How useful are monetary policy rules to deal with inflation: The Spanish case.

The role of monetary policy rules to explain the behaviour of central banks has received an increasing attention during the last few years. The Spanish case could be of interest given that, with an inflation above the European average, was able to conduct its monetary policy and to control the inflation in order to join the European monetary union. But after the adoption of the European Central Bank’s monetary policy in January 1999, a higher inflation can be observed. In this paper we explore whether the monetary policy performed by the Bank of Spain would have follow a monetary policy rule, and to which extent monetary rules contribute to achieve the goal of inflation.Monetary policy rules, inflation.

Seismology of Standing Kink Oscillations of Solar Prominence Fine Structures

We investigate standing kink magnetohydrodynamic (MHD) oscillations in a prominence fine structure modeled as a straight and cylindrical magnetic tube only partially filled with the prominence material, and with its ends fixed at two rigid walls representing the solar photosphere. The prominence plasma is partially ionized and a transverse inhomogeneous transitional layer is included between the prominence thread and the coronal medium. Thus, ion-neutral collisions and resonant absorption are the considered damping mechanisms. Approximate analytical expressions of the period, the damping time, and their ratio are derived for the fundamental mode in the thin tube and thin boundary approximations. We find that the dominant damping mechanism is resonant absorption, which provides damping ratios in agreement with the observations, whereas ion-neutral collisions are irrelevant for the damping. The values of the damping ratio are independent of both the prominence thread length and its position within the magnetic tube, and coincide with the values for a tube fully filled with the prominence plasma. The implications of our results in the context of the MHD seismology technique are discussed, pointing out that the reported short-period (2 - 10 min) and short-wavelength (700 - 8,000 km) thread oscillations may not be consistent with a standing mode interpretation and could be related to propagating waves. Finally, we show that the inversion of some prominence physical parameters, e.g., Alfv\'en speed, magnetic field strength, transverse inhomogeneity length-scale, etc., is possible using observationally determined values of the period and damping time of the oscillations along with the analytical approximations of these quantities.Comment: Accepted for publication in Ap

Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads

We analyse the oscillatory properties of resonantly damped transverse kink oscillations in two-dimensional prominence threads. The fine structures are modelled as cylindrically symmetric magnetic flux tubes with a dense central part with prominence plasma properties and an evacuated part, both surrounded by coronal plasma. The equilibrium density is allowed to vary non-uniformly in both the transverse and the longitudinal directions.We examine the influence of longitudinal density structuring on periods, damping times, and damping rates for transverse kink modes computed by numerically solving the linear resistive magnetohydrodynamic (MHD) equations. The relevant parameters are the length of the thread and the density in the evacuated part of the tube, two quantities that are difficult to directly estimate from observations. We find that both of them strongly influence the oscillatory periods and damping times, and to a lesser extent the damping ratios. The analysis of the spatial distribution of perturbations and of the energy flux into the resonances allows us to explain the obtained damping times. Implications for prominence seismology, the physics of resonantly damped kink modes in two-dimensional magnetic flux tubes, and the heating of prominence plasmas are discussed.Comment: 12 pages, 9 figures, A&A accepte

Kelvin-Helmholtz instability in partially ionized compressible plasmas

The Kelvin-Helmholtz Instability (KHI) has been observed in the solar atmosphere. Ion-neutral collisions may play a relevant role for the growth rate and evolution of the KHI in solar partially ionized plasmas as in, e.g., solar prominences. Here, we investigate the linear phase of the KHI at an interface between two partially ionized magnetized plasmas in the presence of a shear flow. The effects of ion-neutral collisions and compressibility are included in the analysis. We obtain the dispersion relation of the linear modes and perform parametric studies of the unstable solutions. We find that in the incompressible case the KHI is present for any velocity shear regardless the value of the collision frequency. In the compressible case, the domain of instability depends strongly on the plasma parameters, specially the collision frequency and the density contrast. For high collision frequencies and low density contrasts the KHI is present for super-Alfvenic velocity shear only. For high density contrasts the threshold velocity shear can be reduced to sub-Alfvenic values. For the particular case of turbulent plumes in prominences, we conclude that sub-Alfvenic flow velocities can trigger the KHI thanks to the ion-neutral coupling.Comment: Accepted for publication in Ap

Numerical simulations of turbulence in prominence threads induced by torsional oscillations

