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 Physics , 2010, Abstract: Full Stokes spectropolarimetric data (in the 10830 A region) of an active region filament were obtained in July 2005 using the Tenerife Infrared Polarimeter instrument. The polarization profiles in the filament show Zeeman-like signatures. Milne-Eddington inversions were performed to infer the chromospheric magnetic field, inclination, azimuth, velocity and Doppler width from the He I 10830 A multiplet. Field strengths of the order of 600-800 G were found in the filament. Strong transverse fields at chromospheric levels were detected near the polarity inversion line. To our knowledge, these are the highest field strengths reliably measured in these structures. Our findings suggest the possible presence of a flux rope.
 Physics , 2010, DOI: 10.1051/0004-6361/200913421 Abstract: 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.
 Physics , 2015, DOI: 10.1051/0004-6361/201425508 Abstract: Inversion codes are numerical tools used for the inference of physical properties from the observations. Despite their success, the quality of current spectropolarimetric observations and those expected in the near future presents a challenge to current inversion codes. The pixel-by-pixel strategy of inverting spectropolarimetric data that we currently utilize needs to be surpassed and improved. The inverted physical parameters have to take into account the spatial correlation that is present in the data and that contains valuable physical information. We utilize the concept of sparsity or compressibility to develop an new generation of inversion codes for the Stokes parameters. The inversion code uses numerical optimization techniques based on the idea of proximal algorithms to impose sparsity. In so doing, we allow for the first time to exploit the presence of spatial correlation on the maps of physical parameters. Sparsity also regularizes the solution by reducing the number of unknowns. We compare the results of the new inversion code with pixel-by-pixel inversions, demonstrating the increase in robustness of the solution. We also show how the method can easily compensate for the effect of the telescope point spread function, producing solutions with an enhanced contrast.
 Physics , 2010, DOI: 10.1051/0004-6361/201014374 Abstract: 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.
 J. Fukue Physics , 2009, DOI: 10.1093/pasj/60.3.627 Abstract: Radiative transfer in a relativistic plane-parallel flow, e.g., an accretion disk wind, is examined in the fully special relativistic treatment. Under the assumption of a constant flow speed, for the relativistically moving atmosphere we analytically obtain generalized Milne-Eddington solutions of radiative moment equations; the radiation energy density, the radiative flux, and the radiation pressure. In the static limit these solutions reduce to the traditional Milne-Eddington ones for the plane-parallel static atmosphere, whereas the source function nearly becomes constant as the flow speed increases. Using the analytical solutions, we analytically integrate the relativistic transfer equation to obtain the specific intensity. This specific intensity also reduces to the Milne-Eddinton case in the static limit, while the emergent intensity is strongly enhanced toward the flow direction due to the Doppler and aberration effects as the flow speed increases (relativistic peaking).
 Jun Fukue Advances in Astronomy , 2011, DOI: 10.1155/2011/412620 Abstract: Relativistic radiative transfer in a relativistic spherical flow is examined in the fully special relativistic treatment. Under the assumption of a constant flow speed and using a variable (prescribed) Eddington factor, we analytically solve the relativistic moment equations in the comoving frame for several restricted cases, and obtain relativistic Milne-Eddington type solutions. In contrast to the plane-parallel case where the solutions exhibit the exponential behavior on the optical depth, the solutions have power-law forms. In the case of the radiative equilibrium, for example, the radiative flux has a power-law term multiplied by the exponential term. In the case of the local thermodynamic equilibrium with a uniform source function in the comoving frame, the radiative flux has a power-law form on the optical depth. This is because there is an expansion effect (curvature effect) in the spherical wind and the background density decreases as the radius increases. 1. Introduction The research field of radiative transfer has been developed in astrophysics and atmospheric science [1–13]. Relativistic radiative transfer and relativistic radiation hydrodynamics have been also developed in astrophysics and applied to various energetic phenomena in the universe: nova outbursts, gamma-ray bursts, astrophysical jets, black-hole accretion disks, and black-hole winds. In the subrelativistic regime, some researchers adopted the diffusion approximation in the comoving frame (e.g., [14–17]), or proposed the variable Eddington factor (e.g., [18–24]), or performed the numerical simulations using, for example, the flux-limited diffusion (FLD) approximation (e.g., [25–35]). In the highly relativistic regime, however, we cannot treat the relativistic radiative transfer properly. Hence, the research and development of the radiative transfer problem in relativistically moving media is now of great importance in this field. At the present stage, the numerical approach using the FLD approximation is limited within the subrelativistic regime. In addition, even in the subrelativistic regime, the FLD method cannot reproduce the radiative force precisely in the optically thin region [36]. This is because in the optically thin region the radiative flux vector is not generally parallel to the gradient of the radiation energy density due to the effect of the distant radiation source. On the other hand, the analytical approach is very restricted in the special cases. Indeed, even for the nonrelativistic case only a few analytical solutions have been found, but for the relativistic
 Physics , 2009, DOI: 10.1051/0004-6361/200911800 Abstract: We study the vector magnetic field of a filament observed over a compact Active Region Neutral Line. Spectropolarimetric data acquired with TIP-II (VTT, Tenerife, Spain) of the 10830 \AA spectral region provide full Stokes vectors which were analyzed using three different methods: magnetograph analysis, Milne-Eddington inversions and PCA-based atomic polarization inversions. The inferred magnetic field strengths in the filament are of the order of 600 - 700 G by all these three methods. Longitudinal fields are found in the range of 100 - 200 G whereas the transverse components become dominant, with fields as large as 500 - 600 G. We find strong transverse fields near the Neutral Line also at photospheric levels. Our analysis indicates that strong (higher than 500 G, but below kG) transverse magnetic fields are present in Active Region filaments. This corresponds to the highest field strengths reliably measured in these structures. The profiles of the Helium 10830 \AA lines observed in this Active Region filament are dominated by the Zeeman effect.
