High-resolution imaging spectroscopy of two micro-pores and an arch filament system in a small emerging-flux region

Aims. The purpose of this investigation is to characterize the temporal evolution of an emerging flux region, the associated photospheric and chromospheric flow fields, and the properties of the accompanying arch filament system. Methods. This study is based on imaging spectroscopy with the G\"ottingen Fabry-P\'erot Interferometer at the Vacuum Tower Telescope, on 2008 August 7. Cloud model (CM) inversions of line scans in the strong chromospheric absorption H$\alpha$ line yielded CM parameters, which describe the cool plasma contained in the arch filament system. Results. The observations cover the decay and convergence of two micro-pores with diameters of less than one arcsecond and provide decay rates for intensity and area. The photospheric horizontal flow speed is suppressed near the two micro-pores indicating that the magnetic field is sufficiently strong to affect the convective energy transport. The micro-pores are accompanied by an arch filament system, where small-scale loops connect two regions with H$\alpha$ line-core brightenings containing an emerging flux region with opposite polarities. The chromospheric velocity of the cloud material is predominantly directed downwards near the footpoints of the loops with velocities of up to 12 km/s, whereas loop tops show upward motions of about 3 km/s. Conclusions. Micro-pores are the smallest magnetic field concentrations leaving a photometric signature in the photosphere. In the observed case, they are accompanied by a miniature arch filament system indicative of newly emerging flux in the form of $\Omega$-loops. Flux emergence and decay take place on a time-scale of about two days, whereas the photometric decay of the micro-pores is much more rapid (a few hours), which is consistent with the incipient submergence of $\Omega$-loops. The results are representative for the smallest emerging flux regions still recognizable as such.Comment: 15 pages, 16 figures, 3 tables, published in A&

Asymptotically Safe Lorentzian Gravity

The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a non-trivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick-rotation. Within the Einstein-Hilbert approximation, the $\beta$-functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Lorentzian quantum gravity belong to the same universality class at high energies.Comment: 4 pages, 2 figure

An effective action for asymptotically safe gravity

Asymptotically safe theories of gravitation have received great attention in recent times. In this framework an effective action embodying the basic features of the renormalized flow around the non-gaussian fixed point is derived and its implications for the early universe are discussed. In particular, a "landscape" of a countably infinite number of cosmological inflationary solutions characterized by an unstable de Sitter phase lasting for a large enough number of e-folds is found.Comment: 5 pages, to appear as a Rapid Communication in Physical Review

Properties of the inner penumbral boundary and temporal evolution of a decaying sunspot

It was empirically determined that the umbra-penumbra boundaries of stable sunspots are characterized by a constant value of the vertical magnetic field. We analyzed the evolution of the photospheric magnetic field properties of a decaying sunspot belonging to NOAA 11277 between August 28 - September 3, 2011. The observations were acquired with the spectropolarimeter on-board of the Hinode satellite. We aim to proof the validity of the constant vertical magnetic-field boundary between the umbra and penumbra in decaying sunspots. A spectral-line inversion technique was used to infer the magnetic field vector from the full-Stokes profiles. In total, eight maps were inverted and the variation of the magnetic properties in time were quantified using linear or quadratic fits. We found a linear decay of the umbral vertical magnetic field, magnetic flux, and area. The penumbra showed a linear increase of the vertical magnetic field and a sharp decay of the magnetic flux. In addition, the penumbral area quadratically decayed. The vertical component of the magnetic field is weaker on the umbra-penumbra boundary of the studied decaying sunspot compared to stable sunspots. Its value seem to be steadily decreasing during the decay phase. Moreover, at any time of the shown sunspot decay, the inner penumbra boundary does not match with a constant value of the vertical magnetic field, contrary to what was seen in stable sunspots. During the decaying phase of the studied sunspot, the umbra does not have a sufficiently strong vertical component of the magnetic field and is thus unstable and prone to be disintegrated by convection or magnetic diffusion. No constant value of the vertical magnetic field was found for the inner penumbral boundary.Comment: Accepted for publication in Astronomy & Astrophysics, 6 pages, 7 figure

