Magnetic instability in a rotating layer at highly eccentric positions of the critical level

This study follows the numerical results presented in Marsenić & Ševčík (2010) that explored the influence of the critical level position on stability of a system. The model was a horizontal fluid layer between z = ±0.5d rotating with an angular velocity Ω = Ω₀ ž about the vertical axis z . The fluid was considered to be inviscid, finitely electrically conducting and incompressible and was permeated by a horizontal magnetic field B ₀ = ℬ︁₀B₀(z) y̌ , where ℬ︁₀ was the magnitude of the field and the function B₀(z) = tanh [γ (z –z₀)]. When γ is large, the field gradient is concentrated near z = z₀, the critical level, the field being almost homogeneous elsewhere. In this way it controls the width of the magnetic shear layer associated with the current sheet. It was found that at conditions when the magnetic field gradient was large enough (γ = O (10)) and the critical level was placed close enough to the (bottom) perfectly conducting boundary (z₀ < –0.388d for γ = 80), magnetically driven convection appeared localized to a close neighbourhood of the critical level – the so called critical layer. Based on the circumstances of its rise and its properties it was identified with the resistive tearing‐mode instability. This paper presents an analytical treatment of the problem assuming γ ≥ 1. The approach consists in separation of the computational domain into an outer region where the diffusionless limit (Elsasser number Λ → ∞) applies and an inner region (the critical layer) of finite conductivity. According to the tearing‐mode theory in classical systems, the solution in the inner region is sought as long‐wavelength with respect to the width of the critical layer. The obtained solution shows features similar to the one obtained numerically and confirmed relevance of the simplifying physical assumptions made in each region. The convection in the critical layer is strictly conditioned by a sharp magnetic shear. If the shear region is removed by further positioning of the critical level towards the perfectly conducting boundary, the localized convection disappears. It is in compliance with the fact that the system is stabilised by a perfectly conducting boundary with respect to the tearing mode. Stability is then checked numerically in the layer bounded by perfectly conducting boundaries where the critical point of the magnetic field lies on one of them. The existence of a magnetically driven instability is confirmed. Depending on the value γ, it may rise as a stationary convection (for γ < 1.5) or as a wave which for γ > 16 exhibits similarity properties (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The azimuthal magnetorotational instability (AMRI)

We consider the flow of an electrically conducting fluid between differentially rotating cylinders, in the presence of an externally imposed current-free toroidal field B₀(R_in/R) ê _ϕ . It is known that the classical, axisymmetric magnetorotational instability does not exist for such a purely toroidal imposed field.We show here that a nonaxisymmetric magnetorotational instability does exist, having properties very similar to the axisymmetric magnetorotational instability in the presence of an axial field. In the nonlinear regime the magnetic energy of the perturbances is shifted (in the sense of an inverse cascade) to the axisymmetric mode rather than to the modes with m > 1. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Axisymmetry vs. nonaxisymmetry of a Taylor‐Couette flow with azimuthal magnetic fields

The instability of a supercritical Taylor‐Couette flow of a conducting fluid with resting outer cylinder under the influence of a uniform axial electric current is investigated for magnetic Prandtl number Pm = 1. In the linear theory the critical Reynolds number for axisymmetric perturbations is not influenced by the current‐induced axisymmetric magnetic field but all axisymmetric magnetic perturbations decay. The nonaxisymmetric perturbations with m = 1 are excited even without rotation for large enough Hartmann numbers (“Tayler instability”). For slow rotation their growth rates scale with the Alfvén frequency of the magnetic field but for fast rotation they scale with the rotation rate of the inner cylinder. In the nonlinear regime the ratio of the energy of the magnetic m = 1 modes and the toroidal background field is very low for the non‐rotating Tayler instability but it strongly grows if differential rotation is present. For super‐Alfv´enic rotation the energies in the m = 1 modes of flow and field do not depend on the molecular viscosity, they are almost in equipartition and contain only 1.5 % of the centrifugal energy of the inner cylinder. The geometry of the excited magnetic field pattern is strictly nonaxisymmetric for slow rotation but it is of the mixed‐mode type for fast rotation – contrary to the situation which has been observed at the surface of Ap stars. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Excitation of high-m tearing modes at the solar flare site

It is shown that high-m drift tearing modes can be excited under the conditions prevalent at the solar flare sites. Since the growth rate of the high-m tearing modes is larger than that for low-m macroscopic tearing modes and smaller than that of microscopic ion-acoustic instability, these modes warrant accommodation in the scheme of instabilities possibly operating in the hybrid model of solar flares suggested by Spicer.     

