Coronal Leaky Tube Waves and Oscillations Observed with Trace

Leaky tube waves are examined in the context of kink oscillations in coronal loops, observed in recent years using TRACE. It is pointed out that the standard (non-leaky) principal kink mode has a leaky bifurcated counterpart with decay time 4^–4(L/R)² P, where R and L are the loop radius and length, and P is the oscillation period. This is somewhat too long to explain the observed decays, except for very short or thick loops, but may be implicated in the initial excitation. Higher harmonics decay much more rapidly. The external solution takes the form of a wave running nearly parallel to the tube, but with a small outward component. In addition, a number of other leaky modes are described which decay on timescales of seconds, =Ra _e/a ², where a and a _e are the loop and external Alfvén speeds respectively, and which can be identified as being almost radially propagating fast magnetoacoustic waves. These are outside the currently observable range, but are likely to be important energetically.     

On the Excitation of Leaky Modes in Cylindrical Loops

The role of leaky waves in the coronal loop oscillations observed by TRACE is not yet clearly understood. In this work, the excitation of fast waves in solar coronal loops modelled as dense plasma cylindrical tubes in a uniform straight magnetic field is investigated. We study the trapped and especially leaky modes (whose energy escapes from the tube) that result from an initial disturbance by solving the time-dependent problem numerically. We find that the stationary state of the tube motion is given by the trapped normal modes. By contrast, the transient behaviour between the initial and the stationary phase is dominated by wave leakage. The so-called trig leaky modes are clearly identified since the transient behaviour shows periods and damping times that are in agreement with the values calculated from the normal-mode analysis. Consequently, these radiating modes have physical significance. However, we have not found any evidence for the excitation of other types of modes, such as the principal leaky kink mode. J. Andries is postdoctoral Fellow of the National Fund for Scientific Research – Flanders (Belgium) (F.W.O.-Vlaanderen).     

Non-Axisymmetric Oscillations of Thin Prominence Fibrils

We study non-axisymmetric oscillations of thin prominence fibrils. A fibril is modeled by a straight thin magnetic tube with the ends frozen in dense plasmas. The density inside and outside the tube varies only along the tube and it is discontinuous at the tube boundary. Making a viable assumption that the tube radius is much smaller than its length, we show that the squares of the frequencies of non-axisymmetric tube oscillations are given by the eigenvalues of the Sturm–Liouville problem for a second-order ordinary differential equation on a finite interval with the zero boundary conditions. For an equilibrium density that is constant outside the tube and piecewise constant inside we derived a simple dispersion equation determining the frequencies of non-axisymmetric oscillations. We carry out a parametric study of this equation both analytically and numerically, restricting our analysis to the first even mode and the first odd mode. In particular, we obtained a criterion that allows to find out if each of these modes is a normal or leaky mode.     

Helioseismology program for the PICARD satellite

The PICARD mission is a CNES micro‐satellite to be launched in 2009. Its goal is to better understand the Sun and the potential impact of its activity on earth climate by measuring simultaneously the solar total and spectral irradiance, diameter, shape and oscillations. We present the scientific objectives, instrumental requirements and data products of the helioseismology program of PICARD which aims to observe the low to medium l p‐mode oscillations in intensity and search for g‐mode oscillation signatures at the limb. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Spectrum of Torsional Oscillations of the Moon

The diagnostic potentialities of the torsional oscillations for probing the structure of the interiors of the Moon are investigated. Models with no core, a liquid core, and a solid core are considered. The profiles of compressional and shear wave velocities V _P and V _S for the lunar interior estimated by Bills and Ferrari (1977), Goins et al. (1981), and Nakamura (1983) from the Apollo lunar seismic network are used. For all these models, the periods of torsional oscillations for n = 2–100 and four overtones have been calculated. The derivatives of the dimensionless eigenfrequency with respect to the dimensionless shear modulus and density are calculated and tabulated for use. These data can be used to determine corrections to the model density and shear modulus distributions due to their small change. The damping of torsional oscillations is studied. Several trial radial distributions of the dissipative function Q are considered.     

