Wave reflections in the solar atmosphere

The small phase-lag between velocities observed at different chromospheric levels is interpreted as being due to acoustic waves reflected by the very hot atmospheric layers of the chromosphere-corona transition zone. We consider first an isothermal slab, then a realistic solar atmospheric model and calculate weighting functions for velocities in Ca ii lines. It is shown that taking into account these functions and integrating over horizontal wave numbers leads to a good agreement with previous observations (Mein, 1977) in the case of 8498 and 8542 Ca ii lines. For the K line, the less good agreement shows that magnetoacoustic waves become important in the upper chromospheric layers.     

Solar convective zone and acoustic oscillations

The influence of the superadiabatic convection region and the hydrogen-helium ionization region on the spectrum of acoustic oscillations are considered. The spectrum peculiarities are studied by means of the phase-shift function which describes the reflection of the acoustic waves by the outermost layers of the Sun. This function permits us to investigate the influence of the envelope structure upon the oscillations without all the model data. It is shown that in spite of the strong influence of the superadiabatic convection upon acoustic oscillations, its structural changes cannot explain the discrepancy between observations and theory. It is emphasized that the explanation of the discrepancy between observations and standard model calculations requires taking into account the non-ideal nature of the plasma.     

Non-adiabatic effects on the pulsation periods

Weight functions for the non-adiabatic radial pulsations are introduced. It is shown from behavior of these functions that the pulsation periods in classical Cepheids are determined essentially in the adiabatic region of stellar envelopes and, on the other hand, those of low surface-gravity models are strongly affected in the region where the acoustic waves are strongly coupled with the radiation fields. The fact is important for understanding basic difference of the pulsation properties between classical Cepheids and low surfacegravity models.The non-adiabatic weight functions deviate from adiabatic ones in two ways in the stellar envelope layers. In the region where the acoustic waves are tightly coupled with radiation fields, the non-adiabatic weight functions have larger values than the corresponding adiabatic ones. On the contrary, the functions are smaller in the outer isothermal region.These results are discussed from the viewpoint on the propagation of the acoustic waves in radiation nelds.     

Excitation of plasma waves in the ionosphere caused by atmospheric acoustic waves

The transformation of atmospheric acoustic waves into plasma waves in the ionosphere is investigated. The transformation mechanism is based on plasma wave exitation by growing acoustic waves, when a frequency/wavelength matching situation is reached. The interaction of acoustic and plasma waves occurs through collisions of neutral particles with ions. For the case of ion-sound waves, oscillations on ion cyclotron frequency and Alfvén waves is considered. A peculiarity of Alfvén waves is the wide frequency band which may be stimulated through wave-wave interaction.     

Reflectionless propagation of acoustic waves in the solar atmosphere

The possibility that vertical acoustic waves with frequencies lower than the cutoff frequency corresponding to the temperature minimum pass this minimum is investigated. It is shown that the averaged temperature profile in the solar atmosphere can be approximated by several so-called reflectionless profiles on which the acoustic waves propagate without internal reflection. The possibility of the penetration of vertical acoustic waves, including low-frequency ones, into the solar corona is explained in this way.     

Arbitrary Amplitude Ion Acoustic Solitary Waves in An Unmagnetized Two Electron Population Ultra-Relativistic Dense Plasmas

The nonlinear wave structure of arbitrary amplitude ion acoustic solitary waves (IASWs) are studied in the Sagdeev’s pseudopotential framework for an ultra-relativistic degenerate dense plasma comprising cold and hot electrons and inertial ultra-cold ions. By employing standard normal-mode analysis the dispersion relation for linear waves is studied. The numerical results are presented to understand the features of ion acoustic solitary wave structures. It is shown that the present plasma model supports IASWs having positive potential well. Also, it is found that the small amplitude rarefactive double layer solution can exist in such a plasma system in some parametric region. It is shown that solitary structures and double layers are affected by relevant plasma parameters.     

