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.     

The height variation of granular and oscillatory velocities

Previous observations of spatially-resolved vertical velocity variations in ten lines of Fe i spanning the height range 0 h 1000 km are re-analyzed using velocity weighting functions. The amplitudes and scale heights of granular and oscillatory velocities are determined, as well as those of the remaining unresolved velocities. I find that the optimal representation of the amplitude of the outward-decreasing granular velocities is an exponentially decreasing function of height, with a scale height of 150 km and a velocity at zero height of 1.27 km s^–1. The optimal representation of the same quantities for oscillatory velocities is an exponential increase with height, with a scale height of 1100 km and a velocity at zero height of 0.35 km s^–1. The remaining unresolved velocities decrease with height, with a scale height of 380 km and a velocity at zero height of 2.3 km s^–1.     

Measurements of the oscillatory and slowly-varying components of the solar velocity field

Spectroheliograms with high spatial resolution are presented to illustrate the decomposition of the solar velocity field into its oscillatory and slowly-varying components. An analysis of data obtained in the lines Fei λ 5434 and Feii λ 4924 yield essentially the same principal results:

1. Spectroheliograms of the oscillatory component have a mottled appearance of rising and falling elements ranging from 2000 km to 3000 km in size. These elements oscillate vertically with a period in the range 275–300 s and an amplitude of 0.5 km/s. Although most oscillations last two cycles some have been observed for as many as four cycles.
2. Spectroheliograms of the slowly-varying component show a velocity granulation pattern whose spatial properties correspond closely to those of the photospheric granulation visible on direct photographs of the Sun. The velocity granules are approximately 1000 km in diameter and rise relative to their intergranular spaces with speeds that are typically 0.6 km/s, but which may occasionally be as large as 0.9 km/s. Most velocity granules seem to live for at least 10 min with many lasting 10–30 min, and a few of the biggest and fastest moving lasting 30 min to 1 hr.

It is concluded that Spectroheliograms of the slowly-varying component represent the velocity field of the photospheric granulation.     

Inferring the depth extent of the horizontal supergranular flow

The 2D horizontal velocity field determined from local correlation tracking of granulation and its divergence have remarkably different appearances. The 2D horizontal velocity shows the classical 32 Mm supergranular cellular outflow bounded by the chromospheric network, whereas the divergence is dominated by distinct long-lived sources and sinks of about 7 Mm size. The 2D horizontal velocity shows no obvious evidence for 7 Mm cells, and the divergence exhibits little power with the 32 Mm scale. However, by mass continuity for a steady 3D flow in a stratified atmosphere, the divergence of the 2D horizontal component is equal to the vertical velocity divided by a height scale. Thus the 3D steady solar flow field at the bottom of the photosphere has a vertical component consisting primarily of 7 Mm sources and sinks, which define the 2D cellular-like 32 Mm continuous horizontal outflows.Simultaneous Doppler vertical velocity measurements verify the mass-continuity relation, and give a height scale equal to the density scale height in the photosphere within observational error. The observational result is consistent with our theoretical expectation. Any height scale other than the density scale height would indicate a vertical velocity thate-folds on a scale comparable to or smaller than the density scale height, which we argue is unphysical near the top of the convection zone. The continuity relation indicates that vortex-free steady horizontal velocities seen at the solar surface, i.e., the horizontal supergranular flow, must diminish with depth due to the increasing density scale height. We estimate that the horizontal supergranular flow cannot extend much more than onee-fold increase in the density scale height below the visible solar surface, about 2.4 Mm. Therefore the convection below the solar surface should be characterized by the scale of the principal steady vertical velocity component, i.e., by vertical plumes having a dimension of 7 Mm - what we have called mesogranulation - rather than closed 32 Mm cells as is widely believed.Operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with National Science Foundation.     

The reduction of the solar velocity field into its oscillatory and slowly-varying components

Spectroheliogram movies of the solar velocity field have been made in the 4924 line of Feii with a time resolution of 20 sec/frame and a spatial resolution in the range 1–2 sec of arc. A conventional doppler movie has been used to generate two additional movies which show the slowly-varying and oscillatory components of the velocity field separately. A basic result is the simplicity of the field patterns into which the relatively complex velocity field can be decomposed.Operated by the Association of Universities for Research in Astronomy, Inc., under contract to the National Science Foundation.Visiting Astronomer, Solar Division.     

