Phase velocities of gravity waves in the solar photosphere

Space-time variations of pressure in the solar photosphere are reproduced based on the results of observations in the Fe I line. Local internal gravity waves (IGWs) are isolated by means of proper filtering. A method of determination of the phase velocities of IGWs based on 1D observations is developed. Horizontal and vertical projections of the phase velocities of isolated IGWs with different periods are determined. It is shown that the phase velocity of an IGW decreases significantly with a decrease in oscillation frequency. The horizontal wavelengths of gravity waves with periods ranging from 5 to 60 minutes are commensurable with the granulation scales. The dispersive properties of gravity waves are studied.     

Spatial structure of gravity waves in the solar photosphere

Observations of the Fe I line are used to simulate spatial and temporal pressure variations in the solar photosphere. The local internal gravity waves, which are essentially structures that are quasi-periodic in space (on granular and mesogranular scales) and time and propagate along inclined paths at subsonic velocities, are isolated by appropriate filtering. The phase and group velocities of the wave trains are orthogonal; their z-projections are of the opposite sign.     

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.     

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.

     

Some properties of velocity fields in the solar photosphere

Photoelectric records of the Doppler effect (DE) and longitudinal Zeeman effect (LZE) were obtained with the Capri magnetograph of the Fraunhofer Institut photoelectric, using the Fei line λ 5250.22. Each record consists of 65 scans repeated along the same line on the sun. The analysis of 16 records covering a total of 485 oscillating regions (period 300 sec) leads to the following results:

1. (1)
   The mean lifetime of the DE-oscillations outside active regions is 20 min and 32 min in the neighborhood of spotgroups. Discarding the weakest sporadic osculations, one obtains 27 min and 43 min respectively. The most frequent lifetime in both cases is 15 min.     
   
   

Excitation of solar gravity waves

The interaction between convection and gravity waves are simulated numerically in a model closely corresponding to the physical conditions in the solar interior.The penetration of convective elements into the stably stratified interior is shown to generate gravity waves. The energy efficiency of this generation is less than 0.1 %. The simulations also show that the convective overshoot region is very shallow, 0.02–0.06 pressure scaleheights.     

Wave propagation in the photosphere

Using a 32 minutes sequence of observation, brightness and velocity fluctuations in the wings of the Mgi line at 5172.7 Å and Fe ii line at 5197.578 Å are analysed. The analysis of phase shifts and amplitude ratios leads to the following conclusions:

Waves in the solar photosphere

Time-sequences of line profile data have been subjected to a unique analysis which produces an amplitude and phase of the velocity and intensity at several line depths for each time sample and spatial point on the Sun. The data have been filtered to pass only the frequencies and spatial wavenumbers of the 5-min band. Yet, a secondary oscillation emerges, the phase of which propagates downward. Empirical eigenfunctions for velocity and intensity are given, and the kinetic energy flux is computed.Operated by the Association of Universities for Research in Astronomy under contract with the National Science Foundation.     

Inhomogeneities in the solar photosphere

A model of the solar photosphere incorporating a simple two-stream representation of granulation is found to give a small but significant improvement in the continuous radiation field over a homogeneous model. It is common to assume that the pressure does not vary with horizontal position; however, this assumption cannot be valid if the material is in hydrostatic equilibrium, so horizontal pressure differences between the hot and cold columns are allowed. This has a major effect on the structure, and one of the consequences is that temperature fluctuations at equal optical depths are greater than those at equal geometric depths.Now at Georgetown College Observatory, Washington, D.C., U.S.A.     

Molecules in the solar photosphere

A consideration of the dissociation equilibrium of diatomic molecules in the Utrecht Reference Photosphere leads us to conclude that SH, SiO, CS, HF and HCl may show up in enough concentrations in the solar atmosphere. The number above photosphere for these molecules is comparable with or more than that of MgH.     

Temperature variations in the solar photosphere

We reproduced the observed center-to-limb variations of 11 weak line profiles with the HSRA and the microturbulence distribution given by Lites (1973), introducing an anisotropic macroturbulence (vertical component of 1.5 km/sec and horizontal one of 2.3 km/sec).The variations of the profiles with the heliographic latitude cannot be explained with temperature variations (it comes out that T/T 10^–3), but we need instead a very small dependence on of the photospheric turbulence velocity field, the maximum of which, situated around - 40°–60°, is of about 3–4%, above the equatorial value. With the present measurements, however, we are not able to distinguish between variations of the micro- and macroturbulence components of the total velocity field.     

