converted to a thermal spectrum of soft X-rays and γ-rays. By introducing two important parameters: the Landau level-superfluid modified factor and the overal soft X/γ-ray efficiency coefficient, we compute the theoretical luminosity L _X of a magnetar under our model and plot a diagram of L _X as a function of magnetic field strength B. Numerical calculations based on our model agree well with the observed properties of magnetar candidates.     

Gamma-quanta conversion into positronium atoms in a strong magnetic field

The curvature -quanta emitted in the pulsar magnetospheres tangentially to the curved lines of force of the magnetic field are shown to be later canalized along the magnetic field—if it is strong enough,B0.1B _cr =4×10¹²G—by gradually converting into a mutually bound electron-positron pair, i.e. a positronium atom. This happens before the photon reaches the threshold of free-pair creation. The positronium thus arising is stable against the ionizing action of the electric field near the pulsar unless it reaches a critical value about 4×10⁷ CGSE forB10¹³G. This prevents the screening of the electric field up to the distances from the pulsar, where the magnetic field is already below the value of 0.1B _cr and the free pair creation may become essential. This effect provides, at least within the Arons model, a higher theoretical estimate for the total luminosity of pulsars whose field at the surfaceB _s exceeds 0.1B _cr as compared with the conventional one.     

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.     

Gravitation and inertia; a rearrangement of vacuum in gravity

We address gravitation and inertia in the framework of a general gauge principle (GGP) which accounts for the gravitation gauge group G _R generated by a hidden local internal symmetry implemented on the flat space. Following the method of phenomenological Lagrangians, we connect the group G _R to a non-linear realization of the Lie group of the distortion G _D of the local internal properties of six-dimensional flat space, M ₆, which is assumed as a toy model underlying four-dimensional Minkowski space. We study the geometrical structure of the space of parameters and derive the Maurer–Cartan’s structure equations. We treat distortion fields as Goldstone fields, to which the metric and connection are related, and we infer the group invariants and calculate the conserved currents. The agreement between the proposed gravitational theory and available observational verifications is satisfactory. Unlike the GR, this theory is free of fictitious forces, which prompts us to address separately the inertia from a novel view point. We construct a relativistic field theory of inertia, which treats inertia as a distortion of local internal properties of flat space M ₂ conducted under the distortion inertial fields. We derive the relativistic law of inertia (RLI) and calculate the inertial force acting on the photon in a gravitating system. In spite of the totally different and independent physical sources of gravitation and inertia, the RLI furnishes a justification for the introduction of the Principle of Equivalence. Particular attention is given to the realization of the group G _R by the hidden local internal symmetry of the abelian group U ^loc=U(1) _Y ×diag[SU(2)], implemented on the space M ₆. This group has two generators, the third component T ³ of isospin and the hypercharge Y, implying Q ^d =T ³+Y/2, where Q ^d is the distortion charge operator assigning the number −1 to particles, but +1 to anti-particles. This entails two neutral gauge bosons that coupled to T ³ and Y. We address the rearrangement of the vacuum state in gravity resulting from these ideas. The neutral complex Higgs scalar breaks the vacuum symmetry leaving the gravitation subgroup intact. The resulting massive distortion field component may cause an additional change of properties of the spacetime continuum at huge energies above the threshold value.     

The evolutionary behaviour of population III intermediate mass stars

Assuming the Big-Bang nucleosynthesis was responsible for the formation of helium, the evolution of first-generation intermediate-mass stars of 5, 7, and 9M with no metals have been studied from the threshold of stability through the stage of helium exhaustion in the cores of the stars. Hydrogen Main-Sequence positions are marked at effective temperatures higher than those of normal stars. The evolutionary tracks during the hydrogen burning phase start to be similar to those of normal stars when the CN-cycle reactions, which are controlled by the triple-alpha reactions, become operative for hydrogen depletion. Helium Main Sequence of Population III stars of intermediate mass occurs at the high effective temperature region of the H-R diagram and stars stay as blue stars until the end of the core helium exhaustion phase. The total time elapsed is in the range of 3×10⁷ and 10⁸yr. The stars with the initial masses of 5, 7, and 9M developed a moderately electron degenerate complete hydrogen-exhausted region with masses of 0.77, 1.06, and 1.42M , respectively, in which the most abundant element is carbon.     

