A new approach to analyzing solar coronal spectra and updated collisional ionization equilibrium calculations. ii. updated ionization rate coefficients

TL;DR: In this article, a collisional ionization equilibrium (CIE) was calculated using state-of-the-art electron-ion recombination data for all elements from H through Zn and, additionally, Al-through Ar-like ions of Fe.

Abstract: We have re-analyzed Solar Ultraviolet Measurement of Emitted Radiation (SUMER) observations of a parcel of coronal gas using new collisional ionization equilibrium (CIE) calculations These improved CIE fractional abundances were calculated using state-of-the-art electron–ion recombination data for K-shell, L-shell, Na-like, and Mg-like ions of all elements from H through Zn and, additionally, Al- through Ar-like ions of Fe They also incorporate the latest recommended electron impact ionization data for all ions of H through Zn Improved CIE calculations based on these recombination and ionization data are presented here We have also developed a new systematic method for determining the average emission measure (EM) and electron temperature (Te )o f an isothermal plasma With our new CIE data and a new approach for determining average EM and Te ,w e have re-analyzed SUMER observations of the solar corona We have compared our results with those of previous studies and found some significant differences for the derived EM and Te We have also calculated the enhancement of coronal elemental abundances compared to their photospheric abundances, using the SUMER observations themselves to determine the abundance enhancement factor for each of the emitting elements Our observationally derived first ionization potential factors are in reasonable agreement with the theoretical model of Laming

Summary

1. INTRODUCTION

• Investigating the dynamics of the solar corona is crucial if one is to understand fundamental solar and heliospheric physics.
• Gaps remain in their understanding of some of the most fundamental processes taking place in the corona.
• Analyzing the spectral emission of the corona can give the temperature and density of the plasma, as well as information on the complex plasma structures common in this region of the Sun’s atmosphere.
• The authors also investigate here the observed relative elemental abundances and the first ionization potential (FIP) effect.
• Section 8 discusses the consequences of these results, in particular highlighting discrepancies between the results of this paper and those of Landi et al. (2002).

2. OBSERVATIONS

• The spectrum analyzed by Landi et al. (2002), and revisited here, was detected using the Solar Ultraviolet Measurement of Emitted Radiation Spectrometer (SUMER; Wilhelm et al. 1995) onboard the Solar and Heliospheric Observatory (SOHO).
• Known typos in the line assignment labels of Landi et al. (2002) have been corrected; these do not affect their reported results.
• The remaining spectral lines are split into three distinct groups, labeled in the first column of Table 1 as I.
• Transitions between the ground and the first excited configuration: IIa.
• The subdivision of transition Group II is to allow us to investigate a longstanding discrepancy between EMs derived using Li- and Na-like ions and those derived using other isoelectronic sequences (e.g., Dupree 1972; Feldman et al. 1998; Landi et al. 2002).

3. METHOD OF CALCULATING TEMPERATURE AND

• Only those emission lines that have a strong density sensitivity in this range will be affected by the density gradient (Lang et al. 1990).
• (5) This has the same value for all transitions if the constant temperature and density assumption is correct, which the authors label EMc.
• Thus, from the observed line intensities, Iji, and using accurate data for Gji(Te, ne), one can calculate the EM and Te of the emitting region.
• For ease of reading, the authors typically drop these units below.

4. IMPROVED CIE CALCULATIONS

• The plasma conditions of the solar upper atmosphere are often described as being optically thin, low density, dust free, and in steady state or quasi-steady state.
• This is commonly called CIE or coronal equilibrium.
• These conditions are not always the case in the solar upper atmosphere in the event of impulsive heating events but, given the inactivity and low density of the plasma analyzed here, they sufficiently describe the observed conditions.
• At the temperature of peak formation in CIE, DR dominates over RR for most ions.
• Considering all the ions and levels that need to be taken into account, it is clear that vast quantities of data are needed.

4.1. Recombination Rate Coefficients

• The DR and RR rate coefficients used to determine the CIE fractional abundances utilized by Landi et al. (2002) were those recommended by Mazzotta et al. (1998).
• There has been a significant improvement in the recombination rate coefficients since then.
• The RR rate coefficients are in even better agreement, typically within 10% over this temperature range.
• For both DR and RR outside this temperature range, agreement between these two state-of-the-art theories can become significantly worse.
• The DR calculations have also been compared to experimental measurements, where they exist, and found to be in agreement to within 35% in the temperature range where the ion forms in CIE.

4.2. EII Rate Coefficients

• There have also been recent attempts to improve the state of the EII rate coefficients used in CIE calculations.
• The most complete of these studies is that of Dere (2007), who produced recommended rate coefficients for all ionization stages of the elements H through Zn.
• For the ions important to the present work, differences between recent recommended rate coefficients of up to 50% are seen.
• In short, the authors do not see (An extended version of this figure set is available in the online journal.) the uniform agreement between recommended sets of EII data as they do for the state-of-the-art DR and RR calculations.
• Given the large differences between the Dere (2007) and Mattioli et al. (2007) results, the authors believe that further analysis of the EII database is required to resolve these differences.

4.3. Updated CIE Calculations

• Their results show large differences from the Mazzotta et al. (1998) data for certain elements.
• Here the authors revise the work of Bryans et al. (2006) to include these newly recommended EII rate coefficients for all elements from H through Zn and some further updates to the DR and RR rate coefficients for selected ions.
• The authors also include some corrections for Ca-like ions (K. P. Dere 2007, private communication).
• The DR and RR rate coefficients used here are those of Bryans et al. (2006) but updated to include recent corrections to the fitting of some of the rate coefficients (Badnell 2006b).
• Here the authors provide an electronic table of the CIE fractional abundances for all elements from H through Zn calculated using these data (Table 2; Fe shown only to illustrate the format and content).