Tidal interaction in High‐Mass X‐ray Binaries

Our aim is to investigate tidal interaction in High‐Mass X‐ray Binary stars in order to determine in which objects the rotation of the mass donors is synchronized or pseudosynchronized with the orbital motion of the compact companion. We calculate the pseudosynchronization period (P_ps) and compare it with the rotational period of the mass donors (P_rot). We find that (1) the Be/X‐ray binaries are not synchronized, the mass donors rotate faster than the orbital period and the ratio P_ps/P_rot is 2–300; (2) the giant and supergiant systems are close to synchronization and for them the ratio P_ps/P_rot is 0.3–2 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A short wavelength instability in the neutral sheet of the earth's geomagnetic tail

In an earlier paper, Bowers (1973), ion plasma oscillations were found to be unstable in the steady state developed by Cowley (1972) for the neutral sheet in the Earth's geomagnetic tail. In this paper a similar stability analysis is carried out but for a different steady state, suggested by Dungey, with the result that unstable waves with frequencies near the electron plasma frequency are found. In the Dungey steady state the current necessary for magnetic field reversal is carried by plasma originating from both the magnetosheath and the lobes of the tail. This modifies the steady state proposed by Alfvén and subsequently developed by Cowley in which all the current is carried by plasma from the lobes of the tail thereby fixing the cross-tail potential Φ. With magnetosheath plasma present the value of Φ is no longer fixed solely by parameters in the lobes of the tail but the cross-tail electric field is still assumed localised in the dusk region of the sheet as in the Cowley model due to the balance of charge required in the neutral sheet. The value of Φ can be expected to increase as magnetic flux is transported to the tail which inflates and causes flux annihilation because the magneto-sheath plasma in the neutral sheet has insufficient pressure to keep the two lobes of the tail apart. The Vlasov-Maxwell set of equations is perturbed and linearised enabling a critical condition for instability to be found for modes propagating across the tail. Typically, this condition requireseΦ≳KT _m whereT _m is the temperature of magnetosheath electrons. The instability occurs in the presence of cold plasma which hasE×B drifted into the neutral sheet from the lobes of the tail. This contrasts with the usual two stream instability which is stabilised by the cold plasma. Once precipitated the instability may be explosive provided current disruption occurs, for then a further increase in Φ will result which drives a greater range of wave numbers unstable thereby causing even more turbulence and an even larger cross-tail electric field. Because of this behaviour the instability may be a trigger for a substorm.     

Nonlocal density wave theory for gravitational instability of protoplanetary disks without sharp boundaries

The stability of a self‐gravitating infinitesimally thin gaseous disk rotating around a central mass is studied. Our global linear analysis concerns marginal stability, i.e. it yields the critical temperature for the onset of instability for any given ratio of the disk mass to the central mass. Both axisymmetric and low‐m nonaxisymmetric excitations are analysed. When the fractional disk mass increases, the symmetry character of the instability changes from rings (m = 0) to one‐armed trailing spirals (m = 1). The distribution of the surface density along the spiral arms is not uniform, but describes a sequence of maxima that might be identified with forming planets. The number of the mass concentrations decreases with increasing fractional disk mass. We also obtain solutions in the form of global nonaxisymmetric vortices, which are, however, never excited.     

Interaction between sheared flow and resistive tearing mode

We investigate the nonlinear evolution of resistive tearing mode in a current sheet with a sheared flow in a long, thin cylinder. The results show that a hyperbolic secant (sech) flow field will lead to instability of the resistive tearing mode, formation of magnetic islands and rapid release of magnetic energy. The coupling between sheared flow and the tearing mode and interaction between suprathermal instabilities change the degree of shear in the magnetic field (the electric current gradient) and drive the development of the instability. This process may be one of the mechanisms of solar flares.     

The restricted planar isosceles three-body problem with non-negative energy

We consider a restricted three-body problem consisting of two positive equal masses m ₁ = m ₂ moving, under the mutual gravitational attraction, in a collision orbit and a third infinitesimal mass m ₃ moving in the plane P perpendicular to the line joining m ₁ and m ₂. The plane P is assumed to pass through the center of mass of m ₁ and m ₂. Since the motion of m ₁ and m ₂ is not affected by m ₃, from the symmetry of the configuration it is clear that m ₃ remains in the plane P and the three masses are at the vertices of an isosceles triangle for all time. The restricted planar isosceles three-body problem describes the motion of m ₃ when its angular momentum is different from zero and the motion of m ₁ and m ₂ is not periodic. Our main result is the characterization of the global flow of this problem.     

