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Threads are the building blocks of solar prominences and very often show longitudinal oscillatory motions that are strongly attenuated with time. The damping mechanism responsible for the reported oscillations is not fully understood yet. To understand the oscillations and damping of prominence threads it is mandatory to investigate first the nature of the equilibrium solutions that arise under static conditions and under the presence of radiative losses, thermal conduction and background heating. This provides the basis to calculate the eigenmodes of the thread models. The nonlinear ordinary differential equations for hydrostatic and thermal equilibrium under the presence of gravity are solved using standard numerical techniques and simple analytical expressions are derived under certain approximations. The solutions to the equations represent a prominence thread, i.e., a dense and cold plasma region of a certain length that connects with the corona through a prominence corona transition region (PCTR). The solutions can also match with a chromospheric-like layer if a spatially dependent heating function localised around the footpoints is considered. We have obtained static solutions representing prominence threads and have investigated in detail the dependence of these solutions on the different parameters of the model. Among other results, we have shown that multiple condensations along a magnetic field line are possible, and that the effect of partial ionisation in the model can significantly modify the thermal balance in the thread and therefore their length. This last parameter is also shown to be comparable to that reported in the observations when the radiative losses are reduced for typical thread temperatures., Accepted for publication in A&A

Rossby waves are a pervasive feature of the large-scale motions of the Earth’s atmosphere and oceans. These waves (also known as planetary waves and r-modes) also play an important role in the large-scale dynamics of different astrophysical objects such as the solar atmosphere and interior, astrophysical discs, rapidly rotating stars, planetary and exoplanetary atmospheres. This paper provides a review of theoretical and observational aspects of Rossby waves on different spatial and temporal scales in various astrophysical settings. The physical role played by Rossby-type waves and associated instabilities is discussed in the context of solar and stellar magnetic activity, angular momentum transport in astrophysical discs, planet formation, and other astrophysical processes. Possible directions of future research in theoretical and observational aspects of astrophysical Rossby waves are outlined.

The importance of the chromosphere in the mass and energy transport within the solar atmosphere is now widely recognized. This review discusses the physics of magnetohydrodynamic waves and instabilities in large-scale chromospheric structures as well as in magnetic flux tubes. We highlight a number of key observational aspects that have helped our understanding of the role of the solar chromosphere in various dynamic processes and wave phenomena, and the heating scenario of the solar chromosphere is also discussed. The review focuses on the physics of waves and invokes the basics of plasma instabilities in the context of this important layer of the solar atmosphere. Potential implications, future trends and outstanding questions are also delineated.

There is observational evidence of the presence of small-amplitude transverse magnetohydrodynamic (MHD) waves with a wide range of frequencies in the threads of solar prominences. It is believed that the waves are driven at the photosphere and propagate along the magnetic field lines up to prominences suspended in the corona. The dissipation of MHD wave energy in the partially ionized prominence plasma is a heating mechanism whose relevance needs to be explored. Here we consider a simple 1D model for a non-uniform thin thread and investigate the heating associated with dissipation of Alfvén waves. The model assumes an ad hoc density profile and a uniform pressure, while the temperature and ionization degree are self-consistently computed considering either local themodynamical equilibrium (LTE) or non-LTE approximations for the hydrogen ionization. A broadband driver for Alfvén waves is placed at one end of the magnetic field line, representing photospheric excitation. The Alfvénic perturbations along the thread are obtained by solving the linearized MHD equations for a partially ionized plasma in the single-fluid approximation. We find that wave heating in the partially ionized part of the thread is significant enough to compensate for energy losses due to radiative cooling. A greater amount of heating is found in the LTE case because the ionization degree for core prominence temperatures is lower than that in the non-LTE approximation. This results in a greater level of dissipation due to ambipolar diffusion in the LTE case. Conversely, in the hot coronal part of the model, the plasma is fully ionized and wave heating is negligible. The results of this simple model suggest that MHD wave heating can be relevant for the energy balance in prominences. Further studies based on more elaborate models are required.

Partially ionized plasmas are found in many different astrophysical environments. The study of partially ionized plasmas is of great interest for solar physics because some layers of the solar atmosphere (photosphere and chromosphere) as well as solar structures, such as spicules and prominences, are made of these kinds of plasmas. To our knowledge, despite it being known that the adiabatic coefficient,γ, or the first adiabatic exponent, Γ1, depend on the ionization degree, this fact has been disregarded in all the studies related to magnetohydrodynamic waves in solar partially ionized plasmas. However, in other astrophysical areas, the dependence ofγor Γ1on the plasma ionization degree has been taken into account. Therefore, our aim here is to study how, in a plasma with prominence physical properties, the joint action of the temperature, density, and ionization degree modifies the numerical values of the first adiabatic exponent Γ1which affects the adiabatic sound speed and the period of slow waves. In our computations, we have used two different approaches; first of all, we assume local thermodynamic equilibrium (LTE) and, later, we consider a non-local thermodynamic equilibrium (non-LTE) model. When comparing the results in the LTE and non-LTE cases, the numerical values of Γ1are clearly different for both and they are probably strongly dependent on the assumed model which determines how the ionization degree evolves with temperature. Finally, the effect of the ionization degree dependence of Γ1on the period of slow waves has been determined showing that it can be of great importance for seismological studies of partially ionized solar structures.