Flow around sunspots from it p-mode frequency shift measurements

We use five-day helioseimic data from the Taiwan Oscillation Network to study the flow around a sunspot, NOAA 7887. The p-mode oscillations in an annular region centered at the sunspot are decomposed into the modes propagating toward and away from the sunspot. We find that the frequency of an outgoing mode is greater than that of the corresponding incoming mode. This indicates that the plasma is flowing outward from the sunspot. The outflow velocity is estimated to be about 40–80 m s^-1.     

Stability of planar oscillations of a satellite in an elliptic orbit

A problem of stability of odd 2-periodic oscillations of a satellite in the plane of an elliptic orbit of arbitrary eccentricity is considered. The motion is supposed to be only under the influence of gravitational torques.Stability of plane oscillations was investigated earlier (Zlatoustovet al., 1964) in linear approximation. In the present paper a problem of stability is solved in the non-linear mode. Terms up to the forth order inclusive are taken into consideration in expansion of Hamiltonian in a series.It is shown that necessary conditions of stability obtained in linear approximation coincide with sufficient conditions for almost all values of parameters ande (inertial characteristics of the satellite and eccentricity of the orbit). Exceptions represent either values of the parameters ,e when a problem of stability cannot be solved in a strict manner by non-linear approximation under consideration, or values of the parameters which correspond to resonances of the third and fourth orders. At the resonance of the third order oscillations are unstable, but at the resonance of the fourth order both unstability and stability of the satellite's oscillations take place depending on the values of the parameters ,e.     

Long Period (0.9–5.5 Year) Oscillations in Surface Spherical Harmonics of Sunspot Longitudinal Distributions

The temporal changes in the two-dimensional patterns of sunspot groups, spanning 125 years (1650 Carrington Rotations), were previously analyzed using surface spherical harmonics (SSHs) (Juckett, 2003) in an attempt to quantify properties of the active longitudes among sunspot distributions. Common trends in the oscillations of both the amplitudes and spatial phases of sectoral combinations of SSHs were examined. The amplitude analysis revealed strong evidence for the second and third harmonics of the 11-year cycle across all SSHs, plus evidence for other structured variations spanning both longer and shorter time scales. In this report, temporal oscillations above the second harmonic reveal a dispersion relationship with respect to order, m, in the m = l and m = l–1 SSH modes. Furthermore, the relationship between amplitude and abrupt spatial phase transitions for these oscillations is consistent with the behavior of standing waves. Under this assumption, each standing-wave half-cycle is identified by spatial phase transitions between and π. This was used to convert the SSH amplitude series for each mode from a rectified version of the standing wave to an estimate of the full cycle. Spectral analysis yielded a dispersion relation over the SSH order range m = 1 to m = 18 spanning the cycle periods from the 11-year solar cycle down to that of the well-documented, but ill-understood 1.3 and 1.8 year quasi-periodic cycles of the quasi-biennial oscillation. Examination of the spatial phase patterns of the SSH modes suggests that the longitudinal variations in sunspot clustering are a complex phenomena with patterns occurring in several time scales. The standing wave trait of the SSH modes may offer evidence uniting the dynamo waves in the convective zone to interfacial oscillations in the tachocline.     

Pulsational instability of yellow hypergiants

Instability of population I (X = 0.7, Z = 0.02) massive stars against radial oscillations during the post-main-sequence gravitational contraction of the helium core is investigated. Initial stellar masses are in the range 65M _⊙ ≤ M _ZAMS ≤ 90M _⊙. In hydrodynamic computations of self-exciting stellar oscillations we assumed that energy transfer in the envelope of the pulsating star is due to radiative heat conduction and convection. The convective heat transfer was treated in the framework of the theory of time-dependent turbulent convection. During evolutionary expansion of outer layers after hydrogen exhaustion in the stellar core the star is shown to be unstable against radial oscillations while its effective temperature is T _eff > 6700 K for M _ZAMS = 65M _⊙ and T _eff > 7200 K for M _ZAMS = 90M _⊙. Pulsational instability is due to the κ-mechanism in helium ionization zones and at lower effective temperature oscillations decay because of significantly increasing convection. The upper limit of the period of radial pulsations on this stage of evolution does not exceed ≈200 day. Radial oscillations of the hypergiant resume during evolutionary contraction of outer layers when the effective temperature is T _eff > 7300 K for M _ZAMS = 65M _⊙ and T _eff > 7600 K for M _ZAMS = 90M _⊙. Initially radial oscillations are due to instability of the first overtone and transition to fundamental mode pulsations takes place at higher effective temperatures (T _eff > 7700 K for M _ZAMS = 65M _⊙ and T _eff > 8200 K for M _ZAMS = 90M _⊙). The upper limit of the period of radial oscillations of evolving blueward yellow hypergiants does not exceed ≈130 day. Thus, yellow hypergiants are stable against radial stellar pulsations during the major part of their evolutionary stage.     

