Fifteen years in the high-energy life of the solar-type star HD 81809. XMM-Newton observations of a stellar activity cycle

Aims. The data set of the long-term XMM-Newton monitoring program of HD 81809 is analyzed to study its X-ray cycle, to investigate if the latter is related to the chromospheric one, to infer the structure of the corona of HD 81809, and to explore if the coronal activity of HD 81809 can be ascribed to phenomena similar to the solar ones and, therefore, considered an extension of the solar case. Methods. We analyze the observations of HD 81809 performed with XMM-Newton with a regular cadence of 6 months from 2001 to 2016 and representing one of the longest available observational baseline ($\sim 15$~yr) for a solar-like star with a well-studied chromospheric cycle (with a period of $\sim 8$~yr). We investigate the modulation of coronal luminosity and temperature and its relation with the chromospheric cycle. We interpret the data in terms of a mixture of solar-like coronal regions, adopting a methodology originally proposed to study the Sun as an X-ray star. Results. The observations show a well-defined regular cyclic modulation of the X-ray luminosity that reflects the activity level of HD 81809. The data covers approximately two cycles of coronal activity; the modulation has an amplitude of a factor of $\sim 5$ (excluding evident flares, as in the June 2002 observation) and a period of $7.3\pm 1.5$~yr, consistent with that of the chromospheric cycle. We demonstrate that the corona of HD 81809 can be interpreted as an extension of the solar case and it can be modeled with a mixture of solar-like coronal regions along the whole cycle. The activity level is mainly determined by a varying coverage of very bright active regions, similar to cores of active regions observed in the Sun. Evidence of unresolved significant flaring activity is present especially in proximity of cycle maxima.Comment: 11 pages, 5 Figures, A&A accepte

Perfect magnetohydrodynamics as a field theory

We propose the generally covariant action for the theory of a self-coupled complex scalar field and electromagnetism which by virtue of constraints is equivalent, in the regime of long wavelengths, to perfect magnetohydrodynamics (MHD). We recover from it the Euler equation with Lorentz force, and the thermodynamic relations for a prefect fluid. The equation of state of the latter is related to the scalar field's self potential. We introduce 1+3 notation to elucidate the relation between MHD and field variables. In our approach the requirement that the scalar field be single valued leads to the quantization of a certain circulation in steps of $\hbar$; this feature leads, in the classical limit, to the conservation of that circulation. The circulation is identical to that in Oron's generalization of Kelvin's circulation theorem to perfect MHD; we here characterize the new conserved helicity associated with it. We also demonstrate the existence for MHD of two Bernoulli-like theorems for each spacetime symmetry of the flow and geometry; one of these is pertinent to suitably defined potential flow. We exhibit the conserved quantities explicitly in the case that two symmetries are simultaneously present, and give examples. Also in this case we exhibit a new conserved MHD circulation distinct from Oron's, and provide an example.Comment: RevTeX, 16 pages, no figures; clarifications added and typos corrected; version to be published in Phys. Rev.

Topological Landau-Ginzburg Theory for Vortices in Superfluid 4^4He

We propose a new Landau-Ginzburg theory for arbitrarily shaped vortex strings in superfluid $^4$He. The theory contains a topological term and directly describes vortex dynamics. We introduce gauge fields in order to remove singularities from the Landau-Ginzburg order parameter of the superfluid, so that two kinds of gauge symmetries appear, making the continuity equation and conservation of the total vorticity manifest. The topological term gives rise to the Berry phase term in the vortex mechanical actions.Comment: LATEX, 9 page