Absorption of acoustic waves in monolithic and fibril sunspot models

It has been hypothesized that the observation of substantial absorption of acoustic power in the vicinity of sunspots may be explained by the transformation of acoustic oscillations into highly damped shear Alfvén waves in thin resonant layers. Analytical estimates of the efficiency of this process (Hollweg, 1988) are compared with direct one-dimensional numerical simulations of absorption by a magnetic barrier in a viscous medium. After slight modification, the estimate is found to give a good approximation to the numerical absorption rate.Further calculations are performed for scattering from a magnetic field of fibril structure. Such models are better able to explain the spatial structure of the absorbing region implied by the observations. It is found that the existence of a multiplicity of surfaces at which resonant absorption occurs can considerably increase the total energy absorption coefficient. Resonant effects involving the multiple reflection of acoustic waves within such structures can also lead to enhanced absorption. Fibril models, therefore, produce significantly increased absorption over a wide range of plausible parameter values, and are a more plausible explanation for the observed p-mode scattered power deficit than resonant absorption in a monolithic structure.     

Excess heating of corona and chromosphere above magnetic regions by non-linear Alfvén waves

Excess heating of the active region solar atmosphere is interpreted by the decay of MHD slow-mode waves produced in the corona through the non-linear coupling of Alfvén waves supplied from subphotospheric layers. It is stressed that the Alfvén-mode waves may be very efficiently generated directly in the convection layer under the photosphere in magnetic regions, and that such magnetic regions, at the same time, provide the ‘transparent windows’ for Alfvén waves in regard to the Joule and frictional dissipations in the photospheric and subphotospheric layers. Though the Alfvén waves suffer considerable reflection in the chromosphere and in the transition layer, a certain fraction of this large flux is propagated out to the corona, and a large velocity amplitude exceeding the local Alfvén velocity is attained during the propagation along the magnetic tubes of force into a region of lower density and weaker magnetic field. The otherwise divergence-free velocity field in Alfvén waves gets involved in such a case with a compressional component (slow-mode waves) which again is of considerable velocity amplitude relative to the local acoustic velocity when estimated by using the formulation for non-linear coupling between MHD wave modes derived by Kaburaki and Uchida (1971). Therefore, the compressional waves thus produced through the non-linear coupling of Alvén waves will eventually be thermalized to provide a heat source. The introduction of this non-linear coupling process and the subsequent thermalization of thus produced slow-mode waves may provide means of converting the otherwise dissipation-free Alfvén mode energy into heat in the corona. The liberated heat will readily be redistributed by conduction along the magnetic lines of force, with higher density as a consequence of increased scale height, and thus the loop-like structure of the coronal condensations (or probably also the thread-like feature of the general corona) may be explained in a natural fashion.     

Dust-acoustic solitary waves and double layers with two temperature ions in a nonextensive dusty plasma

Small amplitude dust-acoustic solitary waves in an unmagnetized dusty plasma consisting of electrons and two temperature ions obeying the q-nonextensive distribution are investigated. Employing reductive perturbation method, the Korteweg-de Vries (KdV) equation is derived. From the solitonic solutions of KdV equation, the influence of nonextensivity of electrons as well as ions and dust concentration on the amplitude and width of dust-acoustic solitary waves has been studied. It is observed that both positive and negative potential dust acoustic solitary waves occur in this case. The modified KdV (mKdV) equation is derived in order to examine the solitonic solutions for the critical plasma parameters for which KdV theory fails. The parametric regimes for the existence of mKdV solitons and double layers (DLs) have also been determined. Positive potential double layers are found to occur in the present study.     

Physical Properties of Wave Motion in Inclined Magnetic Fields within Sunspot Penumbrae

At the surface of the Sun, acoustic waves appear to be affected by the presence of strong magnetic fields in active regions. We explore the possibility that the inclined magnetic field in sunspot penumbrae may convert primarily vertically-propagating acoustic waves into elliptical motion. We use helioseismic holography to measure the modulus and phase of the correlation between incoming acoustic waves and the local surface motion within two sunspots. These correlations are modeled by assuming the surface motion to be elliptical, and we explore the properties of the elliptical motion on the magnetic-field inclination. We also demonstrate that the phase shift of the outward-propagating waves is opposite to the phase shift of the inward-propagating waves in stronger, more vertical fields, but similar to the inward phase shifts in weaker, more-inclined fields.     