5. A NEW APPROACH TO DERIVE AVERAGE EMS AND TEMPERATURES

• Using the method described in Section 3, the assumption of constant temperature and density, and their updated CIE results, the authors can calculate the EM curve for each of the observed spectral lines listed in Table 1.
• The authors calculate the EM curves using a constant electron density of 1.8 × 108 cm−3 as was reported by Feldman et al. (1999) for the same source region.
• Step 1 of their approach is to take the mean of all crossing points of the EM curves for a given group of lines.
• This can be seen in the left panel of Figure 3.
• Also, because of the shape of the curves, any outlying crossings are far more likely to occur at a higher EM than at a lower EM.

6. CORONAL ABUNDANCE ENHANCEMENT FACTORS

• There they used only a single line, whereas here the authors use two.
• The authors have repeated the analysis using the Mazzotta et al. (1998) CIE fractional abundances.

7. ANALYSIS BY GROUPS

• Using their derived coronal abundances the authors calculate the EM and Te of each of the line categorizations given in Section 2.
• Figures 7–15 show the GEM approach as applied to each of these groups.
• For the Group I and II categorizations, the authors show their individual subcategorizations as well as the groups as a whole.
• In the case of Group IIb, the emission lines have been further subdivided by separating out the N v and O vi lines.
• The authors elaborate on the possible reasons for this in Section 8.

8.1. Updated CIE Fractional Abundances

• One of the aims of this paper is to investigate the effect of their new CIE fractional abundances on the EM analysis.
• The authors also compare with the recently recommended CIE fractional abundances of Bryans et al. (2006) in Figure 2.
• Differences between the current CIE results and those of Mazzotta et al. (1998) are large for all elements other than H, He, and Li. Factors of typically at least 2 difference in abundance are found for at least one ionization stage of each of these elements.
• The authors attribute all these differences primarily to the EII rate coefficients.
• In Sections 8.2 and 8.4 the authors discuss the impact of these updated CIE calculations on the analysis of the present SUMER observation.

8.2. Comparison With FIP Factor Observations

• For this same SUMER observation, FIP factors were also determined by Feldman et al. (1998).
• First, their reference EM value is taken from the crossing of two Ar EM curves whereas Feldman et al. (1998) use the emission from a single Li-like O vi line as their reference value.
• Furthermore, in determining the FIP factor for each element the authors generally use more emission lines than Feldman et al. (1998).
• They estimate log10 Te = 6.13 (the same value at which the authors ultimately arrive) but only calculate these FIP factor versus.
• The error bars on their results for Na and Ca are also relatively large and the Feldman et al. (1998) results lie within these errors.

8.3. Comparison with the FIP Factor Model

• The FIP effect model of Laming (2004, 2009) allows an opportunity to quantitatively compare their derived coronal elemental abundances with those of theory.
• The Laming model builds on that of Schwadron et al. (1999) by explaining the FIP effect in terms of Alfvén waves in the chromosphere.
• The authors results suggest that upward wave energy fluxes in this range best describe the solar conditions at the time of this particular SUMER observation.
• The authors data generally fit the model well, with the exception of K.
• It should also be noted that the low-FIP results of the present work were calculated relative to a high-FIP enhancement of 1, while in the Laming model the high-FIP elements do show a slight abundance variation dependent on their FIP value.

8.4. Groups

• The authors have used the same group splitting as that used by Landi et al. (2002) and thus can compare directly with their results.
• Figure 10 shows the EM curves for the lines in Group IIa.
• Given the disagreement with the other lines in Group IIa, and the lower formation temperature of N v and O vi compared to the other ions in the group, it is possible that the emission lines from these two ions originate from a different region of plasma.
• In addition to the comparison of EM within Group II, the authors also compare the EM from the Li- and Na-like ions (Group IIa∗) with the EM derived from every other ion in the observation (i.e., those from Groups I, IIb, and III).
• The authors results have larger errors, which the authors believe to be more realistic due to their more rigorous method of calculating the mean and standard deviation of EM and Te.

8.5. Other Issues

• There are a number of indications that the observed emission does not come from an isothermal plasma.
• It is also possible that the relatively large errors in EM and Te are suggestive of a non-isothermal plasma.
• This issue has been raised by Feldman & Laming (2000) in reference to Fe8+ emission.
• These authors found that the contribution function of emission from Li-like lines only becomes significantly affected on reaching densities 1011 cm−3, orders of magnitude higher than the density of 1.8 × 108 cm−3 inferred by Feldman et al. (1999) for the observation analyzed here.
• Again, such a study is beyond the scope of this paper.

9. PROPOSALS FOR FUTURE OBSERVATIONS

• The authors work shows that SUMER observations can go a long way toward constraining FIP models such as those of Laming (2004, 2009).
• Even better constraints can be achieved through the simultaneous observation of lines from a number of additional charge states.
• More lines from high-FIP elements such as N, O, Ne, and Ar are required to better determine the EM for these high-FIP elements, which can then be used to normalize the low-FIP elements.
• For N, O, and Ne, emission lines from H- and He-like stages need to be observed to avoid using Li-like ions.
• This may require simultaneous observations using separate, crosscalibrated spectrometers.

10. SUMMARY

• This work has re-analyzed data from a SUMER coronal observation in an attempt to improve upon previous methods of analysis.
• Their results differ from those of Landi et al. (2002) in certain respects.
• Also, the previously reported discrepancy between the EM derived from Li- and Na-like lines and the EM from all other lines (Groups I, IIb, and III) is not supported by their results, rather the two agree at the 1σ level.
• CHIANTI is a collaborative project involving the NRL (USA), RAL (UK), MSSL (UK), the Universities of Florence and Cambridge (UK), and George Mason University (USA).
• P.B. and D.W.S. were supported in part by the NASA Solar and Heliospheric Physics Supporting Research and Technology program and the NASA Astronomy and Physics Research and Analysis Program.

Figures

Figure 1. Ionization fractional abundance vs. Te for all ionization stages of Fe. The upper graph shows our results (solid curves) and the abundances calculated by Mazzotta et al. (1998; dashed curves). The lower graph shows the ratio of the calculated abundances. Comparison is made only for fractional abundances greater than 10−2. We label our results as “New” and those of Mazzotta et al. (1998) as “Old.”

