An observational search for large-scale organization of five-minute oscillations on the Sun

The large-scale solar velocity field has been measured over an aperture of radius 0.8 R on 121 days between April and September, 1976. Measurements are made in the line Fei 5123.730 Å, employing a velocity subtraction technique similar to that of Severny et al. (1976). Comparisons of the amplitude and frequency of the five-minute resonant oscillation with the geomagnetic C9 index and magnetic sector boundaries show no evidence of any relationship between the oscillations and coronal holes or sector structure.     

On spatial characteristics of five-minute oscillations in the sunspot umbra

Using a differential method we have carried out observations of oscillations in six sunspots. Spectral lines Fe i 5434 Å and Fe i 5576 Å were used. Horizontal waves are not observed in the sunspot umbra photosphere. Results obtained indicate that, at least, the sunspot umbra oscillates as a single whole.     

Infrared continuum observations of five-minute oscillations

Infrared continuum observations of the Sun at wavelengths between 10 and 30 show a nonisothermal response of the upper photosphere to compression waves associated with the five-minute oscillations. Observations were made with four broad-band filters with effective transmission wavelengths between 10 and 26 and with a 10 aperture. Further observations at submillimeter wavelengths with a 2 aperture did not resolve oscillatory fluctuations of five-minute period.Comparisons with velocity field data of Howard (1976) suggest that the relaxation time of the photosphere exceeds (300/2) seconds at the height of formation of the 26 continuum (_5000Å 10^-2). The photosphere reponds to 3 mHz oscillatory motion with considerably less compression than expected for simple acoustic modes in an adiabatically responsive atmosphere, confirming the evanescent character of the five-minute oscillations.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Concerning five-minute variations of the global magnetic field of the Sun

For the purpose of identifying five-min oscillations we analyze long-term continuous observations of the solar magnetic field (with a duration from 3 to 11 hours) with 0.5 D spatial resolution obtained with the STOP telescope (Solar Telescope for Operative Predictions) at the Sayan observatory in 1987 and 1989. It is shown that global magnetic field fluctuations with such periods seem to be real, but the character of corresponding power spectra is strongly dependent on the mean field strength in the magnetograph aperture.     

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...     

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.     

Torsional oscillations of the Sun

A series of digitized synoptic observations of solar magnetic and velocity fields has been carried out at the Mount Wilson Observatory since 1967. In recent studies (Howard and LaBonte, 1980; LaBonte and Howard, 1981), the existence of slow, large-scale torsional (toroidal) oscillations of the Sun has been demonstrated. Two modes have been identified. The first is a travelling wave, symmetric about the equator, with wave number 2 per hemisphere. The pattern-alternately slower and faster than the average rotation-starts at the poles and drifts to the equator in an interval of 22 years. At any one latitude on the Sun, the period of the oscillation is 11 years, and the amplitude is 3 m s^-1. The magnetic flux emergence that is seen as the solar cycle occurs on average at the latitude of one shear zone of this oscillation. The amplitude of the shear is quite constant from the polar latitudes to the equator. The other mode of torsional oscillation, superposed on the first mode, is a wave number 1 per hemisphere pattern consisting of faster than average rotation at high latitudes around solar maximum and faster than average rotation at low latitudes near solar minimum. The amplitude of the effect is about 5 m s^-1. For the first mode, the close relationship in latitude between the activity-related magnetic flux eruption and the torsional shear zone suggests strongly that there is a close connection between these motions and the cycle mechanism. It has been suggested (Yoshimura, 1981; Schüssler, 1981) that the effect is caused by a subsurface Lorentz force wave resulting from the dynamo action of magnetic flux ropes. But, this seems unlikely because of the high latitudes at which the shear wave is seen to originate and the constancy of the magnitude of the shear throughout the life time of the wave.     

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.     

On the excitation of oscillations of the Sun (numerical models)

Numerical solutions of the general time-dependent gas-dynamical equations in linear adiabatic approximation are given for initial conditions imitating: (a) a central perturbation, (b) a boundary perturbation (in the convective envelope), and (c) a ‘shrinking’ of the Sun as a whole. For a variety of models of the Sun it is found that at the surface the radial component v _r of velocity is much greater than the tangential component v _t , and that the period T of stationary oscillations does not exceed 131^m. The appearance at the surface of a g mode with period 160^m is found to be improbable. With the initial conditions adopted, a propagating wave is produced which is reflected successively from the centre to the periphery and back, producing 5-min oscillations at the surface of the Sun. Expansion of this wave into separate modes leads to a power spectrum qualitatively similar to that observed.     

Solar five-minute oscillations of low,intermediate, and high degree

The overstability of acoustic modes trapped inside the Sun is studied with mechanical and thermal effects of turbulence included in an approximate manner through the eddy diffusivities. Many of the acoustic modes are found to be overstable with the most rapidly growing modes occupying a region centred around 3.3 mHz and spread over a wide range of length-scales. The numerical results turn out to be in reasonable accord with the observed power-spectrum of the five-minute oscillations of arbitrary degree. It is demonstrated that these oscillations are most likely to be driven by a simultaneous operation of the -mechanism and the convective Cowling mechanism, the dominant contribution to the generation of self-excited acoustic waves arising from the turbulent diffusion.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

On the measurement precision of solar p-mode eigenfrequencies

We make use of 3456 d of observations of the low-ℓ p-mode oscillations of the Sun in order to study the evolution over time of the measurement precision of the radial eigenfrequencies. These data were collected by the ground-based Birmingham Solar-Oscillations Network (BiSON) between 1991 January and 2000 June. When the power spectrum of the complete time series is fitted, the analysis yields frequency uncertainties that are close to those expected from the returned coherence times of the modes. The slightly elevated levels compared with the prediction appear to be consistent with a degradation of the signal-to-noise ratio in the spectrum that is the result of the influence of the window function of the observations (duty cycle 71 per cent). The fractional frequency precision reaches levels of a several parts in 10⁶ for many of the modes. The corresponding errors reported from observations made by the GOLF instrument on board the ESA/NASA SOHO satellite, when extrapolated to the length of the BiSON data set, are shown to be (on average) about ∼25 per cent smaller than their BiSON counterparts owing to the uninterrupted nature of the data from which they were derived.
An analysis of the BiSON data in contiguous segments of different lengths, T , demonstrates that the frequency uncertainties scale as T ^−1/2. This is to be expected in the regime where the coherence (life) times of the modes, τ _{n ℓ}, are smaller than the observing time T (the 'oversampled' regime). We show that mode detections are only now beginning to encroach on the 'undersampled' regime (where   T < τ _{n ℓ})  .