Fast magnetohydrodynamic oscillation of longitudinally inhomogeneous prominence threads: an analogue with quantum harmonic oscillator |
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Teimuraz Zaqarashvili Submitted: 2014-04-11 02:46
Previous works indicate that the frequency ratio of second and first harmonics of kink oscillations tends towards 3 in the case of prominence threads. We aim to study the magnetohydrodynamic oscillations of longitudinally inhomogeneous prominence threads and to shed light on the problem of the frequency ratio. The classical Sturm-Liouville problem is used for the threads with longitudinally inhomogeneous plasma density. We show that the spatial variation of total pressure perturbations along the thread is governed by the stationary Schr?dinger equation, where the longitudinal inhomogeneity of plasma density stands for the potential energy. The Schr?dinger equation appears as the equation of quantum harmonic oscillator for a parabolic profile of plasma density. Consequently, the equation has bounded solutions in terms of Hermite polynomials. Boundary conditions at the thread surface lead to a transcendental dispersion equation with Bessel functions. The thin flux tube approximation of the dispersion equation shows that the frequency of kink waves is proportional to the expression α 2n+1), where α is the density inhomogeneity parameter, and n the longitudinal mode number. Consequently, the ratio of the frequencies of second and first harmonics tends to 3 in prominence threads. The numerical solution of the dispersion equation shows that the ratio decreases only slightly for thicker tubes in the case of less longitudinal inhomogeneity of the external density, therefore the thin flux tube limit is a good approximation for prominence oscillations. However, stronger longitudinal inhomogeneity of external density may lead to the significant shift in the frequency ratio for wider tubes, and therefore the thin tube approximation may fail. The tendency of frequency ratio of second and first harmonics towards 3 in prominence threads is explained by the analogy of the oscillations with quantum harmonic oscillator, where the density inhomogeneity of the threads plays a role as the potential energy.
Authors: Lomineishvili, S.N., Zaqarashvili, T.V., Zhelyazkov, I. and Tevzadze, A.G.
Projects: None
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Publication Status: Accepted in A&A
Last Modified: 2014-04-14 12:51
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Twisted magnetic flux tubes in the solar wind |
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Teimuraz Zaqarashvili Submitted: 2014-02-11 08:51
Magnetic flux tubes in the solar wind can be twisted as they are transported from the solar surface, where the tubes are twisted owing to photospheric motions. It is suggested that the twisted magnetic tubes can be detected as the variation of total (thermal+magnetic) pressure during their passage through observing satellite. We show that the total pressure of several observed twisted tubes resembles the theoretically expected profile. The twist of isolated magnetic tube may explain the observed abrupt changes of magnetic field direction at tube walls. We have also found some evidence that the flux tube walls can be associated with local heating of the plasma and elevated proton and electron temperatures. For the tubes aligned with the Parker spiral, the twist angle can be estimated from the change of magnetic field direction. Stability analysis of twisted tubes shows that the critical twist angle of the tube with a homogeneous twist is 700, but the angle can further decrease owing to the motion of the tube with regards to the solar wind stream. The tubes with a stronger twist are unstable to the kink instability, therefore they probably can not reach 1 AU.
Authors: Zaqarashvili, T.V., V"or"os, Z., Narita, Y., Bruno, R.
Projects: Wind
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Publication Status: ApJL (in press)
Last Modified: 2014-02-11 12:20
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Rossby waves and polar spots in rapidly rotating stars: Implications for stellar wind evolution |
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Teimuraz Zaqarashvili Submitted: 2013-11-20 07:41
Rapidly rotating stars show short-period oscillations in
magnetic activity and polar appearance of starspots. The aim of this paper is to study large-scale shallow water waves in the tachoclines of rapidly rotating stars and their connection to the periodicity and the formation of starspots at high latitudes. Shallow-water magnetohydrodynamic equations were used to study the dynamics of large-scale waves at the rapidly rotating
stellar tachoclines in the presence of toroidal magnetic field. Dispersion relations and latitudinal distribution of wave modes were derived. We found that low-frequency magnetic Rossby waves tend to be located at poles, but high-frequency magnetic Poincar'e waves are concentrated near the equator in rapidly rotating stars. These
results have important implications for the evolution of the stellar wind in young Sun-like stars. Unstable magnetic Rossby waves may lead to the local enhancement of magnetic flux at high latitudes of tachoclines in rapidly rotating stars. The enhanced magnetic flux may rise upwards owing to the magnetic buoyancy in the form of tubes and appear as starspots at polar regions. Magnetic Rossby waves may
also cause observed short-term periodicity in the stellar magnetic activity.
