53 research outputs found
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
Magnetic properties of a long-lived sunspot - Vertical magnetic field at the umbral boundary
Context. In a recent statistical study of sunspots in 79 active regions, the
vertical magnetic field component averaged along the umbral
boundary is found to be independent of sunspot size. The authors of that study
conclude that the absolute value of at the umbral boundary is
the same for all spots.
Aims. We investigate the temporal evolution of averaged along
the umbral boundary of one long-lived sunspot during its stable phase.
Methods. We analysed data from the HMI instrument on-board SDO. Contours of
continuum intensity at , whereby
refers to the average over the quiet sun areas, are used to extract the
magnetic field along the umbral boundary. Projection effects due to different
formation heights of the Fe I 617.3 nm line and continuum are taken into
account. To avoid limb artefacts, the spot is only analysed for heliocentric
angles smaller than .
Results. During the first disc passage, NOAA AR 11591, remains
constant at 1693 G with a root-mean-square deviation of 15 G, whereas the
magnetic field strength varies substantially (mean 2171 G, rms of 48 G) and
shows a long term variation. Compensating for formation height has little
influence on the mean value along each contour, but reduces the variations
along the contour when away from disc centre, yielding a better match between
the contours of G and .
Conclusions. During the disc passage of a stable sunspot, its umbral boundary
can equivalently be defined by using the continuum intensity or
the vertical magnetic field component . Contours of fixed
magnetic field strength fail to outline the umbral boundary.Comment: accepted for publication in A&A; v2 minor edit, correcting statement
regarding one citatio
A 3-D sunspot model derived from an inversion of spectropolarimetric observations and its implications for the penumbral heating
I deduced a 3-D sunspot model that is in agreement with spectropolarimetric
observations, to address the question of penumbral heating by the repetitive
rise of flow channels. I performed inversions of data taken simultaneously in
infrared and visible spectral lines. I used two independent magnetic components
to reproduce the irregular Stokes profiles in the penumbra. I studied the
averaged and individual properties of the two components. By integrating the
field inclination to the surface, I developed a 3-D model of the spot from
inversion results without intrinsic height information. I find that the
Evershed flow is harbored by the weaker of the two field components. This
component forms flow channels that show upstreams in the inner and mid
penumbra, continue horizontally as slightly elevated loops throughout the
penumbra, and finally bend down in the outer penumbra. I find several examples,
where two or more flow channels are found along a radial cut from the umbra to
the outer boundary of the spot. I find that a model of horizontal flow channels
in a static background field is in good agreement with the observed spectra.
The properties of the flow channels correspond very well to the simulations of
Schlichenmaier et al. (1998). From the temporal evolution in intensity images
and the properties of the flow channels in the inversion, I conclude that
interchange convection of rising hot flux tubes in a thick penumbra still seems
a possible mechanism for maintaining the penumbral energy balance.Comment: 17 pages, 21 figures, accepted by A&
Observations of Sunspot Oscillations in G band and Ca II H line with Solar Optical Telescope on Hinode
Exploiting high-resolution observations made by the Solar Optical Telescope
onboard Hinode, we investigate the spatial distribution of power spectral
density of oscillatory signal in and around NOAA active region 10935. The
G-band data show that in the umbra the oscillatory power is suppressed in all
frequency ranges. On the other hand, in Ca II H intensity maps oscillations in
the umbra, so-called umbral flashes, are clearly seen with the power peaking
around 5.5 mHz. The Ca II H power distribution shows the enhanced elements with
the spatial scale of the umbral flashes over most of the umbra but there is a
region with suppressed power at the center of the umbra. The origin and
property of this node-like feature remain unexplained.Comment: 7 pages, 8 figures, accepted for publication in PASJ (Hinode Special
Issue
Single sample soft shadows
Journal ArticleA simple extension to ray tracing is presented that creates visually plausible "soft" shadows with little extra computation. Although these soft shadows are approximate, they are robust and have penumbra widths that behave in a believable way, including accurate placement of singularities where penumbra width is zero. The method has continuous behavior in space and time, so it is appropriate for both static and dynamic image generation
No universal connection between the vertical magnetic field and the umbra-penumbra boundary in sunspots
Context. It has been reported that the boundary between the umbra and the
penumbra of sunspots occurs at a canonical value of the strength of the
vertical magnetic field, independently of the size of the spot. This critical
field strength is interpreted as to be the threshold for the onset of
magnetoconvection.
Aims. Here we investigate the reasons why this criterion, also called the
Jur\v{c}\'ak criterion in the literature, does not always identify the boundary
between umbra and penumbra.
Methods. We perform a statistical analysis of 23 sunspots observed with
Hinode/SOT. We compare the properties of the continuum intensity and the
vertical magnetic field between filaments and spines and how they vary between
spots of different sizes.
Results. We find that the inner boundary of the penumbra is not related to a
universal value of the vertical magnetic field. The properties of spines and
filaments vary between spots of different sizes. Both components are darker in
larger spots and the spines exhibit stronger vertical magnetic field. These
variations of the properties of filaments and spines with spot size are also
the reason for the reported invariance of the averaged vertical magnetic field
at 50% of the mean continuum intensity.
Conclusions. The formation of filaments and the onset of magnetoconvection
are not related to a canonical value of the strength of the vertical magnetic
field. Such a seemingly unique magnetic field strength is rather an effect of
the filling factor of spines and penumbral filaments.Comment: 15 pages, 11 figures. Accepted for publication in Astronomy and
Astrophysic
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