Table 4 Derived Te and EM

Figure 14. Same as Figure 7 but for Group II as a whole, excluding emission lines from N v and O vi.

Figure 13. Same as Figure 7 but for Group IIb.

Figure 3. EM vs. Te curves of all emission lines observed here from Si. The dashed lines indicate the mean log10 EM and log10 Te and the dotted lines show the standard deviations of these values. Asterisks indicate where the curves cross. The left panel shows the results after Step 1 of the analysis, the middle panel shows the results after Step 2, and the right panel shows the results after Step 3. See Section 5 for a description of each step.

Figure 2. Ionization fractional abundance vs. Te for all ionization stages of Fe. The upper graph shows our results (solid curves) and the abundances calculated by Bryans et al. (2006; dashed curves). The lower graph shows the ratio of the calculated abundances. Comparison is made only for fractional abundances greater than 10−2. We label our results as “New” and those of Bryans et al. (2006) as “Old.”

Figure 5. EM vs. Te curves of all the emission lines from each of the elements Ne, Mg, Al, Si, S, Ar, and Fe (excluding Li- and Na-like ions). The Te derived from these elements were used to determine the FIP factors of Na, K, and Ca. Asterisks indicate where the curves cross. The three panels show the three steps of the GEM method as in Figure 3.

Figure 6. Coronal abundance enhancement factor (i.e., FIP factor) used for each of the elements vs. their FIP. Open circles indicate the high-FIP elements O, N, Ne, and Ar where no enhancement was assumed. The elements in squares indicate those which had their enhancement factor determined by matching their mean EM with that of the high-FIP element Ar. Elements marked with diamonds are those that did not have enough crossings to determine their EM in this way (see Section 6 for further details). The data points for Al and Ca overlap. The dotted line is purely to guide the eye. The solid circles are the results of Feldman et al. (1998) for N, O, Ne, Na, Mg, Si, S, Ca, and Fe. Feldman et al. (1998) scaled their results to O and assumed a FIP factor of 1 for this element. We also set the O FIP factor to 1, so their and our FIP factors for O lie directly on top of one another in this plot.

Figure 11. Same as Figure 10 but excluding emission lines from N v and O vi.

Figure 12. Same as Figure 10 but showing only emission lines from N v and O vi.

Table 1 Emission Lines and Intensities Used in the Present Study

Figure 19. Same as Figure 18 but for log10 Te . The upper values of the standard deviation for the thick and thin lines lie on top of one another.

Figure 18. Mean log10 EM values for each of the groups using the GEM method (as listed in Table 4). The numbers in the data points represent the number of EM curve crossings that were used to derive the mean EM. The error bars on the points are ±δ〈log10 EM〉. Group IIa∗ excludes the O vi and N v lines. The dashed and dotted lines indicate the mean and standard deviation, respectively, when every emission line, except N v and O vi, is considered. The thick lines include emission lines from Li- and Na-like ions (Figure 16) and the thin lines exclude emission lines from these ions (Figure 17).

Figure 10. Same as Figure 7 but for Group IIa.

Figure 9. Same as Figure 7 but for Group I as a whole.

Table 3 Inferred FIP Enhancement Factors and Coronal Abundances Used in the Analysis Here

Table 1 Emission Lines and Intensities Used in the Present Study

Figure 20. Coronal abundance enhancement factor (i.e., FIP factor) used for each of the elements vs. their FIP. Open symbols represent the present results; refer to Figure 6 for details. The data points for Al and Ca overlap. The solid circles are the results of the model of Laming (2009) for upward Alfvén wave energy fluxes of 2, 8, and 32 (solid, dashed, and dot-dashed lines, respectively) in units of 106 ergs cm−2 s−1. Lines have been drawn between points only to guide the eye.

Figure 17. Same as Figure 16 but excluding emission lines from all Li- and Na-like ions.

Table 5 Te and EM Values Derived Using the GEM Method and Our Current CIE Fractional Abundances, as well as Using the GEM Method with the Mazzotta et al. (1998) CIE Fractional Abundancesa

Figure 8. Same as Figure 7 but for Group Ib.

Full text

The Astrophysical Journal, 691:1540–1559, 2009 February 1 doi:10.1088/0004-637X/691/2/1540
c

