The Chromospheric Solar Limb Brightening at Radio, Millimeter, Sub-millimeter, and Infrared Wavelengths

Observations of the emission at radio, millimeter, sub-millimeter, and infrared wavelengths in the center of the solar disk validate the auto-consistence of semi-empirical models of the chromosphere. Theoretically, these models must reproduce the emission at the solar limb. In this work, we tested both the VALC and the C7 semi-empirical models by computing their emission spectrum in the frequency range from 2 GHz to 10 THz, at solar limb altitudes. We calculate the Sun's theoretical radii as well as their limb brightening. Non-Local Thermodynamic Equilibrium (NLTE) was computed for hydrogen, electron density, and H-. In order to solve the radiative transfer equation a 3D geometry was employed to determine the ray paths and Bremsstrahlung, H-, and inverse Bremsstrahlung opacity sources were integrated in the optical depth. We compared the computed solar radii with high resolution observations at the limb obtained by Clark (1994). We found that there are differences between observed and computed solar radii of 12000 km at 20 GHz, 5000 km at 100 GHz, and 1000 km at 3 THz for both semi-empirical models. A difference of 8000 km in the solar radii was found comparing our results against heights obtained from H{\alpha} observations of spicules-off at the solar limb. We conclude that the solar radii can not be reproduced by VALC and C7 semi-empirical models at radio - infrared wavelengths. Therefore, the structures in the high chromosphere provides a better measurement of the solar radii and their limb brightening as shown in previous investigations.Comment: Accepted by The Astrophysical Journa

What majority decisions are possible with possible abstaining

Suppose we are given a family of choice functions on pairs from a given finite set. The set is considered as a set of alternatives (say candidates for an office) and the functions as potential "voters". The question is, what choice functions agree, on every pair, with the majority of some finite subfamily of the voters? For the problem as stated, a complete characterization was given in \citet{shelah2009mdp}, but here we allow each voter to abstain. There are four cases.Comment: 23 page

On the Sensitivity of Partial Redistribution Scattering Polarization Profiles to Various Atmospheric Parameters

This paper presents a detailed study of the scattering polarization profiles formed under partial frequency redistribution (PRD) in two thermal models of the solar atmosphere. Particular attention is given to understanding the influence of several atmospheric parameters on the emergent fractional linear polarization profiles. The shapes of these $Q/I$ profiles are interpreted in terms of the anisotropy of the radiation field, which in turn depends on the source function gradient that sets the angular variation of the specific intensity. We define a suitable frequency integrated anisotropy factor for PRD that can be directly related to the emergent linear polarization. We show that complete frequency redistribution is a good approximation to model weak resonance lines. We also show that the emergent linear polarization profiles can be very sensitive to the thermal structure of the solar atmosphere and, in particular, to spatial variations of the damping parameter.Comment: 45 pages, 16 figures, accepted for publication in the Astrophysical Journal (2010

The Relation between the Radial Temperature Profile in the Chromosphere and the Solar Spectrum at Centimeter, Millimeter, Sub-millimeter, and Infrared Wavelengths

Solar observations from millimeter to ultraviolet wavelengths show that there is a temperature minimum between photosphere and chromosphere. Analysis based on semi-empirical models locate this point at about 500 km over the photosphere. The consistency of these models has been tested by means of millimeter to infrared observations. In the present work, we show that variations of the theoretical radial temperature profile near the temperature minimum impacts the brightness temperature at centimeter, submillimeter, and infrared wavelengths, but the millimeter wavelength emission remains unchanged. We found a region between 500 and 1000 km over the photosphere that remains hidden to observations at the frequencies under study in this work.Comment: Accepted in Solar Physic

Measuring Communication in Parallel Communicating Finite Automata

Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of returning centralized systems, when the number of necessary communications during the computations of the system is bounded by a function depending on the length of the input. It is proved that an infinite hierarchy of language families exists, depending on the number of messages sent during their most economical recognitions. Moreover, several properties are shown to be not semi-decidable for the systems under consideration.Comment: In Proceedings AFL 2014, arXiv:1405.527