Meridional motions of magnetic features in the solar photosphere

We cross-correlate pairs of Mt. Wilson magnetograms spaced at intervals of 24–38 days to investigate the meridional motions of small magnetic features in the photosphere. Our study spans the 26-yr period July 1967–August 1993, and the correlations determine longitude averages of these motions, as functions of latitude and time. The time-average of our results over the entire 26-yr period is, as expected, antisymmetric about the equator. It is poleward between 10° and 60°, with a maximum rate of 13 m s^–1, but for latitudes below ±10° it is markedly equatorward, and it is weakly equatorward for latitudes above 60°. A running 1-yr average shows that this complex latitude dependence of the long-term time average comes from a pattern of motions that changes dramatically during the course of the activity cycle. At low latitudes the motion is equatorward during the active phase of the cycle. It tends to increase as the zones of activity move toward the equator, but it reverses briefly to become poleward at solar minimum. On the poleward sides of the activity zones the motion is most strongly poleward when the activity is greatest. At high latitudes, where the results are more uncertain, the motion seems to be equatorward except around the times of polar field reversal. The difference-from-average meridional motions pattern is remarkably similar to the pattern of the magnetic rotation torsional oscillations. The correspondence is such that the zones in which the difference-from-average motion is poleward are the zones where the magnetic rotation is slower than average, and the zones in which it is equatorward are the zones where the rotation is faster.Our results suggest the following characterization: there is a constant and generally prevailing motion which is perhaps everywhere poleward and varies smoothly with latitude. On this is superimposed a cycle-dependent pattern of similar amplitude in which the meridional motions of the small magnetic features are directed away from regions of magnetic flux concentration. This is suggestive of simple diffusion, and of the models of Leighton (1964) and Sheeley, Nash, and Wang (1987). The correspondence between the meridional motions pattern and the torsional oscillations pattern in the magnetic rotation suggests that the latter may be an artifact of the combination of meridional motion and differential rotation.     

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.     
   
   

The study of velocity oscillations in the solar photosphere using the velocity substraction technique

A method of measurement of local line-of-sight velocities in the solar atmosphere by means of polarization optics is described. No spurious signals due to instrumental displacements of the spectrum arise with this method. The sensitivity of the method obtained is 0.3 m s^-1, with a time constant τ = 5 s and input aperture 1.4″ × 4.5″. Some preliminary results of the assessment of spatial characteristics of 5-min oscillations are included. Data are given to illustrate a center-to-limb variation of the spectrum of 5-min oscillations.     

Absolute wavelengths of Fraunhofer lines: Convective motions in the solar photosphere and the gravitational red shift

Absolute wavelengths for Fraunhofer lines are compared with laboratory measurements for several atomic and molecular spectra. The wavelength differences are shown to be consistent with the proposal that the deeper layers of the photosphere are in convective motion: _e -3 km/sec for log ₀> -1.0. Convective motions in the outer layers (log₀< - 1.0) are shown to be very small. Wavelength shifts of Fraunhofer lines formed in these outer layers are in good quantitative agreement with the predictions of the General Theory of Relativity.     

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.     

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.     

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 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.     

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 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.     

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.     

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.     

On the occurrence of convective motions in the upper photosphere

We have examined whether the motion field in the photosphere in the range of optical depths 0.25< ₀< 0.6 is dominated by thermal convection or by vibrations. The observed asymmetries of infrared Fraunhofer lines indicate the presence of motions, and the fact that the asymmetry is zero for lines of low excitation and increases with the excitation potential shows that these motions are chiefly convective in this part of the photosphere: upward moving elements appear to be hotter than downward moving ones.Assuming furthermore that the photosphere can be described by a three-column model, with temperature differences as given by Edmonds (1967), we find that in the range of optical depths given above, where T seems to vary between 80 and 160 °K, average convective velocities of 2.3 to 3.2 km/sec should occur. This result is in numerical agreement with (a) a previous one by the present authors (1967) derived from the variation of line asymmetry with depth in lines of one multiplet, (b) a finding by Lambert and Mallia (1968) deduced from absolute wavelength measurements of Fraunhofer lines, and (c) a recent result of Beckers (1968) found from a comparison of two granulation pictures obtained simultaneously with a narrow-band filter centred on the two wings of a faint line.