Temperature fluctuations in the solar photosphere

The general problem of interpreting granulation data, in particular Edmonds' r.m.s. intensity fluctuation distribution against heliocentric angle , is discussed.A method is developed for investigating a variety of models of inhomogeneous departures from radiative equilibrium using two dimensional solutions of the equation of radiative transfer, and theoretical r.m.s. intensity fluctuation distributions are computed. It is found that only a very narrow range of models yields distributions which exhibit the essential features of Edmonds' distribution (a center-of-disk value of 14 % and a maximum value of 20.5 % at a heliocentric angle of 53°). The feature of these models is a maximum in the temperature fluctuations of about 660 K r.m.s., which represents a temperature difference between hot and cold regions of 2000 K, at a depth of about 250 km below ₅₀₀₀= 0.03. Below this the temperature fluctuations decrease rapidly in the next 70 km.These results are interpreted in terms of convective and radiative transport of energy. Velocities of the order of 8 km/sec are deduced in the essentially convective regime near 320 km, decreasing through 4 km/sec near the temperature fluctuation maximum to negligible values in the radiative region above 200 km.These features are shown to be consistent with modern theoretical and laboratory studies of convection in incompressible fluids. Further, these studies indicate that a second temperature fluctuation should occur at the bottom of a convective layer. For this reason, further photospheric models are studied in which, below the region of small temperature fluctuations near 320 km, the fluctuations increase sharply. For one of these models a theoretical intensity r.m.s. distribution is obtained which closely fits not only the maximum at = 53° in Edmonds' observed distribution but also the initial decrease and smaller minimum near 24°.Of the National Bureau of Standards and the University of Colorado.     

Temperature fluctuations in the solar photosphere

In paper I of this series it was shown that Edmonds' center-limb rms intensity fluctuation data provided strong evidence for the existence of a maximum in the horizontal temperature fluctuation near 250 km (optical depth 0.7). The data also gave a much less reliable indication of a second temperature fluctuation maximum approximately 100 km below this level. Two models, model 1 exhibiting a single temperature fluctuation maximum and model 2 which has two temperature fluctuation maxima, were put forward as worthy of further investigation. In this paper the theoretical mean limb-darkening for these models is compared with the observed limb-darkening. Neither is satisfactory and several modifications are discussed. Models of the first type can be made to fit these data only by making adjustments which appear to be inconsistent with convection as an explanation of the temperature fluctuations. Further, the agreement with the fluctuation data is now less satisfactory. However, a modified model of the second type is developed which is consistent with the convection hypothesis, which is in good agreement with the mean limb-darkening and is in qualitative agreement with the fluctuation data. This is interpreted as providing some evidence that the photospheric granulation arises from a shallow convection layer at the base of the photosphere.     

Horizontal velocities in the solar photosphere

Horizontal macroscopic velocities V _hor in the photosphere are studied. High-resolution spectrograms of quiet regions are analyzed for center-limb variation of rms Doppler shifts. The data are treated to assure that the observed velocities refer to constant size volumes on the Sun (800 × × 3000 × 250 km), independent of μ. Using known height variation of vertical velocities and calculated line formation heights, the height dependence of 〈V _hor〉 is obtained. From a value around 450 m s^?1 it decreases rapidly with increasing height. To study also small-scale velocities, the time evolution of subarcsecond size elements in the photospheric network (solar filigree) is studied on filtergrams. It is concluded that they show proper motions implying 〈V _hor〉 about 1 km s^?1.     

Temperature variations in the solar photosphere

From the variations in equivalent width of a selected set of Fraunhofer lines, we derived the variation of effective temperature and microturbulence velocity between the equator and the regions at heliographic latitude of - 72°. The reliability of the results (T/T = 0 ± 0.6%, / = 6% ± 13%) needs further investigations, but from the analysis of our data we can state that temperature variations, if any, are very small. Some suggestions for more fruitful measurements are also given.     

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.     

Temperature variations in the solar photosphere

We made detailed LTE calculations of the sensitivities of some Fraunhofer lines to local variations of the effective temperature of the Sun, taking also into account the effects of local variations of the microturbulence. The temperature sensitivities we got show a clear dependence upon the mean optical depth at which lines originate and upon the binding energy of the lower level involved in the transition.A list of some selected lines is given, in view of possible measurements either of any pole equator-variation of the effective temperature or of such local effects as those connected with the presence of strong non-spot magnetic fields.Arcetri Astrophysical Observatory, Florence, Italy.     

Radiative damping of trapped gravity waves in the solar atmosphere

The radiative damping of trapped gravity waves in an optically thin atmosphere is studied for a stratified Boussinesq fluid. The character of the atmospheric eigenmodes depends on the distribution of the Brunt-Väisälä frequency N and the radiative relaxation time . The calculations for simple layer models show that if N is large over some finite fraction of the trapping region, then modes of long lifetime can exist. In order to suppress gravity waves entirely, it is necessary that N < 1 over the entire trapping region. Qualitative application of the results to the solar atmosphere leads to the conclusion that gravity wave eigenmodes of the solar atmosphere, although damped, are by no means eliminated by radiative effects.