Between umbra and penumbra

International audienceComputing shadow boundaries is a difficult problem in the case of non-point light sources. A point is in the umbra if it does not see any part of any light source; it is in full light if it sees entirely all the light sources; otherwise, it is in the penumbra. While the common boundary of the penumbra and the full light is well understood, less is known about the boundary of the umbra. In this paper we prove various bounds on the complexity of the umbra and the penumbra cast by a segment or polygonal light source on a plane in the presence of polygon or polytope obstacles. In particular, we show that a single segment light source may cast on a plane, in the presence of two triangles, four connected components of umbra and that two fat convex obstacles of total complexity n can engender Omega(n) connected components of umbra. In a scene consisting of a segment light source and k disjoint polytopes of total complexity n, we prove an Omega(nk^2+k^4) lower bound on the maximum number of connected components of the umbra and a O(nk^3) upper bound on its complexity. We also prove that, in the presence of k disjoint polytopes of total complexity n, some of which being light sources, the umbra cast on a plane may have Omega(n^2k^3 + nk^5) connected components and has complexity O(n^3k^3). These are the first bounds on the size of the umbra in terms of both k and n. These results prove that the umbra, which is bounded by arcs of conics, is intrinsically much more intricate than the full light/penumbra boundary which is bounded by line segments and whose worst-case complexity is in Omega(n alpha(k) +km +k^2) and O(n alpha(k) +km alpha(k) +k^2), where m is the complexity of the polygonal light source

Flow patterns around old sunspots and flare activity

New magnetic flux emerges significantly more probably in already existing solar active regions. Based on the the Debrecen Observatory photographic observations, several active regions are collected, where at least one large, X-class flare was recorded, and emergence of new activity, birth and quick motion of new umbrae was observed in the vicinity of old spots, the new activity emerged in the center of the old active region. Newly emerging magnetic flux in older sunspot groups can be distinguished by its quicker and generally westward proper motions. Umbrae of the new activity do not coalesce with older umbrae of the same polarity, but both elastic and inelastic collisions between them can be observed. Spots of the emerging new activity can flow around old unipolar spots (presumably shallower structures, “ω-loops”) westward, like a hydrodynamic flow around a cylinder, forming a wake behind it. Collision of different polarities in the wake can lead to large flares. The presence of old spots disturbs the normal emergence of the new activity, so motions of the new spots are distorted by the flow, the new emerging “Ω-loop” can be stuck between the umbrae of the old, tight dipole, the orientation of the new dipole can be distorted by as much as 180◦. The general direction of the flow around the old spots seems to depend on the latitude, the angle between the motion axis and the E-W direction grows with the latitude. The intensive flare activity seems to be connected strongly with the newly emerging magnetic flux; interacting of differently oriented dipoles and the difference of the orientation of the emerging new dipole from the ordinary Hale-Nicholson orientation is also significant. Simply large gradients of magnetic fields (δ-configuration) are not enough, dynamical processes (emergence of new flux, shearing or colliding motions of umbrae of different magnetic polarity) must also be present for large flares

High Resolution Helioseismic Imaging of Subsurface Structures and Flows of A Solar Active Region Observed by Hinode

We analyze a solar active region observed by the Hinode CaII H line using the time-distance helioseismology technique, and infer wave-speed perturbation structures and flow fields beneath the active region with a high spatial resolution. The general subsurface wave-speed structure is similar to the previous results obtained from SOHO/MDI observations. The general subsurface flow structure is also similar, and the downward flows beneath the sunspot and the mass circulations around the sunspot are clearly resolved. Below the sunspot, some organized divergent flow cells are observed, and these structures may indicate the existence of mesoscale convective motions. Near the light bridge inside the sunspot, hotter plasma is found beneath, and flows divergent from this area are observed. The Hinode data also allow us to investigate potential uncertainties caused by the use of phase-speed filter for short travel distances. Comparing the measurements with and without the phase-speed filtering, we find out that inside the sunspot, mean acoustic travel times are in basic agreement, but the values are underestimated by a factor of 20-40% inside the sunspot umbra for measurements with the filtering. The initial acoustic tomography results from Hinode show a great potential of using high-resolution observations for probing the internal structure and dynamics of sunspots.Comment: accepted for publication in Ap