There is increasing evidence that magnetohydrodynamic waves play an important role in the propagation and dissipation of energy in the solar atmosphere. Here we investigate how torsional Alfvén waves driven at the photosphere can transport energy to an overlying coronal magnetic loop and explore their ability to heat the plasma. We consider a coronal loop whose feet are embedded in the partially ionized chromosphere. A broadband driver at the photosphere excites torsional Alfvén waves that propagate upward to the coronal loop. By means of numerical computations under the stationary-state assumption, we study the transmission of wave energy to the loop and the heating associated with ohmic diffusion and ion–neutral collisions. We find that wave transmission to the loop is heavily affected by the presence of cavity resonances when the frequency of the driver matches an eigenfrequency of the loop. A tremendous amount of wave energy is channeled to the coronal loop for those particular frequencies. The transmitted energy surpasses by many orders of magnitude the requirements to balance thermal radiation. However, dissipation is so weak in the coronal plasma that only a tiny percentage of the energy budget is converted into heat, which is not enough to compensate for radiative losses. Most of the energy simply leaks back to the chromosphere. Conversely, dissipation is much more efficient in the lower atmosphere, and wave heating can locally balance a significant fraction of radiation in the chromosphere. We argue that nonlinear effects such as turbulence triggered by the Kelvin–Helmholtz instability should enhance the heating efficiency at coronal heights.

Context.Partially ionized plasmas constitute an essential ingredient of the solar atmosphere since layers such as the chromosphere and the photosphere and structures such as prominences and spicules are made of this plasma. On the other hand, ground- and space-based observations have indicated the presence of oscillations in partially ionized layers and structures of the solar atmosphere, which have been interpreted in terms of magnetohydrodynamic (MHD) waves.Aims.Our aim is to study the temporal behavior of nonlinear Alfvén waves, and the subsequent excitation of field-aligned motions and perturbations, in a partially ionized plasma when dissipative mechanisms such as ambipolar diffusion, radiative losses, and thermal conduction are taken into account.Methods.First, we applied the regular perturbations method for small-amplitude initial perturbations to obtain the temporal behavior of perturbations. Then we solved the full set of nonlinear MHD equations for larger values of the initial amplitude.Results.We obtain analytical and numerical solutions to first-, second-, and third-order systems of equations and study the effects produced by ambipolar diffusion and thermal mechanisms on the temporal behavior of Alfvén and slow waves. We also study how the majority of the energy is transferred from the Alfvén waves to plasma internal energy. After numerically solving the full nonlinear equations when a large amplitude is assumed, the profile of the perturbations displays the typical sawtooth profile characteristic of associated shocks.Conclusions.When ambipolar diffusion is taken into account, first-order Alfvén waves are damped in time, while second-order perturbations are undamped. However, due to the release of heat produced by ambipolar diffusion, other physical effects that modify the physical conditions in the spatial domain under consideration appear. On the other hand, the second-order perturbations are damped by thermal effects with a damping time that can be longer or shorter than that of Afvén waves. Therefore, after the initial excitation, Alfvén waves can be quickly damped, while slow waves remain in the plasma for a longer time, and vice versa.

We have catalogued 196 filament oscillations from the GONG $H{\alpha}$ network data during several months near the maximum of solar cycle 24 (January - June 2014). Selected examples from the catalog are described in detail, along with our statistical analyses of all events. Oscillations were classified according to their velocity amplitude: 106 small-amplitude oscillations (SAOs), with velocities $10\mathrm{\, km \; s^{-1}}$. Both SAOs and LAOs are common, with one event of each class every two days on the visible side of the Sun. For nearly half of the events we identified their apparent trigger. The period distribution has a mean value of 58$\pm$15 min for both types of oscillations. The distribution of the damping time per period peaks at $\tau/P=1.75$ and $1.25$ for SAOs and LAOs respectively. We confirmed that LAO damping rates depend nonlinearly on the oscillation velocity. The angle between the direction of motion and the filament spine has a distribution centered at $27^\circ$ for all filament types. This angle agrees with the observed direction of filament-channel magnetic fields, indicating that most of the catalogued events are longitudinal (i.e., undergo field-aligned motions). We applied seismology to determine the average radius of curvature in the magnetic dips, $R\approx89$ Mm, and the average minimum magnetic-field strength, $B\approx16$ G. The catalog is available to the community online, and is intended to be expanded to cover at least 1 solar cycle., Comment: Accepted for publication in The Astrophysical Journal Supplement Series

Annual oscillations have been detected in many indices of solar activity during many cycles. Recent multi spacecraft observations of coronal bright points revealed slow retrograde toroidal phase drift (with the speed of 3 m/s of 1 yr oscillations, which naturally suggested their connection with Rossby-type waves in the interior. We have studied from a theoretical point of view the dynamics of global magneto-Kelvin and magneto-Rossby waves in the solar tachocline with toroidal magnetic field. Using spherical coordinates, the dispersion relations of the waves and latitudinal structure of solutions were obtained analytically. We have also obtained the spectrum of unstable magneto-Rossby wave harmonics in the presence of the latitudinal differential rotation. Estimated periods and phase speeds show that the magneto-Rossby waves rather than the Kelvin waves match with the observations of 1 yr oscillations. On the other hand, Morlet wavelet analysis of Greenwich Royal Observatory sunspot areas for the solar cycle 23 has revealed multiple periodicities with periods of 450-460 days, 370-380 days, 310-320 days, 240-270 days, and 150-175 days in hemispheric and full disk data. Comparison of theoretical results with the observations allow us to conclude that the global magneto-Kelvin waves in the upper overshoot tachocline may be responsible for the periodicity of 450-460 days (1.3 yrs), while the remaining periods can be connected with different harmonics of global fast magneto-Rossby waves., Comment: 13 pages, 8 figures, published in ApJ

Transverse oscillations of thin threads in solar prominences are frequently reported in high-resolution observations. The typical periods of the oscillations are in the range of 3 to 20 min. A peculiar feature of the oscillations is that they are damped in time, with short damping times corresponding to few periods. Theoretically, the oscillations are interpreted as kink magnetohydrodynamic waves. However, the mechanism responsible for the damping is not well known. Here we perform a comparative study between different physical mechanisms that may damp kink waves in prominence threads. The considered processes are thermal conduction, cooling by radiation, resonant absorption, and ion-neutral collisions. We find that thermal conduction and radiative cooling are very inefficient for the damping of kink waves. The effect of ion-neutral collisions is minor for waves with periods usually observed. Resonant absorption is the only process that produces an efficient damping. The damping times theoretically predicted by resonant absorption are compatible with those reported in the observations.