Lunar photoelectron layer dynamics

Possible waves and oscillations in the lunar photoelectron layer (PEL) are investigated. The steady state PEL is reviewed as a basis for discussing PEL motions. Magnetic fields are neglected, so that there are four possible wave modes to consider. The propagation through the PEL of the two electromagnetic modes is discussed. Positive-ion waves, the third mode, are dismissed and plasma waves are considered at length. It is concluded that there are no propagating waves in the PEL other than electromagnetic. However, there is a type of oscillation which appears to be new and which may not be strongly damped. With these oscillations, termed flight-time oscillations, the height of the PEL fluctuates as does the electric field. These oscillations appear to be analogous to the height oscillations of the vertical jet of water in a city park water fountain. If flight-time oscillations are not much damped then it would be simplest to interpret them as plasma oscillations continually driven by the upwelling photoelectron stream. A possible laboratory investigation of these oscillations is discussed. For the surfaces of the Moon and the planet Mercury, the flight-time oscillation frequency,ω _F, is found to be respectively ç 4 × 10⁶ and ç 10⁷ rad s^?1. The PEL's of those surfaces may be in a state of continual vertical ‘quivering’ due to flight-time oscillations, or may be quiescent.     

2005 Photometric observations and multiple frequencies of the <Emphasis Type="Italic">δ</Emphasis> Scuti variable V350 Peg

We present the V light curves of δ Scuti type variable V350 Peg, obtained between August and October 2005 at the Ankara University Observatory (AUG) and the TüBíTAK National Observatory (TUG). By application of multiple-frequency analyses using Period04 to 7878 photometric V measurements (which are consist of our 747 V data and 7131 V data obtained at Monegrillo Observatory) of V350 Peg, a five-frequency solution was found to be fitted well to the data. In accordance with the computed Q values for V350 Peg, it was found that this star has probably radial mode with l=0 and g-mode oscillations.     

Wave propagation in a magnetic cylinder

The nature of oscillations in a magnetic cylinder embedded in a magnetic environment is investigated. It is shown that the standard slender flux tube analysis of a kink mode in a cylinder excludes the possibility of a second mode, which arises under photospheric conditions. Under coronal conditions, two widely separated classes of oscillation can be freely sustained, one on an acoustic time-scale and the other on an Alfvénic time-scale. The acoustic-type oscillations are always present, but the much shorter period, Alfvénic-type, oscillations arise only in high density (strictly, low Alfvén velocity) loops. An application to waves in fibrils is also given, and suggests (following Wentzel, 1979) that they are fast kink waves propagating in a density enhancement.     

On depth-dependence of photospheric oscillations

We report on results from photographic observations of photospheric oscillations as a function of depth. Using rms-values and power-spectra from shifts of entire line-profiles, we find qualitatively an increase of the velocity-amplitude with increasing height. We get more quantitative informations by comparing measured asymmetries of line-profiles with calculated ones derived from Voigt-functions containing a depth dependent velocity-field.We find the scale-height H ₀ of photospheric velocity oscillations to be 930±100 km. This result is to be compared with H ₀ = 1100±200 km obtained by Canfield (1976), who used velocity weighting functions of the line centres.Further, we show that a general observed line asymmetry of medium strong lines (c-shape) does not depend on the phase of oscillations.Mitt. aus dem Kiepenheuer-Institut Nr. 178.     

