Applications of an exact counting formula in the Bousso-Polchinski Landscape

The Bousso-Polchinski (BP) Landscape is a proposal for solving the Cosmological Constant Problem. The solution requires counting the states in a very thin shell in flux space. We find an exact formula for this counting problem which has two simple asymptotic regime one of them being the method of counting low $\Lambda$ states given originally by Bousso and Polchinski. We finally give some applications of the extended formula: a robust property of the Landscape which can be identified with an effective occupation number, an estimator for the minimum cosmological constant and a possible influence on the KKLT stabilization mechanism.Comment: 43 pages, 11 figures, 2 appendices. We have added a new section (3.4) on the influence of the fraction of non-vanishing fluxes in the KKLT mechanism. Other minor changes also mad

Determination of Transverse Density Structuring from Propagating MHD Waves in the Solar Atmosphere

We present a Bayesian seismology inversion technique for propagating magnetohydrodynamic (MHD) transverse waves observed in coronal waveguides. The technique uses theoretical predictions for the spatial damping of propagating kink waves in transversely inhomogeneous coronal waveguides. It combines wave amplitude damping length scales along the waveguide with theoretical results for resonantly damped propagating kink waves to infer the plasma density variation across the oscillating structures. Provided the spatial dependence of the velocity amplitude along the propagation direction is measured and the existence of two different damping regimes is identified, the technique would enable us to fully constrain the transverse density structuring, providing estimates for the density contrast and its transverse inhomogeneity length scale

Spatial deconvolution of spectropolarimetric data: an application to quiet Sun magnetic elements

Observations of the Sun from the Earth are always limited by the presence of the atmosphere, which strongly disturbs the images. A solution to this problem is to place the telescopes in space satellites, which produce observations without any (or limited) atmospheric aberrations. However, even though the images from space are not affected by atmospheric seeing, the optical properties of the instruments still limit the observations. In the case of diffraction limited observations, the PSF establishes the maximum allowed spatial resolution, defined as the distance between two nearby structures that can be properly distinguished. In addition, the shape of the PSF induce a dispersion of the light from different parts of the image, leading to what is commonly termed as stray light or dispersed light. This effect produces that light observed in a spatial location at the focal plane is a combination of the light emitted in the object at relatively distant spatial locations. We aim to correct the effect produced by the telescope's PSF using a deconvolution method, and we decided to apply the code on Hinode/SP quiet Sun observations. We analyze the validity of the deconvolution process with noisy data and we infer the physical properties of quiet Sun magnetic elements after the deconvolution process.Comment: 14 pages, 9 figure

Analysis of Quiet-Sun Internetwork Magnetic Fields Based on Linear Polarization Signals

We present results from the analysis of Fe I 630 nm measurements of the quiet Sun taken with the spectropolarimeter of the Hinode satellite. Two data sets with noise levels of 1.2{\times}10-3 and 3{\times}10-4 are employed. We determine the distribution of field strengths and inclinations by inverting the two observations with a Milne-Eddington model atmosphere. The inversions show a predominance of weak, highly inclined fields. By means of several tests we conclude that these properties cannot be attributed to photon noise effects. To obtain the most accurate results, we focus on the 27.4% of the pixels in the second data set that have linear polarization amplitudes larger than 4.5 times the noise level. The vector magnetic field derived for these pixels is very precise because both circular and linear polarization signals are used simultaneously. The inferred field strength, inclination, and filling factor distributions agree with previous results, supporting the idea that internetwork fields are weak and very inclined, at least in about one quarter of the area occupied by the internetwork. These properties differ from those of network fields. The average magnetic flux density and the mean field strength derived from the 27.4% of the field of view with clear linear polarization signals are 16.3 Mx cm-2 and 220 G, respectively. The ratio between the average horizontal and vertical components of the field is approximately 3.1. The internetwork fields do not follow an isotropic distribution of orientations.Comment: To appear in APJ, Vol 749, 201

The Minimum Description Length Principle and Model Selection in Spectropolarimetry

It is shown that the two-part Minimum Description Length Principle can be used to discriminate among different models that can explain a given observed dataset. The description length is chosen to be the sum of the lengths of the message needed to encode the model plus the message needed to encode the data when the model is applied to the dataset. It is verified that the proposed principle can efficiently distinguish the model that correctly fits the observations while avoiding over-fitting. The capabilities of this criterion are shown in two simple problems for the analysis of observed spectropolarimetric signals. The first is the de-noising of observations with the aid of the PCA technique. The second is the selection of the optimal number of parameters in LTE inversions. We propose this criterion as a quantitative approach for distinguising the most plausible model among a set of proposed models. This quantity is very easy to implement as an additional output on the existing inversion codes.Comment: Accepted for publication in the Astrophysical Journa