The Efficiency of the Magnetic Acceleration in Relativistic Jets

Using steady, axisymmetric, ideal magnetohydrodynamics (MHD) we analyze relativistic outflows by means of examining the momentum equation along the flow and in the transfield direction. We argue that the asymptotic Lorentz factor is γ_∞ ～ μ ? σ _M , and the asymptotic value of the Poynting-to-matter energy flux ratio—the so-called σ function—is given by σ_∞/(1 + σ_∞) ～ σ _M /μ, where σ _M is the Michel's magnetization parameter and μc ² the total energy-to-mass flux ratio. We discuss how these values depend on the conditions near the origin of the flow. By employing self-similar solutions we verify the above result, and show that a Poynting-dominated flow near the source reaches equipartition between Poynting and matter energy fluxes, or even becomes matter-dominated, depending on the value of σ _M /μ.     

The plasma radiation of flare kernels

We survey the mathematics of non-linear Hamiltonian oscillations with emphasis being laid on the more recently discovered Kolmogorov instability. In the context of radial adiabatic oscillations of stars this formalism predicts a Kolmogorov instability even at low oscillation energies, provided that sufficiently high linear asymptotic modes have been excited. Numerical analysis confirms the occurrence of this instability. It is found to show up already among the lowest order modes, although high surface amplitudes are then required (¦δr¦/R ～ 0.5 for an unstable fundamental mode - first harmonic coupling). On the basis of numerical evidence we conjecture that in the Kolmogorov unstable regime the enhanced coupling due to internal resonance effects leads to an equipartition of energy over all interacting degrees of freedom. We also indicate that the power spectrum of such oscillations is expected to display two components: A very broad band of overlapping pseudo-linear frequency peaks spread out over the asymptotic range, and a strictly non-linear l/f-noise type component close to the frequency origin. It is finally argued that the Kolmogorov instability is likely to occur among non-linearly coupled non-radial stellar modes at a surface amplitude much lower than in the radial case. This lends support to the view that this instability might be operative among the solar oscillations.     

The effect of large Larmor radius on nonlinear Alfvén waves

The effect of large Larmor radius on the nonlinear behaviour of Alfvén waves propagating parallel to a uniform magnetic field in a compressible fluid is investigated with the aid of LLR-MHD equations. It is shown that asymptotic evolution of these waves is governed by the modified nonlinear Schrödinger equation. The dispersion is provided by the large Larmor radius effect in the magnetic field equation. It is suggested that these calculations can have a bearing on the investigation of the structure of MHD waves in both laboratory and space plasmas, e.g., imploding pinches, laser-blow-off plasma experiment, recent barium releases in the magnetosphere, plasma flow near small planetary bodies such as comets and plasma dynamic near collisionless shock fronts.     

Asymptotic theory of the transfer of polarized radiation with resonance scattering in the doppler core of the line

In the first of the series of papers by Ivanov et al. it was shown that the model problem of the transfer of polarized radiation as a result of resonance scattering from two-level atoms in a homogeneous plane atmosphere in the absence of LTE comes down, in the approximation of complete frequency redistribution, to the solution of an integral matrix equation of the Wiener-Hopf type for a (2 × 2) matrix source function S(τ). In the second paper in this series, devoted to the vector Milne problem, complete asymptotic expansions of the matrix I(z) [which is essentially a Laplace transform of the matrix S(τ)] for the case of a Doppler profile of the coefficient of absorption, and the coefficients of asymptotic expansions of S(τ) (τ » 1) are expressed in terms of coefficients of the expansions of I(z). We show that asymptotic expansions of S(τ) can be found directly from an integral matrix equation of the Wiener-Hopf type for S(τ). We give new recursive equations for the coefficients of these expansions, as well as a new derivation of asymptotic expansions of the matrix I, including its second column, which was considered only briefly by Ivanov et al.     

An asymptotic representation of unstable gravity modes in stars

An asymptotic representation is developed for high order unstable gravity modes in a star which are associated with a convective zone enclosed between two radiative layers. In the domain which contains both turning points of the differential equation, the solutions are represented by a single asymptotic expansion in terms of Weber functions.     