The parabolic wave equation in local helioseismology

In recent years methods of time-distance helioseismology have been used to produce maps of local flows in the surface layers of the Sun. Usually, these studies rely on ray theory to describe the propagation of sound waves. Ray theory, however, is a poor approximation of the acoustic wavefield near the surface of the Sun. In particular, it is inappropriate for the study of scattering and diffraction by inhomogeneities. But an exact solution of the acoustic wave equation in the Sun is not trivial. In this paper I present an approximation to the full wave equation, which transforms it into a parabolic equation. The parabolic equation is commonly used in ocean acoustics and geoseismology because it is much simpler to solve numerically. Here I discuss the parabolic approximation, its limitations and potential applications in helioseismology. Finally, I present some numerical results to demonstrate the capabilities of this method.     

Influence of the acoustic radiation pressure on the atmosphere of the sun

In addition to the heating the corona by sound waves, there exists a radiation pressure caused by the absorption of acoustic waves as well as plasma waves. Whereas in the hydrostatic balance of the solar atmosphere, the light pressure can be neglected, the radiation pressure due to acoustic waves and Alfvén waves is much higher and has to be taken into account.In the solar atmosphere, the acoustic radiation pressure is generated by (i) absorption of sound energy, (ii) reflection of sound energy, and (iii) change of the sound velocity.The radiation pressure caused by absorption is dominating within the solar corona. The radiation pressure caused by reflection and the wave velocity change probably produce a pressure inversion in the transition zone between chromosphere and corona. Furthermore, the spicule phenomena are due to instationary radiation pressure.     

Heating of Jupiter’s thermosphere by the dissipation of upward propagating acoustic waves

Thunderstorms in Jupiter’s atmosphere are likely to be prodigious generators of acoustic waves, as are thunderstorms in Earth’s atmosphere. Accordingly, we have used a numerical model to study the dissipation in Jupiter’s thermosphere of upward propagating acoustic waves. Model simulations are performed for a range of wave periods and horizontal wavelengths believed to characterize these acoustic waves. The possibility that the thermospheric waves observed by the Galileo Probe might be acoustic waves is also investigated. Whereas dissipating gravity waves can cool the upper thermosphere through the effects of sensible heat flux divergence, it is found that acoustic waves mainly heat the Jovian thermosphere through effects of molecular dissipation, sensible heat flux divergence, and Eulerian drift work. Only wave-induced pressure gradient work cools the atmosphere, an effect that operates at all altitudes. The sum of all effects is acoustic wave heating at all heights. Acoustic waves and gravity waves heat and cool the atmosphere in fundamentally different ways. Though the amplitudes and mechanical energy fluxes of acoustic waves are poorly constrained in Jupiter’s atmosphere, the calculations suggest that dissipating acoustic waves can locally heat the thermosphere at a significant rate, tens to a hundred Kelvins per day, and thereby account for the high temperatures of Jupiter’s upper atmosphere. It is unlikely that the waves detected by the Galileo Probe were acoustic waves; if they were, they would have heated Jupiter’s thermosphere at enormous rates.     

Probing solar convection

In the solar convection zone, acoustic waves are scattered by turbulent sound speed fluctuations. In this paper the scattering of waves by convective cells is treated using Rytov's technique. Particular care is taken to include diffraction effects, which are important, especially for high-degree modes that are confined to the surface layers of the Sun. The scattering leads to damping of the waves and causes a phase shift. Damping manifests itself in the width of the spectral peak of p-mode eigenfrequencies. The contribution of scattering to the linewidths is estimated and the sensitivity of the results to the assumed spectrum of the turbulence is studied. Finally, the theoretical predictions are compared with recently measured linewidths of high-degree modes.     

Seismology of stellar envelopes: probing the outer layers of a star through the scattering of acoustic waves

The outer layers of Sun-like stars are regions of rapid spatial variation which modulate the p-mode frequencies by partially reflecting the constituent acoustic waves. With the accuracy that has been achieved by current solar observations, and that is expected from imminent stellar observations, this modulation can be observed from the spectra of the low-degree modes. We present a new and simple theoretical calculation to determine the leading terms in an asymptotic expansion of the outer phase of these modes, which is determined by the structure of the surface layers of the star. Our procedure is to compare the stellar envelope with a plane-parallel polytropic envelope, which we regard as a smooth reference background state. Then we can isolate a seismic signature of the acoustic phase and relate it to the stratification of the outer layers of the convection zone. One can thereby constrain theories of convection that are used to construct the convection zones of the Sun and Sun-like stars. The accuracy of the diagnostic is tested in the solar case by comparing the predicted outer phase with an exact numerical calculation.     

