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

The Ca II infrared triplet's performance as an activity indicator compared to Ca II H and K

Aims. A large number of Calcium Infrared Triplet (IRT) spectra are expected from the GAIA- and CARMENES missions. Conversion of these spectra into known activity indicators will allow analysis of their temporal evolution to a better degree. We set out to find such a conversion formula and to determine its robustness. Methods. We have compared 2274 Ca II IRT spectra of active main-sequence F to K stars taken by the TIGRE telescope with those of inactive stars of the same spectral type. After normalizing and applying rotational broadening, we subtracted the comparison spectra to find the chromospheric excess flux caused by activity. We obtained the total excess flux, and compared it to established activity indices derived from the Ca II H & K lines, the spectra of which were obtained simultaneously to the infrared spectra. Results. The excess flux in the Ca II IRT is found to correlate well with $R_\mathrm{HK}'$ and $R_\mathrm{HK}^{+}$, as well as $S_\mathrm{MWO}$, if the $B-V$-dependency is taken into account. We find an empirical conversion formula to calculate the corresponding value of one activity indicator from the measurement of another, by comparing groups of datapoints of stars with similar B-V.Comment: 16 pages, 15 figures. Accepted for publication in Astronomy & Astrophysic

Time series of high resolution spectra of SN 2014J observed with the TIGRE telescope

We present a time series of high resolution spectra of the Type Ia supernova 2014J, which exploded in the nearby galaxy M82. The spectra were obtained with the HEROS echelle spectrograph installed at the 1.2 m TIGRE telescope. We present a series of 33 spectra with a resolution of R = 20, 000, which covers the important bright phases in the evolution of SN 2014J during the period from January 24 to April 1 of 2014. The spectral evolution of SN 2014J is derived empirically. The expansion velocities of the Si II P-Cygni features were measured and show the expected decreasing behaviour, beginning with a high velocity of 14,000 km/s on January 24. The Ca II infrared triplet feature shows a high velocity component with expansion velocities of > 20, 000 km/s during the early evolution apart from the normal component showing similar velocities as Si II. Further broad P-Cygni profiles are exhibited by the principal lines of Ca II, Mg II and Fe II. The TIGRE SN 2014J spectra also resolve several very sharp Na I D doublet absorption components. Our analysis suggests interesting substructures in the interstellar medium of the host galaxy M82, as well as in our Milky Way, confirming other work on this SN. We were able to identify the interstellar absorption of M82 in the lines of Ca II H & K at 3933 and 3968 A as well as K I at 7664 and 7698 A. Furthermore, we confirm several Diffuse Interstellar Bands, at wavelengths of 6196, 6283, 6376, 6379 and 6613 A and give their measured equivalent widths.Comment: 11 pages, 10 figures, accepted for publication in MNRA

Simultaneous X-ray and optical spectroscopy of the Oef supergiant lambda Cep

Probing the structures of stellar winds is of prime importance for the understanding of massive stars. Based on their optical spectral morphology and variability, the stars of the Oef class have been suggested to feature large-scale structures in their wind. High-resolution X-ray spectroscopy and time-series of X-ray observations of presumably-single O-type stars can help us understand the physics of their stellar winds. We have collected XMM-Newton observations and coordinated optical spectroscopy of the O6Ief star lambda Cep to study its X-ray and optical variability and to analyse its high-resolution X-ray spectrum. We investigate the line profile variability of the He II 4686 and H-alpha emission lines in our time series of optical spectra, including a search for periodicities. We further discuss the variability of the broadband X-ray flux and analyse the high-resolution spectrum of lambda Cep using line-by-line fits as well as a code designed to fit the full high-resolution X-ray spectrum consistently. During our observing campaign, the He II 4686 line varies on a timescale of ~18 hours. On the contrary, the H-alpha line profile displays a modulation on a timescale of 4.1 days which is likely the rotation period of the star. The X-ray flux varies on time-scales of days and could in fact be modulated by the same 4.1 days period as H-alpha, although both variations are shifted in phase. The high-resolution X-ray spectrum reveals broad and skewed emission lines as expected for the X-ray emission from a distribution of wind-embedded shocks. Most of the X-ray emission arises within less than 2R* above the photosphere.Comment: Accepted for publication in Astronomy & Astrophysic

Reaction-diffusion systems and nonlinear waves

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article.Comment: LaTeX, 16 pages, corrected typo

Solution of generalized fractional reaction-diffusion equations

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.Comment: LaTeX, 18 pages, corrected typo

Variational method and duality in the 2D square Potts model

The ferromagnetic q-state Potts model on a square lattice is analyzed, for q>4, through an elaborate version of the operatorial variational method. In the variational approach proposed in the paper, the duality relations are exactly satisfied, involving at a more fundamental level, a duality relationship between variational parameters. Besides some exact predictions, the approach is very effective in the numerical estimates over the whole range of temperature and can be systematically improved.Comment: 20 pages, 5 EPS figure