Magnetic reconnection in plasmas

A review of the present status of the theory of magnetic reconnection is given. In strongly collisional plasmas reconnection proceeds via resistive current sheets, i.e. quasi-stationary macroscopic Sweet-Parker sheets at intermediate values of the magnetic Reynolds numberR _m , or mirco-current sheets in MHD turbulence, which develops at highR _m . In hot, dilute plasmas the reconnection dynamics is dominated by nondissipative effects, mainly the Hall term and electron inertia. Reconnection rates are found to depend only on the ion mass, being independent of the electron inertia and the residual dissipation coefficients. Small-scale whistler turbulence is readily excited giving rise to an anomalous electron viscosity. Hence reconnection may be much more rapid than predicted by conventional resistive theory.     

A photometric study of the nova‐like variable TT Arietis with the MOST satellite

Variability on all time scales between seconds and decades is typical for cataclysmic variables (CVs). One of the brightest and best studied CVs is TT Ari, a nova‐like variable which belongs to the VY Scl subclass, characterized by occasional low states in their light curves. It is also known as a permanent superhumper at high state, revealing “positive” (P_S > P₀) as well as “negative” (P_S < P₀) superhumps, where PS is the period of the superhump and P₀ the orbital period. TT Ari was observed by the Canadian space telescope MOST for about 230 hours nearly continuously in 2007, with a time resolution of 48 seconds. Here we analyze these data, obtaining a dominant “negative” superhump signal with a period P_S = 0.1331 days and a mean amplitude of 0.09 mag. Strong flickering with amplitudes up to 0.2 mag and peak‐to‐peak time scales of 15–20 minutes is superimposed on the periodic variations. We found no indications for significant quasi‐periodic oscillations with periods around 15 minutes, reported by other authors. We discuss the known superhump behaviour of TTAri during the last five decades and conclude that our period value is at the upper limit of all hitherto determined “negative” superhump periods of TTAri, before and after the MOST run. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of perturbation on the location of libration point in the robe restricted problem of three bodies

The effect of small perturbation in the Coriolis and centrifugal forces on the location of libration point in the ‘Robe (1977) restricted problem of three bodies’ has been studied. In this problem one body,m ₁, is a rigid spherical shell filled with an homogeneous incompressible fluid of densityϱ ₁. The second one,m ₂, is a mass point outside the shell andm ₃ is a small solid sphere of densityϱ ₃ supposed to be moving inside the shell subject to the attraction ofm ₂ and buoyancy force due to fluidϱ ₁. Here we assumem ₃ to be an infinitesimal mass and the orbit of the massm ₂ to be circular, and we also suppose the densitiesϱ ₁, andϱ ₃ to be equal. Then there exists an equilibrium point (−μ + (ɛ′μ)/(1 + 2μ), 0, 0).     

The study of magnetic reconnection in solar spicules

This work is devoted to study the magnetic reconnection instability under solar spicule conditions. Numerical study of the resistive tearing instability in a current sheet is presented by considering the magnetohydrodynamic (MHD) framework. To investigate the effect of this instability in a stratified atmosphere of solar spicules, we solve linear and non-ideal MHD equations in the x?z plane. In the linear analysis it is assumed that resistivity is only important within the current sheet, and the exponential growth of energies takes place faster as plasma resistivity increases. We are interested to see the occurrence of magnetic reconnection during the lifetime of a typical solar spicule.     

Magnetoconvection in Rotating Stars

Linear and nonlinear properties of magnetoconvection in rotating inviscid fluid are investigated. A time dependent one dimensional nonlinear Landau-Gonzburg equation is derived and analyzed at a supercritical pitchfork bifurcation corresponding to a region0 < R _m < R ^* _m (R _m =R ^* _m corresponds to Takens-Bogdanov bifurcation point). This revised version was published online in July 2006 with corrections to the Cover Date.     

