The five-minute oscillations in the solar atmosphere

The acoustic overstability in a polytropic plane-parallel atmosphere with superadiabatic temperature gradient and radiative dissipation is demonstrated for optically thick disturbances. The periods of oscillation are found to be in the range 250–480 s and the associated wavelength of the order of 4000 km. The five-minute oscillations in the solar surface are attributed to self-excited sound waves in a layer in the subphotospheric convection zone of about 1000 km thickness.     

Observational study of the five-minute oscillations in the solar atmosphere

An improved method is described for the measurement of both the solar radius and the height of the chromosphere in any desired wavelength. Possible sources of uncertainty are discussed and a comparison with other methods is made. The first results from the 1972 observing period are given: R = (960.24 ±0.16) for the continuum at 5011.5 Å and R = (966.9 ±0.4) for H ± 0.5 Å. This yields a mean height of Ha emission of (4900 ± 400) km.     

Observational study of the five-minute oscillations in the solar atmosphere

The 5-min oscillations in the photospheric velocity fields have been studied in detail from measurements on 14 absorption lines from three time sequences of spectrograms of high quality. The lines cover a range of heights in the solar atmosphere from log = + 0.2 to -1.2. Regions oscillating coherently are seen to have an average dimension of 8000 km and the oscillations in general last for 2 to 3 periods. The power spectrum analysis of high resolution enabled to determine the period of oscillation at each level very precisely. The period decreases with increase in height, being 304 s at the level log = + 0.2 and 295 s at the level log = -1.2. The low level lines possess considerable power in the low frequency range representing the convective overshoot from below. The oscillatory power increases with height, while the low frequency power decreases and the high frequency component remains substantially constant in the heights studied.The intensity fluctuations in the continuum, the line wing and core of Fe i 6358.695 have also been studied. The continuum power spectrum has practically all the power near the zero frequency range, with a very weak oscillatory component. The line wing intensity fluctuations resemble those in the continuum, whereas the line core clearly shows an oscillatory component similar to the velocity oscillations.     

Trapped gravity waves and the five-minute oscillations of the solar atmosphere

The various modes of hydrodynamic waves are considered for a model of the solar atmosphere which is based on the Bilderberg model and includes the effects of ionization. The atmosphere forms a potential well for internal gravity waves, since the stability is low at the base (near the convection) and low again in the region of partial ionization in the chromosphere. Calculations show that there are two resonant (trapped) modes of internal gravity waves for horizontal wavelengths based on the scale of the granulation. The properties of these modes are in close agreement with the two modes of oscillation observed by Frazier (1968). Trapped acoustic modes are found to have periods too short to account for the observations.Presently Visiting Fellow, Joint Institute for Laboratory Astrophysics, University of Colorado, Boulder, Colo.     

Tunnel-effect and propagation of 5-min oscillations in the solar atmosphere

Summary Tunneling of surface waves (which are also called non-propagating or evanescent mode) in isothermal atmosphere is considered. Tunneling of 5-min oscillations in solar atmosphere is discussed. Phase lead of chromospheric oscillations with respect to photospheric oscillations (Tanenbaum et al., 1971) can be explained by tunneling only.     

Variability in the power spectrum of solar five-minute oscillations

Two-dimensional power spectra of solar five-minute oscillations display prominent ridge structures in (k, ω) space, where k is the horizontal wavenumber and ω is the temporal frequency. The positions of these ridges in k and ω can be used to probe temperature and velocity structures in the subphotosphere. We have been carrying out a continuing program of observations of five-minute oscillations with the diode array instrument on the vacuum tower telescope at Sacramento Peak Observatory (SPO). We have sought to establish whether power spectra taken on separate days show shifts in ridge locations; these may arise from different velocity and temperature patterns having been brought into our sampling region by solar rotation. Power spectra have been obtained for six days of observations of Doppler velocities using the Mgi λ5173 and Fei λ5434 spectral lines. Each data set covers 8 to 11 hr in time and samples a region 256″ × 1024″ in spatial extent, with a spatial resolution of 2″ and temporal sampling of 65 s. We have detected shifts in ridge locations between certain data sets which are statistically significant. The character of these displacements when analyzed in terms of eastward and westward propagating waves implies that changes have occurred in both temperature and horizontal velocity fields underlying our observing window. We estimate the magnitude of the velocity changes to be on the order of 100 m s^-1; we may be detecting the effects of large-scale convection akin to giant cells.     

