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Register a new userLarge-scale horizontal flows in the solar photosphere. IV. On the vertical structure of large-scale horizontal flows
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Michal Svanda
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In the recent papers, we introduced a method utilised to measure the flow field. The method is based on the tracking of supergranular structures. We did not precisely know, whether its results represent the flow field in the photosphere or in some sub-photospheric layers. In this paper, in combination with helioseismic data, we are able to estimate the depths in the solar convection envelope, where the detected large-scale flow field is well represented by the surface measurements. We got a clear answer to question what kind of structures we track in full-disc Dopplergrams. It seems that in the quiet Sun regions the supergranular structures are tracked, while in the regions with the magnetic field the structures of the magnetic field are dominant. This observation seems obvious, because the nature of Doppler structures is different in the magnetic regions and in the quiet Sun. We show that the large-scale flow detected by our method represents the motion of plasma in layers down to ~10 Mm. The supergranules may therefore be treated as the objects carried by the underlying large-scale velocity field.
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We study the influence of large-scale photospheric motions on the estabilization of an eruptive filament, observed on October 6, 7, and 8, 2004, as part of an international observing campaign (JOP 178). Large-scale horizontal flows were invetigated from a series of MDI full-disc Dopplergrams and magnetograms. From the Dopplergrams, we tracked supergranular flow patterns using the local correlation tracking (LCT) technique. We used both LCT and manual tracking of isolated magnetic elements to obtain horizontal velocities from magnetograms. We find that the measured flow fields obtained by the different methods are well-correlated on large scales. The topology of the flow field changed significantly during the filament eruptive phase, suggesting a possible coupling between the surface flow field and the coronal magnetic field. We measured an increase in the shear below the point where the eruption starts and a decrease in shear after the eruption. We find a pattern in the large-scale horizontal flows at the solar surface that interact with differential rotation. We conclude that there is probably a link between changes in surface flow and the disappearance of the eruptive filament.
We propose a useful method for mapping large-scale velocity fields in the solar photosphere. It is based on the local correlation tracking algorithm when tracing supergranules in full-disc dopplergrams. The method was developed using synthetic data. The data processing the data are transformed during the data processing into a suitable coordinate system, the noise is removed, and finally the velocity field is calculated. Resulting velocities are compared with the model velocities and the calibration is done. From our results it becomes clear that this method could be applied to full-disc dopplergrams acquired by the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SoHO).
Recently, we have developed a method useful for mapping large-scale horizontal velocity fields in the solar photosphere. The method was developed, tuned and calibrated using the synthetic data. Now, we applied the method to the series of Michelson Doppler Imager (MDI) dopplergrams covering almost one solar cycle in order to get the information about the long-term behaviour of surface flows. We have found that our method clearly reproduces the widely accepted properties of mean flow field components, such as torsional oscillations and a pattern of meridional circulation. We also performed a periodic analysis, however due to the data series length and large gaps we did not detect any significant periods. The relation between the magnetic activity influencing the mean zonal motion is studied. We found an evidence that the emergence of compact magnetic regions locally accelerates the rotation of supergranular pattern in their vicinity and that the presence of magnetic fields generally decelerates the rotation in the equatorial region. Our results show that active regions in the equatorial region emerge exhibiting a constant velocity (faster by 60 +/- 9 m/s than Carrington rate) suggesting that they emerge from the base of the surface radial shear at 0.95 R_sun, disconnect from their magnetic roots, and slow down during their evolution.
In a recent paper (Svanda et al., 2008, A&A 477, 285) we pointed out that, based on the tracking of Doppler features in the full-disc MDI Dopplergrams, the active regions display two dynamically different regimes. We speculated that this could be a manifestation of the sudden change in the active regions dynamics, caused by the dynamic disconnection of sunspots from their magnetic roots as proposed by Schuessler & Rempel (2005, A&A 441, 337). Here we investigate the dynamic behaviour of the active regions recorded in the high-cadence MDI data over the last solar cycle in order to confirm the predictions in the Schuesslers & Rempels paper. We find that, after drastic reduction of the sample, which is done to avoid disturbing effects, a large fraction of active regions displays a sudden decrease in the rotation speed, which is compatible with the mechanism of the dynamic disconnection of sunspots from their parental magnetic structures.
Wasserstein gradient flows provide a powerful means of understanding and solving many diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over entropy functionals in Wasserstein space. This equivalence, introduced by Jordan, Kinderlehrer and Otto, inspired the so-called JKO scheme to approximate these diffusion processes via an implicit discretization of the gradient flow in Wasserstein space. Solving the optimization problem associated to each JKO step, however, presents serious computational challenges. We introduce a scalable method to approximate Wasserstein gradient flows, targeted to machine learning applications. Our approach relies on input-convex neural networks (ICNNs) to discretize the JKO steps, which can be optimized by stochastic gradient descent. Unlike previous work, our method does not require domain discretization or particle simulation. As a result, we can sample from the measure at each time step of the diffusion and compute its probability density. We demonstrate our algorithms performance by computing diffusions following the Fokker-Planck equation and apply it to unnormalized density sampling as well as nonlinear filtering.
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