Spectroscopic variability of two Oe stars

The Oe stars HD45314 and HD60848 have recently been found to exhibit very different X-ray properties: whilst HD60848 has an X-ray spectrum and emission level typical of most OB stars, HD45314 features a much harder and brighter X-ray emission, making it a so-called gamma Cas analogue. Monitoring the optical spectra could provide hints towards the origin of these very different behaviours. We analyse a large set of spectroscopic observations of HD45314 and HD60848, extending over 20 years. We further attempt to fit the H-alpha line profiles of both stars with a simple model of emission line formation in a Keplerian disk. Strong variations in the strengths of the H-alpha, H-beta, and He I 5876 emission lines are observed for both stars. In the case of HD60848, we find a time lag between the variations in the equivalent widths of these lines. The emission lines are double peaked with nearly identical strengths of the violet and red peaks. The H-alpha profile of this star can be successfully reproduced by our model of a disk seen under an inclination of 30 degrees. In the case of HD45314, the emission lines are highly asymmetric and display strong line profile variations. We find a major change in behaviour between the 2002 outburst and the one observed in 2013. This concerns both the relationship between the equivalent widths of the various lines and their morphologies at maximum strength (double-peaked in 2002 versus single-peaked in 2013). Our simple disk model fails to reproduce the observed H-alpha line profiles of HD45314. Our results further support the interpretation that Oe stars do have decretion disks similar to those of Be stars. Whilst the emission lines of HD60848 are explained by a disk with a Keplerian velocity field, the disk of HD45314 seems to have a significantly more complex velocity field that could be related to the phenomenon that produces its peculiar X-ray emission.Comment: Accepted for Publication in A&

Boundary and Bulk Phase Transitions in the Two Dimensional Q > 4 State Potts Model

The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the surface transition the complete analytical solution of the problem is presented in the $Q \to \infty$ limit, including the critical and tricritical exponents, magnetization profiles and scaling functions. According to the accurate numerical results the universality class of the surface transition is independent of the value of Q > 4. For the bulk transition we have numerically calculated the latent heat and the magnetization discontinuity and we have shown that the correlation lengths in the ordered and in the disordered phases are identical at the transition point.Comment: 11 pages, RevTeX, 6 PostScript figures included. Manuscript substantially extended, details on the analytical and numerical calculations added. To appear in Phys. Rev.

Corner Exponents in the Two-Dimensional Potts Model

The critical behavior at a corner in two-dimensional Ising and three-state Potts models is studied numerically on the square lattice using transfer operator techniques. The local critical exponents for the magnetization and the energy density for various opening angles are deduced from finite-size scaling results at the critical point for isotropic or anisotropic couplings. The scaling dimensions compare quite well with the values expected from conformal invariance, provided the opening angle is replaced by an effective one in anisotropic systems.Comment: 11 pages, 2 eps-figures, uses LaTex and eps

Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models

The q-state Potts model with long-range interactions that decay as 1/r^alpha subjected to an uniform magnetic field on d-dimensional lattices is analized for different values of q in the nonextensive regime (alpha between 0 and d). We also consider the two dimensional antiferromagnetic Ising model with the same type of interactions. The mean field solution and Monte Carlo calculations for the equations of state for these models are compared. We show that, using a derived scaling which properly describes the nonextensive thermodynamic behaviour, both types of calculations show an excellent agreement in all the cases here considered, except for alpha=d. These results allow us to extend to nonextensive magnetic models a previous conjecture which states that the mean field theory is exact for the Ising one.Comment: 10 pages, 4 figure

Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect

Our previous ``exotic'' particle, together with the more recent anomalous anyon model (which has arbitrary gyromagnetic factor $g$) are reviewed. The non-relativistic limit of the anyon generalizes the exotic particle which has $g=0$ to any $g$.When put into planar electric and magnetic fields, the Hall effect becomes mandatory for all $g\neq2$, when the field takes some critical value.Comment: A new reference added. Talk given by P. Horvathy at the International Workshop "Nonlinear Physics: Theory and Experiment. III. July'04, Gallipoli (Lecce, Italy). To be published in Theor. Math. Phys. Latex 9 pages, no figure

Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations

Simple derivation is presented of the four families of infinitely many shape invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi polynomials. Darboux-Crum transformations are applied to connect the well-known shape invariant Hamiltonians of the radial oscillator and the Darboux-P\"oschl-Teller potential to the shape invariant potentials of Odake-Sasaki. Dutta and Roy derived the two lowest members of the exceptional Laguerre polynomials by this method. The method is expanded to its full generality and many other ramifications, including the aspects of generalised Bochner problem and the bispectral property of the exceptional orthogonal polynomials, are discussed.Comment: LaTeX2e with amsmath, amssymb, amscd 26 pages, no figure