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

Stokes Inversion based on Convolutional Neural Networks

Spectropolarimetric inversions are routinely used in the field of Solar Physics for the extraction of physical information from observations. The application to two-dimensional fields of view often requires the use of supercomputers with parallelized inversion codes. Even in this case, the computing time spent on the process is still very large. Our aim is to develop a new inversion code based on the application of convolutional neural networks that can quickly provide a three-dimensional cube of thermodynamical and magnetic properties from the interpretation of two-dimensional maps of Stokes profiles. We train two different architectures of fully convolutional neural networks. To this end, we use the synthetic Stokes profiles obtained from two snapshots of three-dimensional magneto-hydrodynamic numerical simulations of different structures of the solar atmosphere. We provide an extensive analysis of the new inversion technique, showing that it infers the thermodynamical and magnetic properties with a precision comparable to that of standard inversion techniques. However, it provides several key improvements: our method is around one million times faster, it returns a three-dimensional view of the physical properties of the region of interest in geometrical height, it provides quantities that cannot be obtained otherwise (pressure and Wilson depression) and the inferred properties are decontaminated from the blurring effect of instrumental point spread functions for free. The code is provided for free on a specific repository, with options for training and evaluation.Comment: 18 pages, 14 figures, accepted for publication in Astronomy & Astrophysic

Enhancing SDO/HMI images using deep learning

The Helioseismic and Magnetic Imager (HMI) provides continuum images and magnetograms with a cadence better than one per minute. It has been continuously observing the Sun 24 hours a day for the past 7 years. The obvious trade-off between full disk observations and spatial resolution makes HMI not enough to analyze the smallest-scale events in the solar atmosphere. Our aim is to develop a new method to enhance HMI data, simultaneously deconvolving and super-resolving images and magnetograms. The resulting images will mimic observations with a diffraction-limited telescope twice the diameter of HMI. Our method, which we call Enhance, is based on two deep fully convolutional neural networks that input patches of HMI observations and output deconvolved and super-resolved data. The neural networks are trained on synthetic data obtained from simulations of the emergence of solar active regions. We have obtained deconvolved and supper-resolved HMI images. To solve this ill-defined problem with infinite solutions we have used a neural network approach to add prior information from the simulations. We test Enhance against Hinode data that has been degraded to a 28 cm diameter telescope showing very good consistency. The code is open source.Comment: 13 pages, 10 figures. Accepted for publication in Astronomy & Astrophysic

Spectropolarimetric analysis of an active region filament. I. Magnetic and dynamical properties from single component inversions

The determination of the magnetic filed vector in solar filaments is possible by interpreting the Hanle and Zeeman effects in suitable chromospheric spectral lines like those of the He I multiplet at 10830 A. We study the vector magnetic field of an active region filament (NOAA 12087). Spectropolarimetric data of this active region was acquired with the GRIS instrument at the GREGOR telescope and studied simultaneously in the chromosphere with the He I 10830 A multiplet and in the photosphere with the Si I 10827 A line. As it is usual from previous studies, only a single component model is used to infer the magnetic properties of the filament. The results are put into a solar context with the help of the Solar Dynamic Observatory images. Some results clearly point out that a more complex inversion had to be done. Firstly, the Stokes $V$ map of He I does not show any clear signature of the presence of the filament. Secondly, the local azimuth map follows the same pattern than Stokes $V$ as if the polarity of Stokes $V$ were conditioning the inference to very different magnetic field even with similar linear polarization signals. This indication suggests that the Stokes $V$ could be dominated by the below magnetic field coming from the active region, and not, from the filament itself. Those and more evidences will be analyzed in depth and a more complex inversion will be attempted in the second part of this series.Comment: 18 pages, 19 figures, accepted for publication in A&

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