2009. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
A NEW APPROACH TO ANALYZING SOLAR CORONAL SPECTRA AND UPDATED COLLISIONAL
IONIZATION EQUILIBRIUM CALCULATIONS. II. UPDATED IONIZATION RATE COEFFICIENTS
P. Bryans
1,3
, E. Landi
2
, and D. W. Savin
1
1
Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA
2
US Naval Research Laboratory, Space Science Division, 4555 Overlook Avenue, SW, Code 7600A, Washington, DC 20375, USA
Received 2008 May 21; accepted 2008 October 12; published 2009 February 5
ABSTRACT
We have re-analyzed Solar Ultraviolet Measurement of Emitted Radiation (SUMER) observations of a parcel
of coronal gas using new collisional ionization equilibrium (CIE) calculations. These improved CIE fractional
abundances were calculated using state-of-the-art electron–ion recombination data for K-shell, L-shell, Na-like,
and Mg-like ions of all elements from H through Zn and, additionally, Al- through Ar-like ions of Fe. They
also incorporate the latest recommended electron impact ionization data for all ions of H through Zn. Improved
CIE calculations based on these recombination and ionization data are presented here. We have also developed
a new systematic method for determining the average emission measure (EM) and electron temperature (T
e
)of
an isothermal plasma. With our new CIE data and a new approach for determining average EM and T
e
,wehave
re-analyzed SUMER observations of the solar corona. We have compared our results with those of previous studies
and found some significant differences for the derived EM and T
e
. We have also calculated the enhancement
of coronal elemental abundances compared to their photospheric abundances, using the SUMER observations
themselves to determine the abundance enhancement factor for each of the emitting elements. Our observationally
derived first ionization potential factors are in reasonable agreement with the theoretical model of Laming.
Key words: atomic data – atomic processes – plasmas – Sun: corona – Sun: UV radiation
Online-only material: figure sets, machine-readable table
1. INTRODUCTION
Investigating the dynamics of the solar corona is crucial if one
is to understand fundamental solar and heliosphericphysics. The
corona also greatly influences the Sun–Earth interaction, as it
is from here that the solar wind originates. Explosive events in
the corona can deposit up to 2 × 10
16
g of ionized particles into
the solar wind (Hundhausen 1993). These can have a profound
effect on the Earth’s magnetosphere and ionosphere. Hence the
investigation of the corona is of obvious importance.
Over the years there has been a significant amount of re-
search invested in developing our understanding of the corona
(reviewed by Aschwanden 2004 and Foukal 2004). However,
gaps remain in our understanding of some of the most funda-
mental processes taking place in the corona. For example, the
so-called coronal heating problem remains unsolved (Gudiksen
& Nordlund 2005; Klimchuk 2006) and we are still unable to
explain the onset processes that cause solar flares and coronal
mass ejections (Forbes 2000; Priest & Forbes 2002).
One of the most powerful tools for understanding the prop-
erties of the solar corona is spectroscopy (Tandberg-Hanssen &
Emslie 1988; Foukal 2004). Analyzing the spectral emission of
the corona can give the temperature and density of the plasma, as
well as information on the complex plasma structures common
in this region of the Sun’s atmosphere. One common approach
to this end is to calculate the emission measure (EM) of the gas
(e.g., Raymond & Doyle 1981).
The EM technique is particularly useful for studying the prop-
erties of the upper solar atmosphere. In this region, conditions
are such that the plasma can often be described as low den-
sity and in steady state and the emitting region as constant in
3
Present Address: US Naval Research Laboratory, Space Science Division,
4555 Overlook Avenue, SW, Code 7670, Washington, DC 20375, USA.
density and temperature. These relatively simple conditions al-
low one to neglect density effects and to assume all emission
is from an isothermal plasma. For example, Landi et al. (2002)
compared off-disk spectral observations of the solar corona with
predictions from the CHIANTI version 3 atomic database (Dere
et al. 1997, 2001). Landi et al. (2002) calculated the EM of the
plasma based on the observed intensities using the atomic data
assembled together in CHIANTI. From this, they also infer the
electron temperature (T
e
) of the emitting plasma. However, the
power of this spectroscopic diagnostic can be limited by our
understanding of the underlying atomic physics that produce
the observed spectrum.
Reliable EM calculations require accurate fractional abun-
dances for the ionization stages of the elements present in the
plasma. For a plasma in collisional ionization equilibrium (CIE;
sometimes also called coronal equilibrium), the atomic data
needed for such a spectral analysis includes rate coefficients
for electron–ion recombination and electron impact ionization
(EII). These data directly affect the calculated ionic fractional
abundances of the gas. The fractional abundances, in turn, are
used to determine the EM. Hence the reliability of the CIE
calculations is critical.
The recommended CIE calculations at the time of the work
by Landi et al. (2002) were those of Mazzotta et al. (1998).
Recently, however, state-of-the-art electron–ion recombination
data have been published for K-shell, L-shell, and Na-like
ions of all elements from H through Zn (Badnell et al. 2003;
Badnell 2006a, 2006b, 2006c;Gu2003a, 2003b, 2004). Based
on these new recombination data, a significant update of
the recommended CIE fractional abundances was published
recently by Bryans et al. (2006, Paper I in this series). Since
then additional recombination data have been published for Mg-
like ions of H through Zn (Altun et al. 2007) and Al- through
Ar-like ions of Fe (Badnell 2006d, 2006e). EII data have also
1540

No. 2, 2009 UPDATED IONIZATION RATE COEFFICIENTS 1541
been updated recently by Suno & Kato (2006), Dere (2007),
and Mattioli et al. (2007). Of these three, the recommended EII
data of Dere (2007), which we adopt, provide the only complete
available set of rate coefficients for all ions of H through Zn. Here
we have updated the results of Bryans et al. (2006) using these
new recombination and ionization data. One of the motivations
behind this paper is to investigate the effects of the recent
improvements in CIE calculations on solar observations.
Since the Landi et al. (2002) paper there have been other
improved atomic data (e.g., the improvement of the model for
N-like ions). These have been made available in a more recent
CHIANTI release—version 5.2 (Landi et al. 2006). It is this
version we use here.
We also investigate here the observed relative elemental abun-
dances and the first ionization potential (FIP) effect. The FIP
effect is the discrepancy between the coronal and photospheric
elemental abundances, possibly explained by the pondermotive
force induced by the propagation of Alfv
´
en waves through the
chromosphere (Laming 2004, 2009). Elements with a FIP below
∼ 10 eV appear to have a coronal abundance that is enhanced
by a factor of a few over their photospheric abundance (see, e.g.,
the review by Feldman & Laming 2000). Often, the FIP effect
is accounted for by multiplying the abundance of the low-FIP
elements by a single scaling factor (such as 3.5, as was done
in Landi et al. 2002). In the present work, we investigate the
reliability of this approach by quantifying the FIP effect based
on the observations themselves. We determine the EM from the
high-FIP element Ar and then scale the elemental abundances of
the moderate- and low-FIP elements so that their derived EMs
match that of Ar. We compare our derived abundances with those
of a previous analysis of the same observation (Feldman et al.
1998) as well as with theoretical predictions (Laming 2009).
An important aspect of this paper is the development of a
sound mathematical method of determining the average EM and
T
e
of an isothermal plasma. Previous studies have done this in a
less rigorous manner. Landi et al. (2002), for example, evaluate
plots of EM versus T
e
curves and give a “by-eye” estimate of
the average value of the EM and T
e
and their associated errors.
This method allows human bias to become important when
deciding which curve crossings to include in the selection. In
addition, it is unclear to what this “average” actually corresponds
mathematically. The fact that the analysis is performed on graphs
with logarithmic axes suggests that by-eye average is closer
to the geometric mean than the arithmetic mean. Finally, no
account is taken of the reliability of the atomic data used to
calculate fractional abundances. Bryans et al. (2006)showed
that CIE results are unreliable at temperatures where the ionic
fractional abundances are less than 1%. Previous studies have
failed to account for this when using the CIE data in the EM
analysis.
Taking the above four paragraphs into account, we have re-
analyzed the observations of Landi et al. (2002). The rest of this
paper is organized as follows. In Section 2 we give a descrip-
tion of the observing sequence, the observed lines, and their
categorizations by Landi et al. (2002). Section 3 defines the
EM and explains the method we use to determine the plasma
temperature from the observed line intensities. In Section 4
we review the recent developments in the understanding of
dielectronic and radiative recombinations (DR and RR) and
EII, and the subsequent improvement in CIE calculations. We
also present updated tables of these CIE calculations, which
supersede those of Bryans et al. (2006). In Section 5 we de-
scribe our new approach for determining the EM and temper-
ature of an isothermal plasma based on the observed spectral
line intensities. Section 6 discusses our method of determining
the elemental abundance enhancement factors due to the FIP
effect. In Section 7 we present the results of our EM calcula-
tions for each of the categorizations introduced by Landi et al.
(2002). Section 8 discusses the consequences of these results, in
particular highlighting discrepancies between the results of this
paper and those of Landi et al. (2002). In Section 9 we propose
future observations needed to address some of the remaining
issues raised by our results here. Concluding remarks are given
in Section 10.
2. OBSERVATIONS
The spectrum analyzed by Landi et al. (2002), and revisited
here, was detected using the Solar Ultraviolet Measurement of
Emitted Radiation Spectrometer (SUMER; Wilhelm et al. 1995)
onboard the Solar and Heliospheric Observatory (SOHO). The
observation spans over 5 hr, from 21:16 UT on 1996 November
21 to 02:28 UT on 1996 November 22, and was collected in
61 spectral sections. The observing slit imaged at a height h of
1.03 R

