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 the variations in the parameters of high-degree acoustic modes with solar cycle

We analyze the pattern of behavior of p-mode wave packets with solar cycle using TON one-day helioseismic data with a high spatial resolution. The time—distance method is used to perform this task. We make an attempt to determine the variations in the travel time of acoustic waves at maximum and minimum solar activity; at maximum activity, this time decreases by 2 s compared to that at minimum activity to a depth of 0.8R_⊙. In addition, the correlation amplitudes of acoustic wave packets from minimum to maximum solar activity were found to decrease by 10–20% for all angular distances.     

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.     

Wave propagation in a non-isothermal atmosphere and the solar five-minute oscillations

This paper presents a detailed discussion of the properties of linear, periodic acoustic waves that propagate vertically in a non-isothermal atmosphere. In order to retain the basic feature of the solar atmosphere we have chosen a temperature profile presenting a minimum. An analytical solution of the problem is possible if T/, being the mean molecular weight, varies parabolically with height. The purpose of this study is to point out the qualitative differences existing between the case treated here and the customary analysis based on a locally isothermal treatment. The computed velocity amplitude and the temperature-perturbation as functions of the wave period exhibit a sharp peak in the region between 180 and 300 s, thus showing the possibility of interpreting the five-minute oscillations as a resonant phenomenon. The propagating or stationary nature of the waves is investigated by a study of the phase of the proposed analytical solution.     

Acoustic wave ducting along magnetic flux tubes in the sunspot regions

The acoustic waves generated in the solar atmosphere propagate globally as well as upwards. These waves interact with the solar magnetic field structures and are ducted upwards. The velocity of these modified acoustic waves is shown to vary in a modelled solar atmosphere. The solar plasma propagating upwards with these waves are likely to alter the observed features of spicules, granules, and supergranules during changing phases of sunspot regions.     

Probing sunspot magnetic fields with p-mode absorption and phase shift data

Long-standing observations of incoming and outgoing f- and p-modes in annuli around sunspots reveal that the spots partially absorb and substantially shift the phase of waves incident upon them. The commonly favoured absorption mechanism is partial conversion to slow magneto-acoustic waves that disappear into the solar interior channelled by the magnetic field of the sunspot. However, up until now, only f-mode absorption could be accounted for quantitatively by this means. Based on vertical magnetic field models, the absorption of p-modes was insufficient. In this paper, we use the new calculations of Crouch & Cally for inclined fields, and a simplified model of the interaction between spot interior and exterior. We find excellent agreement with phase shift data assuming field angles from the vertical in excess of 30° and Alfvén/acoustic equipartition depths of around 600–800 km. The absorption of f-modes produced by such models is considerably larger than is observed, but consistent with numerical simulations. On the other hand, p-mode absorption is generally consistent with observed values, up to some moderate frequency dependent on radial order. Thereafter, it is too large, assuming absorbing regions comparable in size to the inferred phase-shifting region. The excess absorption produced by the models is in stark contrast with previous calculations based on a vertical magnetic field, and is probably due to finite mode lifetimes and excess emission in acoustic glories. The excellent agreement of phase shift predictions with observational data allows some degree of probing of subsurface field strengths, and opens up the possibility of more accurate inversions using improved models. Most importantly, though, we have confirmed that slow mode conversion is a viable, and indeed the likely, cause of the observed absorption and phase shifts.     

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.     

Low frequency turbulence in the solar corona and fundamental radiation of type III solar radio burst

On the basis of the previous numerical simulations, a new mechanism for the emission of the fundamental radio waves of solar radio type III bursts is presented. This hypothesis is to attribute the fundamental radio emission to the coalescence of the plasma waves with the low frequency turbulence, whistler or ion acoustic waves, pre-existing on the way of the electron beam which excite the plasma waves.It is estimated that ion acoustic waves could be occasionally unstable in the solar corona due to that drifting bi-Maxwellian distribution of electrons as observed in the solar wind, which is probably caused by collision-less heat conduction.It is also suggested that the reduced damping of the ion acoustic waves in such a distorted electron distribution in the corona may decrease the threshold electric current to cause the anomalous resistivity to be the onset of the solar flares.     

