\documentclass[11pt]{article} \usepackage[dvips]{graphicx} %% FOR INCLUDING GRAPHICS \usepackage{natbib} \usepackage{epsf} %% ---------------------------------------------------------------------- %% Add specials here %% ---------------------------------------------------------------------- \def\ion#1#2{#1\,{\sc #2}\relax} %% \newcommand{\calss}{CALIB\_SLIT\_SLOT} \newcommand{\as}{$^{\prime\prime}$} %% ---------------------------------------------------------------------- %% Modify: %% Note number, version number and date %% Title %% Author and affiliation %% ---------------------------------------------------------------------- \setlength{\oddsidemargin}{0in} % 1 inch (0 + 1) from left. \setlength{\topmargin}{-0.5in} % 1 inch (1.5 - 0.5) from top. \setlength{\textwidth}{6.5in} % 1 inch (8.5 - 1 - 6.5) from right. \setlength{\textheight}{9in} % 1 inch (11 - 1 - 9) from bottom. \addtolength{\parskip}{0.5\baselineskip} % The environment centerpage centers text vertically on the page. This is % useful within a titlepage environment. \newenvironment{centerpage}{\mbox{} \protect\vspace*{\fill}}{ \protect\vspace*{\fill} \mbox{} \protect\\ \mbox{}} \newcommand{\lam}{$\lambda$} \newcommand{\arcsec}{$^{\prime\prime}$} \begin{document} %\bibliographystyle{plain} % Define bibliography style. \begin{titlepage} \hrule \noindent\textbf{EUV IMAGING SPECTROMETER}\\ \vspace{-0.7\baselineskip}\\ {\noindent\Huge\bf Hinode} \vspace{2mm} \hrule \vspace{3mm} \centerline{\bf EIS SOFTWARE NOTE No. 7} \vspace{3mm} \hrule \noindent Version 1.0 \hfill 24 October 2011 \vspace{2mm} \hrule \begin{centerpage} \begin{center} {\Large\bf Instrumental line widths for the narrow slits of EIS}\\ \mbox{}\\ \mbox{}\\ Peter Young\\ George Mason University\\ 4400 University Drive\\ Fairfax, VA 22030 U.S.A.\\ \mbox{}\\ pyoung@ssd5.nrl.navy.mil\\ \end{center} \end{centerpage} \end{titlepage} %% ---------------------------------------------------------------------- %% The document! %% ---------------------------------------------------------------------- \section{Overview} The EIS emission lines have widths that are dominated by an instrumental component, and this instrumental width is found to vary with CCD Y-pixel position. An IDL routine called \verb|eis_slit_width.pro| is provided to EIS users that yields the instrumental width for the 1\arcsec\ and 2\arcsec\ slits as a function of CCD Y-pixel number. The present EIS software note describes how the instrumental width was obtained and gives background information related to the instrumental width. \section{Previous work} \citet{korendyke06} and \citet{lang06} report a pre-launch line width of 0.056~\AA\ for the \ion{He}{ii} \lam256.32 line which we take to be a measure of the instrumental broadening only. \citet{doschek07} compared the width of the \ion{Fe}{xii} \lam193.51 line above the limb in quiet Sun with the width of the \ion{Fe}{xii} \lam1242 forbidden line observed with \emph{Skylab} and SUMER and came up with the same value for the instrumental width (56~m\AA). Note that this implies the instrumental width is independent of wavelength. \citet{brown08} gave more details on the pre-launch laboratory measurements and cited widths of 47~m\AA\ for \ion{Mg}{iii} \lam187 in the SW band, and widths of 56 and 58~m\AA\ for \ion{He}{ii} \lam256 and \ion{Ne}{iii} \lam267, respectively. Correcting for the thermal broadening from the $10^4$~K plasma within the calibration lamp yields instrumental widths of 47, 55 and 57~m\AA\ for the three lines. Based on the solar spectra obtained with EIS, \citet{brown08} estimate an instrumental width of 54~m\AA\ for the SW band based on the \ion{Fe}{x} \lam190.04 width, and widths of around 55~m\AA\ for the LW band based on several lines. The conclusion is that the instrumental width for the SW band has become a little worse since launch, and the instrumental widths should be taken as 54~m\AA\ and 55~m\AA\ for the SW and LW bands, respectively. None of these works considered the variation of the line width with Y-position on the EIS