 h  1.3 R

above the western limb. The resulting
spectrum covers the entire SUMER spectral range of 660–1500
Å. Landi et al. (2002) give a full description of the observation
sequence and data reduction.
Table 1 lists the coronal lines identified in the spectrum and
their corresponding transitions (reproduced from Landi et al.
2002). Known typos in the line assignment labels of Landi et al.
(2002) have been corrected; these do not affect their reported
results. Landi et al. estimate uncertainties on the extracted
line intensities of 25%–30%. Twelve of the emission lines
observed in this run are omitted from the table here due to their
being blended with other emission lines or having uncertain
intensities. The remaining spectral lines are split into three
distinct groups, labeled in the first column of Table 1 as
I. Forbidden transitions within the ground configuration:
Ia. Non-N-like transitions.
Ib. N-like transitions.
II. Transitions between the ground and the first excited con-
figuration:
IIa. Allowed 2s–2p transitions in the Li-like isoelectronic
sequence and allowed 3s–3p transitions in the Na-like
isoelectronic sequence.
IIb. Intercombination transitions in the Be-, B-, C-, and
Mg-like isoelectronic sequences.
III. Transitions between the first and second excited configura-
tion.
Within each group and subgroup we have derived the average
T
e
and EM. Categorizing the transitions in this way helps us to
better identify any trends in the EM with respect to the transition
type. Group I transitions have been further divided into non-
N-like and N-like transitions. This separation was originally
proposed by Landi et al. (2002) due to the poor agreement they
found for the T
e
derived within each of these transition types.
This is discussed further in Sections 6 and 8. The subdivision of
transition Group II is to allow us to investigate a longstanding
discrepancy between EMs derived using Li- and Na-like ions
and those derived using other isoelectronic sequences (e.g.,
Dupree 1972; Feldman et al. 1998; Landi et al. 2002). We also
discuss this further in Sections 6 and 8.

