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Register a new userIncorporating Uncertainties in Atomic Data Into the Analysis of Solar and Stellar Observations: A Case Study in Fe XIII
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Information about the physical properties of astrophysical objects cannot be measured directly but is inferred by interpreting spectroscopic observations in the context of atomic physics calculations. Ratios of emission lines, for example, can be used to infer the electron density of the emitting plasma. Similarly, the relative intensities of emission lines formed over a wide range of temperatures yield information on the temperature structure. A critical component of this analysis is understanding how uncertainties in the underlying atomic physics propagates to the uncertainties in the inferred plasma parameters. At present, however, atomic physics databases do not include uncertainties on the atomic parameters and there is no established methodology for using them even if they did. In this paper we develop simple models for the uncertainties in the collision strengths and decay rates for Fe XIII and apply them to the interpretation of density sensitive lines observed with the EUV Imagining spectrometer (EIS) on Hinode. We incorporate these uncertainties in a Bayesian framework. We consider both a pragmatic Bayesian method where the atomic physics information is unaffected by the observed data, and a fully Bayesian method where the data can be used to probe the physics. The former generally increases the uncertainty in the inferred density by about a factor of 5 compared with models that incorporate only statistical uncertainties. The latter reduces the uncertainties on the inferred densities, but identifies areas of possible systematic problems with either the atomic physics or the observed intensities.
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We consider three recent large-scale calculations for the radiative and electron-impact excitation data of N IV, carried out with different methods and codes. The scattering calculations employed the relativistic Dirac $R$-matrix (DARC) method, the intermediate coupling frame transformation (ICFT) $R$-matrix method, and the B-spline $R$-matrix (BSR) method. These are all large-scale scattering calculations with well-tested and sophisticated codes, which use the same set of target states. One concern raised in previous literature is related to the increasingly large discrepancies in the effective collision strengths between the three sets of calculations for increasingly weak and/or high-lying transitions. We have built three model ions and calculated the intensities of all the main spectral lines in this ion. We have found that, despite such large differences, excellent agreement (to within $pm$~20%) exists between all the spectroscopically-relevant line intensities. This provides confidence in the reliability of the calculations for plasma diagnostics. We have used the differences in the radiative and excitation rates amongst the three sets of calculations to obtain a measure of the uncertainty in each rate. Using a Monte Carlo approach, we have shown how these uncertainties affect the main theoretical ratios which are used to measure electron densities and temperatures.
In this paper, we discuss the temperature distribution and evolution of a microflare, simultaneously observed by Hinode XRT, EIS, and SDO AIA. We find using EIS lines that during peak emission the distribution is nearly isothermal and peaked around 4.5 MK. This temperature is in good agreement with that obtained from the XRT filter ratio, validating the use of XRT to study these small events, invisible by full-Sun X-ray monitors such as GOES. The increase in the estimated Fe XVIII emission in the AIA 94 {AA} band can mostly be explained with the small temperature increase from the background temperatures. The presence of Fe XVIII emission does not guarantee that temperatures of 7 MK are reached, as is often assumed. We also revisit with new atomic data the temperatures measured by a SoHO SUMER observation of an active region which produced microflares, also finding low temperatures (3 - 4 MK) from an Fe XVIII / Ca XIV ratio.
The nonthermal broadening of spectral lines formed in the solar corona is often used to seek the evidence of Alfven waves propagating in the corona. To have a better understanding of the variation of line widths at different altitudes, we measured the line widths of the strong Fe textsc{xii} 192.4, 193.5, and 195.1 mbox{AA} and Fe textsc{xiii} 202.0 mbox{AA} in an off-limb southern coronal hole up to 1.5 $R_odot$ observed by the Extreme Ultraviolet Spectrometer (EIS) on board the textit{Hinode} satellite. We compared our measurements to the predictions from the Alfven Wave Solar Model (AWSoM) and the SPECTRUM module. We found that the Fe textsc{xii} and Fe textsc{xiii} line widths first increase monotonically below 1.1 $R_odot$, and then keep fluctuating between 1.1 and 1.5 $R_odot$. The synthetic line widths of Fe textsc{xii} and Fe textsc{xiii} below 1.3 $R_odot$ are notably lower than the observed ones. We found that the emission from a streamer in the line of sight significantly contaminates the coronal hole line profiles even up to 1.5 $R_odot$ both in observations and simulations. We suggest that either the discrepancy between the observations and simulations is caused by insufficient nonthermal broadening at the streamer in the AWSoM simulation or the observations are less affected by the streamer. Our results emphasize the importance of identifying the origin of the coronal EUV emission in off-limb observations.
The purpose of this paper is to analyze the variation in the line width with height in the inner corona (region above 1.1 Rsun), by using the spectral data from LASCO-C1 aboard SOHO. We used data acquired at activity minimum (August - October 1996) and during the ascending phase of the solar cycle (March 1998). Series of images acquired at different wavelengths across the Fe X 637.6 nm (red) and Fe XIV 530.3 nm (green) coronal lines by LASCO-C1 allowed us to build radiance and width maps of the off-limb solar corona. In 1996, the line width of Fe XIV was roughly constant or increased with height up to around 1.3 Rsun and then it decreased. The Fe X line width increased with height up to the point where the spectra were too noisy to allow line width measurements (around 1.3 Rsun). Fe X showed higher effective temperatures as compared with Fe XIV. In 1998 the line width of Fe XIV was roughly constant with height above the limb (no Fe X data available).
The Extreme Ultraviolet Variability Experiment (EVE) on the Solar Dynamics Observatory obtains extreme-ultraviolet (EUV) spectra of the full-disk Sun at a spectral resolution of ~1 A and cadence of 10 s. Such a spectral resolution would normally be considered to be too low for the reliable determination of electron density (N_e) sensitive emission line intensity ratios, due to blending. However, previous work has shown that a limited number of Fe XXI features in the 90-60 A wavelength region of EVE do provide useful N_e-diagnostics at relatively low flare densities (N_e ~ 10^11-10^12 cm^-3). Here we investigate if additional highly ionised Fe line ratios in the EVE 90-160 A range may be reliably employed as N_e-diagnostics. In particular, the potential for such diagnostics to provide density estimates for high N_e (~10^13 cm^-3) flare plasmas is assessed. Our study employs EVE spectra for X-class flares, combined with observations of highly active late-type stars from the Extreme Ultraviolet Explorer (EUVE) satellite plus experimental data for well-diagnosed tokamak plasmas, both of which are similar in wavelength coverage and spectral resolution to those from EVE. Several ratios are identified in EVE data which yield consistent values of electron density, including Fe XX 113.35/121.85 and Fe XXII 114.41/135.79, with confidence in their reliability as N_e-diagnostics provided by the EUVE and tokamak results. These ratios also allow the determination of density in solar flare plasmas up to values of ~10^13 cm^-3.
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