Prominence oscillations have been mostly detected using Doppler velocity, although there are also claimed detections by means of the periodic variations of half-width or line intensity. Our main aim here is to explore the relationship between spectral indicators such as Doppler shift, line intensity and line half-width and the linear perturbations excited in a simple prominence model.

Partially ionized plasmas are found across the Universe in many different astrophysical environments. They constitute an essential ingredient of the solar atmosphere, molecular clouds, planetary ionospheres and protoplanetary disks, among other environments, and display a richness of physical effects which are not present in fully ionized plasmas. This review provides an overview of the physics of partially ionized plasmas, including recent advances in different astrophysical areas in which partial ionization plays a fundamental role. We outline outstanding observational and theoretical questions and discuss possible directions for future progress., Comment: 163 pages, submitted to Space Science Reviews

Rieger-type periodicity has been detected in different activity indices over many solar cycles. It was recently shown that the periodicity correlates with solar activity having a shorter period during stronger cycles. Solar activity level is generally asymmetric between northern and southern hemispheres, which could suggest the presence of a similar behavior in the Rieger-type periodicity. We analyse the sunspot area/number and the total magnetic flux data for northern and southern hemispheres during solar cycles 19-23 which had remarkable north-south asymmetry. Using wavelet analysis of sunspot area and number during the north-dominated cycles (19-20) we obtained the periodicity of 160-165 days in the stronger northern hemisphere and 180-190 days in the weaker southern hemisphere. On the other hand, south-dominated cycles (21-23) display the periodicity of 155-160 days in the stronger southern hemisphere and 175-188 days in the weaker northern hemisphere. Therefore, the Rieger-type periodicity has the north-south asymmetry in sunspot area/number data during solar cycles with strong hemispheric asymmetry. We suggest that the periodicity is caused by magnetic Rossby waves in the internal dynamo layer. Using the dispersion relation of magnetic Rossby waves and observed Rieger periodicity we estimated the magnetic field strength in the layer as 45-49 kG in more active hemispheres (north during the cycles 19-20 and south during the cycles 21-23) and 33-40 kG in weaker hemispheres. The estimated difference in the hemispheric field strength is around 10 kG, which provides a challenge for dynamo models. Total magnetic flux data during the cycle 20-23 reveals no clear north-south asymmetry which needs to be explained in the future., Comment: 22 pages, 7 figures

Observations have shown that magnetohydrodynamic waves over a large frequency range are ubiquitous in solar prominences. The waves are probably driven by photospheric motions and may transport energy up to prominences suspended in the corona. Dissipation of wave energy can lead to heating of the cool prominence plasma, so contributing to the local energy balance within the prominence. Here we discuss the role of Alfv\'en wave dissipation as a heating mechanism for the prominence plasma. We consider a slab-like quiescent prominence model with a transverse magnetic field embedded in the solar corona. The prominence medium is modelled as a partially ionized plasma composed of a charged ion-electron single fluid and two separate neutral fluids corresponding to neutral hydrogen and neutral helium. Friction between the three fluids acts as a dissipative mechanism for the waves. The heating caused by externally-driven Alfv\'en waves incident on the prominence slab is analytically explored. We find that the dense prominence slab acts as a resonant cavity for the waves. The fraction of incident wave energy that is channelled into the slab strongly depends upon the wave period, $P$. Using typical prominence conditions, we obtain that wave energy trapping and associated heating are negligible when $P \gtrsim 100$ s, so that it is unlikely that those waves have a relevant influence on prominence energetics. When $1$ s $\lesssim P \lesssim 100$ s the energy absorption into the slab shows several sharp and narrow peaks, that can reach up to 100%, when the incident wave frequency matches a cavity resonance of the slab. Wave heating is enhanced at those resonant frequencies. Conversely, when $P \lesssim 1$ s cavity resonances are absent, but the waves are heavily damped by the strong dissipation. We estimate that wave heating may compensate for about 10% of radiative losses of the prominence plasma., Comment: Accepted for publication in A&A

Ground- and space-based observations have confirmed the presence of oscillatory motions in prominences and they have been interpreted in terms of magnetohydrodynamic (MHD) waves. This interpretation opens the door to perform prominence seismology, whose main aim is to determine physical parameters in magnetic and plasma structures (prominences) that are difficult to measure by direct means. Here, two prominence seismology applications are presented.