1542 BRYANS, LANDI, & SAVIN Vol. 691
Tab le 1
Emission Lines and Intensities Used in the Present Study
Group Ion Sequence Wavelength Transition Intensity
(Å) (ergs cm
−2
s
−1
sr
−1
)
IIa N v Li 1238.82 2s
2
S
1/2
–2p
2
P
3/2
2.520
IIa N v Li 1242.80 2s
2
S
1/2
–2p
2
P
1/2
1.420
IIa O vi Li 1031.91 2s
2
S
1/2
–2p
2
P
3/2
63.000
IIa O vi Li 1037.62 2s
2
S
1/2
–2p
2
P
1/2
28.500
IIa Ne viii Li 770.41 2s
2
S
1/2
–2p
2
P
3/2
30.700
IIa Ne viii Li 780.32 2s
2
S
1/2
–2p
2
P
1/2
14.200
IIb Ne vii Be 895.17 2s
21
S
0
–2s2p
3
P
1
0.132
III Ne vii Be 973.33 2s2p
1
P
1
–2p
21
D
2
0.070
IIa Na ix Li 681.72 2s
2
S
1/2
–2p
2
P
3/2
4.515
IIa Na ix Li 694.13 2s
2
S
1/2
–2p
2
P
1/2
2.600
IIb Na viii Be 789.78 2s
21
S
0
–2s2p
3
P
1
0.074
III Na viii Be 847.91 2s2p
1
P
1
–2p
21
D
2
0.058
IIa Mg x Li 609.79 2s
2
S
1/2
–2p
2
P
3/2
153.000
IIa Mg x Li 624.94 2s
2
S
1/2
–2p
2
P
1/2
91.700
IIb Mg ix Be 693.98 2s
21
S
0
–2s2p
3
P
2
0.898
IIb Mg ix Be 706.06 2s
21
S
0
–2s2p
3
P
1
8.160
III Mg ix Be 749.55 2s2p
1
P
1
–2p
21
D
2
1.490
IIb Mg viii B 762.66 2s
2
2p
2
P
1/2
–2s2p
24
P
3/2
0.047
IIb Mg viii B 769.38 2s
2
2p
2
P
1/2
–2s2p
24
P
1/2
0.152
IIb Mg viii B 772.28 2s
2
2p
2
P
3/2
–2s2p
24
P
5/2
0.670
IIb Mg viii B 782.36 2s
2
2p
2
P
3/2
–2s2p
24
P
3/2
0.357
IIb Mg viii B 789.43 2s
2
2p
2
P
3/2
–2s2p
24
P
1/2
0.099
IIb Mg vii C 868.11 2s
2
2p
23
P
2
–2s2p
35
S
2
0.048
IIa Al xi Li 549.98 2s
2
S
1/2
–2p
2
P
3/2
7.820
IIa Al xi Li 568.18 2s
2
S
1/2
–2p
2
P
1/2
5.050
IIb Al x Be 637.76 2s
21
S
0
–2s2p
3
P
1
2.070
III Al x Be 670.01 2s2p
1
P
1
–2p
21
D
2
0.265
IIb Al ix B 688.25 2s
2
2p
2
P
1/2
–2s2p
24
P
1/2
0.076
IIb Al ix B 691.54 2s
2
2p
2
P
3/2
–2s2p
24
P
5/2
0.441
IIb Al ix B 703.65 2s
2
2p
2
P
3/2
–2s2p
24
P
3/2
0.205
IIb Al ix B 712.23 2s
2
2p
2
P
3/2
–2s2p
24
P
1/2
0.058
IIb Al viii C 756.70 2s
2
2p
23
P
1
–2s2p
35
S
2
0.036
IIb Al viii C 772.54 2s
2
2p
23
P
2
–2s2p
35
S
2
0.055
Ib Al vii N 1053.84 2s
2
2p
34
S
3/2
–2s
2
2p
32
P
3/2
0.017
Ia Al viii C 1057.85 2s
2
2p
23
P
1
–2s
2
2p
21
S
0
0.036
IIa Si xii Li 499.40 2s
2
S
1/2
–2p
2
P
3/2
19.200
IIa Si xii Li 520.67 2s
2
S
1/2
–2p
2
P
1/2
9.160
III Si x B 551.18 2s2p
22
P
3/2
–2p
32
D
5/2
0.200
IIb Si xi Be 564.02 2s
21
S
0
–2s2p
3
P
2
1.110
IIb Si xi Be 580.91 2s
21
S
0
–2s2p
3
P
1
16.000
III Si xi Be 604.15 2s2p
1
P
1
–2p
21
D
2
1.840
IIb Si x B 611.60 2s
2
2p
2
P
1/2
–2s2p
24
P
3/2
0.553
IIb Si x B 624.70 2s
2
2p
2
P
3/2
–2s2p
24
P
5/2
6.970
IIb Si x B 638.94 2s
2
2p
2
P
3/2
–2s2p
24
P
3/2
5.210
IIb Si x B 649.19 2s
2
2p
2
P
3/2
–2s2p
24
P
1/2
1.510
IIb Si ix C 676.50 2s
2
2p
23
P
1
–2s2p
35
S
2
1.560
IIb Si ix C 694.70 2s
2
2p
23
P
2
–2s2p
35
S
2
3.550
Ib Si viii N 944.38 2s
2
2p
34
S
3/2
–2s
2
2p
32
P
3/2
2.030
Ib Si viii N 949.22 2s
2
2p
34
S
3/2
–2s
2
2p
32
P
1/2
0.870
Ia Si ix C 950.14 2s
2
2p
23
P
1
–2s
2
2p
21
S
0
1.920
Ia Si vii O 1049.22 2s
2
2p
43
P
1
–2s
2
2p
41
S
0
0.045
Ib Si viii N 1440.49 2s
2
2p
34
S
3/2
–2s
2
2p
32
D
5/2
0.176
Ib Si viii N 1445.76 2s
2
2p
34
S
3/2
–2s
2
2p
32
D
3/2
2.090
IIb S xi C 552.12 2s
2
2p
23
P
1
–2s2p
35
S
2
0.190
IIb S xi C 574.89 2s
2
2p
23
P
2
–2s2p
35
S
2
0.470
Ib S x N 776.25 2s
2
2p
34
S
3/2
–2s
2
2p
32
P
3/2
1.910
Ia S xi C 782.96 2s
2
2p
23
P
1
–2s
2
2p
21
S
0
0.4005
Ib S x N 787.56 2s
2
2p
34
S
3/2
–2s
2
2p
32
P
1/2
0.946
Ia S ix O 871.73 2s
2
2p
43
P
1
–2s
2
2p
41
S
0
0.440
Ib S x N 1196.26 2s
2
2p
34
S
3/2
–2s
2
2p
32
D
5/2
1.590
Ib S x N 1212.93 2s
2
2p
34
S
3/2
–2s
2
2p
32
D
3/2
3.410
IIa Ar viii Na 700.25 3s
2
S
1/2
–3p
2
P
3/2
0.635
IIa Ar viii Na 713.81 3s
2
S
1/2
–3p
2
P
1/2
0.310
Ib Ar xii N 1018.89 2s
2
2p
34
S
3/2
–2s
2
2p
32
D
5/2
0.274
Ib Ar xii N 1054.57 2s
2
2p
34
S
3/2
–2s
2
2p
32
D
3/2
0.056