Cutoff frequency and the reflection of vertically propagating magnetoacoustic gravity waves in the solar atmosphere

Based on a plane-parallel isothermal model solar atmosphere stratified in the field of gravity, we investigate the main patterns of vertical propagation of magnetoacoustic gravity waves (MAGWs) in the approximation of a horizontal potential magnetic field. We have established that the cutoff frequency for MAGWs below which they cannot propagate does not depend on the magnetic field strength and is equal to that for acoustic gravity waves, the Lamb frequency. The cutoff frequency is shown to be unaffected by the linear interaction between counterpropagating MAGWs that results from a nonuniform height distribution of the Alfvén velocity and that causes the reflection of propagating waves at relatively large heights.     

Imaging bright-spots in the accretion flow near the black hole horizon of Sgr A*

Solar active regions are distinguished by their strong magnetic fields. Modern local helioseismology seeks to probe them by observing waves which emerge at the solar surface having passed through their interiors. We address the question of how an acoustic wave from below is partially converted to magnetic waves as it passes through a vertical magnetic field layer where the sound and Alfvén speeds coincide (the equipartition level), and find that (i) there is no associated reflection at this depth, either acoustic or magnetic, only transmission and conversion to an ongoing magnetic wave; and (ii) conversion in active regions is likely to be strong, though not total, at frequencies typically used in local helioseismology, with lower frequencies less strongly converted. A simple analytical formula is presented for the acoustic-to-magnetic conversion coefficient.     

Three-Dimensional MHD Wave Propagation and Conversion to Alfvén Waves near the Solar Surface. I. Direct Numerical Solution

The efficacy of fast?–?slow MHD mode conversion in the surface layers of sunspots has been demonstrated over recent years using a number of modelling techniques, including ray theory, perturbation theory, differential eigensystem analysis, and direct numerical simulation. These show that significant energy may be transferred between the fast and slow modes in the neighbourhood of the equipartition layer where the Alfvén and sound speeds coincide. However, most of the models so far have been two dimensional. In three dimensions the Alfvén wave may couple to the magnetoacoustic waves with important implications for energy loss from helioseismic modes and for oscillations in the atmosphere above the spot. In this paper, we carry out a numerical “scattering experiment,” placing an acoustic driver 4 Mm below the solar surface and monitoring the acoustic and Alfvénic wave energy flux high in an isothermal atmosphere placed above it. These calculations indeed show that energy conversion to upward travelling Alfvén waves can be substantial, in many cases exceeding loss to slow (acoustic) waves. Typically, at penumbral magnetic field strengths, the strongest Alfvén fluxes are produced when the field is inclined 30°?–?40° from the vertical, with the vertical plane of wave propagation offset from the vertical plane containing field lines by some 60°?–?80°.     

Propagation of acoustic waves in the non‐isothermal solar atmosphere

The acoustic cutoff frequency was originally introduced by Lamb in the study of the propagation of acoustic waves in a stratified, isothermal medium. In this paper, we use a new method to generalize Lamb's result for a stratified, non‐isothermal medium and obtain the local acoustic cutoff frequency, which describes the propagation of acoustic waves in such a medium. The main result is that the cutoff frequency is a local quantity and that its value at a given atmospheric height determines the frequency acoustic waves must have in order to propagate at this height. Application of this result to specific physical problems like the solar atmosphere is discussed. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Response of an optically thin,isothermal atmosphere to a convective overshoot

Radiation is believed to be hostile to the generation of gravity waves by granulation at the base of photosphere where the radiation is effective. A convective overshoot from subphotosphere seems able to penetrate to a height where the solar temperature is minimum and to excite the gravity waves in a stable region there.The response of the solar atmosphere to a Gaussian disturbance characterizing such a convective overshoot is studied in an unbounded isothermal atmosphere. Radiative effects are included, but only in regions which are optically thin. The response is measured in terms of mean vertical kinetic energy density (E _z) and mean vertical external energy flux (Q _z). E _z and Q _z were calculated for a wide range of frequencies centered at the observed 5-min velocity oscillation period. The computed sharp and broad power spectra at the lower chromosphere and the upper photosphere, respectively, are attributed to the combined effects of space damping and source function. Low-frequency waves (2000 s or longer) are found to be not responsible for depositing energy in the upper solar atmosphere.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

