The power spectrum of solar convection flows from high-resolution observations and 3D simulations

Abstract

Context. Understanding solar surface magnetoconvection requires the study of the Fourier spectra of the velocity fields. Nowadays, observations are available that resolve very small spatial scales, well into the subgranular range, almost reaching the scales routinely resolved in numerical magnetoconvection simulations. Comparison of numerical and observational data at present can provide an assessment of the validity of the observational proxies. Aims. Our aims are: (1) to obtain Fourier spectra for the photospheric velocity fields using the spectropolarimetric observations with the highest spatial resolution so far (~120 km), thus reaching for the first time spatial scales well into the subgranular range; (2) to calculate corresponding Fourier spectra from realistic 3D numerical simulations of magnetoconvection and carry out a proper comparison with their observational counterparts considering the residual instrumental degradation in the observational data; and (3) to test the observational proxies on the basis of the numerical data alone, by comparing the actual velocity field in the simulations with synthetic observations obtained from the numerical boxes. Methods. (a) For the observations, data from the SUNRISE/IMaX spectropolarimeter are used. (b) For the simulations, we use four series of runs obtained with the STAGGER code for different average signed vertical magnetic field values (0, 50, 100, and 200 G). Spectral line profiles are synthesized from the numerical boxes for the same line observed by IMaX (Fe I 5250.2 Å) and degraded to match the performance of the IMaX instrument. Proxies for the velocity field are obtained via Dopplergrams (vertical component) and local correlation tracking (LCT, for the horizontal component). Fourier power spectra are calculated and a comparison between the synthetic and observational data sets carried out. (c) For the internal comparison of the numerical data, velocity values on constant optical depth surfaces are used instead of on horizontal planes. Results. A very good match between observational and simulated Fourier power spectra is obtained for the vertical velocity data for scales between 200 km and 6 Mm. Instead, a clear vertical shift is obtained when the synthetic observations are not degraded to emulate the degradation in the IMaX data. The match for the horizontal velocity data is much less impressive because of the inaccuracies of the LCT procedure. Concerning the internal comparison of the direct velocity values of the numerical boxes with those from the synthetic observations, a high correlation (0.96) is obtained for the vertical component when using the velocity values on the log τ500 =-1 surface in the box. The corresponding Fourier spectra are near each other. A lower maximum correlation (0.5) is reached (at log τ500 = 0) for the horizontal velocities as a result of the coarseness of the LCT procedure. Correspondingly, the Fourier spectra for the LCT-determined velocities is well below that from the actual velocity components. Conclusions. As measured by the Fourier spectra, realistic numerical simulations of surface magnetoconvection provide a very good match to the observational proxies for the photospheric velocity fields at least on scales from several Mm down to around 200 km. Taking into account the spatial and spectral instrumental blurring is essential for the comparison between simulations and observations. Dopplergrams are an excellent proxy for the vertical velocities on constant-τ isosurfaces, while LCT is a much less reliable method of determining the horizontal velocities. © 2014 ESO.