1,073 research outputs found
Inferring the magnetic field vector in the quiet Sun. II. Interpreting results from the inversion of Stokes profiles
In a previous paper, we argued that the inversion of Stokes profiles applied
to spectropolarimetric observations of the solar internetwork yield
unrealistically large values of the inclination of the magnetic field vector
(). This is because photon noise in Stokes and are interpreted
by the inversion code as valid signals, that leads to an overestimation of the
transverse component , thus the inclination . However, our
study was based on the analysis of linear polarization signals that featured
only uncorrelated noise. In this paper, we develop this idea further and study
this effect in Stokes and profiles that also show correlated noise. In
addition, we extend our study to the three components of the magnetic field
vector, as well as the magnetic filling factor . With this, we confirm
the tendency to overestimate when inverting linear polarization
profiles that, although non-zero, are still below the noise level. We also
establish that the overestimation occurs mainly for magnetic fields that are
nearly vertical . This indicates that a reliable
inference of the inclination of the magnetic field vector cannot be achieved by
analyzing only Stokes and . In addition, when inverting Stokes and
profiles below the noise, the inversion code retrieves a randomly uniform
distribution of the azimuth of the magnetic field vector . To avoid these
problems, we propose only inverting Stokes profiles for which the linear
polarization signals are sufficiently above the noise level. However, this
approach is also biased because, in spite of allowing for a very accurate
retrieval of the magnetic field vector from the selected Stokes profiles, it
selects only profiles arising from highly inclined magnetic fields.Comment: Accepted for publication in Astronomy and Astrophysics. 14 pages. 7
color figure
Inferring the magnetic field vector in the quiet Sun. III. Disk variation of the Stokes profiles and isotropism of the magnetic field
We have studied the angular distribution of the magnetic field vector in the
solar internetwork employing high-quality data (noise level in units of the quiet-Sun intensity) at different latitudes
recorded with the Hinode/SP instrument. Instead of applying traditional
inversion codes of the radiative transfer equation to retrieve the magnetic
field vector at each spatial point on the solar surface and studying the
resulting distribution of the magnetic field vector, we surmised a theoretical
distribution function of the magnetic field vector and used it to obtain the
theoretical histograms of the Stokes profiles. These histograms were then
compared to the observed ones. Any mismatch between them was ascribed to the
theoretical distribution of the magnetic field vector, which was subsequently
modified to produce a better fit to the observed histograms. With this method
we find that Stokes profiles with signals above (in units of
the continuum intensity) cannot be explained by an isotropic distribution of
the magnetic field vector. We also find that the differences between the
histograms of the Stokes profiles observed at different latitudes cannot be
explained in terms of line-of-sight effects. However, they can be explained by
a distribution of the magnetic field vector that inherently varies with
latitude. We note that these results are based on a series of assumptions that,
although briefly discussed in this paper, need to be considered in more detail
in the future.Comment: Accepted for publication in Astronomy and Astrophysics. 14 pages, 8
color figure
Modified p-modes in penumbral filaments?
Aims: The primary objective of this study is to search for and identify wave
modes within a sunspot penumbra.
Methods: Infrared spectropolarimetric time series data are inverted using a
model comprising two atmospheric components in each spatial pixel. Fourier
phase difference analysis is performed on the line-of-sight velocities
retrieved from both components to determine time delays between the velocity
signals. In addition, the vertical separation between the signals in the two
components is calculated from the Stokes velocity response functions.
