212 research outputs found
String Branchings on Complex Tori and Algebraic Representations of Generalized Krichever-Novikov Algebras
The propagation differential for bosonic strings on a complex torus with
three symmetric punctures is investigated. We study deformation aspects between
two point and three point differentials as well as the behaviour of the
corresponding Krichever-Novikov algebras. The structure constants are
calculated and from this we derive a central extension of the Krichever-Novikov
algebras by means of b-c systems. The defining cocycle for this central
extension deforms to the well known Virasoro cocycle for certain kinds of
degenerations of the torus.
AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40Comment: 11 pages, amste
Searching for overturning convection in penumbral filaments: slit spectroscopy at 0.2 arcsec resolution
Recent numerical simulations of sunspots suggest that overturning convection
is responsible for the existence of penumbral filaments and the Evershed flow,
but there is little observational evidence of this process. Here we carry out a
spectroscopic search for small-scale convective motions in the penumbra of a
sunspot located 5 deg away from the disk center. The position of the spot is
very favorable for the detection of overturning downflows at the edges of
penumbral filaments. Our analysis is based on measurements of the Fe I 709.0 nm
line taken with the Littrow spectrograph of the Swedish 1 m Solar Telescope
under excellent seeing conditions. We compute line bisectors at different
intensity levels and derive Doppler velocities from them. The velocities are
calibrated using a nearby telluric line, with systematic errors smaller than
150 m/s. Deep in the photosphere, as sampled by the bisectors at the 80%-88%
intensity levels, we always observe blueshifts or zero velocities. The maximum
blueshifts reach 1.2 km/s and tend to be cospatial with bright penumbral
filaments. In the line core we detect blueshifts for the most part, with small
velocities not exceeding 300 m/s. Redshifts also occur, but at the level of
100-150 m/s, and only occasionally. The fact that they are visible in high
layers casts doubts on their convective origin. Overall, we do not find
indications of downflows that could be associated with overturning convection
at our detection limit of 150 m/s. Either no downflows exist, or we have been
unable to observe them because they occur beneath tau=1 or the spatial
resolution/height resolution of the measurements is still insufficient.Comment: Accepted for publication in Ap
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
Absolute velocity measurements in sunspot umbrae
In sunspot umbrae, convection is largely suppressed by the strong magnetic
field. Previous measurements reported on negligible convective flows in umbral
cores. Based on this, numerous studies have taken the umbra as zero reference
to calculate Doppler velocities of the ambient active region. To clarify the
amount of convective motion in the darkest part of umbrae, we directly measured
Doppler velocities with an unprecedented accuracy and precision. We performed
spectroscopic observations of sunspot umbrae with the Laser Absolute Reference
Spectrograph (LARS) at the German Vacuum Tower Telescope. A laser frequency
comb enabled the calibration of the high-resolution spectrograph and absolute
wavelength positions. A thorough spectral calibration, including the
measurement of the reference wavelength, yielded Doppler shifts of the spectral
line Ti i 5713.9 {\AA} with an uncertainty of around 5 m s-1. The measured
Doppler shifts are a composition of umbral convection and magneto-acoustic
waves. For the analysis of convective shifts, we temporally average each
sequence to reduce the superimposed wave signal. Compared to convective
blueshifts of up to -350 m s-1 in the quiet Sun, sunspot umbrae yield a
strongly reduced convective blueshifts around -30 m s-1. {W}e find that the
velocity in a sunspot umbra correlates significantly with the magnetic field
strength, but also with the umbral temperature defining the depth of the
titanium line. The vertical upward motion decreases with increasing field
strength. Extrapolating the linear approximation to zero magnetic field
reproduces the measured quiet Sun blueshift. Simply taking the sunspot umbra as
a zero velocity reference for the calculation of photospheric Dopplergrams can
imply a systematic velocity error.Comment: 10 pages, 7 figures, 2 tables, Appendix with 5 figure
Evolution of a magnetic flux tube in a sunspot penumbra
The motion of an individual magnetic flux tube inside the penumbra of a sunspot is studied numerically. Here, we present preliminary results. The thin flux tube approximation together with a simplified radiative heat exchange with the surroundings is used to study the evolution of a flux tube embedded into a background given by a global magneto-static sunspot model. The investigation is undertaken in order to verify the conjecture that convection in sunspot penumbrae occurs by an interchange of magnetic flux tubes. The code being developed can be used to study dynamic aspects of filamentary structure in the penumbra: the temporal and spatial fluctuations of the temperature and the magnetic field, the motion of bright penumbral grains, or the Evershed effect. Here we present the evolution of a wave formed by the tube whose fragment emerges in the penumbral photosphere and migrates towards the umbra. The properties of this wave show qualitative features of the observed bright penumbral grains with corresponding upward velocity and its correlation with brightness and the inclination of the magnetic field, and also of the Evershed effect
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