Prominence threads are expected to be cold plasma condensations in a long magnetic tube. Because of this density inhomogeneity along the magnetic field, the ratio of the fundamental transverse mode period to twice that of its first overtone, P{sub 1}/2P{sub 2}, must differ from 1. We investigate the dependence of this ratio on the equilibrium parameters of prominence threads and its possible use as a diagnostic tool for prominence seismology. Using the low-beta plasma approximation, we follow the procedure of previous works to obtain the frequencies and spatial distribution of the modes. We also check the thin tube approximation and find it reasonably accurate. The period ratio P{sub 1}/2P{sub 2} is found to be greater than unity, in contrast with coronal loops, for which the effect of inhomogeneities is to make this ratio smaller than 1. The ratio is very sensitive to the thread length, while the dependence on other parameters is less important for threads than for coronal loops. Hence, the period ratio can be used to obtain an estimation of the length of the supporting magnetic tube, since the thread length is known from observations. The obtained value of the tube length does not depend on other parameters,more » so their potential for prominence seismology may be great.« less

The presence of small-amplitude oscillations in prominences is well-known from long time ago. These oscillations, whose exciters are still unknown, seem to be of local nature and are interpreted in terms of magnetohydrodynamic (MHD) waves. During last years, observational evidence about the damping of these oscillations has grown and several mechanisms able to damp these oscillations have been the subject of intense theoretical modelling. Among them, the most efficient seem to be radiative cooling and ion-neutral collisions. Radiative cooling is able to damp slow MHD waves efficiently, while ion-neutral collisions, in partially ionised plasmas like those of solar prominences, can also damp fast MHD waves. In this paper, we plan to summarize our current knowledge about the time and spatial damping of small-amplitude oscillations in prominences.

Observations and models of solar prominences are reviewed. We focus on non-eruptive prominences, and describe recent progress in four areas of prominence research: (1) magnetic structure deduced from observations and models, (2) the dynamics of prominence plasmas (formation and flows), (3) Magneto-hydrodynamic (MHD) waves in prominences and (4) the formation and large-scale patterns of the filament channels in which prominences are located. Finally, several outstanding issues in prominence research are discussed, along with observations and models required to resolve them., Comment: 75 pages, 31 pictures, review paper

Material flows are typical features of prominences and are routinely observed in H α , UV and EUV lines. Therefore, including a magnetic field-aligned background flow, we study the effect of flows on the damping of non-adiabatic magnetohydrodynamic (MHD) waves in a magnetised unbounded prominence medium, and we explore the observational implications. We have linearised the non-adiabatic MHD equations and, considering only field-aligned propagation, we focus our study in the behaviour of thermal and slow waves. When a flow with a constant speed is present, two slow waves, with different periods, appear, while the damping time remains unchanged. On the other hand, the thermal wave becomes in this case a propagating wave, with finite period, while its damping time remains also unmodified. As a consequence of the changes in the periods produced by the flow, the damping per period of the different waves is modified. In the case of slow waves, and for a fixed flow speed, the damping per period of the high-period slow wave is increased while the opposite happens for the low-period slow wave, and the strongest finite damping per period, for the high-period slow wave, is obtained for flow speeds close to the non-adiabatic sound speed. In the case of the thermal wave, a finite value for the damping per period is obtained for any non-zero flow speed, and in this case the strongest finite damping per period is obtained for values of the flow speed close to zero. Furthermore, we point out that there is the possibility to have slow and thermal waves having the same period, the same damping time, or both simultaneously, which makes the proper identification of the waves for an external observer extremely difficult. Then, if flows are ubiquitous in prominences the observational determinations of periods and damping per period, made by an external observer, include its effect, and for a proper identification, information about the wavelength, flow speed and perturbations should be needed, which constitutes a truly difficult observational task.

Small-amplitude prominence oscillations are usually damped after a few periods. We study the attenuation of non-adiabatic magnetoacoustic waves in a slab prominence embedded in the coronal medium. We assume an equilibrium configuration with a transverse magnetic field to the slab axis and investigate wave damping by thermal conduction and radiative losses. The differential MHD equations that govern linear slow and fast modes are numerically solved to obtain the complex oscillatory frequency and the corresponding eigenfunctions. We find that coronal thermal conduction and radiative losses from the prominence plasma reveal as the most relevant damping mechanisms. Both mechanisms govern together the attenuation of hybrid modes, whereas prominence radiation is responsible for the damping of internal modes and coronal conduction essentially dominates the attenuation of external modes. In addition, the energy transfer between the prominence and the corona caused by thermal conduction has a noticeable effect on the wave stability, radiative losses from the prominence plasma being of paramount importance for the thermal stability of fast modes. We conclude that slow modes are efficiently damped, with damping times compatible with observations. On the contrary, fast modes are less attenuated by non-adiabatic effects and their damping times are several orders of magnitude larger than those observed. The presence of the corona causes a decrease of the damping times with respect to those of an isolated prominence slab, but its effect is still insufficient to obtain damping times of the order of the period in the case of fast modes., Accepted for publication in New Astronomy

High resolution observations of solar filaments suggest the presence of groups of prominence threads, i.e. the fine-structures of prominences, which oscillate coherently (in phase). In addition, mass flows along threads have been often observed. Here, we investigate the effect of mass flows on the collective fast and slow nonadiabatic magnetoacoustic wave modes supported by systems of prominence threads. Prominence fine-structures are modeled as parallel, homogeneous and infinite cylinders embedded in a coronal environment. The magnetic field is uniform and parallel to the axis of threads. Configurations of identical and nonidentical threads are both explored. We apply the T-matrix theory of acoustic scattering to obtain the oscillatory frequency and the eigenfunctions of linear magnetosonic disturbances. We find that the existence of wave modes with a collective dynamics, i.e. those that produce significant perturbations in all threads, is only possible when the Doppler-shifted individual frequencies of threads are very similar. This can be only achieved for very particular values of the plasma physical conditions and flow velocities within threads., Comment: Submitted in ApJ

Aims. We study the joint effect of ion-neutral collisions and thermal mechanisms on the damping of MHD waves in a partially ionised prominence plasma. Methods. Thermal conduction, radiation, and heating were included in the energy equation of the one-fluid MHD set of equations we derived earlier for an adiabatic, partially ionised plasma. Then, assuming small perturbations, these equations were linearised and the dispersion relation for magnetoacoustic, Alfven, and thermal waves obtained. Results. Compared with the non-adiabatic, fully ionised, and the adiabatic, partially ionised cases, the main result is that there is an increase in the efficiency of the damping of magnetoacoustic waves in prominence oscillations within the observed range of wavelengths for the magnetoacoustic waves. On the other hand, the Alfven wave is only damped by the ion-neutral collision mechanism, and this damping becomes important for almost neutral plasmas. Conclusions. The coupling of non-adiabatic mechanisms with the ion-neutral collisions mechanism offers a more complete model for the damping of magnetoacoustic waves with those values compatible with those observed in prominence oscillations. Furthermore, the ion-neutral collisions mechanism is able to damp the Alfven wave in an efficient way.