Overstability of acoustic modes and the solar five-minute oscillations

The stability of linear convective and acoustic modes in solar envelope models is investigated by incorporating the thermal and mechanical effects of turbulence through the eddy transport coefficients. With a reasonable value of the turbulent Prandtl number it is possible to obtain the scales of motion corresponding to granulation, supergranulation and the five-minute oscillations. Several of the acoustic modes trapped in the solar convection zone are found to be overstable and the most unstable modes, spread over a region centred predominantly around a period of 300 s with a wide range of horizontal length scales, are in reasonable accord with the observed power-spectrum of the five-minute oscillations. It is demonstrated that these oscillations are driven by a simultaneous action of the -mechanism and the radiative and turbulent conduction mechanisms operating in the strongly superadiabatic region in the hydrogen ionization zone, the turbulent transport being the dominant process in overstabilizing the acoustic modes.     

Detection of solar five-minute oscillations of low degree

Solar five-minute oscillations of degree l = 3, 4, and 5 have been observed at Stanford, in the Doppler shift of the Fe 5124 line. The frequencies and amplitudes are in broad agreement with previous observations of modes with l ≤ 3, though we note that there are some systematic discrepancies between the results of different observers.     

Rotational splitting of solar five-minute oscillations of low degree

Solar Physics - An analysis of 28 contiguous days of whole disk observations of the solar surface by means of optical resonant scattering in the K 769.9 nm line, taken at the Teide Observatory at...     

Non-divergent oscillations in the solar atmosphere

Non-divergent oscillations having the form of deep water waves are shown to form normal modes or free oscillations of the solar atmosphere under two approximations: the chromosphere-coronal interface behaves like a free surface, and the density scale height is sufficiently large in the convective zone. These modes show the temporal and spatial characteristics of the 300 second chromospheric oscillations.     

Velocity oscillations in the solar atmosphere

From a series of long duration continuous Doppler records of selected spectral lines, characteristics of solar velocity oscillations have been studied. Statistical distribution of the durations of the bursts of oscillations has been estimated. From the nature of distortion of the waveforms of the oscillation, the presence of disturbing impulses has been speculated. Constancy and homogeneity of the oscillations have been examined from detailed spectral density plots. Duration indices for the oscillations at different heights in the solar atmosphere have been derived by estimating mean spectral densities of characteristic oscillation amplitudes during several individual bursts and comparing them with corresponding spectral densities from long records. The variation among experimental results has been explained as due to the limitations of the power spectral analysis method on short records.     

Wave propagation in a magnetically structured atmosphere

The solar atmosphere, from the photosphere to the corona, is structured by the presence of magnetic fields. We consider the nature of such inhomogeneity and emphasis that the usual picture of hydromagnetic wave propagation in a uniform medium may be misleading if applied to a structured field. We investigate the occurrence of magnetoacoustic surface waves at a single magnetic interface and consider in detail the case where one side of the interface is field-free. For such an interface, a slow surface wave can always propagate. In addition, a fast surface wave may propagate if the field-free medium is warmer than the magnetic atmosphere.     