The Cepheid impostor HD 18391 and its anonymous parent cluster

New and existing photometry for the G0 Ia supergiant HD 18391 is analyzed in order to confirm the nature of the variability previously detected in the star, which lies off the hot edge of the Cepheid instability strip. Small‐amplitude variability at a level of δV = 0.016 ± 0.002 is indicated, with a period of P = 123^d.04 ± 0^d.06. A weaker second signal may be present at P = 177^d.84 ± 0^d.18 with δV = 0.007 ± 0.002, likely corresponding to fundamental mode pulsation if the primary signal represents overtone pulsation (123.04/177.84 = 0.69). The star, with a spectroscopic reddening of E_B–V = 1.02 ± 0.003, is associated with heavily‐reddened B‐type stars in its immediate vicinity that appear to be outlying members of an anonymous young cluster centered ∼10′ to the west and 1661 ± 73 pc distant. The cluster has nuclear and coronal radii of r_n = 3.5′ and R_c = 14′, respectively, while the parameters for HD 18391 derived from membership in the cluster with its outlying B stars are consistent with those implied by its Cepheid‐like pulsation, provided that it follows the semi‐period‐luminosity relation expected of such objects. Its inferred luminosity as a cluster member is M_V = –7.76 ± 0.10, its age (9 ± 1) × 10⁶ years, and its evolutionary mass ∼19 M_⊙. HD 18391 is not a classical Cepheid, yet it follows the Cepheid period‐luminosity relation closely, much like another Cepheid impostor, V810 Cen (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

剪切流动和电阻撕裂模的相互作用

本文在细长柱位形下数值研究了具有剪切流动的电流片中电阻撕裂模不稳定性的非线性演化。结果表明，电流片附近Ｓｅｃｈ形式的剪切流动，将导致电阻撕裂模不稳定性的发展，且不稳定性增长率随着剪切参数Ｒｒ的增加而增长，导致磁岛的形成和快速的磁能释放。这种剪切流动和撕裂模的耦合过程以及超热不稳定性的相互作用，改变了磁拱中的磁场剪切强度或者说电流密度梯度，从而驱动电阻撕裂模不稳定性的发展，这种过程对于等离子体电流密     

Three Periods in Asteroid 4197 Brightness Variations

In 1996, photometric observations of the near-Earth asteroid NEA 4197 (1982 TA) were performed at the Crimean Astrophysical Observatory. More than 2000 brightness measurements in the V band were made. The harmonic data analysis at a fairly high significance level revealed two close periods, P ₁= 3^h _.5372 ± 0^h _.0005 (amplitude 0 ^m _.4) and P ₂= 4^h _.367 ± 0^h _.001 (amplitude 0 ^m _.2). The third period, P ₃= 20^h _.26 ± 0^h _.05 (amplitude about 0 ^m _.15), was found at a lower significance level. The conclusion was drawn that the asteroid is a binary system. Its components rotate with the periods P ₁and P ₂, and P ₃is probably related to the orbital motion of the components. Assuming that the diameters of both components are equal to 2 km, the orbital radius equals 4.4 km.     

The S3–4 ionospheric irregularities satellite experiment: Probe detection of multi-ion component plasmas and associated effects on instability processes

The pulsed plasma probe technique has been expanded to include simultaneous determinations of absolute electron density, density fluctuations, electron temperature, and mean-ion-mass with resolution limited only by probe geometry, sheath size, and telemetry. The technique has been designed to test for coupling of electron density variations and ion composition irregularities in multi-component plasmas by the comparison of electron density fluctuation power spectraP _N(k) and a newly-developed diagnostic parameter, the mean-ion-mass fluctuation spectraM _i/M _iP _M(k). In addition, the experiment extends satellite-borne irregularity spectral analyses down to the 5–20 m range while attempting to identify F-region plasma instability processes on the basis of characteristics inN _e,T _e, N _e,P _N,M _i, andP _M. Initial results demonstrate the expanded diagnostic capability for high spatial resolution measurements of mean-ion-mass and provide experimental evidence for the role of ion composition in multi-stepped plasma instability processes. Specific results include a spectral indexX _n inP _N=A _nf^–X _n of 1.6–2.9 over the wavelength range from 1 km to 6 m under conditions identified with an unstable equatorial nighttime ionosphere. Simultaneous measurements ofM _i/M _i(P _M=A _M f ^–X _m) andN _e/N _e(P _N=A _n f ^–X _n) have shown a general behavior tending to lower power (A _m<A _n) and softer spectra (X _m<X _n) in ion mass fluctuations when compared with fluctuations in total plasma density. Limited analyses of the two power spectral elements raise hopes for the differentiation between plasma mechanisms that can lead to similar indices inP _N.Paper originally submitted to the journalSpace Science Instrumentation.     