High-resolution observations show that oscillations and waves in prominence threads are common and that they are attenuated in a few periods. In addition, observers have also reported the presence of material flows in such prominence fine-structures. Here we investigate the time damping of non-leaky oscillations supported by a homogeneous cylindrical prominence thread embedded in an unbounded corona and with a steady mass flow. Thermal conduction and radiative losses are taken into account as damping mechanisms, and the effect of these non-ideal effects and the steady flow on the attenuation of oscillations is assessed. We solve the general dispersion relation for linear, non-adiabatic magnetoacoustic and thermal waves supported by the model, and find that slow and thermal modes are efficiently attenuated by non-adiabatic mechanisms. On the contrary, fast kink modes are much less affected and their damping times are much larger than those observed. The presence of flow has no effect on the damping of slow and thermal waves, whereas fast kink waves are more (less) attenuated when they propagate parallel (anti-parallel) to the flow direction. Although the presence of steady mass flows improves the efficiency of non-adiabatic mechanisms on the attenuation of transverse, kink oscillations for parallel propagation to the flow, its effect is still not enough to obtain damping times compatible with observations., Accepted for publication in ApJ

High-resolution observations provide evidence about the existence of small-amplitude transverse oscillations in solar filament fine structures. These oscillations are believed to represent fast magnetohydrodynamic (MHD) waves and the disturbances are seen to be damped in short timescales of the order of 1 to 4 periods. In this Letter we propose that, due to the highly inhomogeneous nature of the filament plasma at the fine structure spatial scale, the phenomenon of resonant absorption is likely to operate in the temporal attenuation of fast MHD oscillations. By considering transverse inhomogeneity in a straight flux tube model we find that, for density inhomogeneities typical of filament threads, the decay times are of a few oscillatory periods only., 11 pages, 2 figures, ApJL accepted

Recent observations with the Hinode Solar Optical Telescope display an active region prominence whose fine threads oscillate in the vertical direction as they move along a path parallel to the photosphere. A seismological analysis of this event is carried out by taking advantage of the small radius of these structures compared to the total length of magnetic field lines, i.e. by using the thin tube approximation. This analysis reveals that the oscillatory period is only slightly modified by the existence of the flow and that the difference between the period of a flowing thread and a static one is below the error bars of these observations. Moreover, although it is not possible to obtain values of the physical parameters, a lower bound for the Alfv\'en speed (ranging between 120 km s$^{-1}$ and 350 km s$^{-1}$) is obtained for each of the threads. Such Alfv\'en speeds agree with the intense magnetic fields and large densities usually found in active region prominences.

The solar corona is a complex magnetic environment where several kinds of waves can propagate. In this work, the properties of fast, Alfven, and slow magnetohydrodynamic waves in a simple curved structure are investigated. We consider the linear regime, i.e., small-amplitude waves. We study the time evolution of impulsively generated waves in a coronal arcade by solving the ideal magnetohydrodynamic equations. We use a numerical code specially designed to solve these equations in the low-beta regime. The results of the simulations are compared with the eigenmodes of the arcade model. Fast modes propagate nearly isotropically through the whole arcade and are reflected at the photosphere, where line-tying conditions are imposed. On the other hand, Alfven and slow perturbations are very anisotropic and propagate along the magnetic field lines. Because of the different physical properties in different field lines, there is a continuous spectrum of Alfven and slow modes. Curvature can have a significant effect on the properties of the waves. Among other effects, it considerably changes the frequency of oscillation of the slow modes and enhances the possible dissipation of the Alfven modes due to phase mixing.

The temporal evolution of a solar prominence inserted in a three-dimensional magnetic flux rope is investigated numerically. Using the model of Titov Demoulin (1999) under the regime of weak twist, the cold and dense prominence counteracts gravity by modifying the initially force-free magnetic configuration. In some cases a quasi-stationary situation is achieved after the relaxation phase, characterized by the excitation of standing vertical oscillations. These oscillations show a strong attenuation with time produced by the mechanism of continuum damping due to the inhomogeneous transition between the prominence and solar corona. The characteristic period of the vertical oscillations does not depend strongly on the twist of the flux rope. Nonlinearity is the responsible for triggering the Kelvin-Helmholtz instability associated to the vertical oscillations and that eventually produces horizontal structures. Contrary to other configurations in which the longitudinal axis of the prominence is permeated by a perpendicular magnetic field, like in unsheared arcades, the orientation of the prominence along the flux rope axis prevents the development of Rayleigh-Taylor instabilities and therefore the appearance of vertical structuring along this axis., Comment: Submitted to ApJ