No. 2, 2009 UPDATED IONIZATION RATE COEFFICIENTS 1543
Tab le 1
(Continued)
Group Ion Sequence Wavelength Transition Intensity
(Å) (ergs cm
−2
s
−1
sr
−1
)
Ia Ar xi O 1392.11 2s
2
2p
43
P
2
–2s
2
2p
41
D
2
0.134
IIa K ix Na 636.29 3s
2
S
1/2
–3p
2
P
1/2
0.133
IIa Ca x Na 557.76 3s
2
S
1/2
–3p
2
P
3/2
8.000
IIa Ca x Na 574.00 3s
2
S
1/2
–3p
2
P
1/2
4.880
IIb Ca ix Mg 691.41 3s
21
S
0
–3s3p
3
P
1
0.109
III Ca ix Mg 821.23 3s3p
1
P
1
–3p
21
D
2
0.048
Ia Fe xii P 1242.00 3s
2
3p
34
S
3/2
–3s
2
3p
32
P
3/2
11.840
Ia Fe xii P 1349.36 3s
2
3p
34
S
3/2
–3s
2
3p
32
P
1/2
5.353
Ia Fe xi S 1467.06 3s
2
3p
43
P
1
–3s
2
3p
41
S
0
3.390
Notes. We list here all the emission lines of the SUMER 1996 November 21 21:16 UT to 1996 November 22
02:28 UT observation that are used in the analysis here. This table is reproduced from Landi et al. (2002) with
known transition assignment errors corrected. Lines that are blended or have uncertain intensities have also been
omitted.
3. METHOD OF CALCULATING TEMPERATURE AND
EM
The intensity of an observed spectral line due to a transition
from level j to level i in element X of ionization state +m can be
written as
I
ji
=
1
4πd
2

V
G
ji
(T
e
,n
e
)n
2
e
dV, (1)
where n
e
is the electron density, V is the emitting volume along
the line of sight, and d is the distance to the source. G
ji
(T
e
,n
e
)
is the contribution function, which is defined as
G
ji
(T
e
,n
e
) =
n
j
(X
+m
)
n(X
+m
)
n(X
+m
)
n(X)
n(X)
n(H)
n(H)
n
e
A
ji
n
e
, (2)
where n
j
(X
+m
)/n(X
+m
) is the population of the upper level
j relative to all levels in X
+m
, n(X
+m
)/n(X) is the fractional
abundance of the ionization stage +m relative to the sum of all
ionization stages of X, n(X)/n(H) is the abundance of element X
relative to hydrogen, and n(H)/n
e
is the abundance of hydrogen
relative to the electron density. A
ji
is the spontaneous emission
coefficient for the transition.
For the observation analyzed here, the emitting plasma was
found to be isothermal by Feldman et al. (1998) and Landi et al.
(2002). For the moment we assume this to be correct but we
revisit the validity of the isothermal assumption in Section 8.4.
One can also make the assumption that the region emitting
the observed line intensities is at a constant density. While the
line of sight of the observation covers plasma where densities
vary by orders of magnitude, the emission is dominated by a
region with a small range of densities around the peak density.
Only those emission lines that have a strong density sensitivity
in this range will be affected by the density gradient (Lang
et al. 1990). Feldman et al. (1999) inferred a density of 1.8 ×
10
8
cm
−3
for this observation. A density-dependent study of the
74 lines observed here is beyond the scope of our paper. Here we
use the inferred density of Feldman et al. (1999) in our analysis.
If we now assume that all the emission comes from the same
parcel of gas of nearly constant temperature, T
c
, and density, we
can approximate
I
ji
=
G
ji
(T
c
,n
e
)
4πd
2
EM, (3)
where the EM is defined as
EM =

n
2
e
dV (4)
and can be evaluated from the observed line intensity as
EM = 4πd
2
I
ji
G
ji
(T
c
,n
e
)
. (5)
This has the same value for all transitions if the constant
temperature and density assumption is correct, which we label
EM
c
. Thus, from the observed line intensities, I
ji
, and using
accurate data for G
ji
(T
e
,n
e
), one can calculate the EM and T
e
of the emitting region. This is done by plotting the EM against
T
e
. The resulting curves for each observed line should intersect
at a common point yielding [T
c
, EM
c
]. But this depends on the
assumption of constant temperature and density being correct
and on the accuracy of the underlying atomic data. Here, one
of the issues we are investigating is the effect on solar coronal
observations of the newly calculated fractional abundances
f
m
=
n(X
+m
)
n(X)
. (6)
The units used throughout this paper for EM and T
e
are cm
−3
and K, respectively. For ease of reading, we typically drop these
units below.
4. IMPROVED CIE CALCULATIONS
The plasma conditions of the solar upper atmosphere are
often described as being optically thin, low density, dust free,
and in steady state or quasi-steady state. Under these conditions
the effects of any radiation field can be ignored, three-body
collisions are unimportant, and the ionization balance of the gas
is time-independent. This is commonly called CIE or coronal
equilibrium. These conditions are not always the case in the
solar upper atmosphere in the event of impulsive heating events
but, given the inactivity and low density of the plasma analyzed
here, they sufficiently describe the observed conditions. For a
thorough discussion of plasma conditions where one must treat
the timescales and density effects more carefully, we direct the
reader to Summers et al. (2006).
In CIE, recombination is due primarily to DR and RR. At
the temperature of peak formation in CIE, DR dominates over

