On Fabry P\'erot Etalon based Instruments. I. The Isotropic Case

Here we assess the spectral and imaging properties of Fabry P\'erot etalons when located in solar magnetographs. We discuss the chosen configuration (collimated or telecentric) for both ideal and real cases. For the real cases, we focus on the effects caused by the polychromatic illumination of the filter by the irregularities in the optical thickness of the etalon and by deviations from the ideal illumination in both setups. We first review the general properties of Fabry P\'erots and we then address the different sources of degradation of the spectral transmission profile. We review and extend the general treatment of defects followed by different authors. We discuss the differences between the point spread functions (PSFs) of the collimated and telecentric configurations for both monochromatic and (real) quasi-monochromatic illumination of the etalon. The PSF corresponding to collimated mounts is shown to have a better performance, although it varies from point to point due to an apodization of the image inherent to this configuration. This is in contrast to the (perfect) telecentric case, where the PSF remains constant but produces artificial velocities and magnetic field signals because of its strong spectral dependence. We find that the unavoidable presence of imperfections in the telecentrism produces a decrease of flux of photons and a shift, a broadening and a loss of symmetrization of both the spectral and PSF profiles over the field of view, thus compromising their advantages over the collimated configuration. We evaluate these effects for different apertures of the incident beam.Comment: 20 pages 22 figures 2 Appendice

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

Detection of emission in the Si i 1082.7 nm line core in sunspot umbrae

We analyze spectropolarimetric sunspot umbra observations taken in the near-infrared Si i 1082.7 nm line taking NLTE effects into account. The data were obtained with the GRIS instrument installed at the German GREGOR telescope. A point spread function (PSF) was constructed using prior Mercury observations with GRIS and the information provided by the adaptive optics system of the GREGOR telescope. The data were then deconvolved from the PSF using a principal component analysis deconvolution method and were analyzed via the NICOLE inversion code. The Si i 1082.7 nm line seems to be in emission in the umbra of the observed sunspot after the effects of scattered light are removed. We show how the spectral line shape of umbral profiles changes dramatically with the amount of scattered light. Indeed, the continuum levels range, on average, from 44% of the quiet Sun continuum intensity to about 20%. The inferred levels are in line with current model predictions and empirical umbral models. Current umbral empirical models are not able to reproduce the emission in the deconvolved umbral Stokes profiles. The results of the NLTE inversions suggests that to obtain the emission in the Si i 1082.7 nm line, the temperature stratification should first have a hump located at about log tau -2 and start rising at lower heights when moving into the transition region. This is, to our knowledge, the first time the Si i 1082.7 nm line is seen in emission in sunspot umbrae. The results show that the temperature stratification of current umbral models may be more complex than expected with the transition region located at lower heights above sunspot umbrae. Our finding might provide insights into understanding why the sunspot umbra emission in the millimeter spectral range is less than that predicted by current empirical umbral models

Milne-Eddington inversion of the Fe I line pair at 630~nm

The iron lines at 630.15 and 630.25 nm are often used to determine the physical conditions of the solar photosphere. A common approach is to invert them simultaneously under the Milne-Eddington approximation. The same thermodynamic parameters are employed for the two lines, except for their opacities, which are assumed to have a constant ratio. We aim at investigating the validity of this assumption, since the two lines are not exactly the same. We use magnetohydrodynamic simulations of the quiet Sun to examine the behavior of the ME thermodynamic parameters and their influence on the retrieval of vector magnetic fields and flow velocities. Our analysis shows that the two lines can be coupled and inverted simultaneously using the same thermodynamic parameters and a constant opacity ratio. The inversion of two lines is significantly more accurate than single-line inversions because of the larger number of observables.Comment: Accepted for publication in Astronomy and Astrophysics (Research Note

Applicability of Milne-Eddington inversions to high spatial resolution observations of the quiet Sun

