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\usepackage{longtable}
\usepackage{rotating}
\usepackage{epsfig}
\usepackage{psfig}

\begin{document}

\title{Estimating AR electron densities at coronal 
temperatures with CDS and CHIANTI}

\centerline{  G. Del Zanna  }
\centerline{DAMTP, University of Cambridge, Cambridge  UK}
\centerline{April 2003}

\tableofcontents

\section{Introduction}

The material presented here is still largely 
{\bf unpublished}, and was collected for a presentation
given at NAM 2003 in Dublin at the CDS user meeting.

Part of the material presented here is contained in 
Del Zanna, PhD Thesis (1999).
Readers are {\bf strongly recommended} to read the various 
words of caution described in Del Zanna, PhD Thesis (1999).


A lot of issues make density estimates complex.
For example: 

\begin{itemize}
\item In some cases, temperature effects should be taken 
 into account.

\item In some cases (e.g. at low densities), 
photoexcitation needs to be taken into account.

\item In most (if not all!) cases, the lines 
 {\bf can be blended}, depending on the thermal 
 structure of the source. 
In the CDS post-recovery case, proper line fitting 
becomes crucial.

\item For some ions, the atomic data are yet 
{\bf not reliable}. 
For example, {\bf do not use Fe~XII !!}.


\item Only ions that have peak emissivity at the 
 temperatures where the source emits can be 
expected to give meaningful results. 

\item The densites that are obtained do depend on the 
 chosen instrument calibration. The various calibrations 
do agree within 30\% on average, but larger departures
are present in some cases (see Del Zanna et al. 2001).


\end{itemize}


Here, all the atomic data and programs used are from 
the CHIANTI package. 
Readers interested in using CHIANTI for density diagnostics
can find relevant information 
in the CHIANTI user guide, that can be found in the 
WWW pages, e.g.:

\begin{itemize}
\item
 DAMTP, UK: \url{http://www.damtp.cam.ac.uk/user/astro/chianti/}
\end{itemize}


Here, only  density diagnostics that can be applied 
to study  active regions at coronal temperatures are
discussed.

 \begin{figure}[!htbp]
\centerline{\epsfig{file=a2_AR_25_sep_97_NIS1_res.ps, width=9.0cm , angle=0 }}
  \caption{A NIS pre-recovery spectrum of an active region, showing 
 strong Si~IX, Si~X, Fe~XIII, Fe~XIV useful for density diagnostics.}
  \label{fig:}
\end{figure}
% Figure~\ref{fig:}


\begin{table}[htbp]
\caption{Density sensitive line ratios observed  by CDS, 
ordered by the temperature 
 of maximum of the contribution functions shown in column 4,
 calculated with the 
ionization equilibrium calculations of Arnaud and Rothenflug (1985).
 The ranges for which the ratios can be used are shown in column 5.
The numbers in parentheses indicate the number of transitions that 
compose the self-blends.
The lines indicated with a (!)  have problems in either their  observation 
or in the atomic physics. 
The lines indicated with a (*) are the best selection within 
a wider choice. 
The detectors in parentheses indicate that the lines are also visible
 in second order. 
N means NIS, and G means GIS; 
}


\begin{center}
%

\begin{tabular}{|llllcl|}
\hline
Ion       &Ratio (\AA) &Detector& log T$_{\rm max}$ & log N$_{\rm e}$ &  \\
\hline
\hline

Si IX (*)    & 349.9 (3) / 341.949 & N 1 (G 4) & 6.02 &\hbox{7.5 -- 9.5\hskip 4.5pt} & \\
Si IX     & 345.100 / 341.949 & N 1   (G 4) & 6.02 &\hbox{7.5 -- 9.5\hskip 4.5pt} & \\
Si IX     & 349.9 (3) / 345.100 & N 1 (G 4) & 6.02 &\hbox{7.5 -- 9.5\hskip 4.5pt} &  \\   

Si X      & 356.0 (2) / 347.402 & N 1 (G 4)& 6.12 &8.0 -- 10.0 &  \\

Fe XII    & 338.278 (!) / 364.467  & N 1 (G 4)& 6.16 &7.0 -- 12.0 &  \\

Fe XIII   & 321.4   / 320.80 & N 1 & 6.21 &8 -- 10    &   \\
Fe XIII   & 318.12 / 320.80 & N 1 & 6.21 &8 -- 10    &   \\
Fe XIII   & 359.6 (2) (!) / 348.18 & N 1 (G 4) & 6.21 &8 -- 10 &  \\
Fe XIII (*)  & 320.8  (bl) / 348.18 & N 1 & 6.21 & 8 -- 10 &  \\

Fe XIII (*)   &203.8 (2) / 202.044   & G 1 &6.21 &8.5 -- 10.5   &  \\

Fe XIV    & 353.83 (!) / 334.17 & N 1 (G 4)& 6.25 &9.0 -- 11.0 &   \\ 

\hline

\end{tabular}
\end{center}
\label{tab:dens_pairs}
%Table~\ref{tab:dens_pairs}
\normalsize
\end{table}

Table~\ref{tab:dens_pairs}  presents  a list of 
useful density-sensitive line ratios  available within the   CDS channels.
Only the principal usable ratios are listed, involving pairs of  lines seen by the 
same spectrometer and detector.