The pre-penumbral magnetic canopy in the solar atmosphere

Penumbrae are the manifestation of magnetoconvection in highly inclined (to the vertical direction) magnetic field. The penumbra of a sunspot tends to form, initially, along the arc of the umbra antipodal to the main region of flux emergence. The question of how highly inclined magnetic field can concentrate along the antipodal curves of umbrae, at least initially, remains to be answered. Previous observational studies have suggested the existence of some form of overlying magnetic canopy which acts as the progenitor for penumbrae. We propose that such overlying magnetic canopies are a consequence of how the magnetic field emerges into the atmosphere and are, therefore, part of the emerging region. We show, through simulations of twisted flux tube emergence, that canopies of highly inclined magnetic field form preferentially at the required locations above the photosphere

Wave dynamics in a sunspot umbra

The high spatial and time resolution data obtained with SDO/AIA for the sunspot in active region NOAA 11131 on 08 December 2010 were analysed with the time-distance plot technique and the pixelised wavelet filtering method. Oscillations in the 3 min band dominate in the umbra. The integrated spectrum of umbral oscillations contains distinct narrowband peaks at 1.9 min, 2.3 min, and 2.8 min. The power significantly varies in time, forming distinct oscillation trains. The oscillation power distribution over the sunspot in the horizontal plane reveals that the enhancements of the oscillation amplitude, or wave fronts, have a distinct structure consisting of an evolving two-armed spiral and a stationary circular patch at the spiral origin, situated near the umbra centre. This structure is seen from the temperature minimum to the corona. In time, the spiral rotates anti-clockwise. The wave front spirality is most pronounced during the maximum amplitude phases of the oscillations. In the low-amplitude phases the spiral breaks into arc-shaped patches. The 2D cross-correlation function shows that the oscillations at higher atmospheric levels occur later than at lower layers. The phase speed is estimated to be about 100 km/s. The fine spectral analysis shows that the central patch corresponds to the high-frequency oscillations, while the spiral arms highlight the lower-frequency oscillations in the 3-min band. The vertical and horizontal radial structure of the oscillations is consistent with the model that interprets umbral oscillations as slow magnetoacoustic waves filtered by the atmospheric temperature non-uniformity in the presence of the magnetic field inclination from the vertical. The mechanism for the polar-angle structure of the oscillations, in particular the spirality of the wave fronts, needs to be revealed.Comment: 8 pages, 9 figures, Astronomy and Astrophysics, 201

Stable Umbral Chromospheric Structures

Aims. To understand the morphology of the chromosphere in sunspot umbra. We investigate if the horizontal structures observed in the spectral core of the Ca II H line are ephemeral visuals caused by the shock dynamics of more stable structures, and examine their relationship with observables in the H-alpha line. Methods. Filtergrams in the core of the Ca II H and H-alpha lines as observed with the Swedish 1-m Solar Telescope are employed. We utilise a technique that creates composite images and tracks the flash propagation horizontally. Results. We find 0"15 wide horizontal structures, in all of the three target sunspots, for every flash where the seeing was moderate to good. Discrete dark structures are identified that are stable for at least two umbral flashes, as well as systems of structures that live for up to 24 minutes. We find cases of extremely extended structures with similar stability, with one such structure showing an extent of 5". Some of these structures have a correspondence in H-alpha but we were unable to find a one to one correspondence for every occurrence. If the dark streaks are formed at the same heights as umbral flashes then there are systems of structures with strong departures from the vertical for all three analysed sunspots. Conclusions. Long-lived Ca II H filamentary horizontal structures are a common and likely ever-present feature in the umbra of sunspots. If the magnetic field in the chromosphere of the umbra is indeed aligned with the structures, then the present theoretical understanding of the typical umbra needs to be revisited.Comment: Accepted to Astronomy and Astrophysics. Online material (Fig3.mov and Fig4.mov) will be available at A&

Image patch analysis and clustering of sunspots: a dimensionality reduction approach

Sunspots, as seen in white light or continuum images, are associated with regions of high magnetic activity on the Sun, visible on magnetogram images. Their complexity is correlated with explosive solar activity and so classifying these active regions is useful for predicting future solar activity. Current classification of sunspot groups is visually based and suffers from bias. Supervised learning methods can reduce human bias but fail to optimally capitalize on the information present in sunspot images. This paper uses two image modalities (continuum and magnetogram) to characterize the spatial and modal interactions of sunspot and magnetic active region images and presents a new approach to cluster the images. Specifically, in the framework of image patch analysis, we estimate the number of intrinsic parameters required to describe the spatial and modal dependencies, the correlation between the two modalities and the corresponding spatial patterns, and examine the phenomena at different scales within the images. To do this, we use linear and nonlinear intrinsic dimension estimators, canonical correlation analysis, and multiresolution analysis of intrinsic dimension.Comment: 5 pages, 7 figures, accepted to ICIP 201