CCD. \section{EIS field of view} The EIS CCDs are 1024 pixels high (solar-Y direction) and the EIS slit, projected onto the CCD, extends for almost the complete height of the CCD. On board software restrictions prevent the entire CCD height from being obtained in a single exposure -- the maximum size is 512 pixels. In addition, up to April 2008 software restrictions allowed only the central 512 pixels to be downloaded, i.e., pixels from 256 to 767. When this restriction was relaxed, the full CCD height could be observed by using two exposures, one covering the bottom of the CCD, the other covering the top of the CCD. The position of an EIS exposure on the CCD is usually determined by the pointing selected by the EIS Chief Observer (CO). That is, the EIS planning software takes a requested solar-Y pointing and converts it to a pixel position on the CCD. The CO can manually choose where the exposure appears on the CCD by specifying a YIP (Y Initial Position) value, which is the pixel corresponding to the bottom of the EIS raster. YIP takes a value between 1 and 1023. The very bottom pixel, YIP=0, can not be selected. Normally EIS observes the same region observed by SOT. The center of the SOT field of view is approximately YIP=560. Therefore an EIS raster 200 pixels high centered on the SOT field of view will extend from YIP=460 to YIP=659 (approximately). As shown in the following sections, the EIS instrumental line width has its minimum around YIP=200--300, and so this is where the instrumental width is smallest. \section{The routine EIS\_SLIT\_WIDTH} The routine \verb|eis_slit_width.pro| is available within the EIS branch of \emph{Solarsoft} and yields the instrumental width, in \AA, as follows: % \begin{verbatim} IDL> wid=eis_slit_width(ypix,slit_ind=slit_ind) \end{verbatim} % The input YPIX is the CCD Y-pixel number, which varies from 0 to 1023 (bottom to top of the CCD). The optional input SLIT\_IND allows the EIS slit to be specified: 0 for the 1\arcsec\ slit (the default), and 2 for the 2\arcsec\ slit. \begin{figure} \centerline{\epsfxsize=12cm\epsfbox{plot_eis_slit_width.eps}} \caption{Output from the routine eis\_slit\_width showing the variation of the instrumental widths with CCD Y-pixel position for the 1\arcsec\ (solid line) and 2\arcsec\ (dashed line) slits.} \label{fig.slit-width} \end{figure} The widths returned by \verb|eis_slit_width.pro| (as of 2011 October) are shown in Fig.~\ref{fig.slit-width}. For a particular data-set, the CCD Y-pixel values can be obtained from an EIS data object as follows: % \begin{verbatim} IDL> yws=obj->getinfo('YWS') IDL> ny=obj->getinfo('YW') IDL> ypix=indgen(ny)+yws \end{verbatim} % From an EIS windata structure they are obtained with % \begin{verbatim} IDL> yws=windata.hdr.yws IDL> ny=windata.hdr.yw IDL> ypix=indgen(ny)+yws \end{verbatim} If the \verb|eis_auto_fit| suite of routines is used, then the Gaussian fits to the data are automatically corrected for the instrumental widths with the command: % \begin{verbatim} IDL> wid=eis_get_fitdata(fit,/wid) \end{verbatim} % see EIS Software Note No.~16 for more details. The method for deriving the instrumental widths is described below. \section{Deriving the instrumental widths} The method described here requires measurements of the \ion{Fe}{xii} \lam193.51 line above the quiet Sun limb at the equator. The observations were obtained with the study CALIB\_SLIT\_SLOT. \subsection{The CALIB\_SLIT\_SLOT study} A study, \calss\ (ID 352), was designed to obtain narrow rasters using the 40\arcsec, 1\arcsec\ and 2\arcsec\ slits and taking the full 512 pixel height in Y. It was intended to be run twice, the first covering the top half of the CCD (Y-pixels 512 to 1023) and the second covering the bottom half (Y-pixels 1 to 512). Each run of \calss\ yields three different rasters. The first is a raster with the 40\arcsec\ slit which has three scan positions separated by 32\arcsec\, and an exposure time of 20~s. The second raster is obtained with the 1\arcsec\ slit, has 15 scan positions and a 40~s exposure time. The third raster uses the 2\arcsec\ slit, has 15 scan positions and a 20~s exposure time. The two narrow slit rasters use the same line list, consisting of the three core lines, \ion{Fe}{viii} \lam185.21, \ion{Fe}{xii} \lam193.51, \ion{Fe}{xiii} \lam\lam202.04, 203.82, \ion{Si}{vii} \lam275.35 and \ion{Fe}{xv} \lam284.16. The dates on which \calss\ observed both the top and bottom of the CCD are given in Table~\ref{tbl.runs}. For the period Nov.