Wave propagation in a magnetically structured atmosphere

The propagation of waves in a magnetic slab embedded in a magnetic environment is investigated. The possible modes of propagation are examined from the general dispersion relation, both analytically and numerically, for disturbances which are evanescent in the environment. Approximate dispersion relations governing propagation in a slender slab of field are derived both from the general dispersion relation and from an application of the slender flux tube approximation.Several different situations, representative of both photospheric and coronal conditions, are considered. In general, the structures are found to support both fast and slow, body and surface, waves. Under coronal conditions, for two dimensional propagation, disturbances propagate as fast and slow body waves. The fast body waves are analogous to the ducted shear waves of seismology (Love waves).     

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.     

Wave propagation in the quiet solar chromosphere

In order to precise previous results about wave propagation in the quiet chromosphere (N. Mein and P. Mein, 1976), we study the behaviour of Doppler shifts and intensity fluctuations in 3 lines of Ca ii. We use the same observation as in our previous work, that is to say a sequence of spectra lasting 27 mn, taken at Sacramento Peak Observatory solar tower. Results can be summarized as follows:

1. Phase-lag between intensity fluctuations and dopplershifts is always near 90° in the Ca ii lines, even for frequencies as high as 15 mHz, and whatever is the location in the chromospheric network.
2. Magneto-acoustic waves propagating vertically in a vertical or horizontal magnetic field could account for the observations only if they were, on one hand reflected in the upper atmosphere, on the other hand propagating with a very high sound or Alfvén speed. The lower limit for the speed (70 km s^-1) does not seem to be realistic. Oblique waves could be investigated for better agreement.

     

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.     

Redistribution of energy by vertical oscillations in the solar atmosphere

The effect of vertical oscillations with periods between 90 s and 300 s on a solar atmosphere governed by heat conduction and radiation loss is examined. The effect is found to be primarily a redistribution, rather than a net addition or subtraction, of energy within the low corona, mainly by long period (180 to 300 s) oscillations. The redistribution of energy is found to affect the time-averaged temperature and density profiles of such an atmosphere, particularly in the low corona. The amount of energy redistributed is found to increase with increasing period.     

Darkening and visibility functions for the global five-minute oscillations

A theory for the brightness fluctuations of the Sun as a star under the effect of its global oscillations has been developed. Formulas for the darkening and visibility of p-modes are derived and their calculations are performed in the local approximation for adiabatic oscillations. Observational data from the DIFOS multichannel photometer onboard the CORONAS-F satellite are used to solve the inverse problem of determining the amplitude of the five-minute temperature fluctuations in the solar photosphere as a function of the height. Analysis of the solution and comparison with the results of other authors suggest that the predicted temperature waves resulting from a linear transformation of p-modes in the photosphere exist in the photosphere. The wavelength and phase velocity of the temperature waves are considerably smaller than those of acoustic waves. It turns out that the solar brightness fluctuations should be produced mainly by the temperature waves in the photosphere, not by the p-modes themselves. The darkening function for the brightness fluctuations is oscillatory in behavior, while the visibility function can differ markedly from that for the Doppler shifts of spectral lines produced by p-modes. These properties are important for interpreting the observations of stellar oscillations based on stellar brightness fluctuations.     

The origin of the solar five-minute oscillation

Two absorption lines formed in the lower photosphere were used to study simultaneous velocity and intensity fluctuations. No significant correspondence was found between the locations of granules and those of oscillation, even when a time lag was included. This result supports the explanation of the origin of the oscillations as a self-excited sound wave rather than the local response to a granule excitation.     

Solar seeing and the spatial properties of the five-minute oscillations

A numerical simulation of observations of the spatial properties of the five-minute oscillations is carried out, assuming the oscillations are internal gravity waves excited by granular convection according to the theory of Thomas et al. (1971). The simulation includes the effects of seeing and finite aperture. The details of the simulation are chosen to model the observational method of Frazier (1968a, b). The results show that the peak in the observed power spectrum of the oscillations can occur at a wavelength considerably longer than the true wavelength of the oscillations. In particular, the peak in Frazier's observed power spectra at wavelength 5000 km is consistent with the considerably shorter true wavelength 1500 km predicted by the gravity wave theory.