Authors: Zaqarashvili, T.V., Oliver, R., Ballester, J.L., Carbonell, M., Khodachenko, M.L., Lammer, H., Leitzinger, M. and Odert, P.
Projects: None
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Publication Status: Published in A&A
Last Modified: 2013-11-20 07:48
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Radio seismology of the outer solar corona |
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Teimuraz Zaqarashvili Submitted: 2013-11-20 07:25
Observed oscillations of coronal loops in extreme ultraviolet (EUV) lines have been successfully used to estimate plasma parameters in the inner corona (< 0.2 R, where R is the solar radius). However, coronal seismology in EUV lines fails for higher altitudes because of rapid decrease in line intensity. We aim to use radio observations to estimate the plasma parameters of the outer solar corona (> 0.2 R). We used the large Ukrainian radio telescope URAN-2 to observe type IV radio bursts at the frequency range of 8-32 MHz during the time interval of 09:50-12:30 UT on April 14, 2011. The burst was connected to C2.3 flare, which occurred in AR 11190 during 09:38-09:49 UT. The dynamic spectrum of radio emission shows clear quasi-periodic variations in the emission intensity at almost all frequencies. Wavelet analysis at four different frequencies (29 MHz, 25 MHz, 22 MHz, and 14 MHz) shows the quasi-periodic variation of emission intensity with periods of 34 min and 23 min. The periodic variations can be explained by the first and second harmonics of vertical kink oscillation of transequatorial coronal loops, which were excited by the same flare. The apex of transequatorial loops may reach up to 1.2 R altitude. We derive and solve the dispersion relation of trapped magnetohydrodynamic (MHD) oscillations in a longitudinally inhomogeneous magnetic slab. The analysis shows that a thin (with width to length ratio of 0.1), dense (with the ratio of internal and external densities of > 20) magnetic slab with weak longitudinal inhomogeneity may trap the observed oscillations. Seismologically estimated Alfvén speed inside the loop at the height of 1 R is 1000 km s/s. The magnetic field strength at this height is estimated as 0.9 G. Extrapolation of magnetic field strength to the inner corona gives 10 G at the height of 0.1 R. Radio observations can be successfully used for the sounding of the outer solar corona, where EUV observations of coronal loops fail. Therefore, radio seismology of the outer solar corona is complementary to EUV seismology of the inner corona.
Authors: Zaqarashvili, T.V., Melnik, V.N., Brazhenko, A.I., Panchenko, M., Konovalenko, A.A., Franzuzenko, A.V., Dorovskyy, V.V., Rucker, H.O.
Projects: None
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Publication Status: Published in A&A
Last Modified: 2013-11-20 07:48
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Torsional Alfvén waves in partially ionized solar plasma: effects of neutral helium and stratification |
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Teimuraz Zaqarashvili Submitted: 2013-11-20 07:19
Ion-neutral collisions may lead to the damping of Alfvén waves in chromospheric and prominence plasmas. Neutral helium atoms enhance the damping in certain temperature intervals, where the ratio of neutral helium and neutral hydrogen atoms is increased. Therefore, the height dependence of the ionization degrees of hydrogen and helium may influence the damping rate of Alfvén waves. We aim to study the effect of neutral helium on the damping of Alfvén waves in stratified, partially ionized plasma of the solar chromosphere. We consider a magnetic flux tube, which is expanded up to 1000 km height and then becomes vertical owing to merging with neighboring tubes, and study the dynamics of linear torsional Alfvén waves in the presence of neutral hydrogen and neutral helium atoms. We start with a three-fluid description of plasma and subsequently derive single-fluid magnetohydrodynamic (MHD) equations for torsional Alfvén waves. Thin flux tube approximation allows us to obtain the dispersion relation of the waves in the lower part of tubes, while the spatial dependence of steady-state Alfvén waves is governed by a Bessel-type equation in the upper parts of the tubes. Consecutive derivation of single-fluid MHD equations results in a new Cowling diffusion coefficient in the presence of neutral helium, which is different from the previously used one. We find that shorter period (< 5 s) torsional Alfvén waves damp quickly in the chromospheric network owing to ion-neutral collision. On the other hand, longer period (> 5 s) waves do not reach the transition region because they become evanescent at lower heights in the network cores. Propagation of torsional Alfvén waves through the chromosphere into the solar corona should be considered with caution: low-frequency waves are evanescent owing to the stratification, while high-frequency waves are damped by ion-neutral collisions.