 Physics , 2014, DOI: 10.1051/0004-6361/201424584 Abstract: Milne-Eddington (M-E) inversion codes for the radiative transfer equation are the most widely used tools to infer the magnetic field from observations of the polarization signals in photospheric and chromospheric spectral lines. Unfortunately, a comprehensive comparison between the different M-E codes available to the solar physics community is still missing, and so is a physical interpretation of their inferences. In this contribution we offer a comparison between three of those codes (VFISV, ASP/HAO, and HeLIx$^+$). These codes are used to invert synthetic Stokes profiles that were previously obtained from realistic non-grey three-dimensional magnetohydrodynamical (3D MHD) simulations. The results of the inversion are compared with each other and with those from the MHD simulations. In the first case, the M-E codes retrieve values for the magnetic field strength, inclination and line-of-sight velocity that agree with each other within $\sigma_B \leq 35$ (Gauss), $\sigma_\gamma \leq 1.2\deg$, and $\sigma_{\rm v} \leq 10$ ms$^{-1}$, respectively. Additionally, M-E inversion codes agree with the numerical simulations, when compared at a fixed optical depth, within $\sigma_B \leq 130$ (Gauss), $\sigma_\gamma \leq 5\deg$, and $\sigma_{\rm v} \leq 320$ ms$^{-1}$. Finally, we show that employing generalized response functions to determine the height at which M-E codes measure physical parameters is more meaningful than comparing at a fixed geometrical height or optical depth. In this case the differences between M-E inferences and the 3D MHD simulations decrease to $\sigma_B \leq 90$ (Gauss), $\sigma_\gamma \leq 3\deg$, and $\sigma_{\rm v} \leq 90$ ms$^{-1}$.
 Physics , 2015, Abstract: NASA's Solar Dynamics Observatory is delivering vector field observations of the full solar disk with unprecedented temporal and spatial resolution; however, the satellite is in a highly inclined geostationary orbit. The relative spacecraft-Sun velocity varies by $\pm3$~km/s over a day which introduces major orbital artifacts in the Helioseismic Magnetic Imager data. We demonstrate that the orbital artifacts contaminate all spatial and temporal scales in the data. We describe a newly-developed three stage procedure for mitigating these artifacts in the Doppler data derived from the Milne-Eddington inversions in the HMI Pipeline. This procedure was applied to full disk images of AR11084 to produce consistent Dopplergrams. The data adjustments reduce the power in the orbital artifacts by 31dB. Furthermore, we analyze in detail the corrected images and show that our procedure greatly improve the temporal and spectral properties of the data without adding any new artifacts. We conclude that this new and easily implemented procedure makes a dramatic improvement in the consistency of the HMI data and in its usefulness for precision scientific studies.
 Physics , 2010, Abstract: We report the discovery of the first HeI*\lambda 10830 broad absorption line quasar FBQS J1151+3822. Using new infrared and optical spectra, as well as the SDSS spectrum, we extracted the apparent optical depth profiles as a function of velocity of the 3889A and 10830A HeI* absorption lines. Since these lines have the same lower levels, inhomogeneous absorption models could be used to extract the average true HeI* column density; the log of that number was 14.9. The total hydrogen column density was obtained using Cloudy models. A range of ionization parameters and densities were allowed, with the lower limit on the ionization parameter of log U=-1.4 determined by the requirement that there be sufficient HeI*, and the upper limit on the density of log n=8 determined by the lack of Balmer absorption. Simulated UV spectra showed that the ionization parameter could be further constrained in principle using a combination of low and high ionization lines (such as MgII and PV), but the only density-sensitive line predicted to be observable and not significantly blended was CIII\lambda 1176. We estimated the outflow rate and kinetic energy, finding them to be consistent but on the high side compared with analysis of other objects. Assuming that radiative line driving is the responsible acceleration mechanism, a force multipler model was constructed. A dynamical argument using the model results strongly constrained the density to be log n >= ~7. Consequently, the log hydrogen column density is constrained to be between 21.7 and 22.9, the mass outflow rate to be between 11 and 56 solar masses per year, the ratio of the mass outflow rate to the accretion rate to be between 1.2 and 5.8, and the kinetic energy to be between 1 and 5 x 10^44 erg/s. We discuss the advantages of using HeI* to detect high-column-density BALQSOs and and measure their properties. (Abridged)
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