Threads are the main constituents of prominences and are subjected to oscillations that might be interpreted as MHD waves. Moreover, the Kelvin-Helmholtz instability (KHI) has been reported in prominences. Both waves and KHI may affect the thermodynamic state of the threads. We investigate the triggering of turbulence in a thread caused by the nonlinear evolution of standing torsional Alfv\'en waves as well as possible observational signatures of this dynamics and the plasma heating. We modeled the thread as a radially and longitudinally nonuniform cylindrical flux tube with a uniform axial magnetic field embedded in a coronal environment. We perturbed the flux tube with the longitudinally fundamental mode of standing torsional Alfv\'en waves and numerically solved the 3D MHD equations to study the temporal evolution in both ideal and dissipative scenarios. We also performed forward modeling to calculate the synthetic H{\alpha} imaging. Standing torsional Alfv\'en waves undergo phase-mixing owing to the radially nonuniform density. The phase-mixing generates azimuthal shear flows that eventually trigger the KHI and, later, turbulence. If nonideal effects are included, plasma heating is localized in an annulus region at the thread boundary and does not increase the temperature in the cool core. Instead, the average temperature in the thread decreases owing to the mixing of internal and external plasmas. In the synthetic observations, first we find periodic pulsations in the H{\alpha} intensity caused by the integration of the phase-mixing flows along the line of sight. Later, we find fine strands that may be associated with the KHI vortices. Turbulence can be generated by standing torsional Alfv\'en waves in a thread after the onset of KHI, but this mechanism is not enough to heat globally the structure. The dynamics could be seen in high-resolution H{\alpha} observations.Comment: Accepted in Astronomy & Astrophysic

Transition to turbulence in nonuniform coronal loops driven by torsional Alfv\'en waves. II. Extended analysis and effect of magnetic twist

It has been shown in a previous work that torsional Alfv\'en waves can drive turbulence in nonuniform coronal loops with a purely axial magnetic field. Here we explore the role of the magnetic twist. We model a coronal loop as a transversely nonuniform straight flux tube, anchored in the photosphere, and embedded in a uniform coronal environment. We consider that the magnetic field is twisted and control the strength of magnetic twist by a free parameter of the model. We excite the longitudinally fundamental mode of standing torsional Alfv\'en waves, whose temporal evolution is obtained by means of high-resolution three-dimensional ideal magnetohydrodynamic numerical simulations. We find that phase mixing of torsional Alfv\'en waves creates velocity shear in the direction perpendicular to the magnetic field lines. The velocity shear eventually triggers the Kelvin-Helmholtz instability (KHi). In weakly twisted magnetic tubes, the KHi is able to grow nonlinearly and, subsequently, turbulence is driven in the coronal loop in a similar manner as in the untwisted case. Provided that magnetic twist remains weak, the effect of magnetic twist is to delay the onset of the KHi and to slow down the development of turbulence. In contrast, magnetic tension can suppress the nonlinear growth of the KHi when magnetic twist is strong enough, even if the KHi has locally been excited by the phase-mixing shear. Thus, turbulence is not generated in strongly twisted loopsComment: Published in A&A. 12 pages. 12 figure

Kink oscillations of flowing threads in solar prominences

Recent observations by Hinode/SOT show that MHD waves and mass flows are simultaneously present in the fine structure of solar prominences. We investigate standing kink magnetohydrodynamic (MHD) waves in flowing prominence threads from a theoretical point of view. We model a prominence fine structure as a cylindrical magnetic tube embedded in the solar corona with its ends line-tied in the photosphere. The magnetic cylinder is composed of a region with dense prominence plasma, which is flowing along the magnetic tube, whereas the rest of the flux tube is occupied by coronal plasma. We use the WKB approximation to obtain analytical expressions for the period and the amplitude of the fundamental mode as functions of the flow velocity. In addition, we solve the full problem numerically by means of time-dependent simulations. We find that both the period and the amplitude of the standing MHD waves vary in time as the prominence thread flows along the magnetic structure. The fundamental kink mode is a good description for the time-dependent evolution of the oscillations, and the analytical expressions in the WKB approximation are in agreement with the full numerical results. The presence of flow modifies the period of the oscillations with respect to the static case. However, for realistic flow velocities this effect might fall within the error bars of the observations. The variation of the amplitude due to the flow leads to apparent damping or amplification of the oscillations, which could modify the real rate of attenuation caused by an additional damping mechanism.Comment: Accepted for publication in A&

Resonantly Damped Kink Magnetohydrodynamic Waves in a Partially Ionized Filament Thread

Transverse oscillations of solar filament and prominence threads have been frequently reported. These oscillations have the common features of being of short period (2-10 min) and being damped after a few periods. Kink magnetohydrodynamic (MHD) wave modes have been proposed as responsible for the observed oscillations, whereas resonant absorption in the Alfven continuum and ion-neutral collisions are the best candidates to be the damping mechanisms. Here, we study both analytically and numerically the time damping of kink MHD waves in a cylindrical, partially ionized filament thread embedded in a coronal environment. The thread model is composed of a straight and thin, homogeneous filament plasma, with a transverse inhomogeneous transitional layer where the plasma physical properties vary continuously from filament to coronal conditions. The magnetic field is homogeneous and parallel to the thread axis. We find that the kink mode is efficiently damped by resonant absorption for typical wavelengths of filament oscillations, the damping times being compatible with the observations. Partial ionization does not affect the process of resonant absorption, and the filament plasma ionization degree is only important for the damping for wavelengths much shorter than those observed. To our knowledge, this is the first time that the phenomenon of resonant absorption is studied in a partially ionized plasma.Comment: Submitted in Ap