The vector approach to the problem of physical libration of the Moon: the linearized problem

A flexible and informative vector approach to the problem of physical libration of the rigid Moon has been developed in which three Euler differential equations are supplemented by 12 kinematic ones. A linearized system of equations can be split into an even and odd systems with respect to the reflection in the plane of the lunar equator, and rotational oscillations of the Moon are presented by superposition of librations in longitude and latitude. The former is described by three equations and consists of unrestricted oscillations with a period of T ₁ = 2.878 Julian years (amplitude of 1.855″) and forced oscillations with periods of T ₂ = 27.201 days (15.304″), one stellar year (0.008″), half a year (0.115″), and the third of a year (0.0003″) (five harmonics altogether). A zero frequency solution has also been obtained. The effect of the Sun on these oscillations is two orders of magnitude less than that of the Earth. The libration in latitude is presented by five equations and, at pertrubations from the Earth, is described by two harmonics of unrestricted oscillations (T ₅ ≈ 74.180 Julian years, T ₆ ≈ 27.347 days) and one harmonic of forced oscillations (T ₃ = 27.212 days). The motion of the true pole is presented by the same harmonics, with the maximum deviation from the Cassini pole being 45.3″. The fifth (zero) frequency yields a stationary solution with a conic precession of the rotation axis (previously unknown). The third Cassini law has been proved. The amplitudes of unrestricted oscillations have been determined from comparison with observations. For the ratio $ \frac{{\sin I}} {{\sin \left( {I + i} \right)}} \approx 0.2311 $ \frac{{\sin I}} {{\sin \left( {I + i} \right)}} \approx 0.2311 , the theory gives 0.2319, which confirms the adequacy of the approach. Some statements of the previous theory are revised. Poinsot’s method is shown to be irrelevant in describing librations of the Moon. The Moon does not have free (Euler) oscillations; it has oscillations with a period of T ₅ ≈ 74.180 Julian years rather than T ≈ 148.167 Julian years.     

Observational Study of Sunspot Oscillations in Stokes I,Q, U,and V

Time series of 2-dimensional spectro-polarmetric data were obtained with the intent of studying the temporal behavior of velocity, magnetic flux, and characteristics of the Stokes V profile in a small region of a larger sunspot. Full Stokes profiles in I, Q, U, and V were obtained. Velocity oscillations were found at frequencies of 3.3 mHz in each of the profiles. Acoustic power maps indicate that locations of highest power correspond to areas in which the polarization signal was greatest, therefore no conclusion about the type of wave mode participating in the oscillations can be made. Velocity amplitudes were I: 71 m s^–1, Q: 47 m s^–1, U: 65 m s^–1 and V: 86 m s^–1. Oscillatory behavior was also detected in longitudinal field strength, with an r.m.s. amplitude of 22 G, at 2.6 and 3.3 mHz. The power was localized at the umbral/penumbral boundary. A phase analysis indicates a –130° phase difference with Stokes V velocity oscillations at 3.3 mHz and a 75° difference at 2.6 mHz. Results are consistent with magnetic field lines swaying in response to a p-mode driver. No oscillatory behavior was seen in Stokes V asymmetry or amplitude splitting.     

Nonradial oscillations of low-mass stars in the presence of a magnetic field

Nonradial oscillations of a partially degenerate standard model, approximating a class of low-mass stars, have been studied in the presence of a weak poloidal magnetic field. The magnetic field in the interior of the configuration is taken to be continuous across the equilibrium surface and is matched with an external dipole field. Using a variational formulation, corrections to the oscillation frequencies of the Kelvin mode have been found for different values of the central degeneracy. It has been noted that the effect of the magnetic field is to increase the frequency of nonradial (l=2) mode of pulsation.     

