1,225 research outputs found
Evolution of the flow field in decaying active regions, Transition from a moat flow to a supergranular flow
We investigate the evolution of the horizontal flow field around sunspots
during their decay by analysing its extension and horizontal velocity around
eight spots using SDO/HMI Doppler maps. By assuming a radially symmetrical flow
field, the applied analysis method determines the radial dependence of the
azimuthally averaged flow field. For comparison, we studied the flow in
supergranules using the same technique. All investigated, fully fledged
sunspots are surrounded by a flow field whose horizontal velocity profile
decreases continuously from 881 m s at 1.1 Mm off the spot boundary,
down to 199 m s at a mean distance of 11.9 Mm to that boundary. Once the
penumbra is fully dissolved, however, the velocity profile of the flow changes:
The horizontal velocity increases with increasing distance to the spot boundary
until a maximum value of about 398 m s is reached. Then, the horizontal
velocity decreases for farther distances to the spot boundary. In
supergranules, the horizontal velocity increases with increasing distance to
their centre up to a mean maximum velocity of 355 m s. For larger
distances, the horizontal velocity decreases. We thus find that the velocity
profile of naked sunspots resembles that of supergranular flows. The evolution
of the flow field around individual sunspots is influenced by the way the
sunspot decays and by the interplay with the surrounding flow areas.
Observations of the flow around eight decaying sunspots suggest that as long as
penumbrae are present, sunspots with their moat cell are embedded in network
cells. The disappearance of the penumbra (and consequently the moat flow) and
the competing surrounding supergranular cells, both have a significant role in
the evolution of the flow field: The moat cell transforms into a supergranule,
which hosts the remaining naked spot.Comment: accepted for publication in A&A, 11 pages, 6 figures, 3 tables;
appendix with 9 figures and 8 online movie
Geodesics for a class of distances in the space of probability measures
In this paper, we study the characterization of geodesics for a class of
distances between probability measures introduced by Dolbeault, Nazaret and
Savar e. We first prove the existence of a potential function and then give
necessary and suffi cient optimality conditions that take the form of a coupled
system of PDEs somehow similar to the Mean-Field-Games system of Lasry and
Lions. We also consider an equivalent formulation posed in a set of probability
measures over curves
Infinite-horizon problems under periodicity constraint
We study so{\`u}e infinite-horizon optimization problems on spaces of
periodic functions for non periodic Lagrangians. The main strategy relies on
the reduction to finite horizon thanks in the introduction of an avering
operator.We then provide existence results and necessary optimality conditions
in which the corresponding averaged Lagrangian appears
Weighted interpolation inequalities: a perturbation approach
We study optimal functions in a family of Caffarelli-Kohn-Nirenberg
inequalities with a power-law weight, in a regime for which standard
symmetrization techniques fail. We establish the existence of optimal
functions, study their properties and prove that they are radial when the power
in the weight is small enough. Radial symmetry up to translations is true for
the limiting case where the weight vanishes, a case which corresponds to a
well-known subfamily of Gagliardo-Nirenberg inequalities. Our approach is based
on a concentration-compactness analysis and on a perturbation method which uses
a spectral gap inequality. As a consequence, we prove that optimal functions
are explicit and given by Barenblatt-type profiles in the perturbative regime
Optimal transportation for the determinant
Among -valued triples of random vectors having fixed marginal
probability laws, what is the best way to jointly draw in such a way
that the simplex generated by has maximal average volume? Motivated
by this simple question, we study optimal transportation problems with several
marginals when the objective function is the determinant or its absolute value
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
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