Phase transition in Schwarzschild-de Sitter spacetime

Using a static massive spherically symmetric scalar field coupled to gravity in the Schwarzschild-de Sitter (SdS) background, first we consider some asymptotic solutions near horizon and their local equations of state (E.O.S.) on them. We show that near cosmological and event horizons our scalar field behaves as a dust. At the next step near two pure de Sitter or Schwarzschild horizons we obtain a coupling dependent pressure to energy density ratio. In the case of a minimally coupling this ratio is ?1 which springs to the mind thermodynamical behavior of dark energy. If having a negative pressure behavior near these horizons we concluded that the coupling constant must be ξ<¼. Therefore we derive a new constraint on the value of our coupling ξ. These two different behaviors of unique matter in the distinct regions of spacetime at present era can be interpreted as a phase transition from dark matter to dark energy in the cosmic scales and construct a unified scenario.     

Magneto-convection in sunspot penumbrae

Finite amplitude convection in the presence of a horizontal magnetic field has been investigated in a region where thermal diffusivity (κ) is less than magnetic diffusivity (η) and whenκ/η > 1,Q ≤Q _c, where $$Q_c = \frac{{(1 + \sigma _1 )(\pi ^2 + q_c^2 )^2 }}{{q_c^2 (\sigma _2 - \sigma _1 )}}$$ ,Q is the Chandrasekhar number,σ ₁ the Prandtl number,σ ₂ the magnetic Prandtl number, andq _c the critical wave number at the onset of stationary convection. We have derived a nonlinear time-dependent Landau—Ginzburg equation near the onset of supercritical stationary convection and a nonlinear, second-order equation at the Takens—Bogdanov bifurcation. We have obtained steady-state solutions of these equations, which describe the nonlinear behaviour near the onset of stationary convection.     

Binary asteroid population. 2. Anisotropic distribution of orbit poles of small,inner main-belt binaries

Our photometric observations of 18 main-belt binary systems in more than one apparition revealed a strikingly high number of 15 having positively re-observed mutual events in the return apparitions. Our simulations of the survey showed that it cannot be due to an observational selection effect and that the data strongly suggest that poles of mutual orbits between components of binary asteroids in the primary size range 3–8 km are not distributed randomly: The null hypothesis of an isotropic distribution of the orbit poles is rejected at a confidence level greater than 99.99%. Binary orbit poles concentrate at high ecliptic latitudes, within 30° of the poles of the ecliptic. We propose that the binary orbit poles oriented preferentially up/down-right are due to either of the two processes: (i) the YORP tilt of spin axes of their parent bodies toward the asymptotic states near obliquities 0° and 180° (pre-formation mechanism) or (ii) the YORP tilt of spin axes of the primary components of already formed binary systems toward the asymptotic states near obliquities 0° and 180° (post-formation mechanism). The alternative process of elimination of binaries with poles closer to the ecliptic by dynamical instability, such as the Kozai effect due to gravitational perturbations from the Sun, does not explain the observed orbit pole concentration. This is because for close binary asteroid systems, the gravitational effects of primary’s irregular shape dominate the solar-tide effect.     

Wave disturbances near the temperature jump in the transition region of the solar atmosphere

We theoretically analyzed the properties of surface waves near the temperature jump in the solar atmosphere whose dispersion relation is identical in form to the equation for waves on deep water. We found an exact solution to the model equation for the vertical velocity of the medium in such a wave. Based on the derived space-time dependence of the vertical velocity of the medium, we quantitatively explained one of the events recorded in the SOI/MDI experiment onboard the SOHO spacecraft that accompanied coronal mass ejection.     

Convection in a rapidly rotating system: the smallinclination limit and its planetary applications

An asymptotic method based on a continuous superposition of waves is used to studythe linear stability of convection in a rapidly rotating system. The method gives a uniformrepresentation of the solutions which allows us to impose the boundary conditions and then tominimize the Rayleigh number. This study was done for Prandtl numbers between 0.01 and 100.In the spherical case, for a self-gravitating, internally heated fluid in the small inclination limit,six branches are unveiled. In these branches, infinitesimal amplitude convection takes placepreferentially near the surface of a cylinder coaxial with the axis of rotation in a zone ofthickness ∝ T^−1⧸12, T being the Taylor number. The Rayleigh number ofthree of these flows differs at the most by sixty percent; however, in some intervals of the Prandtlnumber the difference is less than ten percent. Since these flows are located at different radialdistances, this method predicts mixed-modes convection in separate zones at slightlysupercritical values of the Rayleigh number for all Prandtl numbers. A solution exhibitingconvection in separate zones at low supercritical Rayleigh numbers is proposed for the first time.Applications to atmospheres and dynamos of the planets and the starts are discussed.     