Local Modulation of Solar Oscillations by Magnetic Fields

The amplitudes of solar oscillations measured in Doppler velocity are modulated by the presence of a strong photospheric magnetic field. Here we show that the amount of modulation cannot be predicted solely on the local photospheric magnetic field strength. Qualitatively, magnetic fields of similar strength have similar effects on the oscillations. Quantitatively, however, we find a neighborhood effect, so that the presence of a nearby sunspot affects oscillations in the area in its vicinity that has normal quiet-Sun magnetic field strength. Thus, different types of magnetic regions alter the oscillatory power to a varying degree, and the p-mode power within regions of similar magnetic field strength is more reduced if there is a sunspot present. The neighborhood effect falls off with distance from the sunspot. We also show that our measurements of the power modulation, in which we look at the effects on oscillations pixel by pixel, can be made consistent with results of amplitude modulation of modes as obtained from ring-diagram analysis of active regions, but only if the neighborhood effect on quiet-Sun regions is taken into account.     

Studies of granular velocities

Continuum brightness and Doppler velocity fluctuations in the lines 6301.5 and 6302.5 Å of Fei, measured in two selected spectrograms, are analysed by standard statistical (power- and coherence spectrum) methods. It is shown qualitatively that the oscillatory component of the velocity fluctuations (at spatial wavelengths > 4) decreases, while the supposedly granular component (at spatial wavelengths < 4) as well as the coherence between brightness and velocity fluctuations increases with optical depth.The spatial resolution of the spectrograms is estimated by comparing the observed power spectrum of brightness fluctuations with spectra found in the literature, assuming the combined instrumental and seeing spread function to be Gaussian. The resolution thus determined is = 1.24 ± 0.07. If the measured values are corrected accordingly, we obtain a true brightness rms of 10 to 14%, depending upon the shape of the power spectrum chosen for comparison, and a velocity rms at continuum optical depth of 1.3 km/sec. It is shown, however, that using the same correction function for the velocity power spectrum as for the brightness possibly gives rise to misestimating the velocity rms.Mitteilungen aus dem Fraunhofer Institut Nr. 100.     

Studies of granular velocities

The two available methods for determining the rms amplitude of the granular convective velocity field, namely the interpretation of line profiles, and direct measurements of velocity fluctuations in highly resolved spectra, give values ( 2 km/sec, and 0.4 km/sec, resp.) which are apparently inconsistent both in magnitude and in their dependence upon optical depth. We give both theoretical and observational evidence for the working hypothesis, that the best resolved spectra mainly show velocity fluctuations due to the oscillation of the solar atmosphere, whereas the contribution of the granular velocity field is greatly reduced because of atmospheric seeing and can be found only as a weak superposition to the oscillatory velocity field. Realistic assumptions for the typical size of the granulation (2.5) and for the seeing parameter (1), together with a simplified model of the granular velocity field, lead to correction factors of 30 to 40 between the true and observed amplitudes of the granular velocities.Mitteilungen aus dem Fraunhofer Institut, Nr. 95.     

Vertical velocities and horizontal wave propagation in the solar photosphere

We used the Sacramento Peak Doppler-Zeeman Analyzer to study the velocity and magnetic fields in 60 × 300 areas on the solar disk. We map the steady component of the line-of-sight velocity and longitudinal magnetic fields and compare them with the coarse Ca⁺ network. The collective phase behavior of the 5-min oscillations is studied in detail. We find large scale phase coherence, including waves with typical horizontal phase velocities of 100 km/sec which can be followed up to 50 000 km. The important oscillatory features are interpreted in terms of the properties of modified sound waves. We find no apparent relationship between the steady and oscillatory fields.     

Recurrency and the origin of the vertical component of the interplanetary magnetic field

The autocorrelation functions of the solar wind velocity and of the IMF components as well as of the geomagnetic activity indices are studied for two periods: August–December, 1965 and January–May, 1974. The vertical component of the IMF is shown to exhibit a rather definite recurrency relatively independent of the recurrency of the solar wind velocity.The daily mean values of the Z-component of the IMF are shown to correlate ( = -0.5) with the intensity of the meridional component of the large scale solar magnetic field with time delay of about 5 days with respect to the latter. This result is interpreted as an evidence for the Z- component of the IMF to be carried away by the solar wind from the Sun.     

Studies of granular velocities

The process of measuring granular velocity fields with an instrument having finite spectral and spatial resolution is investigated for the case that (1) a weak Fraunhofer line is used, (2) the velocity is constant with height in the solar atmosphere, (3) the original Doppler shifts are of the same order of magnitude as the intrinsic width of the line (width observed with infinitely high spectral and spatial resolution), (4) continuum brightness and line strength fluctuations are superimposed onto the velocity field.It is shown that using a spectral instrumental profile which is large compared to both the intrinsic line width and the rms Doppler shifts (as in the case of filtergrammes), the shift-induced brightness signal is always a linear function of the shift and corrections for finite spatial resolution can be applied to the measured shifts in the usual straightforward way.If the spectral instrumental profile is not large (as in the case of slit-spectrogrammes), the observed line profile is shown to depend upon the spatial resolution as well. It is altered (broadened, made asymmetric) by (1) spatially unresolved Doppler shifts and higher moments of the Doppler shift amplitude distribution, (2) by local correlation between continuum brightness, line strength, and velocity fluctuation. A value of the Doppler shift which is unaffected by nonlinearities, can be measured at a certain position in the line wing. Knowledge of the intrinsic line width is necessary, however, to determine this position, as well as the order of magnitude of the nonlinearity effects producing asymmetries in the observed line profile. Finally, the conditions are discussed under which a complete deconvolution of a spectrum could be accomplished.On leave from Fraunhofer Institut, Freiburg.     