Evolutionary status of the primary component of YZ Cassiopeiae

The models of non-rotating and rotating 2.31M _\ stars of Population I composition have been calculated, starting at the threshold of stability. A 2.31M _\ star was chosen to compare the results with the observational parameters of the primary component of the well-known detached binary YZ Cassiopeiae. The effects of rotation on the internal structure during the evolution of the star were studied by constructing sequences of axisymmetric rotating models under the assumption that angular momentum was conserved according to a predetermined angular velocity distribution depending on the structure of the star.The first section of this paper deals with effects of rotation on the evolutionary behaviours of the 2.31M _\ star through the pre-Main-Sequence evolution as well as the zero-age Main Sequence.In the second section of this paper, the evolutionary studies have been extended up to near-hydrogen exhaustion phase in order to obtain a theoretical model corresponding to the given mass and radius of the primary component of YZ Cassiopeiae. The theoretical models were found to be in a good agreement with observational parameters. The computed rotating models of the primary of YZ Cassiopeiae indicates that its evolutionary age is 6.01×10⁸ years; and the central hydrogen content 0.183 — which means that about 75% of its original value was depleted.     

The cosmic ray primary composition between 10 and 10 eV from Extensive Air Showers electromagnetic and TeV muon data

The cosmic ray primary composition in the energy range between 10¹⁵ and 10¹⁶ eV, i.e., around the “knee” of the primary spectrum, has been studied through the combined measurements of the EAS-TOP air shower array (2005 m a.s.l., 10⁵ m² collecting area) and the MACRO underground detector (963 m a.s.l., 3100 m w.e. of minimum rock overburden, 920 m² effective area) at the National Gran Sasso Laboratories. The used observables are the air shower size (N_e) measured by EAS-TOP and the muon number (N_μ) recorded by MACRO. The two detectors are separated on average by 1200 m of rock, and located at a respective zenith angle of about 30°. The energy threshold at the surface for muons reaching the MACRO depth is approximately 1.3 TeV. Such muons are produced in the early stages of the shower development and in a kinematic region quite different from the one relevant for the usual N_μ−N_e studies. The measurement leads to a primary composition becoming heavier at the knee of the primary spectrum, the knee itself resulting from the steepening of the spectrum of a primary light component (p, He) of Δγ=0.7±0.4 at E₀4×10¹⁵ eV. The result confirms the ones reported from the observation of the low energy muons at the surface (typically in the GeV energy range), showing that the conclusions do not depend on the production region kinematics. Thus, the hadronic interaction model used (CORSIKA/QGSJET) provides consistent composition results from data related to secondaries produced in a rapidity region exceeding the central one. Such an evolution of the composition in the knee region supports the “standard” galactic acceleration/propagation models that imply rigidity dependent breaks of the different components, and therefore breaks occurring at lower energies in the spectra of the light nuclei.     

Twenty-Seven-Day Variation of Galactic Cosmic Rays

Neutron monitor data observed at Climax (CL) and Huancayo/Haleakala (HU/HAL) have been used to calculate the amplitude A of the 27-day variation of galactic cosmic rays (CRs). The median primary rigidity of response, R _m, for these detectors encompasses the range 18 ≤R _m≤46 GV and the threshold rigidity R ₀ covers the range 2.97≤R ₀≤12.9 GV. The daily average values of CR counts have been harmonically analyzed for each Bartels solar rotation (SR) during the period 1953 – 2001. The amplitude of the 27-day CR variation is cross-correlated to solar activity as measured by the sunspot number R, the interplanetary magnetic field (IMF) strength B, the z-component B _z of the IMF vector, and the tilt angle ψ of the heliospheric current sheet (HCS). It is anticorrelated to the solar coronal hole area (CHA) index as well as to the solar wind speed V. The wind speed V leads the amplitude by 24 SRs. The amplitude of the 27-day CR variation is better correlated to each of the these parameters during positive solar polarity (A>0) than during negative solar polarity (A<0) periods. The CR modulation differs during A>0 from that during A<0 owing to the contribution of the z-component of the IMF. It differs during A ₁>0 (1971 – 1980) from that during A ₂>0 (1992 – 2001) owing to solar wind speed.