Uncertainties in the solar photospheric oxygen abundance

The purpose of this work is to better understand the confidence limits of the photospheric solar oxygen abundance derived from three-dimensional models using the forbidden [OI] line at 6300 \AA , including correlations with other parameters involved. We worked with a three-dimensional empirical model and two solar intensity atlases. We employed Bayesian inference as a tool to determine the most probable value for the solar oxygen abundance given the model chosen. We considered a number of error sources, such as uncertainties in the continuum derivation, in the wavelength calibration and in the abundance/strength of Ni. Our results shows correlations between the effects of several parameters employed in the derivation. The Bayesian analysis provides robust confidence limits taking into account all of these factors in a rigorous manner. We obtain that, given the empirical three-dimensional model and the atlas observations employed here, the most probable value for the solar oxygen abundance is $\log(\epsilon_O) = 8.86\pm0.04$. However, we note that this uncertainty does not consider possible sources of systematic errors due to the model choice.Comment: Accepted for publication in Astronomy and Astrophysic

Heating of the magnetized solar chromosphere by partial ionization effects

In this paper, we study the heating of the magnetized solar chromosphere induced by the large fraction of neutral atoms present in this layer. The presence of neutrals, together with the decrease with height of the collisional coupling, leads to deviations from the classical MHD behavior of the chromospheric plasma. A relative net motion appears between the neutral and ionized components, usually referred to as ambipolar diffusion. The dissipation of currents in the chromosphere is enhanced orders of magnitude due to the action of ambipolar diffusion, as compared to the standard ohmic diffusion. We propose that a significant amount of magnetic energy can be released to the chromosphere just by existing force-free 10--40 G magnetic fields there. As a consequence, we conclude that ambipolar diffusion is an important process that should be included in chromospheric heating models, as it has the potential to rapidly heat the chromosphere. We perform analytical estimations and numerical simulations to prove this idea.Comment: Accepted for publication by The Astrophysical Journa

Análisis didáctico del proceso matemático de modelización en alumnos de secundaria

En este trabajo se analiza didácticamente el proceso matemático de modelización en relación con las dificultades y errores de un grupo de alumnos de educación secundaria. Se consideran dos situaciones problemáticas relativas a este proceso, que se estudian desde las perspectivas epistemológica, semiótica y fenomenológica que propone el Enfoque Lógico Semiótico (ELOS) (Socas, 2007). Se concluye relacionando estas dificultades y errores de los alumnos con la organización de la enseñanza de la modelización en la secundaria, mostrando también el papel que juegan en dicho proceso otros como la sustitución formal y la generalización, así como las estructuras y las operaciones matemáticas implicadas en el mismo

A Hot Downflowing Model Atmosphere For Umbral Flashes And The Physical Properties Of Their Dark Fibrils

We perform NLTE inversions in a large set of umbral flashes, including the dark fibrils visible within them, and in the quiescent umbra by using the inversion code NICOLE on a set of full Stokes high-resolution Ca II 8542 A observations of a sunspot at disk center. We find that the dark structures have Stokes profiles that are distinct from those of the quiescent and flashed regions. They are best reproduced by atmospheres that are more similar to the flashed atmosphere in terms of velocities, even if with reduced amplitudes. We also find two sets of solutions that finely fit the flashed profiles: a set that is upflowing, featuring a transition region that is deeper than in the quiescent case and preceded by a slight dip in temperature, and a second solution with a hotter atmosphere in the chromosphere but featuring downflows close to the speed of sound at such heights. Such downflows may be related, or even dependent, on the presence of coronal loops, rooted in the umbra of sunspots, as is the case in the region analyzed. Similar loops have been recently observed to have supersonic downflows in the transition region and are consistent with the earlier "sunspot plumes" which were invariably found to display strong downflows in sunspots. Finally we find, on average, a magnetic field reduction in the flashed areas, suggesting that the shock pressure is moving field lines in the upper layers.Comment: Accepted in June for publication at ApJ. Comments to [email protected] or [email protected]

Non-local thermodynamic equilibrium inversions from a 3D MHD chromospheric model

The structure of the solar chromosphere is believed to be governed by magnetic fields, even in quiet-Sun regions that have a relatively weak photospheric field. During the past decade inversion methods have emerged as powerful tools for analyzing the chromosphere of active regions. The applicability of inversions to infer the stratification of the physical conditions in a dynamic 3D solar chromosphere has not yet been studied in detail. This study aims to establish the diagnostic capabilities of non-local thermodynamical equilibrium (NLTE) inversion techniques of Stokes profiles induced by the Zeeman effect in the Ca II 8542 line. We computed the Ca II atomic level populations in a snapshot from a 3D radiation-MHD simulation of the quiet solar atmosphere in non-LTE using the 3D radiative transfer code Multi3d. These populations were used to compute synthetic full-Stokes profiles in the Ca II 8542 line using 1.5D radiative transfer and the inversion code Nicole. The profiles were then spectrally degraded to account for finite filter width and Gaussian noise was added to account for finite photon flux. These profiles were inverted using Nicole and the results were compared with the original model atmosphere. Our NLTE inversions applied to quiet-Sun synthetic observations provide reasonably good estimates of the chromospheric magnetic field, line-of-sight velocities and somewhat less accurate, but still very useful, estimates of the temperature. Three dimensional scattering of photons cause cool pockets in the chromosphere to be invisible in the line profile and consequently they are also not recovered by the inversions. To successfully detect Stokes linear polarization in this quiet snapshot, a noise level below 10^{-3.5} is necessary.Comment: Accepted for publication in Astronomy & Astrophysic

Análisis y clasificación de errores cometidos por alumnos de secundaria en los procesos de sustitución formal, generalización y modelización en álgebra

Presentamos un estudio con alumnos de educación secundaria sobre tres procesos específicos del lenguaje algebraico: la sustitución formal, la generalización y la modelización. A partir de las respuestas a un cuestionario, realizamos una clasificación de los errores cometidos y se analizan sus posibles orígenes. Finalmente, formulamos algunas consecuencias didácticas que se derivan de estos resultados

On the validity of the 630 nm Fe I nm lines for the magnetometry of the internetwork quiet Sun

The purpose of this work is to analyze the reliability of the magnetic field strengths inferred from the 630 nm pair of Fe I lines at internetwork quiet Sun regions. Some numerical experiments have been performed that demonstrate the inability of these lines to recover the magnetic field strength in such low flux solar regions. It is shown how different model atmospheres, with magnetic field strengths ranging from few hundred Gauss to kiloGauss, give rise to Stokes profiles that can not be distinguished. The reasons for this degeneracy are discussed.Comment: Accepted for publication in A&

Análisis y clasificación de errores cometidos por alumnos de secundaria en los procesos de sustitución formal, generalización y modelización en álgebra

EN esta ponencia se presenta un estudio con alumnos de Educación Secundaria sobre tres procesos específicos del lenguaje algebraico: la sustitución formal, la generalización y la modelización. A partir de las respuestas dadas a un cuestionario diseñado para esta investigación, se realiza una clasificación de los errores cometidos y se analizan los posibles orígenes de dichos errores

La transformación de hankel clifford en ciertos espacios de distribuciones

The main objective of this paper is to show that the study of two Hankel-Clifford integral transformations on certain spaces of generalized functions allows to solve a class of partial differential equations of the Kepinski type for any real value of its parameter. Distributional theorems of inversion and uniqueness are also established