The physical conditions of the solar photosphere change on very small spatial scales both horizontally and vertically. Such a complexity may pose a serious obstacle to the accurate determination of solar magnetic fields. We examine the applicability of Milne-Eddington (ME) inversions to high spatial resolution observations of the quiet Sun. Our aim is to understand the connection between the ME inferences and the actual stratifications of the atmospheric parameters. We use magnetoconvection simulations of the solar surface to synthesize asymmetric Stokes profiles such as those observed in the quiet Sun. We then invert the profiles with the ME approximation. We perform an empirical analysis of the heights of formation of ME measurements and analyze the uncertainties brought about by the ME approximation. We also investigate the quality of the fits and their relationship with the model stratifications. The atmospheric parameters derived from ME inversions of high-spatial resolution profiles are reasonably accurate and can be used for statistical analyses of solar magnetic fields, even if the fit is not always good. We also show that the ME inferences cannot be assigned to a specific atmospheric layer: different parameters sample different ranges of optical depths, and even the same parameter may trace different layers depending on the physical conditions of the atmosphere. Despite this variability, ME inversions tend to probe deeper layers in granules as compared with intergranular lanes.Comment: Accepted for publication in Astronomy and Astrophysic

Quiet Sun magnetic fields from space-borne observations: simulating Hinode's case

We examine whether or not it is possible to derive the field strength distribution of quiet Sun internetwork regions from very high spatial resolution polarimetric observations in the visible. In particular, we consider the case of the spectropolarimeter attached to the Solar Optical Telescope aboard Hinode. Radiative magneto-convection simulations are used to synthesize the four Stokes profiles of the \ion{Fe}{1} 630.2 nm lines. Once the profiles are degraded to a spatial resolution of 0\farcs32 and added noise, we infer the atmospheric parameters by means of Milne-Eddington inversions. The comparison of the derived values with the real ones indicates that the visible lines yield correct internetwork field strengths and magnetic fluxes, with uncertainties smaller than $\sim$150 G, when a stray light contamination factor is included in the inversion. Contrary to the results of ground-based observations at 1\arcsec, weak fields are retrieved wherever the field is weak in the simulation.Comment: Accepted for publication in ApJ Letter

Solar polarimetry through the K I lines at 770 nm

We characterize the K I D1 & D2 lines in order to determine whether they could complement the 850 nm window, containing the Ca II infrared triplet lines and several Zeeman sensitive photospheric lines, that was studied previously. We investigate the effect of partial redistribution on the intensity profiles, their sensitivity to changes in different atmospheric parameters, and the spatial distribution of Zeeman polarization signals employing a realistic magnetohydrodynamic simulation. The results show that these lines form in the upper photosphere at around 500 km and that they are sensitive to the line of sight velocity and magnetic field strength at heights where neither the photospheric lines nor the Ca II infrared lines are. However, at the same time, we found that their sensitivity to the temperature essentially comes from the photosphere. Then, we conclude that the K I lines provide a complement to the lines in the 850 nm window for the determination of atmospheric parameters in the upper photosphere, especially for the line of sight velocity and the magnetic field.Comment: 10 pages, 9 figures, main journal publicatio

Granular Scale Magnetic Flux Cancellations in the Photosphere

We investigate the evolution of 5 granular-scale magnetic flux cancellations just outside the moat region of a sunspot by using accurate spectropolarimetric measurements and G-band images with the Solar Optical Telescope aboard Hinode. The opposite polarity magnetic elements approach a junction of the intergranular lanes and then they collide with each other there. The intergranular junction has strong red shifts, darker intensities than the regular intergranular lanes, and surface converging flows. This clearly confirms that the converging and downward convective motions are essential for the approaching process of the opposite-polarity magnetic elements. However, motion of the approaching magnetic elements does not always match with their surrounding surface flow patterns in our observations. This suggests that, in addition to the surface flows, subsurface downward convective motions and subsurface magnetic connectivities are important for understanding the approach and collision of the opposite polarity elements observed in the photosphere. We find that the horizontal magnetic field appears between the canceling opposite polarity elements in only one event. The horizontal fields are observed along the intergranular lanes with Doppler red shifts. This cancellation is most probably a result of the submergence (retraction) of low-lying photospheric magnetic flux. In the other 4 events, the horizontal field is not observed between the opposite polarity elements at any time when they approach and cancel each other. These approaching magnetic elements are more concentrated rather than gradually diffused, and they have nearly vertical fields even while they are in contact each other. We thus infer that the actual flux cancellation is highly time dependent events at scales less than a pixel of Hinode SOT (about 200 km) near the solar surface.Comment: Accepted for publication in the Astrophysical Journa