Solar activity undergoes a variation over time scales of several months known as Rieger-type periodicity, which usually occurs near maxima of sunspot cycles. An early analysis showed that the periodicity appears only in some cycles, and is absent in other cycles. But the appearance/absence during different cycles has not been explained. We performed a wavelet analysis of sunspot data from the Greenwich Royal Observatory and the Royal Observatory of Belgium during cycles 14-24. We found that the Rieger-type periods occur in all cycles, but they are cycle-dependent: shorter periods occur during stronger cycles. Our analysis revealed a periodicity of 185-195 days during the weak cycles 14-15 and 24, and a periodicity of 155-165 days during the stronger cycles 16-23. We derived the dispersion relation of the spherical harmonics of the magnetic Rossby waves in the presence of differential rotation and a toroidal magnetic field in the dynamo layer near the base of the convection zone. This showed that the harmonic of fast Rossby waves with m=1 and n=4, where m (n) indicate the toroidal (poloidal) wavenumbers, respectively, perfectly fit with the observed periodicity. The variation of the toroidal field strength from weaker to stronger cycles may lead to the different periods found in those cycles, which explains the observed enigmatic feature of the Rieger-type periodicity. Finally, we used the observed periodicity to estimate the dynamo field strength during cycles 14-24. Our estimations suggest a field strength of 40 kG for the stronger cycles, and 20 kG for the weaker cycles., Comment: 23 pages, 4 figures, accepted in ApJ

Oscillations of magnetic structures in the solar corona have often been interpreted in terms of magnetohydrodynamic waves. We study the adiabatic magnetoacoustic modes of a prominence plasma slab with a uniform longitudinal magnetic field, surrounded by a prominence-corona transition region (PCTR) and a coronal medium. Considering linear small-amplitude oscillations, the dispersion relation for the magnetoacoustic slow and fast modes is deduced assuming evanescent-like perturbations in the coronal medium. In the system without PCTR, a classification of the oscillatory modes according to the polarisation of their eigenfunctions is made in order to distinguish modes with fast-like or slow-like properties. Internal and external slow modes are governed by the prominence and coronal properties respectively, and fast modes are mostly dominated by prominence conditions for the observed wavelengths. In addition, the inclusion of an isothermal PCTR does not substantially influence the mode frequencies, but new solutions (PCTR slow modes) are present., Accepted for publication in Solar Physics

The main aim of this study is to point out the difficulties found when trying to assess the statistical significance of the North-South asymmetry (hereafter SSNSA) of the most usually considered time series of solar activity. First of all, we distinguish between solar activity time series composed by integer or non-integer and dimensionless data, or composed by non-integer and dimensional data. For each of these cases, we discuss the most suitable statistical tests which can be applied and highlight the difficulties to obtain valid information about the statistical significance of solar activity time series. Our results suggest that, apart from the need to apply the suitable statistical tests, other effects such as the data binning, the considered units and the need, in some tests, to consider groups of data, affect substantially the determination of the statistical significance of the asymmetry. Our main conclusion is that the assessment of the statistical significance of the N-S asymmetry of solar activity is a difficult matter and that an absolute answer cannot be given, since many different effects influence the results given by the statistical tests. In summary, the quantitative results about the statistical significance of the N-S asymmetry of solar activity provided by different authors, as well as the studies about its behaviour, must be considered with care because they depend from the chosen values of different parameters or from the considered units., Comment: Astronomy and Astrophysics Latex, 9 pages, 4 figures

One of the typical features shown by observations of solar prominence oscillations is that they are quickly damped in time by one or several not well-known mechanisms. In addition, recent high resolution observations have revealed that the prominence fine structures, called fibrils, can oscillate with their own periods, independently from the rest of the prominence. The main aim of the present work is to study the attenuation of oscillations supported by a single prominence fibril. We consider an equilibrium made of a prominence plasma Cartesian slab of finite width embedded in a coronal medium, and assume non-adiabatic effects (thermal conduction, radiation losses and heating) as damping mechanisms. The magnetic field is taken uniform and parallel to the slab axis. We find that the efficiency of the non-adiabatic effects as damping mechanisms is different for each magnetoacoustic mode. The obtained values of the damping time are compatible with those observed in the case of the slow modes, but the fast modes are much less attenuated.

We study the excitation and damping of transverse oscillations in a complex multi-stranded model of a coronal loop. By numerically solving the time-dependent magnetohydrodynamic (MHD) equations in two dimensions, we show how the global motion of the whole bundle of tubes, produced by an external disturbance, is converted into localised motions due to the process of resonant absorption. At any location in the structure two dominant frequencies are found, the frequency of the global mode (different from the kink frequency of the individual strands) and the local Alfvén frequency. The mechanism of mode conversion is not affected by the complicated geometry of the system and for certain configurations the energy conversion does not only take place at the external edge of the composite loop but also inside the structure.

Recent high-resolution observations have pointed out that prominences are made of small threads (also named fibrils) piled up to form the body of the prominence. These fine structures also seem to support their own oscillatory modes, while their effect on the global modes of the prominences are less certain. We study the effect of adding a smooth transition layer between the prominence material and the corona along the magnetic field line, since previous studies have considered a jump in density in this interface. Then we compare the results with previous models and check that these transition layers do not affect significantly the periods of the modes.

We present results on the oscillatory properties (periods, damping rates, and spatial distribution of perturbations) for resonantly damped oscillations in a system of two inhomogeneous coronal slabs and compare them to the properties found in single slab loop models. A system of two identical coronal loops is modelled, in Cartesian geometry, as being composed by two density enhancements. The linear magnetohydrodynamic (MHD) wave equations for oblique propagation of waves are solved and the damping due to resonant absorption is computed. Due to the interaction between the loops, the normal modes of oscillation present in a single slab split into symmetric and antisymmetric oscillations when a system of two identical slabs is considered. The frequencies of these solutions may differ from the single slab results when the distance between the loops is of the order of a few slab widths. Oblique propagation of waves weakens this interaction, since solutions become more confined to the edges of the slabs. The damping is strong for surface-like oscillations, while sausage body-like solutions are unaffected.

