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.     

Fluctuations of brightness and vertical velocity at various heights in the photosphere

In a spectrogram of exceptionally high spatial resolution, brightness and velocity fluctuations in seven weak to medium-strong Fe i lines have been measured and analyzed. Heights of formation of these lines have been computed using the Harvard-Smithsonian Reference Atmosphere (Gingerich et al., 1972), taking into account departures from LTE.The results show that granular velocity fluctuations decrease with increasing height up to the vicinity of the temperature minimum. If extrapolated downward to the height of formation of the continuum, the rms velocity fluctuation is 0.8 km s^-1 with an estimated error of ± 0.2 km s^-1.The correlation of continuum brightness fluctuations with velocity fluctuations decreases rapidly with height, and even becomes slightly negative at h > 160 km. This finding is consistent with the picture of the granulation consisting of convective elements overshooting into a stable atmosphere.On leave from Fraunhofer Institut, Freiburg, F.R.G.     

Observations of photospheric faculae at the center of the solar disk

Methods for the determination of the average optical depth of formation of weak Fraunhofer lines are compared, and their relative merits are discussed. Distinction should be made between the region of origin of the emergent radiation, and of the line depression. For weak or fairly weak lines the average optical depth of formation of the line depression is the relevant quantity; it should be determined by using a computational scheme based on the classical weighting functions of line formation; other methods give physically unsignificant or conflicting results.

     

On the rms intensity fluctuation of solar granulation

Using a selected high definition granulation photograph obtained with a 40 cm aperture telescope from the ground, a new determination of the rms intensity fluctuation is attempted. We find, at 5500 Å, a value of 0.058 without, of 0.067 with correction for theoretical diffraction only, and 0.095 ± 0.015 as the most probable value, if the differences between our power spectrum and those given in the literature is interpreted as due to a residual seeing of = 0.3 in our photograph.Mitteilungen aus dem Fraunhofer Institut Nr. 104.     

On the proper motion of small pores in sunspot groups

The possibility of measuring pore positions and proper motions with high accuracy, using time series of short exposure photographs, is discussed. Preliminary measurements of a series covering a time span of 110 min. show that positions of small pores may be defined, and horizontal velocities determined, to within 0.1, or 30 m s^–1, respectively.Mitteilungen aus dem Kiepenheuer-Institut No. 173.     

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.     

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.