Why the Sun may appear oblate

If the Sun loses angular momentum from its core, due to core contraction, into the solar wind at the observed rate, then an 0.7 day rotational period for the core of the Sun is required for temporal equilibrium. The rotational power released in the core contraction process can equal the observed magnetic energy released in the solar activity cycle if the Sun's core rotates with a period near 1.4 to 4 days. The rotational power released from a rotating object is , where is the torque on the object and is its angular velocity. Fitting this to the solar wind torque and core rotation rate provides an 0.5 to 5 day rotation period for the Sun's core. A gravitational Pannekoek-Rosseland electric field in the Sun makes the Ferraro theorem inapplicable in such a way that rather than a constant angular velocity with radius, an inverse square radial dependence occurs. This results in a two day rotational period for the region in the Sun where most of the angular momentum resides. The consistency of the above four methods suggests that the Sun's observed oblateness is due to a rapidly rotating solar core. The oblateness of the photosphere is estimated to be near 3.4×10^–5.     

Generation of waves by the solar magnetic field polarity reversal

In this paper an excitation of waves is considered during the time interval in which the undisturbed magnetic field changes its direction. If this interval is taken to be 2 years, which is shorter than the 11-year cycle, then the undisturbed components of the magnetic field may be linearly dependent on time and independent of the coordinates. The excitation of waves is due to the undisturbed stationaryV ₀ flow with divV ₀ = 0 and with (V ₀ rot₀) = constant.We use the local Cartesian coordinate system, which is immovable towards the solar centre, and consider the case when the toroidal component of the undisturbed magnetic field changes its sign simultaneously with one of the axial components. The third component does not change its direction.The efficiency of the enhancement of the magnetic field and velocity disturbances depends on the Alfvén wave frequency, _A. When _A = 0, the component of the disturbed velocity, which is directed along the constant component of the undisturbed magnetic field, increases. In this case the shear waves excite the carrier (high) frequency (KV ₀), whereK is the wave vector. Due to the shear instability the amplitude of the velocity increases during 1 year before the moment of reversal of the global magnetic field polarity (RGMFP) for an arbitrary latitude. It reaches a maximum at RGMFP and decreases in the next year. When _A > 0, then the amplitudes of the disturbed values reach maxima before the moment of RGMFP, and when _A < 0, they reach maxima after it.We argue that the shear waves propagate from middle latitudes to the pole and equator. Using the results of the analytical solutions and leaning on the evidence of the observational data (Gigolashvili and Japaridze, 1992), we derive the result that the component of the undisturbed magnetic field, which is perpendicular to the solar surface, changes its sign simultaneously with the toroidal component.     

A model of the magnetized solar wind

A steady state, inviscid, single fluid model of the solar win d in the equatorial plane is developed using magneto-hydrodynamics and including the heat equation wit h thermal conduction but no non-thermal heating (i.e. a conduction model). The effects of solar rotation and magnetic field are included enabling both radial and azimuthal components of the velocity and magnetic fields to be found in a conduction model for the first time.The magnetic field cuts off the thermal conduction far from the sun and leads to an increased temperature at 1 AU and relatively small changes to the radial velocity and density. Models have been found which fit the experimental electron densities in 2 R < r < 16 R . These models predict at 1 AU a radial velocity of 300–380 km·sec^-1 and a density of 8 protons·cm^-3. The latter velocity corresponds to a density profile obtained by Blackwell and Petford (1966) during the last sunspot minimum, and is about 100 km·sec^-1 above that found in previous conduction models which fit the coronal electron densities. The radial velocities are now consistent with the mean quiet solar wind, as are the densities when the experimental values are averaged over a magnetic sector. However, the azimuthal velocity at 1 AU is only 1–2 km·sec^-1 which is low compared to the experimental values, as found by previous authors.     

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.     

On the temporal variation of the solar continuous brightness fluctuations

From a sequence of white-light photographs of solar granulation at the centre of the disk, obtained by Spectro-Stratoscope on May 17, 1975, two-dimensional spatial power spectra of photospheric intensity fluctuations were deduced. These show periodicities of 1000 s, 250–450 s (5-min oscillation), and shorter ones in the range 30–120 s. The reality of the shorter periods, however, seems to be questionable.The weighted mean wavenumber of the spatial power spectra and rms of the intensity fluctuation (I _rms) are also computed, showing the same periodicities as the power.Mitteilungen aus dem Kiepenheuer-Institut Nr. 188.On leave of absence from the Institute of Geophysics, University of Tehran.     