Relativistic and Newtonian diskoseismology

The normal mode oscillations of thin accretion disks around black holes and other compact objects are analyzed and contrasted with those in stars. For black holes, the most robust modes are gravitationally trapped near the radius at which the radial epicyclic frequency is maximum. Their eigenfrequencies depend mainly on the mass and angular momentum of the black hole. The fundamental g-mode has recently been seen in numerical simulations of black hole accretion disks. For stars such as white dwarfs, the modes are trapped near the inner boundary (magnetospheric or stellar) of the accretion disk. Their eigenfrequencies are approximately multiples of the (Keplerian) angular velocity of the inner edge of the disk. The relevance of these modes to the high frequency quasi-periodic oscillations observed in the power spectra of accreting binaries will be discussed. In contrast to most stellar oscillations, most of these modes are unstable in the presence of viscosity (if the turbulent viscosity induced by the magnetorotational instability acts hydrodynamically).     

Recent observations of high-degree solar p-mode oscillations at the Kitt Peak National Observatory

A brief summary is given of a program which is currently being carried out with the McMath telescope of the Kitt Peak National Observatory in order to study high-degree (l ≳ 150) solar p-mode oscillations. This program uses a 244 × 248 pixel CID camera and the main spectrograph of the McMath telescope to obtain velocity-time maps of the oscillations which can be converted into two-dimensional (k _h - ω) power spectra of the oscillations. Several different regions of the solar spectrum have been used in order to study the oscillations at different elevations in the solar atmosphere. The program concentrates on eastward- and westward-propagating sectoral harmonic waves so that measurements can be made of the absolute rotational velocities of the solar photospheric and shallow sub-photospheric layers. Some preliminary results from this program are now available. First, we have been unable to confirm the existence of a radial gradient in the equatorial rotational velocity as was previously suggested. Second, we have indeed been able to confirm the presence of p-mode waves in the solar chromosphere as was first suggested by Rhodes et al. (1977). Third, we have been able to demonstrate differences in photospheric and chromospheric power spectra.

     

Present and Future Observing Trends in Atmospheric Magnetoseismology

With modern imaging and spectral instruments observing in the visible, EUV, X-ray, and radio wavelengths, the detection of oscillations in the solar outer atmosphere has become a routine event. These oscillations are considered to be the signatures of a wave phenomenon and are generally interpreted in terms of magnetohydrodynamic (MHD) waves. With multiwavelength observations from ground- and space-based instruments, it has been possible to detect waves in a number of different wavelengths simultaneously and, consequently, to study their propagation properties. Observed MHD waves propagating from the lower solar atmosphere into the higher regions of the magnetized corona have the potential to provide excellent insight into the physical processes at work at the coupling point between these different regions of the Sun. High-resolution wave observations combined with forward MHD modeling can give an unprecedented insight into the connectivity of the magnetized solar atmosphere, which further provides us with a realistic chance to reconstruct the structure of the magnetic field in the solar atmosphere. This type of solar exploration has been termed atmospheric magnetoseismology. In this review we will summarize some new trends in the observational study of waves and oscillations, discussing their origin and their propagation through the atmosphere. In particular, we will focus on waves and oscillations in open magnetic structures (e.g., solar plumes) and closed magnetic structures (e.g., loops and prominences), where there have been a number of observational highlights in the past few years. Furthermore, we will address observations of waves in filament fibrils allied with a better characterization of their propagating and damping properties, the detection of prominence oscillations in UV lines, and the renewed interest in large-amplitude, quickly attenuated, prominence oscillations, caused by flare or explosive phenomena.     

Coupling modes of hydromagnetic oscillations in non-uniform, finite pressure plasmas: Two-fluids model

Within a framework of the two-fluids approximation, basic modes constituting hydromagnetic coupling oscillations in non-uniform, finite-β plasmas are examined. It is shown that the oscillations consist of a coupling between a localized mode and a propagating one, and a strong peak appears at a resonance point. In the case of isothermal plasma (T_e = T_i), there are two localized modes, the Alfvén (or drift Alfvén) and the ion drift modes, and a propagating mode being known as the fast magnetosonic wave. Coupling oscillations associated with the Alfvén mode exhibit a nearly incompressible character, whereas those with the ion drift mode are compressional and diamagnetic. Furthermore, the slow magnetosonic wave also couples with the localized mode in the case of T_e > T_i. Based on characteristics of these oscillations, the origin of geomagnetic pulsations is discussed in connection with the distribution of plasma parameters in the outer magnetosphere.