Modulation of Acoustic Waves by Solar Convection

Amplitude and phase of an acoustic oscillation in the solar convection zone vary in response to the local variation of the speed of sound and the convection velocity. Such wave modulation is considered by means of a two-dimensional periodic model, with alternating vertical channels of hot rising and cool sinking gas. According to this model, vertically propagating waves show only amplitude modulation. For low wave frequencies the amplitude is larger in the upflow channels, for high frequencies it is larger in the downflow channels. The transition occurs at a frequency for which the vertical wavelength is approximately equal to the horizontal period of the model. Waves with an inclined propagation direction show a similar amplitude modulation but, in addition, a modulation of their phase. The present results are compared with recent observational studies. There is evidence that wave modulation indeed occurs on the Sun, on the granular as well as on the mesogranular scale, in addition to the episodic amplitude enhancement that has been interpreted in terms of local acoustic events.     

Oscillatory Response of the 3D Solar Atmosphere to the Leakage of Photospheric Motion

The direct propagation of acoustic waves, driven harmonically at the solar photosphere, into the three-dimensional solar atmosphere is examined numerically in the framework of ideal magnetohydrodynamics. It is of particular interest to study the leakage of 5-minute global solar acoustic oscillations into the upper, gravitationally stratified and magnetised atmosphere, where the modelled solar atmosphere possesses realistic temperature and density stratification. This work aims to complement and bring further into the 3D domain our previous efforts (by Erdélyi et al., 2007, Astron. Astrophys. 467, 1299) on the leakage of photospheric motions and running magnetic-field-aligned waves excited by these global oscillations. The constructed model atmosphere, most suitable perhaps for quiet Sun regions, is a VAL IIIC derivative in which a uniform magnetic field is embedded. The response of the atmosphere to a range of periodic velocity drivers is numerically investigated in the hydrodynamic and magnetohydrodynamic approximations. Among others the following results are discussed in detail: i) High-frequency waves are shown to propagate from the lower atmosphere across the transition region, experiencing relatively low reflection, and transmitting most of their energy into the corona; ii) the thin transition region becomes a wave guide for horizontally propagating surface waves for a wide range of driver periods, and particularly at those periods that support chromospheric standing waves; iii) the magnetic field acts as a waveguide for both high- and low-frequency waves originating from the photosphere and propagating through the transition region into the solar corona. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

The effect of mechanical waves on empirical solar models

Empirical solar models contain the effect of heating due to radiative energy loss from acoustic waves. We estimate here the temperature difference between the radiative equilibrium model and the empirical model. At optical depth ₅₀₀₀ = 0.1 this difference is small, but near the temperature minimum (₅₀₀₀ = 10^–4) it reaches between 53 and 83 K. The temperature difference between the equator and the poles caused by a hypothetical difference in the heating is estimated.     

No Evidence Supporting Flare-Driven High-Frequency Global Oscillations

The underlying physics that generates the excitations in the global low-frequency (<?5.3?mHz) solar acoustic power spectrum is a well-known process that is attributed to solar convection; however, a definitive explanation as to what causes excitations in the high-frequency regime (>?5.3?mHz) has yet to be found. Karoff and Kjeldsen (Astrophys. J. 678, 73??C?76, 2008) concluded that there is a correlation between solar flares and the global high-frequency solar acoustic waves. We have used Global Oscillation Network Group (GONG) helioseismic data in an attempt to verify the Karoff and Kjeldsen (2008) results as well as compare the post-flare acoustic power spectrum to the pre-flare acoustic power spectrum for 31 solar flares. Among the 31 flares analyzed, we observe that a decrease in acoustic power after the solar flare is just as likely as an increase. Furthermore, while we do observe variations in acoustic power that are most likely associated with the usual p-modes associated with solar convection, these variations do not show any significant temporal association with flares. We find no evidence that consistently supports flare-driven high-frequency waves.     

Ion-acoustic waves in the solar atmosphere

A model for ion-acoustic waves in the solar atmosphere is presented. In the limit of strongly magnetized plasma this model leads to the Zakharov-Kuznetsov equation which possesses a flat solitary wave solution. An initial-value problem for this equation is solved numerically to show a transition of the flat solitary waves into spherical solitary waves. The paper suggests further developments of an ion-acoustic wave theory that may improve our knowledge of ion-acoustic waves and lead to the possibility of their being detected in the solar atmosphere.     

Reflection and Ducting of Gravity Waves Inside the Sun

Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward and downward traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an α-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection.