H. Schleicher

Dynamics of the solar granulation. IX. A global approach

Based on a series of spectrograms taken with the German Vacuum Tower Telescope (VTT) at the Observatorio del Teide (Tenerife), we study the temporal evolution of granular dynamics and energy transport in the photospheric layers. We consider the ensemble of the granules cut by the spectrograph slit, modulated by wave motion, as a complex system. We describe this ensemble by the rms of the fluctuations of the observables along the slit: continuum intensity I, gas velocity v measured from line center Doppler shifts with respect to the mean profile, and line width w. The history of the rms of the observables v and w reflects the dynamical change of the system over the 20 min observation time. We find a burst-like change for both observables. However, the cross-correlation between I and v remains virtually constant, with the exception of two gaps. Using six lines of different strength we measure the rms of v in the deep photospheric layers. On the basis of this v variation we derive an upper limit of the kinetic energy flux as a function of height in the photosphere for different times during the observation. The shape of the variation with height is constant over time. A limit for the convective enthalpy flux is calculated using the temperature variations of our earlier models. Its shape remains the same over time. Taken together, these results quantify the different roles that the lower and higher photospheric layers play in the energetics of convective overshoot.

Two-dimensional spectroscopy of sunspots II. Search for propagating waves and drifting velocity filaments in photospheric layers

Aims. Running penumbral waves are often reported from observations in chromospheric lines or lines formed in the upper photosphere. In this work we investigate whether they can be detected in a line formed in the mid to lower photosphere. Methods. We used time series of two-dimensional spectra of an iron line that is insensitive to the magnetic field and that is formed in the lower to mid photosphere. Results. No running penumbral waves are detected in this line formed in the lower and mid photosphere. In the moat, outward moving velocity features are detected. They are slightly faster than the plasma motions but much slower than running penumbral waves. Conclusions. Running penumbral waves are a phenomenon occurring in higher layers, i.e. the lower chromosphere and the upper photosphere, but not in the mid photosphere or below. In the moat, we found long-living filamentary velocity features drifting outwards.

Dynamics of the solar granulation - VII. A nonlinear approach

We investigate the attractor underlying the granular phenomenon by applying nonlinear methods to series of spectrograms from 1994 and 1999. In the three-dimensional phase space spanned by intensity, Doppler velocity, and turbulence (line broadening), the granulation attractor does not ll the entire phase space, as expected from the high Reynolds and Rayleigh numbers of the photospheric plasma, but rather shows a highly structured form. This could be due to the correlations between intensity, turbulence, and velocity, which represent also the Reynolds stress. To obtain insight into the dimensionality of the attractor, we use the time lag method, a nonlinear method that enables us to get information about the underlying attractor of a dynamical system (granulation) from the measurement of one physical quantity only. By applying this method to the observed Doppler velocities, we show that the granulation attractor can be described by three independent variables. The dimension of the granulation attractor seems to be independent of the appearance of big granules and shear flow. Furthermore, the power analysis of the Doppler velocity shows power down to the spatial resolution of the instrument (0.3 arcsec). In order to decide whether the power at the smallest scales is real or noise, we use again the time lag method in combination with either a high pass digital or wavelet lter, which lters out the large wave numbers. It appears that the power at the smallest scales represents a real signal.

Anisotropy and dynamics of photospheric velocity patterns: 2D power and coherence analyses

Context. The dynamical and topological properties of a fluid define its hydrodynamical state and energy transfer. By means of twodimensional (2D) spectroscopy and 2D power and coherence analyses we study these properties in the solar photosphere. Aims. To obtain insight into the change of the velocity field with height in the solar photosphere we analyze 2D spectroscopic observations. Methods. Maps of the vertical velocity at four different photospheric heights are studied by means of 2D power and coherence analyses, in order to characterize the dynamical and topological properties of the velocity field in the 2D wave number domain (kx,ky). (i) The power analysis shows the power amplitude and its distribution over the (kx,ky) domain for each velocity map and thus height level. We use the mean azimuthal presentation to provide a quick 1D overview. (ii) The cross-amplitude spectrum shows interrelationships between two velocity maps. We use the cross-amplitude spectrum to visualize and quantify changes of the velocity patterns with height in the photosphere. (iii) The square coherence is the normalized cross power spectrum; it represents the correlation in the (kx,ky) domain. The degree of isotropy of this quantity signifies the existence of velocity patterns with different shapes. To facilitate the visualization of the 2D power and coherence maps we calculate their 1D mean azimuthal values. Results. The 2D power and coherence analyses reveal that the velocity fields of the higher photospheric layers are different from the deeper granular layers. The loss of similarity is found to occur in the mid photosphere. The highest photospheric layers are characterized by (i) a diminution of the velocity power; (ii) a disappearance of the small velocity structures; and (iii) a tendency for larger upflow velocity structures to become asymmetric.

Dynamics of the Solar Granulation: Its Interaction with the Magnetic Field

The dynamics of the granulation manifests itself in the Doppler shift fluctuations of the cores of spectral lines, which are associated with spatially resolved intensity structures (granules). Another part of the dynamical behavior of the granulation, especially the dynamics of the intergranular space, leads to unresolved Doppler velocity fluctuations detectable as line broadening enhancements of magnetically insensitive absorption lines.