Comparison of the classical and the global solutions of the Ideal Resonance Problem

The Ideal Resonance Problem is defined by the Hamiltonian $$F = B(y) + 2\varepsilon A(y) \sin ^2 x,\varepsilon \ll 1.$$ The classical solution of the Problem, expanded in powers of ε, carries the derivativeB′ as a divisor and is, therefore, singular at the zero ofB′, associated with resonance. With α denoting theresonance parameter, defined by $$\alpha \equiv - B'/|4AB''|^{1/2} \mu ,\mu = \varepsilon ^{1/2} ,$$ it is shown here that the classical solution is valid only for $$\alpha ^2 \geqslant 0(1/\mu ).$$ In contrast, the global solution (Garfinkelet al., 1971), expanded in powers ofμ=ε^1/2, removes the classical singularity atB′=0, and is valid for all α. It is also shown here that the classical solution is an asymptotic approximation, for largeα ², of the global solution expanded in powers ofα ^?2. This result leads to simplified expressions for resonancewidth and resonantamplification. The two solutions are compared with regard to their general behavior and their accuracy. It is noted that the global solution represents a perturbed simple pendulum, while the classical solution is the limiting case of a pendulum in a state offast circulation.     

General polytropic magnetofluid under self-gravity: Voids and shocks

We study the self-similar magnetohydrodynamics (MHD) of a quasi-spherical expanding void (viz. cavity or bubble) surrounding the centre of a self-gravitating gas sphere with a general polytropic equation of state. We show various analytic asymptotic solutions near the void boundary in different parameter regimes and obtain the corresponding void solutions by extensive numerical explorations. We find novel void solutions of zero density on the void boundary. These new void solutions exist only in a general polytropic gas and feature shell-type density profiles. These void solutions, if not encountering the magnetosonic critical curve (MCC), generally approach the asymptotic expansion solution far from the central void with a velocity proportional to radial distance. We identify and examine free-expansion solutions, Einstein–de Sitter expansion solutions, and thermal-expansion solutions in three different parameter regimes. Under certain conditions, void solutions may cross the MCC either smoothly or by MHD shocks, and then merge into asymptotic solutions with finite velocity and density far from the centre. Our general polytropic MHD void solutions provide physical insight for void evolution, and may have astrophysical applications such as massive star collapses and explosions, shell-type supernova remnants and hot bubbles in the interstellar and intergalactic media, and planetary nebulae.     

String black holes as particle accelerators to arbitrarily high energy

We show that an extremal Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole may act as a particle accelerator with arbitrarily high energy when two uncharged particles falling freely from rest to infinity on the near horizon. We show that the center of mass energy of collision is independent of the extreme fine tuning of the angular momentum of the colliding particles. We further show that the center of mass energy of collisions of particles at the ISCO (r _ISCO ) or at the photon orbit (r _ph ) or at the marginally bound circular orbit (r _mb ) i.e. at r≡r _ISCO =r _ph =r _mb =2M could be arbitrarily large for the aforementioned space-time, which is quite different from the Schwarzschild and the Reissner-Nordstrøm space-time. For non-extremal GMGHS space-time the CM energy is finite and depends upon the asymptotic value of the dilation field (? ₀).     

Millstone Hill Thomson scatter results for 1966 and 1967

Thomson (incoherent) scatter radar measurements of F-region electron densities and temperatures were made approximately twice per month throughout 1966 and 1967 at Millstone Hill for periods of 24 hr. Owing to the increase in sunspot activity the results display a rich variety of different types of behaviour. Geomagnetically quiet days tended to follow patterns observed near sunspot minimum. Thus in winter there is typically a marked diurnal variation in electron density with a peak near noon and often a smaller secondary maximum between 02 and 04 EST. In summer there is less day-to-night variation and the peak density is encountered near ground sunset. Usually h_maxF2 is higher in summer than winter and the layer thickness is larger also.Some magnetically disturbed days follow a distinct pattern in which N_max and h_max are normal during the first day of the storm until afternoon when they both increase to very high values. There is then a corresponding decrease in electron temperature. During the night the electron temperature often reaches abnormally high values, providing evidence of nocturnal heating. On the following day N_max and h_max are abnormally low.During 1967 instances in which the trough of low electron density moved south to occupy a position over Millstone became frequent. The electron temperature rose to particularly high values on these occasions. These morphological features are discussed in terms of current theoretical ideas. The results are also employed to derive seasonal variations of electron temperature and protonospheric heat flux. It is shown that since 1964 the protonospheric heat flux has been larger in winter than summer and displays a clear sunspot cycle variation.     