Results: The inversion yields two atmospheric components, one permeated by a
nearly horizontal magnetic field, the other with a less-inclined magnetic
field. Time delays between the oscillations in the two components in the
frequency range 2.5-4.5 mHz are combined with speeds of atmospheric wave modes
to determine wave travel distances. These are compared to expected path lengths
obtained from response functions of the observed spectral lines in the
different atmospheric components. Fast-mode (i.e., modified p-mode) waves
exhibit the best agreement with the observations when propagating toward the
sunspot at an angle ~50 degrees to the vertical.Comment: 8 pages, 12 figures, accepted for publication in Astronomy &
Astrophysic
The uncombed penumbra
The uncombed penumbral model explains the structure of the sunspot penumbra
in terms of thick magnetic fibrils embedded in a magnetic surrounding
atmosphere. This model has been successfully applied to explain the
polarization signals emerging from the sunspot penumbra. Thick penumbral
fibrils face some physical problems, however. In this contribution we will
offer possible solutions to these shortcomings.Comment: 6 pages, 2 figures. to appear in the proceedings of the Solar
Polarization Workshop I
Penumbral thermal structure below the visible surface
. The thermal structure of the penumbra below its visible surface
(i.e., ) has important implications for our present understanding
of sunspots and their penumbrae: their brightness and energy transport, mode
conversion of magneto-acoustic waves, sunspot seismology, and so forth. .
We aim at determining the thermal stratification in the layers immediately
beneath the visible surface of the penumbra: ( km below the visible continuum-forming layer). . We analyzed
spectropolarimetric data (i.e., Stokes profiles) in three Fe \textsc{i} lines
located at 1565 nm observed with the GRIS instrument attached to the 1.5-meter
solar telescope GREGOR. The data are corrected for the smearing effects of
wide-angle scattered light and then subjected to an inversion code for the
radiative transfer equation in order to retrieve, among others, the temperature
as a function of optical depth . . We find that the
temperature gradient below the visible surface of the penumbra is smaller than
in the quiet Sun. This implies that in the region the penumbral
temperature diverges from that of the quiet Sun. The same result is obtained
when focusing only on the thermal structure below the surface of bright
penumbral filaments. We interpret these results as evidence of a thick
penumbra, whereby the magnetopause is not located near its visible surface. In
addition, we find that the temperature gradient in bright penumbral filaments
is lower than in granules. This can be explained in terms of the limited
expansion of a hot upflow inside a penumbral filament relative to a granular
upflow, as magnetic pressure and tension forces from the surrounding penumbral
magnetic field hinder an expansion like this.Comment: 5 pages; 2 figures; accepted for publication in Astronomy and
Astrophysics Letter
Ranking efficient DMUs using cooperative game theory
The problem of ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) has been widely studied in the literature. Some of the proposed approaches use cooperative game theory as a tool to perform the ranking. In this paper, we use the Shapley value of two different cooperative games in which the players are the efficient DMUs and the characteristic function represents the increase in the discriminant power of DEA contributed by each efficient DMU. The idea is that if the efficient DMUs are not included in the modified reference sample then the efficiency score of some inefficient DMUs would be higher. The characteristic function represents, therefore, the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient units is dropped from the sample. Alternatively, the characteristic function of the cooperative game can be defined as the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient DMUs are the only efficient DMUs that are included in the sample. Since the two cooperative games proposed are dual games, their corresponding Shapley value coincide and thus lead to the same ranking. The more an ef- ficient DMU impacts the shape of the efficient frontier, the higher the increase in the efficiency scores of the inefficient DMUs its removal brings about and, hence, the higher its contribution to the overall discriminant power of the method. The proposed approach is illustrated on a number of datasets from the literature and compared with existing methods
Convective motions and net circular polarization in sunspot penumbrae
We have employed a penumbral model, that includes the Evershed flow and
convective motions inside penumbral filaments, to reproduce the azimuthal
variation of the net circular polarization (NCP) in sunspot penumbrae at
different heliocentric angles for two different spectral lines. The theoretical
net circular polarization fits the observations as satisfactorily as penumbral
models based on flux-tubes. The reason for this is that the effect of
convective motions on the NCP is very small compared to the effect of the
Evershed flow. In addition, the NCP generated by convective upflows cancels out
the NCP generated by the downflows. We have also found that, in order to fit
the observed NCP, the strength of the magnetic field inside penumbral filaments
must be very close to 1000 G. In particular, field-free or weak-field filaments
fail to reproduce both the correct sign of the net circular polarization, as
well as its dependence on the azimuthal and heliocentric angles.Comment: Accepted for publication in the Astrophysical Journal. 10 pages, 7
figures (3 in color). Uses emulatedap
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