Context. The geometry and physical conditions in solar coronal loops are complicated and still not understood well. Recent high-resolution observations obtained with TRACE indicate the existence of sub-resolution transverse structuring not accessible to direct observation. This ingredient has not yet been taken into account in the previous theoretical models used for the study of transversal coronal loop oscillations and of their damping due to resonant conversion of energy. Aims. This study aims to assess the effect of the possibly unresolved internal structure of a coronal loop on the properties of its transverse oscillations and on the efficiency of resonant absorption as a damping mechanism of these oscillations. Methods. The equilibrium configuration of a single coronal loop with internal density structuring is modelled by considering the loop as composed of two very close, parallel, identical coronal slabs in Cartesian geometry. The period of the oscillation and the damping time are computed for the resonantly damped fundamental kink mode. These quantities are then compared to those obtained for two models for a single equivalent slab without internal density structuring. Results. We find that the period and the damping time of a coronal loop with internal density structuring change by less than 15%, when compared to the same oscillatory properties of a single coronal loop with either the same density contrast or a single coronal loop with the same total mass. Conclusions. Therefore the internal density structuring of a coronal loop does not affect its oscillatory properties very much. However, the sub-resolution structuring of a coronal loop with different densities in its components or with different widths could vary these results.

Aims. The role of collisions between ions, electrons and neutrals in a partially ionised plasma is assessed as a possible wave damping mechanism. The relevance of this mechanism in the damping of small amplitude prominence oscillations is evaluated. Methods. A one-fluid MHD set of equations taking into account various effects in a partially ionised solar plasma (collisions between different species and Joule dissipation) is derived. Assuming small perturbations, these equations are next linearised about a uniform equilibrium configuration and the dispersion relation of magnetoacoustic waves in an unbounded medium is obtained. Results. The presence of neutrals in the plasma only affects the fast wave in a relevant way. An approximate expression for the damping rate is obtained which shows that the strongest damping takes place in a medium with strong magnetic field, low density and low ionisation fraction. Wave attenuation arises mostly from collisions between ions and neutrals. Conclusions. Given the poor knowledge about the values of the density and ionisation fraction in prominences, it is hard to judge the importance of the physics of partial ionisation in the damping of fast waves in solar prominences. Nevertheless, note that a very idealised case, with no stratification and no equilibrium currents, is considered here, so the addition of these features to the model may change the results of this work.

We study the kink modes of oscillation of a curved coronal loop using a toroidal model with a power-law density profile. We find that there are two kink modes and that their velocity polarization is either mainly horizontal or mainly vertical with respect to the photosphere. It is found that the damping by resonant absorption in an inhomogeneous layer between the loop and the coronal environment is slightly more efficient than for the straight magnetic cylinder and that the period and damping time of the two kink modes are very similar. In an equilibrium with nonuniform Alfven frequency, the kink modes display two additional features, namely, the coupling to an Alfven mode of the external medium (which gives rise to resonant absorption in the corona) and wave leakage by tunneling at some distance from the loop. Hence, in general the modes are resonantly damped and leaky at the same time, although our results point out that resonant absorption at the loop boundary is the dominant damping mechanism.

Aims. We study fast magnetohydrodynamic waves in a system of two coronal loops modeled as smoothed, dense plasma slabs in a uniform magnetic field. This allows us to analyse in a simple configuration the collective behaviour of the structure due to the interaction between the slabs. Methods. We first calculate the normal modes of the system and find analytical expressions for the dispersion relation of the two-slab configuration. Next, we study the time-dependent problem of the excitation of slab oscillations by numerically solving the initial value problem. We investigate the behaviour of the system for several shapes of the initial disturbances. Results. The symmetric mode respect to the centre of the structure is the only trapped mode for all distances between the slabs while the antisymmetric mode is leaky for small slab separations. Nevertheless, there is a wide range of slab separations for which the fundamental symmetric and antisymmetric trapped modes are allowed and have very close frequencies. These modes are excited according to the parity of the initial perturbation. Conclusions. We find that for any initial disturbance the slabs oscillate with the normal modes of the coupled slab system, which are different from the modes of the individual slabs. We show that it is possible to excite the symmetric and antisymmetric trapped modes at the same time. This kind of excitation can produce the beating phenomenon, characterised by a continuous exchange of energy between the individual slabs.

Aims. We study the spatial damping of linear non-adiabatic magnetoacoustic waves in a homogeneous, isothermal, and unbounded medium permeated by a uniform magnetic field, with physical properties akin to those of solar prominences.unbounded Methods. We consider an energy equation with optically thin radiative losses, thermal conduction, and heating, and linearize the MHD equations to obtain a sixth-order polynomial in the wavenumber k, which represents the dispersion relation for slow, fast, and thermal MHD waves. Since we are interested in the spatial damping, we have taken as real and have numerically solved the dispersion relation to obtain complex solutions for the wavenumber k corresponding to fast, slow, and thermal waves. Results. The thermal wave shows the strongest spatial damping, while the fast wave shows the weakest spatial damping. At periods greater than 1 s the spatial damping of magnetoacoustic waves is dominated by radiation, while at shorter periods the spatial damping is dominated by thermal conduction. For very short periods the isothermal regime is attained and the damping length becomes almost constant. Conclusions. Radiative effects on linear magnetoacoustic slow waves can be a viable mechanism for the spatial damping of short period prominence oscillations, while thermal conduction does not play any role. In particular, short-period oscillations (5-15 min) observed in quiescent limb prominences, which seem to be due to internal fundamental slow modes, have damping lengths in the range 10 4 -5 × 10 4 km, in good agreement with our results.