Influence of cosmological expansion on the threshold effects in the annihilation reaction of hard photons with CMB photons

The redshift (z) dependence of the dispersion relations for free particles is analyzed by taking into account the Lorentz invariance violation. A nonlinear algebraic equation is derived for the momenta of the particles involved in the annihilation reaction of a hard photon from a γ-ray source with a soft cosmic microwave background (CMB) photon near the threshold of this reaction. The solutions of this threshold equation are constructed and analyzed as a function of the redshift. We show that the threshold of the reaction under consideration tends to decrease with increasing z; the energy spectra of γ-ray sources at energies of ～10 TeV must be cut off in accordance with the calculated z dependence. We also calculate the time delay of the light signals from γ-ray sources that corresponds to the Lorentz invariance violation for photons. We discuss the possibility of improving the standard constraints on the Lorentz invariance violation parameters for fields of various physical natures.     

Convection driven by tidal and radiogenic heating in medium size icy satellites

Convection is one of the most important processes responsible for the formation of the surface features on many planetary bodies. Observations of some icy satellites indicate that the satellites’ surfaces are modified due to the internally driven tectonic activity. The tidal heating could be an important source of energy responsible for such internal activity. This suggestion is supported by the correlation of the tidal parameter ψ and tectonic features. Consequently, the tidal and the radiogenic heat sources seem to be of primary importance for the medium size icy satellites. Our research deals with convection in a non-differentiated body. The convection is a results of both uniform radiogenic heating and non-uniform and non-spherically symmetric tidal heating. To investigate the problem a 3D model of convection is developed based on the Navier-Stokes equation, the equation of thermal conductivity, the equation of continuity, and the equation of state. The 3D formulae for the tidal heat generation based on the results of Peale and Cassen [1978. Icarus 36, 245-269] and others are used in the model. To measure the relative importance of radiogenic heating versus tidal heating a dimensionless number C_t is introduced. The systematic investigation of a steady-state convection is performed for different values of the Rayleigh number and for the full range of C_t. The results indicate that for low and moderate value of the Rayleigh number, convection pattern driven by the tidal heating and by the radioactivity in the medium size icy satellites consists of one cell or of two cells. For C_t>0 the critical value of Rayleigh number Ra_cr=0. The one-cell pattern is specific for low Rayleigh numbers but it could be observed for the full range of number C_t. It means that the pattern of convection does not fully follow the pattern of heating. This rather unexpected result could be of great importance for the final stage of convection. All patterns of tidally driven convection are oriented with respect to the direction to the planet. For two-cell patterns the regions of downward motion are situated in the centers of the near and far sides of the satellite, respectively.     

A numerical model of the Martian polar cap winds

An investigation of the Martian polar cap winds and their response to a variety of factors is carried out by a series of numerical experiments based on a zonally symmetric primitive equation model. These factors are the seasonal thermal forcing, mass exchange between polar caps and atmosphere, large-scale topography, and polar cap size. The thermal forcing sets up a circulation whose surface winds adjust to achieve angular momentum balance, with low-latitude easterlies and high-latitude westerlies. The maximum westerlies occur roughly where the horizontal temperature gradients are largest. This pattern changes when cap and atmosphere exchange mass. Corriolis forces acting on the net outflow or inflow produce easterlies at the surface during spring (outflow) and westerlies during winter (inflow). Topography appears to have a small effect, but cap size does play a role, the circulation intensity increasing with cap size. Peak surface winds occur when outflow or inflow is a maximum and are 20 m sec^?1 during spring and 30 m sec^?1 during winter for the northern hemisphere. The model results show that surface winds near the edge of a retreating polar cap are substantially enhanced, a result which is consistent with the Viking observations of local dust storm activity near the edge of the south polar cap during spring. The results also indicate that the surficial wind indicators near the south pole are formed during spring and those near the north pole during winter. The implication is that the high-latitude dune fields in the northern hemisphere are formed at a time when the terrain is being covered with frost. It is therefore suggested that the saltating particles are “snowflakes” which have formed by the mechanism proposed by Pollack etal. The model results for the winter simulation, which have formed by the mechanism transport by large-scale eddies, compare favorably with general circulation model (GCM) calculations. This suggests that the eddy transports may be less important than those associated with the net mass flow, and that 2-D climate modeling may be more succesful for Mars than Earth.