--Dec.\ 2009 the study was run in quiet off-limb regions above the equator. \begin{table}[h] \caption{\calss\ runs.} \begin{center} \begin{tabular}{llp{5cm}} \noalign{\hrule} \noalign{\smallskip} \noalign{\hrule} Date & Location & Comment \\ \noalign{\hrule} \noalign{\smallskip} 5-Nov-2009 & East limb & \\ 13-Nov-2009 & East limb & AR loops in north of raster?\\ 19-Nov-2009 & West limb & \\ 26-Nov-2009 & East limb & \\ 11-Dec-2009 & West limb & \\ \noalign{\hrule} \end{tabular} \end{center} \label{tbl.runs} \end{table} An example of the quality of data from \calss\ is shown in Fig.~\ref{fig.nov19}, obtained from the 2009 November 19 data-set. \begin{figure}[t] \centerline{\epsfxsize=12cm\epsfbox{plot_av_width.eps}} \caption{Variation of intensity (upper panel) and full width at half maximum (FWHM; lower panel) over the CCD height for \ion{Fe}{xii} \lam193.51, as obtained from the 2009 November 19 \calss\ data-set. Both the intensity and FWHM have been averaged over 15 pixels in the X-direction. The \lam193.51 line is affected by a dust particle on the CCD at Y-pixels 560--580.} \label{fig.nov19} \end{figure} \subsection{Method} A single \calss\ data-set is processed with the following steps: \begin{itemize} \item The \lam193.51 line is fit with a Gaussian at every spatial pixel in both the top and bottom rasters using the routine EIS\_AUTO\_FIT. \item The line widths are extracted from the fits, and averaged over blocks of 15 $\times$ 16 pixels, leaving a 1D array with 32 elements of line widths as a function of Y-position. \item The top and bottom data-sets are combined to yield a 64 element array of average widths covering the complete CCD height. \end{itemize} The results from multiple data-sets are then combined by constructing a single 64 element array of widths that contains the minimum width from the data-sets. For example, if the widths at Y-position 10 from three data-sets are 63, 60 and 65~m\AA, then the final array will contain the value 60~m\AA. The idea being that the minimum width will always be closest to the true instrumental width. The final step is to subtract a thermal width from the widths, and a value of 0.0232~\AA\ is used. This was computed for the \ion{Fe}{xii} \lam193.51 line by assuming a temperature of $\log\,T=6.2$. With the final 64 element array constructed, a fourth order polynomial is fit to the data-points. The coefficients of this polynomial are then coded into the routine EIS\_SLIT\_WIDTH. \subsection{Results} The runs of \calss\ from 2009 November 19 and 16, and December 11 were considered the best. The method described above yields the results shown in Fig.~\ref{fig.results}. The crosses represent the final 64 element arrays obtained from finding the minimum widths across the three data-sets. The solid lines are the polynomial fits to these arrays. \begin{figure} \centerline{\epsfxsize=12cm\epsfbox{plot_results.eps}} \caption{Instrumental widths (crosses) derived from the \calss\ data-sets for the 1\arcsec\ (top) and 2\arcsec\ (bottom) slits. The solid curves represent fourth order polynomial fits to the data.} \label{fig.results} \end{figure} The instrumental widths are estimated to be accurate to about 3~m\AA. Further measurements are required to give improved statistics for determining the widths. % \section{2009 November 19 data-set} % This data-set is used to illustrate the variation of line width with Y % pixel position. Although \ion{Fe}{xii} \lam195.12 is the strongest EIS % line above the limb, it has a weak blend in the red wing which affects % width measurements. The next strongest line is \ion{Fe}{xii} % \lam193.51 which is believed to be unblended and so is used for the % analysis. Fig.