Authors: Zaqarashvili, T.V., Khodachenko, M.L. and Soler, R.
Projects: None
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Publication Status: published in A&A
Last Modified: 2013-11-20 07:48
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Cut-off wavenumber of Alfvén waves in partially ionized plasmas of the solar atmosphere |
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Teimuraz Zaqarashvili Submitted: 2013-11-20 07:14
Alfvén wave dynamics in partially ionized plasmas of the solar atmosphere shows that there is indeed a cut-off wavenumber, i.e. the Alfvén waves with wavenumbers higher than the cut-off value are evanescent. The cut-off wavenumber appears in single-fluid magnetohydrodynamic (MHD) approximation but it is absent in a multi-fluid approach. Up to now, an explanation for the existence of the cut-off wavenumber is still missing. The aim of this paper is to point out the reason for the appearance of a cut-off wavenumber in single-fluid MHD. Beginning with three-fluid equations (with electrons, protons and neutral hydrogen atoms), we performed consecutive approximations until we obtained the usual single-fluid description. We solved the dispersion relation of linear Alfvén waves at each step and sought the approximation responsible of the cut-off wavenumber appearance. We have found that neglecting inertial terms significantly reduces the real part of the Alfvén frequency although it never becomes zero. Therefore, the cut-off wavenumber does not exist at this stage. However, when the inertial terms together with the Hall term in the induction equation are neglected, the real part of the Alfvén frequency becomes zero. The appearance of a cut-off wavenumber, when Alfvén waves in partially ionized regions of the solar atmosphere are studied, is the result of neglecting inertial and Hall terms, therefore it has no physical origin.
Authors: Zaqarashvili, T. V., Carbonell, M., Ballester J. L. and Khodachenko, M. L.
Projects: None
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Publication Status: published in A&A
Last Modified: 2013-11-20 07:48
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Damping of Alfvén waves in solar partially ionized plasmas: effect of neutral helium in multi-fluid approach |
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Teimuraz Zaqarashvili Submitted: 2011-09-07 04:18
Chromospheric and prominence plasmas contain neutral atoms, which may change the plasma dynamics through collision with ions. Most of the atoms are neutral hydrogen, but a significant amount of neutral helium may also be present in the plasma with a particular temperature. Damping of MHD waves due to ion collision with neutral hydrogen is well studied, but the effects of neutral helium are largely unknown. We aim to study the effect of neutral helium in the damping of Alfvén waves in solar partially ionized plasmas. We consider three-fluid magnetohydrodynamic (MHD) approximation, where one component is electron-proton-singly ionized helium and other two components are the neutral hydrogen and neutral helium atoms. We derive the dispersion relation of linear Alfvén waves in isothermal and homogeneous plasma. Then we solve the dispersion relation and derive the damping rates of Alfvén waves for different plasma parameters. The presence of neutral helium significantly enhances the damping of Alfvén waves compared to the damping due to neutral hydrogen at certain values of plasma temperature (10000-40000 K) and ionization. Damping rates have a peak near the ion-neutral collision frequency, but decrease for the higher part of wave spectrum. Collision of ions with neutral helium atoms can be of importance for the damping of Alfvén waves in chromospheric spicules and in prominence-corona transition regions.
Authors: Zaqarashvili, T.V., Khodachenko, M.L., and Rucker, H.O.
