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

Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, 79104 Freiburg, Germany
e-mail: nesis@kis.uni-freiburg.de

Received: 5 July 2011
Accepted: 21 January 2012

Abstract

Context. The dynamical and topological properties of a fluid define its hydrodynamical state and energy transfer. By means of two-dimensional (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 (k_x,k_y). (i) The power analysis shows the power amplitude and its distribution over the (k_x,k_y) 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 (k_x,k_y) 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.