Nonaxisymmetric instabilities of self-gravitating disks. I toroids

We perform an extensive linear investigation of the nonaxisymmetric disk modes referred to in the literature as P, I, and J modes in self-gravitating polytropic toroids with power law angular velocity distributions. For selected models, we also follow the development of instability from the linear regime through the quasi-linear regime to deep into the nonlinear regime. We consider modes with azimuthal dependence e ^imφ , where m is an integer and φ is the azimuthal angle. We find that instability sets in through m=2 barlike I modes at T/|W|∼0.16–0.18 depending upon the chosen angular velocity law where T is the rotational kinetic energy and W is the gravitational energy of the toroid. Instability in the barlike I mode peaks in strength around T/|W|=0.22–0.23 after which it weakens, eventually stabilizing around T/|W|∼0.25–0.26. One-armed modes (m=1 modes) become unstable just after instability in the m=2I modes sets in; instability in m=1 modes sets in at T/|W|∼0.19. They dominate the barlike I modes in toroids with T/|W|≳0.25. However, almost immediately after the m=1 mode overtakes the barlike I mode, higher-m J modes appear. J modes with m=2, 3, and 4 become unstable for T/|W|≳0.25–0.26, 0.23–0.25, and 0.25–0.26, respectively. m≥3J modes dominate the m=1 mode in toroids with T/|W|≳0.27. As T/|W| increases further, nonaxisymmetric instability sets in through higher and higher m modes. We find quantitative agreement between the early nonlinear behavior of the tested unstable toroids and our linear results. Quasi-linear modeling suggests that a gravitational self-interaction torque which arises early in the nonlinear regime saturates growth of the mode and leads to significant transport of mass and angular momentum. Neither I mode nor J mode instabilities produce prompt fission in toroids.     

Rotation,activity, and lithium abundance in cool binary stars

We have used two robotic telescopes to obtain time‐series high‐resolution optical echelle spectroscopy and VI and/or by photometry for a sample of 60 active stars, mostly binaries. Orbital solutions are presented for 26 double‐lined systems and for 19 single‐lined systems, seven of them for the first time but all of them with unprecedented phase coverage and accuracy. Eighteen systems turned out to be single stars. The total of 6609 R = 55000 échelle spectra are also used to systematically determine effective temperatures, gravities, metallicities, rotational velocities, lithium abundances and absolute Hα‐core fluxes as a function of time. The photometry is used to infer unspotted brightness, V – I and/or b – y colors, spot‐induced brightness amplitudes and precise rotation periods. An extra 22 radial‐velocity standard stars were monitored throughout the science observations and yield a new barycentric zero point for our STELLA/SES robotic system. Our data are complemented by literature data and are used to determine rotation‐temperature‐activity relations for active binary components. We also relate lithium abundance to rotation and surface temperature. We find that 74% of all known rapidly‐rotating active binary stars are synchronized and in circular orbits but 26% (61 systems) are rotating asynchronously of which half have P_rot > P_orb and e > 0. Because rotational synchronization is predicted to occur before orbital circularization active binaries should undergo an extra spin‐down besides tidal dissipation. We suspect this to be due to a magnetically channeled wind with its subsequent braking torque. We find a steep increase of rotation period with decreasing effective temperature for active stars, P_rot α T^–7_eff, for both single and binaries, main sequence and evolved. For inactive, single giants with P_rot > 100 d, the relation is much weaker, P_rot α T^‐1.12_eff. Our data also indicate a period‐activity relation for Hα of the form R_Hα α P_0.24^rot for binaries and R_Hα α P_‐0.14^rot for singles. Its power‐law difference is possibly significant. Lithium abundances in our (field‐star) sample generally increase with effective temperature and are paralleled with an increase of the dispersion. The dispersion for binaries can be 1–2 orders of magnitude larger than for singles, peaking at an absolute spread of 3 orders of magnitude near T_eff ≈ 5000 K. On average, binaries of comparable effective temperature appear to exhibit 0.25 dex less surface lithium than singles, as expected if the depletion mechanism is rotation dependent. We also find a trend of increased Li abundance with rotational period of form log n (Li) α –0.6 log P_rot but again with a dispersion of as large as 3‐4 orders of magnitude (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)