The lines indicated with a (!)  have problems in either their  observation 
or in the atomic physics.  This is based on experience gained in analysing  different source 
regions (e.g. on-disc, off-limb, coronal holes, quiet sun, active regions) 
with the different detectors, and on the best possible line identification,
with $DEM$ analysis of the various regions. 



\section{Pre- vs. post-recovery CDS spectra}

 \begin{figure}[!htbp]
\centerline{\epsfig{file=may_4_97_off_mir5_wlab_NIS1_zoom.ps, width=9.0cm , angle=0 }}
\centerline{\epsfig{file=23_may_99_wlab_NIS1_zoom.ps, width=9.0cm , angle=0 }}
  \caption{
Part of quiet-Sun off-limb spectra, taken pre- vs. post-recovery,
and showing some of the lines useful for 
density-diagnostics (Si~IX, Si~X, Fe~XIII, Fe~XIV).
Note the strong blending of the lines, due to the
    broadened profiles in the post-recovery case. 
Any NIS study that has extraction windows has to be analysed with
         extreme care, because the background estimate is problematic 
even in  full-wavelength spectra. 
}
  \label{fig:}
\end{figure}
% Figure~\ref{fig:}





\section{Comments on the single ions}

\subsection{Si IX}

CDS observes many Si IX lines, 
but only those visible in NIS 1 are usable, because those
seen in GIS 2 are affected by {\it ghosts} or are weak.
The lines visible in NIS 1 are seen at
341.949, 345.1, and 349.9 \AA.
 The last  
is a complex self-blend of three transitions.
These lines are  free of blends and  close in wavelength.
The best ratio is indicated in the Table.

Photoexcitation is significant for this ion, at low densities.

Atomic data appear to be reliable.

 \begin{figure}[!htbp]
\centerline{\epsfig{file=si_9.ps, width=9.0cm , angle=0 }}
  \caption{Emissivities calculated with CHIANTI
}
  \label{fig:}
\end{figure}
% Figure~\ref{fig:}


\subsection{Si X}

CDS observes many Si X lines, but only the two
visible in NIS 1 can safely  be used. 
They are free from blends and were found to give densities 
in close agreement with those derived from Si IX.
The line at 356.0 \AA\ (a self-blend of two transitions)
lies close to other lines, so its intensity must be
carefully measured.

Atomic data appear to be reliable.

 \begin{figure}[!htbp]
\centerline{\epsfig{file=si_10.ps, width=9.0cm , angle=0 }}
  \caption{Emissivities calculated with CHIANTI
}
  \label{fig:}
\end{figure}
% Figure~\ref{fig:}


\subsection{Fe XII}

Fe XII is a complex case (see Del Zanna, PhD Thesis),
for a number of reasons.
Currently, the atomic data are such that 
any density-diagnostic is unreliable. 


\subsection{Fe XIII}

 Fe XIII emits a large number of strong lines in the CDS 
wavelength ranges, in active region spectra.

The Fe XIII  359.7 \AA (359.642  + 359.842 \AA) line is close 
to  the Ne V  359.382
 \AA\ line, and therefore can be 
reliably used only in off-limb or active region observations.
In any case, densities obtained with this line are at 
odds (higher) compared to those obtained from other ions or 
other lines of Fe XIII.

Fe XIII  320.809 can be  a blend with O III 320.976 \AA\ and Mg IV 320.994 %\AA\ 
lines. It can only be used reliably when these contributions can be neglected
(e.g.  with  observations of active regions or off-limb). 

In general, all the other lines give consistent results, 
when blends are not present.

 \begin{figure}[!htbp]
\centerline{\epsfig{file=fe_13.ps, width=9.0cm , angle=0 }}
  \caption{Emissivities calculated with CHIANTI
}
  \label{fig:}
\end{figure}
% Figure~\ref{fig:}


\subsection{ Fe XIV}

Fe  XIV has  been a problem in EUV spectroscopy for a long time.
Although tens of bright Fe XIV lines are present in the NIS and GIS spectra,
 especially in active regions, disagreement  between  observations
and theory was reported by numerous authors.


Only recently,  new calculations (Storey et al., 1999) 
 have shed  light on the Fe XIV problem.
Now, the agreement between theory and NIS/GIS observations is quite good
(see Del Zanna et al. 2001).

One density diagnostic ratio is reported, but should be used with caution, since
the Fe XIV   353.83 \AA\ could be blended with an Ar~XVI  353.920 \AA\ line
in active region spectra. 
Also, note that this ratio is only useful at very high densities, 
higher than those normally found in active regions.

 \begin{figure}[!htbp]
\centerline{\epsfig{file=fe_14.ps, width=9.0cm , angle=0 }}
  \caption{Emissivities calculated with CHIANTI
}
  \label{fig:}
\end{figure}
% Figure~\ref{fig:}


%\subsection{

\end{document}
