Tracking granules at the Sun's surface and reconstructing velocity fields. II. Error analysis

The determination of horizontal velocity fields at the solar surface is crucial to understanding the dynamics and magnetism of the convection zone of the sun. These measurements can be done by tracking granules. Tracking granules from ground-based observations, however, suffers from the Earth's atmospheric turbulence, which induces image distortion. The focus of this paper is to evaluate the influence of this noise on the maps of velocity fields. We use the coherent structure tracking algorithm developed recently and apply it to two independent series of images that contain the same solar signal. We first show that a k-\omega filtering of the times series of images is highly recommended as a pre-processing to decrease the noise, while, in contrast, using destretching should be avoided. We also demonstrate that the lifetime of granules has a strong influence on the error bars of velocities and that a threshold on the lifetime should be imposed to minimize errors. Finally, although solar flow patterns are easily recognizable and image quality is very good, it turns out that a time sampling of two images every 21 s is not frequent enough, since image distortion still pollutes velocity fields at a 30% level on the 2500 km scale, i.e. the scale on which granules start to behave like passive scalars. The coherent structure tracking algorithm is a useful tool for noise control on the measurement of surface horizontal solar velocity fields when at least two independent series are available.Comment: in press in Astronomy and Astrophysics, 9 page

Mesoscale dynamics on the Sun's surface from HINODE observations

Aims: The interactions of velocity scales on the Sun's surface, from granulation to supergranulation are still not understood, nor are their interaction with magnetic fields. We thus aim at giving a better description of dynamics in the mesoscale range which lies between the two scales mentioned above. Method: We analyse a 48h high-resolution time sequence of the quiet Sun photosphere at the disk center obtained with the Solar Optical Telescope onboard Hinode. The observations, which have a field of view of 100 \arcsec$\times$ 100 \arcsec, typically contain four supergranules. We monitor in detail the motion and evolution of granules as well as those of the radial magnetic field. Results: This analysis allows us to better characterize Trees of Fragmenting Granules issued from repeated fragmentation of granules, especially their lifetime statistics. Using floating corks advected by measured velocity fields, we show their crucial role in the advection of the magnetic field and in the build up of the network. Finally, thanks to the long duration of the time series, we estimate that the turbulent diffusion coefficient induced by horizontal motion is approximately $430 \mathrm{km}^2 \mathrm{s}^{-1}$. Conclusions: These results demonstrate that the long living families contribute to the formation of the magnetic network and suggest that supergranulation could be an emergent length scale building up as small magnetic elements are advected and concentrated by TFG flows. Our estimate for the magnetic diffusion associated with this horizontal motion might provide a useful input for mean-field dynamo models.Comment: to appear in A&A - 8 pages, 13 figures (degraded quality) - Full resolution version available @ http://www.ast.obs-mip.fr/users/rincon/hinode_roudier_aa09.pd

Tropical Crops and Resilience to Climate Change

It is anticipated that agricultural output will have to increase by 70% to feed a global population of more than 9 billion by the year 2050 (Benkeblia 2012). The capacity of global high-intensity farming systems to continue to guarantee productive returns while maintaining system stability will eventually decline, and thus new opportunities for agriculture are being realized in tropical environments. As population growth is greatest in tropical regions, and commensurate with rapid industrialization and change in traditional land use practices, it is presumed that equatorial production systems will be some of the most vulnerable to climate change

Quasi full-disk maps of solar horizontal velocities using SDO/HMI data

For the first time, the motion of granules (solar plasma on the surface on scales larger than 2.5 Mm) has been followed over the entire visible surface of the Sun, using SDO/HMI white-light data. Horizontal velocity fields are derived from image correlation tracking using a new version of the coherent structure tracking algorithm.The spatial and temporal resolutions of the horizontal velocity map are 2.5 Mm and 30 min respectively . From this reconstruction, using the multi-resolution analysis, one can obtain to the velocity field at different scales with its derivatives such as the horizontal divergence or the vertical component of the vorticity. The intrinsic error on the velocity is ~0.25 km/s for a time sequence of 30 minutes and a mesh size of 2.5 Mm.This is acceptable compared to the granule velocities, which range between 0.3 km/s and 1.8 km/s. A high correlation between velocities computed from Hinode and SDO/HMI has been found (85%). From the data we derive the power spectrum of the supergranulation horizontal velocity field, the solar differential rotation, and the meridional velocity.Comment: 8 pages, 11 figures, accepted in Astronomy and Astrophysic

Acoustic Events in the Solar Atmosphere from Hinode/SOT NFI observations

We investigate the properties of acoustic events (AEs), defined as spatially concentrated and short duration energy flux, in the quiet sun using observations of a 2D field of view (FOV) with high spatial and temporal resolution provided by the Solar Optical Telescope (SOT) onboard \textit{Hinode}. Line profiles of Fe \textsc{i} 557.6 nm were recorded by the Narrow band Filter Imager (NFI) on a $82" \times 82"$ FOV during 75 min with a time step of 28.75 s and 0.08$"$ pixel size. Vertical velocities were computed at three atmospheric levels (80, 130 and 180 km) using the bisector technique allowing the determination of energy flux in the range 3-10 mHz using two complementary methods (Hilbert transform and Fourier power spectra). Horizontal velocities were computed using local correlation tracking (LCT) of continuum intensities providing divergences. The net energy flux is upward. In the range 3-10 mHz, a full FOV space and time averaged flux of 2700 W m$^{-2}$ (lower layer 80-130 km) and 2000 W m$^{-2}$ (upper layer 130-180 km) is concentrated in less than 1% of the solar surface in the form of narrow (0.3$"$) AE. Their total duration (including rise and decay) is of the order of $10^{3}$ s. Inside each AE, the mean flux is $1.6 10^{5}$ W m$^{-2}$ (lower layer) and $1.2 10^{5}$ W m$^{-2}$ (upper). Each event carries an average energy (flux integrated over space and time) of $2.5 10^{19}$ J (lower layer) to $1.9 10^{19}$ J (upper). More than $10^{6}$ events could exist permanently on the Sun, with a birth and decay rate of 3500 s$^{-1}$. Most events occur in intergranular lanes, downward velocity regions, and areas of converging motions.Comment: 18 pages, 10 figure

Solar supergranulation revealed by granule tracking

Context: Supergranulation is a pattern of the velocity field at the surface of the Sun, which has been known about for more than fifty years, however, no satisfactory explanation of its origin has been proposed. Aims: New observational constraints are therefore needed to guide theoretical approaches which hesitate between scenarios that either invoke a large-scale instability of the surface turbulent convection or a direct forcing by buoyancy. Method: Using the 14-Mpixel CALAS camera at the Pic-du-Midi observatory, we obtained a 7.5h-long sequence of high resolution images with unprecedented field size. Tracking granules, we have determined the velocity field at the Sun's surface in great detail from a scale of 2.5Mm up to 250Mm. Results: The kinetic energy density spectrum shows that supergranulation peaks at 36Mm and spans on scales ranging between 20Mm and 75Mm. The decrease of supergranular flows in the small scales is close to a $k^{-2}$-power law, steeper than the equipartition Kolmogorov one. The probability distribution function of the divergence field shows the signature of intermittency of the supergranulation and thus its turbulent nature.Comment: 4 pages, accepted in Astronomy and Astrophysics (Letters