Temperature waves in the solar atmosphere

The properties of five-minute temperature waves in the photosphere are investigated. The phase and amplitude relations of temperature and acoustic waves are deduced. It is expected that the five-minute oscillations represent a mixture of acoustic and temperature waves. The temperature waves are generated due to linear interaction with acoustic waves.It is well known that concurrent with the acoustic waves, temperature or heat waves can appear in the case of nonadiabatic disturbances (Landau and Lifshitz, 1959). The temperature waves are dissipative damped waves. Propagation of nonadiabatic hydrodynamic waves in a stratified medium have been considered by Zhugzdha (1983). If stratification of heat exchange exists, a linear interaction of hydrodynamic and temperature waves arises. The temperature waves must be present in the solar atmosphere.     

On existence conditions of dust-acoustic solitary waves in a plasma with positively charged dust

Dust acoustic (DA) solitary wave existence conditions are investigated for positively charged dust particles in the presence of nonthermal electrons. Once Sagdeev pseudo-potential derived through fluid equations, for large amplitude DA waves, the lower limit on Mach number is calculated analytically using the necessary condition for the solitary waves existence. The double layers conditions provides the upper limit on Mach number. This allowed us to numerically investigate the effect of the temperature, density and nonthermal parameters on the solitary waves’ characteristics. The present study is devoted to a complex plasma subject to ultraviolet radiations such as the one in the lower earth’s ionosphere.     

Compressive and rarefactive double layers in non-uniform plasma with $$-nonextensive distributed electrons

Electrostatic solitary waves and double layers (DLs) formed by the coupled ion acoustic (IA) and drift waves have been investigated in non-uniform plasma using \(q\)-nonextensive distribution function for the electrons and assuming ions to be cold \(T_{i}< T_{e}\). It is found that both compressive and rarefactive nonlinear structures (solitary waves and DLs) are possible in such a system. The steeper gradients are supportive for compressive solitary (and double layers) and destructive for rarefactive ones. The \(q\)-nonextensivity parameter \(q\) and the magnitudes of gradient scale lengths of density and temperature have significant effects on the amplitude of the double layers (and double layers) as well as on the speed of these structures. This theoretical model is general which has been applied here to the \(F\)-region ionosphere for illustration.     

Equatorially trapped Rossby waves in radiative stars

Observations by recent space missions reported the detection of Rossby waves (r-modes) in light curves of many stars (mostly A, B, and F spectral types) with outer radiative envelope. This article aims to study the theoretical dynamics of Rossby-type waves in such stars. Hydrodynamic equations in a rotating frame were split into horizontal and vertical parts connected by a separation constant (or an equivalent depth). Vertical equations were solved analytically for a linear temperature profile and the equivalent depth was derived through free surface boundary condition. It is found that the vertical modes are concentrated in the near-surface layer with a thickness of several tens of surface density scale height. Then with the equivalent width, horizontal structure equations were solved, and the corresponding dispersion relation for Rossby, Rossby-gravity, and inertia-gravity waves was obtained. The solutions were found to be confined around the equator, leading to the equatorially trapped waves. It was shown that the wave frequency depends on the vertical temperature gradient as well as on stellar rotation. Therefore, observations of wave frequency in light curves of stars with known parameters (radius, surface gravity, rotation period) could be used to estimate the temperature gradient in stellar outer layers. Consequently, the Rossby mode may be considered as an additional tool in asteroseismology apart from acoustic and gravity modes.     

Global Acoustic Resonance in a Stratified Solar Atmosphere

The upward propagation of linear acoustic waves in a gravitationally stratified solar atmosphere is studied. The wave motion is governed by the Klein?–?Gordon equation, which contains a cutoff frequency introduced by stratification. The acoustic cutoff may act as a potential barrier when the temperature decreases with height. It is shown that waves trapped below the barrier could be subject to a resonance that extends into the entire unbounded atmosphere of the Sun. The parameter space characterizing the resonance is explored.