Björn Löptien

A low upper limit on the subsurface rise speed of solar active regions

Comparison of observations and simulations provides a strong upper limit on the subsurface rise speed of solar active regions. Magnetic field emerges at the surface of the Sun as sunspots and active regions. This process generates a poloidal magnetic field from a rising toroidal flux tube; it is a crucial but poorly understood aspect of the solar dynamo. The emergence of magnetic field is also important because it is a key driver of solar activity. We show that measurements of horizontal flows at the solar surface around emerging active regions, in combination with numerical simulations of solar magnetoconvection, can constrain the subsurface rise speed of emerging magnetic flux. The observed flows imply that the rise speed of the magnetic field is no larger than 150 m/s at a depth of 20 Mm, that is, well below the prediction of the (standard) thin flux tube model but in the range expected for convective velocities at this depth. We conclude that convective flows control the dynamics of rising flux tubes in the upper layers of the Sun and cannot be neglected in models of flux emergence.

Data compression for local correlation tracking of solar granulation

Context. Several upcoming and proposed space missions, such as Solar Orbiter, will be limited in telemetry and thus require data compression. Aims. We test the impact of data compression on local correlation tracking (LCT) of time-series of continuum intensity images. We evaluate the effect of several lossy compression methods (quantization, JPEG compression, and a reduced number of continuum images) on measurements of solar differential rotation with LCT. Methods. We apply the different compression methods to tracked and remapped continuum intensity maps obtained by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. We derive 2D vector velocities using the local correlation tracking code FLCT and determine the additional bias and noise introduced by compression to differential rotation. Results. We find that probing differential rotation with LCT is very robust to lossy data compression when using quantization. Our results are severely affected by systematic errors of the LCT method and the HMI instrument. The sensitivity of LCT to systematic errors is a concern for Solar Orbiter.

The shrinking Sun: a systematic error in local correlation tracking of solar granulation

Context. Local correlation tracking of granulation (LCT) is an important method for measuring horizontal flows in the photosphere. This method exhibits a systematic error that looks like a flow converging towards disk center, also known as the shrinking-Sun effect. Aims. We aim at studying the nature of the shrinking-Sun effect for continuum intensity data and at deriving a simple model that can explain its origin. Methods. We derived LCT flow maps by running the local correlation tracking code FLCT on tracked and remapped continuum intensity maps provided by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory. We also computed flow maps from synthetic continuum images generated from STAGGER code simulations of solar surface convection. We investigated the origin of the shrinking-Sun effect by generating an average granule from synthetic data from the simulations. Results. The LCT flow maps derived from HMI and from the simulations exhibit a shrinking-Sun effect of comparable magnitude. The origin of this effect is related to the apparent asymmetry of granulation originating from radiative transfer effects when observing with a viewing angle inclined from vertical. This causes, in combination with the expansion of the granules, an apparent motion towards disk center.

Measuring solar active region inflows with local correlation tracking of granulation

Context. Local helioseismology has detected spatially extended converging surface flows into solar active regions. These play an important role in flux-transport models of the solar dynamo. Aims. We aim to validate the existence of the inflows by deriving horizontal flow velocities around active regions with local correlation tracking of granulation. Methods. We generate a six-year long-time series of full-disk maps of the horizontal velocity at the solar surface by tracking granules in continuum intensity images provided by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). Results. On average, active regions are surrounded by inflows extending up to 10 deg from the center of the active region of magnitudes of 20-30 m/s, reaching locally up to 40 m/s, which is in agreement with results from local helioseismology. By computing an ensemble average consisting of 243 individual active regions, we show that the inflows are not azimuthally symmetric but converge predominantly towards the trailing polarity of the active region with respect to the longitudinally and temporally averaged flow field.

Image compression in local helioseismology

Context. Several upcoming helioseismology space missions are very limited in telemetry and will have to perform extensive data compression. This requires the development of new methods of data compression. Aims. We give an overview of the influence of lossy data compression on local helioseismology. We investigate the e ects of several lossy compression methods (quantization, JPEG compression, and smoothing and subsampling) on power spectra and time-distance measurements of supergranulation flows at disk center. Methods. We applied di erent compression methods to tracked and remapped Dopplergrams obtained by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory. We determined the signal-to-noise ratio of the travel times computed from the compressed data as a function of the compression e ciency. Results. The basic helioseismic measurements that we consider are very robust to lossy data compression. Even if only the sign of the velocity is used, time-distance helioseismology is still possible. We achieve the best results by applying JPEG compression on spatially subsampled data. However, our conclusions are only valid for supergranulation flows at disk center and may not be valid for all helioseismology applications.

Global-scale equatorial Rossby waves as an essential component of solar internal dynamics

The Sun’s complex dynamics is controlled by buoyancy and rotation in the convection zone. Large-scale flows are dominated by vortical motions1 and appear to be weaker than expected in the solar interior2. One possibility is that waves of vorticity due to the Coriolis force, known as Rossby waves3 or r modes4, remove energy from convection at the largest scales5. However, the presence of these waves in the Sun is still debated. Here, we unambiguously discover and characterize retrograde-propagating vorticity waves in the shallow subsurface layers of the Sun at azimuthal wavenumbers below 15, with the dispersion relation of textbook sectoral Rossby waves. The waves have lifetimes of several months, well-defined mode frequencies below twice the solar rotational frequency, and eigenfunctions of vorticity that peak at the equator. Rossby waves have nearly as much vorticity as the convection at the same scales, thus they are an essential component of solar dynamics. We observe a transition from turbulence-like to wave-like dynamics around the Rhines scale6 of angular wavenumber of approximately 20. This transition might provide an explanation for the puzzling deficit of kinetic energy at the largest spatial scales.Analysis of a six-year time series of SDO/HMI images of the solar photosphere reveals the existence of global-scale equatorial Rossby waves in the Sun, which contain a large fraction of the radial vorticity at these scales.

Measuring the Wilson depression of sunspots using the divergence-free condition of the magnetic field vector

Context: The Wilson depression is the difference in geometric height of unit continuum optical depth between the sunspot umbra and the quiet Sun. Measuring the Wilson depression is important for understanding the geometry of sunspots. Current methods suffer from systematic effects or need to make assumptions on the geometry of the magnetic field. This leads to large systematic uncertainties of the derived Wilson depressions. Aims: We aim at developing a robust method for deriving the Wilson depression that only requires the information about the magnetic field that is accessible from spectropolarimetry, and that does not rely on assumptions on the geometry of sunspots or on their magnetic field. Methods: Our method is based on minimizing the divergence of the magnetic field vector derived from spectropolarimetric observations. We focus on large spatial scales only in order to reduce the number of free parameters. Results: We test the performance of our method using synthetic Hinode data derived from two sunspot simulations. We find that the maximum and the umbral averaged Wilson depression for both spots determined with our method typically lies within 100 km of the true value obtained from the simulations. In addition, we apply the method to Hinode observations of a sunspot. The derived Wilson depression (about 600 km) is consistent with results typically obtained from the Wilson effect. We also find that the Wilson depression obtained from using horizontal force balance gives 110 - 180 km smaller Wilson depressions than both, what we find and what we deduce directly from the simulations. This suggests that the magnetic pressure and the magnetic curvature force contribute to the Wilson depression by a similar amount.