Temporal evolution of arch filaments as seen in He I 10830 \r{A}

We study the evolution of an arch filament system (AFS) and of its individual arch filaments to learn about the processes occurring in them. We observed the AFS at the GREGOR solar telescope on Tenerife at high cadence with the very fast spectroscopic mode of the GREGOR Infrared Spectrograph (GRIS) in the He I 10830 \AA\ spectral range. The He I triplet profiles were fitted with analytic functions to infer line-of-sight (LOS) velocities to follow plasma motions within the AFS. We tracked the temporal evolution of an individual arch filament over its entire lifetime, as seen in the He I 10830 \AA\ triplet. The arch filament expanded in height and extended in length from 13" to 21". The lifetime of this arch filament is about 30 min. About 11 min after the arch filament is seen in He I, the loop top starts to rise with an average Doppler velocity of 6 km/s. Only two minutes later, plasma drains down with supersonic velocities towards the footpoints reaching a peak velocity of up to 40 km/s in the chromosphere. The temporal evolution of He I 10830 \AA\ profiles near the leading pore showed almost ubiquitous dual red components of the He I triplet, indicating strong downflows, along with material nearly at rest within the same resolution element during the whole observing time. We followed the arch filament as it carried plasma during its rise from the photosphere to the corona. The material then drained toward the photosphere, reaching supersonic velocities, along the legs of the arch filament. Our observational results support theoretical AFS models and aids in improving future models.Comment: Accepted for publication in Astronomy & Astrophysics, 12 pages, 15 figures, 1 online movi

Efectos de la aplicación de secuencias didácticas en el aprendizaje del concepto de función bajo la teoría de las representaciones semióticas con docentes en formación

El concepto matemático más importante en la transición de la educación media a la educación superior, es el de función. Al ingresar a la universidad los estudiantes inician con el curso de cálculo diferencial donde este concepto se hace imprescindible para el desarrollo de los contenidos. Investigaciones precedidas a esta permitieron identificar debilidades en los estudiantes recurrentes en los últimos cuatro semestres, por ello, se propone una serie de secuencias didácticas con el fin de mejorar el aprendizaje de la temática a abordar. Partiendo desde las investigaciones que afirman que el estudiante tiene total apropiación del concepto cuando hace transformaciones coherentes entre los diferentes registros de representación, se definen las secuencias didácticas bajo la teoría de las representaciones semióticas. Para esta investigación se tomó como población a los docentes en formación del programa de Licenciatura en Matemáticas de la Universidad Francisco de Paula Santander matriculados en el I semestre de 2018

Ca II 8542 \AA\ brightenings induced by a solar microflare

We study small-scale brightenings in Ca II 8542 \AA\ line-core images to determine their nature and effect on localized heating and mass transfer in active regions. High-resolution 2D spectroscopic observations of an active region in the Ca II 8542 \AA\ line were acquired with the GFPI attached to the 1.5-meter GREGOR telescope. Inversions of the spectra were carried out using NICOLE. We identified three brightenings of sizes up to 2"x2". We found evidence that the brightenings belonged to the footpoints of a microflare (MF). The properties of the observed brightenings disqualified the scenarios of Ellerman bombs or IRIS bombs. However, this MF shared some common properties with flaring active-region fibrils or flaring arch filaments (FAFs): (1) FAFs and MFs are both apparent in chromospheric and coronal layers according to the AIA channels, and (2) both show flaring arches with lifetimes of about 3.0-3.5 min and lengths of about 20". The inversions revealed heating by 600 K at the footpoint location in the ambient chromosphere during the impulsive phase. Connecting the footpoints, a dark filamentary structure appeared in the Ca II line-core images. Before the start of the MF, the spectra of this structure already indicated average blueshifts, meaning upward motions of the plasma along the LOS. During the impulsive phase, these velocities increased up to -2.2 km/s. Downflows dominated at the footpoints. However, in the upper photosphere, slight upflows occurred during the impulsive phase. Hence, bidirectional flows are present in the footpoints of the MF. Conclusions: We detected Ca II brightenings that coincided with the footpoint location of an MF. The MF event led to a rise of plasma in the upper photosphere, both before and during the impulsive phase. Excess mass, previously raised to at most chromospheric layers, slowly drained downward along arches toward the footpoints of the MF.Comment: Accepted for publication in Astronomy & Astrophysics, 13 pages, 6 figures, 1 online movi