In this paper we study how the normal fast modes of a coronal loop are modified by the addition of density structure along the loop axis. Using isobaric and thermal equilibria with different heating functions, a density profile for a loop is derived, and then its oscillatory modes are studied with techniques similar to those in our previous works. The main result is that the frequency and spatial structure of the trapped modes are very sensitive to density variations inside the loop, especially at the apex, where the density depends strongly on the footpoint density and the ratio of heating to thermal conduction. Moreover, different tested heating profiles do not introduce important differences with respect to the case of uniform heating along the loop.

Prominence seismology is a rapidly developing topic which seeks to infer the internal structure and properties of solar prominences from the study of its oscillations. Two-dimensional high-resolution observations suggest that filaments can be considered as made by small scale fibrils, having a cool region, stacked one after another in the vertical and horizontal directions. An extense observational background about oscillations in filaments has been gathered during the last 20 years and these observations point out that fibrils or groups of fibrils can oscillate independently. From the theoretical point of view, small amplitude oscillations in single and multifibril configurations have been studied as a first step to explain observational features.

Prominence seismology is a rapidly developing topic which seeks to infer the internal structure and properties of solar prominences from the study of their oscillations. An extense observational background about oscillations in quiescent solar prominences has been gathered during the last 70 years. These observations point out the existence of two different types of oscillations: flare-induced oscillations (winking filaments) which affect the whole prominence and are of large amplitude and small amplitude oscillations which seem to be of local nature. From the theoretical point of view, few models have been set up to explain the phenomenon of winking filaments while, on the contrary, for small amplitude oscillations a large number of models trying to explain the observed features have been proposed. Here, recent theoretical and observational developments on both types of oscillations are reviewed, and suggestions about future research topics which should provide us with a more in-depth knowledge of solar prominences are made.

The excitation and damping of transversal coronal loop oscillations is studied using one-and two-dimensional models of line-tied cylindrical loops. By solving the time-dependent magnetohydrodynamic equations it is shown how an initial disturbance generated in the solar corona induces kink mode oscillations. We investigate the effect of the disturbance on a loop with a non-uniform boundary layer. In particular, a strong damping of transversal oscillations due to resonant absorption is found, such as predicted by previous works based on normal mode analysis.

Prominence seismology is a rapidly developing topic which seeks to infer the internal structure and properties of solar prominences from the study of its oscillations. An extensive observational background about oscillations in quiescent solar prominences has been gathered during the last 70 years. These observations point out the existence of two different types of oscillations: Flare-induced oscillations (winking filaments) which affect the whole prominence and are of large amplitude and small amplitude oscillations which seem to be of local nature. From the theoretical point of view, few models have been set up to explain the phenomenon of winking filaments while, on the contrary, for small amplitude oscillations a large number of models trying to explain the observed features have been proposed.

We study the excitation of fast waves in solar coronal loops modeled as smoothed, dense plasma slabs in a uniform magnetic field. We analyse the features of the trapped and leaky modes which result from an initial disturbance generated in the loop. By solving the time-dependent problem we find that the stationary state of the slab motion is described by the trapped normal modes and that the transient between the initial and the stationary phase is dominated by wave leakage. The period and duration of this transient (what we call the impulsive leaky phase) are in perfect agreement with the corresponding values of leaky modes calculated from the normal mode analysis.

Observations of quiescent filaments show very fine structures which suggests that they can be composed of small-scale threads or fibrils. Two-dimensional, high-resolution observations point out that individual fibrils or groups of fibrils may oscillate independently with their own periods. In this paper, we study the fast magnetohydrodynamic modes of oscillation of multifibril Cartesian systems to represent the oscillations of the fibril structure of a real prominence. In the case of a system made of equal fibrils, our results show that the only non-leaky mode is the symmetric one, which means that all the fibrils oscillate in spatial phase with the same frequency. On the other hand, in a system made of non-equal fibrils, i.e. with different Alfven speeds, the results show that the amplitudes of oscillation are higher in the denser fibrils, that the frequency of oscillation of the only non-leaky mode is slightly smaller than that of the dominant fibril considered alone, and that all the fibrils also oscillate in phase.

We study the time damping of linear non-adiabatic magnetoacoustic waves in a homogeneous, isothermal and bounded magnetic slab of plasma with physical properties akin to those of quiescent solar prominences. Because of the chosen configuration, our results are related to short or intermediate period prominence oscillations and show that the damping times of fast modes are very long compared to those of slow modes. In an attempt to mimic optically thick prominences, differ- ent prominence regimes have been considered by reducing radiative losses. Then, when the temperature and/or density of the prominence are modified, the damping time varies in a complex way which also depends on the prominence regime considered. In all the prominence regimes, a minimum of the damping time can be obtained for a certain value of temperature and density. Finally, the consideration of different heating mechanisms, the case of no heating included, can modify the damping times in a substantial way while the periods are only slightly affected.

We suggest that the periodic shaking of coronal magnetic field lines due to photospheric periodic motions may induce the parametric excitation of slow magnetoacoustic waves in short coronal magnetic structures (with length < 50−70 Mm). Considering the periodic shaking of field lines as an external transversal periodic action on the coronal plasma we show that the temporal behaviour of slow wave spatial Fourier harmonics in the low plasma β limit is governed by the Mathieu equation. Consequently, harmonics of slow magnetoacoustic waves with half the frequency of the photospheric driver have an exponential growth in time. The growth rate of slow waves is proportional to the amplitude of photospheric motions and to the value of the plasma β in the corona. The mechanism may explain the existence of slow magnetoacoustic waves at least in short coronal loop systems (Nightingale et al. 1999, Sol. Phys., 190, 249).