Some properties of velocity fields in the solar photosphere

Photoelectric measurements of Doppler shifts of various Fraunhofer lines obtained with the Capri magnetograph were analysed. The height dependence of the supergranular and oscillatory motions, as well as the two dimensional structure of these velocity fields is investigated. The most interesting results are the following:

1. The oscillatory and supergranular motions are still clearly present in very deep photospheric layers as detected e.g. by means of the Ci line at 5380.3 Å.
2. Whereas the vertical motions (both of oscillation and supergranulation) increase with height, the horizontal component of the supergranular flow is found to be decreasing slightly.
3. Aperiodic horizontal motions are observed in the photospheric layers, which are probably connected with the process of excitation of the oscillatory field.
4. There is no simple way of describing the oscillatory field in terms of independently oscillating ‘cells’, since the two-dimensional pattern changes its appearance drastically already in a fraction of one oscillation period.
5. The correlation obtained by previous observers between vertical stationary motions, the chromospheric network and magnetic fields in particular is confirmed.

     

Application of Non-linear Analysis to Intensity Oscillations of the Chromospheric Bright Points

We have applied several nonlinear techniques to the intensity oscillations of the chromospheric bright points observed at the Vacuum Tower Telescope (VTT) of the Sacramento Peak Observatory. A 35-min time sequence obtained in the Caii H line over a quiet region at the center of the solar disk under high spatial, spectral, and temporal resolution has been used. A relatively new approach is used to detect the hidden periodicity and to extract the associated periodic component(s) from an apparently irregular time series. The unique feature of this approach is that the constituent component(s) can be non-sinusoidal in nature. The periodicity analysis shows that time series of intensity oscillations of most of the bright points can be composed of two non-sinusoidal periodic components with periodicity varying between 2.4 min and 5.8 min. With the help of a multivariate embedding technique, globally significant spatial nonlinear correlation is found. The identification of the nonlinear interaction between bright points is performed by using the methods of dynamical phase synchronization and the similarity index. The analysis indicates that bright points are interconnected in the sense that some bright points are more active and can influence the other relatively passive bright points.     

Grain motions in the solar nebula

Isotopic analyses of meteorites suggest the possibility that some interaction between supernova ejecta and grains occurred in the solar nebula. In particular, the dynamics of grain motions in the solar nebula can explain the observed mixing of nucleosynthetic components. The effect of a shock wave on the motions of grains are examined. A steady-state, plane shock propagating into a uniform region of gas and dust grains is followed by a zone of gas/grain slip, in which the grains are accelerated by drag forces from the pre-shock to the post-shock gas velocity, i.e. reducing the relative velocity between the gas and grains to zero. On the basis of these calculations, it is estimated that if grains carried the isotopic anomalies investigated by Lee, Papanastassoiu, and Wasserburg (1978), then those grains could be no bigger than 2×10^–4 cm in size. A scenario is suggested in which the sluggishness of grains provides a natural way to concentrate and mix the nucleosynthetic components carried by grains in the ejecta and in the solar nebula.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Oxygen ion escape at Mars in a hybrid model: High energy and low energy ions

We have studied the escape and energization of several O⁺ populations and an population at Mars by using a hybrid model. The quasi-neutral hybrid model, HYB-Mars model, included five oxygen ion populations making it possible to distinguish photoions from oxygen ions originating from charge exchange processes and from the ionosphere.We have identified two high-energy ion components and one low-energy ion component of oxygen. They have different spatial and energy distributions near Mars. The two high-energy oxygen ion components, consisting of a high-energy “beam” and a high-energy “halo”, have different origins. (1) The high-energy (>∼100 eV) “beam” of O⁺ and ions are originating from the ionosphere. These ions form a highly asymmetric spatial distribution of escaping oxygen ions with respect to the direction of the convective electric field in the solar wind. (2) The high-energy (>∼100 eV) “halo” component contains O⁺ ions which are formed from the oxygen neutral exosphere by extreme ultraviolet radiation (EUV) and by charge exchange processes. These energetic halo ions can be found all around Mars. (3) The low energy O⁺ and ions (<∼100 eV) form a relatively symmetric spatial distribution around the Mars-Sun line. They originate from the ionosphere and from charge exchange processes between protons and exospheric oxygen atoms.The existence of the low- and the high-energy oxygen components is in agreement with recent in situ plasma measurements made by the ASPERA-3 instrument on the Mars Express mission. The analysis of the escaping oxygen ions suggests that the global energization of escaping planetary ions in the martian tail is controlled by the convective electric field.