1544 BRYANS, LANDI, & SAVIN Vol. 691
RR for most ions. Ionization is primarily a result of EII. At
temperatures low enough for both atoms and ions to exist,
charge transfer (CT) can be both an important recombination
and ionization process (Arnaud & Rothenflug 1985; Kingdon
& Ferland 1996). CT is not expected to be important at solar
coronal temperatures and is not included in the work of Mazzotta
et al. (1998), Bryans et al. (2006), or this paper. Considering all
the ions and levels that need to be taken into account, it is clear
that vast quantities of data are needed. Generating them to the
accuracy required pushes atomic theoretical and experimental
methods to the edge of what is currently achievable and often
beyond. For this reason, the CIE data used by the solar physics
and astrophysics communities have gone through numerous
updates over the years as more reliable atomic data have become
available.
4.1. Recombination Rate Coefficients
The DR and RR rate coefficients used to determine the
CIE fractional abundances utilized by Landi et al. (2002)
were those recommended by Mazzotta et al. (1998). However,
there has been a significant improvement in the recombination
rate coefficients since then. Badnell et al. (2003) and Badnell
(2006a, 2006b, 2006c) have calculated DR and RR rate coeffi-
cients for all ionization stages from bare through Na-like for all
elements from H through Zn and Gu (2003a, 2003b, 2004)fora
subset of these elements. The methods of Badnell and Gu are of
comparable sophistication and their DR results for a given ion
agree with one another typically to better than 35% at the elec-
tron temperatures where the CIE fractional abundance of that
ion is  1%. The RR rate coefficients are in even better agree-
ment, typically within 10% over this temperature range. These
differences for the DR and RR rate coefficients do not appear to
be systematic in any way (Bryans et al. 2006). For both DR and
RR outside this temperature range, agreement between these
two state-of-the-art theories can become significantly worse.
The DR calculations have also been compared to experimental
measurements, where they exist, and found to be in agreement
to within 35% in the temperature range where the ion forms in
CIE. For a fuller discussion of the agreement between recent
theories and the agreement between theory and experiment, we
direct the reader to Bryans et al. (2006).
4.2. EII Rate Coefficients
There have also been recent attempts to improve the state
of the EII rate coefficients used in CIE calculations. The most
complete of these studies is that of Dere (2007), who produced
recommended rate coefficients for all ionization stages of the
elements H through Zn. These data are based on a combina-
tion of laboratory experiments and theoretical calculations. In
addition, there have been works by Suno & Kato (2006) and
Mattioli et al. (2007) that also address the issue of updating the
EII database. These works are less complete than that of Dere
(2007). Suno & Kato (2006) provides EII cross sections for all
ionization stages of C. Mattioli et al. (2007) provide EII cross
sections for all ionization stages of H through O plus Ne and a
selection of other ions up to Ge.
Between these recent compilations there remain sizable
differences in the EII rate coefficients for certain elements, often
in the temperature range where an ion forms in CIE. For the
ions important to the present work, differences between recent
recommended rate coefficients of up to 50% are seen. Larger
differences, of up to a factor of ∼ 4, are found for other ions not
observed in this SUMER observation. In short, we do not see
Tab le 2
CIE Fractional Abundances (Iron)
log(T )Fe
0+
Fe
1+
4.00 0.901 0.058
4.10 1.416 0.020
4.20 1.932 0.085
4.30 2.825 0.587
4.40 3.877 1.291
4.50 4.692 1.794
4.60 5.580 2.399
4.70 6.502 3.061
4.80 7.319 3.639
4.90 8.194 4.290
5.00 9.169 5.056
5.10 10.239 5.927
5.20 11.367 6.865
5.30 12.564 7.879
5.40 13.890 9.028
5.50 15.000 10.326
5.60 15.000 11.714
5.70 15.000 13.149
5.80 15.000 14.619
5.90 15.000 15.000
6.00 15
.000 15.000
6.10 15.000 15.000
6.20 15.000 15.000
6.30 15.000 15.000
6.40 15.000 15.000
6.50 15.000 15.000
6.60 15.000 15.000
6.70 15.000 15.000
6.80 15.000 15.000
6.90 15.000 15.000
7.00 15.000 15.000
7.10 15.000 15.000
7.20 15.000 15.000
7.30 15.000 15.000
7.40 15.000 15.000
7.50 15.000 15.000
7.60 15.000 15.000
7.70 15.000 15.000
7.80 15.000 15.000
7.90 15.000 15.000
8.00 15.
000 15.000
8.10 15.000 15.000
8.20 15.000 15.000
8.30 15.000 15.000
8.40 15.000 15.000
8.50 15.000 15.000
8.60 15.000 15.000
8.70 15.000 15.000
8.80 15.000 15.000
8.90 15.000 15.000
9.00 15.000 15.000
Notes. Calculated − log
10
of the fractional abundance for
ionization stages of iron. We only show the first two ion-
ization stages here. All ionization stages are available in the
online version of the table. We use the DR rate coefficients
of Badnell (2006b) and the RR rate coefficients of Badnell
(2006c) where they exist and use the DR and RR rate co-
efficients of Mazzotta et al. (1998) for ions not calculated
by Badnell (2006b, 2006c). The EII rate coefficients of Dere
(2007) are used. Fractional abundances are cut off at 10
−15
.
For ease of machine readability, values less than 10
−15
are
given − log
10
values of 15.
(This table is available in its entirety in a machine-readable
form in the online journal. A portion is shown here for
guidance regarding its form and content.)

Frequently asked questions

Q1. What are the contributions mentioned in the paper "A new approach to analyzing solar coronal spectra and updated collisional ionization equilibrium calculations. ii. updated ionization rate coefficients" ?

The authors have re-analyzed Solar Ultraviolet Measurement of Emitted Radiation ( SUMER ) observations of a parcel of coronal gas using new collisional ionization equilibrium ( CIE ) calculations. With their new CIE data and a new approach for determining average EM and Te, the authors have re-analyzed SUMER observations of the solar corona. The authors have compared their results with those of previous studies and found some significant differences for the derived EM and Te. Their observationally derived first ionization potential factors are in reasonable agreement with the theoretical model of Laming. 

Q2. What is the effect of the Alfvén waves on the chromosphere?

These Alfvén waves drive a pondermotive force on their reflection or transmission at the chromosphere–corona boundary which results in the elemental fractionation. 

Q3. What is the powerful tool for understanding the properties of the solar corona?

One of the most powerful tools for understanding the properties of the solar corona is spectroscopy (Tandberg-Hanssen & Emslie 1988; Foukal 2004). 

Q4. What is the contribution function of emission from Li-like lines?

These authors found that the contribution function of emission from Li-like lines only becomes significantly affected on reaching densities 1011 cm−3, orders of magnitude higher than the density of 1.8 × 108 cm−3 inferred by Feldman et al. (1999) for the observation analyzed here. 

Q5. Why is there no common intersection of all EM curves at a single?

Due to oversimplifications of the plasma model, uncertainties in the observations, and errors in the atomic data, there is no common intersection of all EM curves at a single [Tc, EMc]. 

Q6. What does the fieldman et al. (1998) use to determine the FIP factors?

Feldman et al. (1998), however, use only one or two emission lines to determine the FIP factors for each of the elements they consider. 

Q7. What is the EM curve for each of the observed spectral lines?

Using the method described in Section 3, the assumption of constant temperature and density, and their updated CIE results, the authors can calculate the EM curve for each of the observed spectral lines listed in Table 1.