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Register a new userThe Lorentz force in atmospheres of CP stars: $theta$ Aurigae
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Several dynamical processes may induce considerable electric currents in the atmospheres of magnetic chemically peculiar (CP) stars. The Lorentz force, which results from the interaction between the magnetic field and the induced currents, modifies the atmospheric structure and induces characteristic rotational variability of the hydrogen Balmer lines. To study this phenomena we have initiated a systematic spectroscopic survey of the Balmer lines variation in magnetic CP stars. In this paper we continue presentation of results of the program focusing on the high-resolution spectral observations of A0p star aur (HD 40312). We have detected a significant variability of the H$alpha$, H$beta$, and H$gamma$ spectral lines during full rotation cycle of the star. This variability is interpreted in the framework of the model atmosphere analysis, which accounts for the Lorentz force effects. Both the inward and outward directed Lorentz forces are considered under the assumption of the axisymmetric dipole or dipole+quadrupole magnetic field configurations. We demonstrate that only the model with the outward directed Lorentz force in the dipole+quadrupole configuration is able to reproduce the observed hydrogen line variation. These results present new strong evidences for the presence of non-zero global electric currents in the atmosphere of an early-type magnetic star.
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The presence of electric currents in the atmospheres of magnetic chemically peculiar (mCP) stars could bring important theoretical constrains about the nature and evolution of magnetic field in these stars. The Lorentz force, which results from the interaction between the magnetic field and the induced currents, modifies the atmospheric structure and induces characteristic rotational variability of pressure-sensitive spectroscopic features, that can be analysed using phase-resolved spectroscopic observations. In this work we continue the presentation of results of the magnetic pressure studies in mCP stars focusing on the high-resolution spectroscopic observations of Bp star 56Ari. We have detected a significant variability of the Halpha, Hbeta, and Hgamma spectral lines during full rotation cycle of the star. Then these observations are interpreted in the framework of the model atmosphere analysis, which accounts for the Lorentz force effects. We used the LLmodels stellar model atmosphere code for the calculation of the magnetic pressure effects in the atmosphere of 56Ari taking into account realistic chemistry of the star and accurate computations of the microscopic plasma properties. The Synth3 code was employed to simulate phase-resolved variability of Balmer lines. We demonstrate that the model with the outward-directed Lorentz force in the dipole+quadrupole configuration is likely to reproduce the observed hydrogen lines variation. These results present strong evidences for the presence of non-zero global electric currents in the atmosphere of this early-type magnetic star.
The brightest magnetic chemically peculiar stars theta Aur and eps UMa were targeted by numerous studies of their photometric and spectroscopic variability. Detailed maps of chemical abundance spots were repeatedly derived for both stars. However, very little information on the magnetic field geometries of these stars is available. In this study we aim to determine detailed magnetic field topologies of theta Aur and eps UMa based on modern, high-resolution spectropolarimetric observations. Both targets were observed in all four Stokes parameters using the Narval and ESPaDOnS spectropolarimeters. A multi-line technique of least-squares deconvolution was employed to detect polarisation signatures in spectral lines. These signatures were modelled with a Zeeman-Doppler imaging code. We succeeded in detecting variable circular and linear polarisation signatures for theta Aur. Only circular polarisation was detected for eps UMa. We obtained new sets of high-precision longitudinal magnetic field measurements using mean circular polarisation metal line profiles as well as hydrogen line cores, which are consistent with historical data. Magnetic
The weak coupling region of CP$^{N-1}$ lattice field theory with the $theta$-term is investigated. Both the usual real theta method and the imaginary theta method are studied. The latter was first proposed by Bhanot and David. Azcoiti et al. proposed an inversion approach based on the imaginary theta method. The role of the inversion approach is investigated in this paper. A wide range of values of $h=-{rm Im} theta$ is studied, where $theta $ denotes the magnitude of the topological term. Step-like behavior in the $x$-$h$ relation (where $x=Q/V$, $Q$ is the topological charge, and $V$ is the two dimensional volume) is found in the weak coupling region. The physical meaning of the position of the step-like behavior is discussed. The inversion approach is applied to weak coupling regions.
The Fokker-Planck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial coefficient, which reflects the anisotropy of the particles motion. This tensor, however, can not be interpreted as a diffusion tensor; there are antisymmetric terms which give rise to fluxes perpendicular to the density gradients. Here, we show that for an inhomogeneous magnetic field these nondiffusive fluxes have finite divergence and therefore affect the density evolution of the system. Only in the special cases of a uniform magnetic field or carefully chosen initial condition with the same symmetry as the magnetic field can these fluxes be ignored in the density evolution.
We study the motion of a Brownian particle subjected to Lorentz force due to an external magnetic field. Each spatial degree of freedom of the particle is coupled to a different thermostat. We show that the magnetic field results in correlation between different velocity components in the stationary state. Integrating the velocity autocorrelation matrix, we obtain the diffusion matrix that enters the Fokker-Planck equation for the probability density. The eigenvectors of the diffusion matrix do not align with the temperature axes. As a consequence the Brownian particle performs spatially correlated diffusion. We further show that in the presence of an isotropic confining potential, an unusual, flux-free steady state emerges which is characterized by a non-Boltzmann density distribution, which can be rotated by reversing the magnetic field. The nontrivial steady state properties of our system result from the Lorentz force induced coupling of the spatial degrees of freedom which cease to exist in equilibrium corresponding to a single-temperature system.
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