Projects: None
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Publication Status: Accepted in A&A
Last Modified: 2011-09-07 05:43
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Magnetohydrodynamic waves in solar partially ionized plasmas: two-fluid approach |
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Teimuraz Zaqarashvili Submitted: 2011-01-21 02:17
Partially ionized plasma is usually described by single-fluid approach, where the ion-neutral collision effects are expressed by Cowling conductivity in the induction equation. However, the single-fluid approach is not valid for the time-scales less than ion-neutral collision time. For these time-scales the two-fluid description is better approximation. We derive the dynamics of magnetohydrodynamic waves in two-fluid partially ionized plasmas and to compare the results with those obtained under single-fluid description. Two-fluid magnetohydrodynamic equations are used, where ion-electron plasma and neutral particles are considered as separate fluids. Dispersion relations of linear magnetohydrodynamic waves are derived for simplest case of homogeneous medium. Frequencies and damping rates of waves are obtained for different parameters of background plasma. We found that two- and single-fluid descriptions give similar results for low frequency waves. However, the dynamics of MHD waves in two-fluid approach is significantly changed when the wave frequency becomes comparable or higher than ion-neutral collision frequency. Alfvén and fast magneto-acoustic waves attain their maximum damping rate at particular frequencies (for example, the peak frequency equals 2.5 ion-neutral collision frequency for 50 % of neutral Hydrogen) in wave spectrum. The damping rates are reduced for higher frequency waves. The new mode of slow magneto-acoustic wave appears for higher frequency branch, which is connected to neutral hydrogen fluid. The single-fluid approach perfectly deals with slow processes in partially ionized plasmas, but fails for time-scales smaller than ion-neutral collision time. Therefore, two-fluid approximation should be used for the description of relatively fast processes. Some results of single-fluid description, for example the damping of high-frequency Alfvén waves in the solar chromosphere due to ion-neutral collisions, should be revised in future.
Authors: Zaqarashvili, T. V., Khodachenko, M. K., Rucker, H. O.
Projects: None
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Publication Status: A&A (accepted)
Last Modified: 2011-01-21 08:46
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Magnetic Rossby waves in the solar tachocline and Rieger-type periodicities |
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Teimuraz Zaqarashvili Submitted: 2009-11-25 07:29
Apart from the 11-year solar cycle, another periodicity around 155-160 days was discovered during solar cycle 21 in high energy solar flares, and its presence in sunspot areas and strong magnetic flux has been also reported. This periodicity has an elusive and enigmatic character, since it usually appears only near the maxima of solar cycles, and seems to be related with a periodic emergence of strong magnetic flux at the solar surface. Therefore, it is probably connected with the tachocline, a thin layer located near the base of the solar convection zone, where strong dynamo magnetic field is stored. We study the dynamics of Rossby waves in the tachocline in the presence of a toroidal magnetic field and latitudinal differential rotation. Our analysis shows that the magnetic Rossby waves are generally unstable and that the growth rates are sensitive to the magnetic field strength and to the latitudinal differential rotation parameters. Variation of the differential rotation and the magnetic field strength throughout the solar cycle enhance the growth rate of a particular harmonic in the upper part of the tachocline around the maximum of the solar cycle. This harmonic is symmetric with respect to the equator and has a period of 155-160 days. A rapid increase of the wave amplitude could give place to a magnetic flux emergence leading to observed periodicities in solar activity indicators related with magnetic flux.
Authors: Zaqarashvili, T.V. , Carbonell, M., Oliver, R. and Ballester, J.L.
Projects: None
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Publication Status: Accepted in ApJ
Last Modified: 2009-11-25 10:56
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Acoustic oscillations in the field-free, gravitationally stratified cavities under solar bipolar magnetic canopies |
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Teimuraz Zaqarashvili Submitted: 2009-06-10 05:48
The main goal is to study the dynamics of the gravitationally stratified, field-free cavities in the solar atmosphere, located under small-scale, cylindrical magnetic canopies, in response to explosive events in the lower-lying regions (due to granulation, small-scale magnetic reconnection, etc.). We derive the two-dimensional Klein-Gordon equation for isothermal density perturbations in cylindrical coordinates. The equation is first solved by a standard normal mode analysis in order to obtain the free oscillation spectrum of the cavity. Then, the equation is solved in the case of impulsive forcing associated to a pressure pulse specified in the lower-lying regions. The normal mode analysis shows that the entire cylindrical cavity of granular dimensions tends to oscillate with frequencies of 5-8 mHz and also with the atmospheric cut-off frequency. Furthermore, the passage of a pressure pulse, excited in the convection zone, sets up a wake in the cavity oscillating with the same cut-off frequency. The wake oscillations can resonate with the free oscillation modes, which leads to an enhanced observed oscillation power. The resonant oscillations of these cavities explain the observed power halos near magnetic network cores and active regions.
Authors: Kuridze, D., Zaqarashvili, T.V., Shergelashvili, B.M. and Poedts, S.
Projects: None
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Publication Status: A&A (accepted)
Last Modified: 2009-06-10 09:18
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