~\ref{fig.nov19} shows how the intensity and full width at half % maximum (FWHM) varies % with CCD height. Both quantities have been averaged over 15 pixels in % the X-direction. The heights around Y-pixel 500 are closest to the % limb and so the brightest, although significant structure is seen in % the Y direction. The FWHM plot demonstrates that the width is smallest % around Y-pixels 150 to 300 and increases to smaller and larger % Y-pixels. At the largest heights on the CCD the FWHM is around 30\%\ % larger than the smallest FWHM values. Note the FWHM plotted here % includes the thermal component of the line width. % For Y-pixels 1--10, the intensity is seen to fall sharply. This marks % the end of the slit (as projected onto the CCD). % A complication in deriving the instrumental width from a plot such as % Fig.~\ref{fig.nov19} comes from real structure in the line width % variation. For example, there is a bump around 230 that is likely due % to a real enhancement in the non-thermal broadening. % \begin{figure}[t] % \centerline{\epsfxsize=12cm\epsfbox{plot_av_width.eps}} % \caption{Variation of intensity (upper panel) and full width at half % maximum (FWHM; lower panel) over the CCD height for \ion{Fe}{xii} \lam193.51, as obtained from % the 2009 November 19 \calss\ data-set. Both the intensity and FWHM % have been averaged over 15 pixels in the X-direction. The % \lam193.51 line is affected by a dust particle on the CCD at % Y-pixels 560--580.} % \label{fig.nov19} % \end{figure} % \section{The 2\as\ slit} % The instrumental width for the 2\as\ slit is larger than that for the % 1\as\ slit, but not by a factor two. The following analysis was % performed to investigate the difference. % To compare line widths from the 1\as\ and 2\as\ slits, two quiet Sun rasters % taken at disk center 1 day apart were studied. The \ion{Fe}{xii} \lam195.12 line % was fit with a Gaussian in both data-sets, and histograms of the line % width created. These are shown in Fig.~\ref{fig.hist}. In each case a thermal width % of 21~m\AA\ was subtracted out from the measured % width. Taking the weighted average of the histogram distributions % gives 65.0~m\AA\ for the 1\as\ slit and 72.0~m\AA\ for the 2\as\ slit. The % instrumental width for the 2\as\ slit is thus 7~m\AA\ larger than that for % the 1\as\ slit. Taking the 1\as\ instrumental width of 54~m\AA\ from % \citet{brown08} thus implies a 2\as\ instrumental width of % 61~m\AA\ for the SW wavelength band. % \begin{figure}[h] % \centerline{\epsfxsize=10cm\epsfbox{plot_hist.eps}} % \caption{The solid line shows the histogram of FWHM values for % \ion{Fe}{xii} \lam195.12 from a quiet Sun raster obtained with the % 1\as\ slit. The dashed lines shows the histogram obtained with the % 2\as\ slit.} % \label{fig.hist} % \end{figure} % The data-sets used were 2008 January 21 16:02 (SYNOP002, 1\as) and 2008 % January 22 16:00 (cam\_qs\_2as\_context, 2\as). Both were obtained close to % Sun centre. The two rasters have different sizes in the Y-direction % (184\as\ and 360\as, respectively) which may account for the different % shapes of the width distributions, since the instrumental widths are % known to vary with Y position. % Note that the 2\as\ instrumental width varies with CCD Y-position in a similar manner to % the 1\as, but the variation may be different. The difference in % instrumental widths could thus be a function of Y-position. \begin{thebibliography}{} \bibitem[Brown et al.(2008)]{brown08} Brown, C. M., Feldman, U., \& Seely, J. F. 2008, ApJS, 176, 511 \bibitem[Doschek et al.(2007)]{doschek07} Doschek, G. A., Mariska, J. T., Warren, H. P., et al. 2007, ApJ, 667, L109 \bibitem[Korendyke et al.(2006)]{korendyke06} Korendyke, C. M., Brown, C. M., Thomas, R. J., et al. 2006, Appl. Optics, 45, 8674 \bibitem[Lang et al.(2006)]{lang06} Lang, J., Kent, B. J., Paustian, W., et al., 2006, Appl. Optics, 45, 8689 \end{thebibliography} \end{document}