3 Plasma diagnostics

3.1 Computation of the line ratios

The intensities of the three component lines (resonance, forbidden and intercombination) are calculated from atomic data presented in the former section. The ratios $R(n_{\rm e}$) and $G(T_{\rm e}$) are calculated for C V, N VI, O VII, Ne IX, Mg XI, and Si XIII. The wavelengths of these three lines for each He-like ion treated in this paper are reported in Table 14.

 

 

Table 9: Effective collisions strengths ($\Upsilon$) for each 1s²-1s2l transition of C V

$T_{\rm e}$/Z3	$^{3} {\rm S}_{1}$	$^{3} {\rm P}_{0}$	$^{3} {\rm P}_{1}$	$^{3} {\rm P}_{2}$	$^{1} {\rm S}_{0}$	$^{1} {\rm P}_{1}$
400	8.48(-03)$^{\rm a}$	4.95(-03)	1.48(-02)	2.47(-02)	1.42(-02)	4.05(-02)
	7.53(-06)$^{\rm b}$	7.67(-07)	2.31(-06)	3.88(-06)	4.32(-07)	9.86(-06)
600	9.09(-03)	5.04(-03)	1.51(-02)	2.51(-02)	1.46(-02)	4.26(-02)
	8.96(-05)	6.94(-06)	2.09(-05)	3.50(-05)	4.40(-06)	7.09(-05)
900	9.46(-03)	5.02(-03)	1.50(-02)	2.51(-02)	1.50(-02)	4.48(-02)
	4.76(-04)	3.12(-05)	9.37(-05)	1.57(-04)	2.28(-05)	2.73(-04)
1350	9.39(-03)	4.85(-03)	1.46(-02)	2.42(-02)	1.52(-02)	4.76(-02)
	1.45(-03)	8.59(-05)	2.58(-04)	4.32(-04)	7.53(-05)	6.95(-04)
2000	8.91(-03)	4.56(-03)	1.37(-02)	2.27(-02)	1.55(-02)	5.13(-02)
	2.97(-03)	1.64(-04)	4.93(-04)	8.26(-04)	1.80(-04)	1.31(-03)
3000	8.14(-03)	4.15(-03)	1.25(-02)	2.08(-02)	1.58(-02)	5.65(-02)
	4.75(-03)	2.51(-04)	7.54(-04)	1.26(-03)	3.62(-04)	2.10(-03)
4500	7.23(-03)	3.68(-03)	1.11(-02)	1.84(-02)	1.62(-02)	6.40(-02)
	6.23(-03)	3.20(-04)	9.60(-04)	1.61(-03)	6.36(-04)	2.97(-03)
6700	6.30(-03)	3.20(-03)	9.60(-03)	1.60(-02)	1.68(-02)	7.38(-02)
	7.08(-03)	3.56(-04)	1.07(-03)	1.79(-03)	1.01(-03)	3.88(-03)
10000	5.37(-03)	2.70(-03)	8.09(-03)	1.34(-02)	1.76(-02)	8.70(-02)
	7.23(-03)	3.59(-04)	1.08(-03)	1.80(-03)	1.50(-03)	4.82(-03)

$^{\rm a}$

Direct + resonance contribution inferred from the data for O VII (from Zhang & Sampson 1987, see Table 10) with the scaling reported in Fig. 4.

$^{\rm b}$

Cascade contribution calculated in this paper.

Note: here a+b corresponds to the total collision strength which populates the level considered.

 

 

Table 10: Effective collisions strengths ($\Upsilon$) for each 1s²-1s2l transition of O VII

$T_{\rm e}$/Z3	$^{3} {\rm S}_{1}$	$^{3} {\rm P}_{0}$	$^{3} {\rm P}_{1}$	$^{3} {\rm P}_{2}$	$^{1} {\rm S}_{0}$	$^{1} {\rm P}_{1}$
	4.06(-03)$^{\rm a}$	2.51(-03)	7.50(-03)	1.25(-02)	7.35(-03)	2.10(-02)
400	5.01(-04)$^{\rm b}$	1.53(-04)	4.60(-04)	7.71(-04)	2.92(-04)	7.53(-04)
	1.82(-05)$^{\rm c}$	1.32(-06)	3.95(-06)	6.67(-06)	9.42(-07)	1.26(-05)
	4.06(-03)	2.48(-03)	7.41(-03)	1.23(-02)	7.45(-03)	2.19(-02)
600	8.27(-04)	2.31(-04)	6.97(-04)	1.16(-03)	4.06(-04)	9.84(-04)
	1.33(-04)	8.38(-06)	2.51(-05)	4.23(-05)	6.68(-06)	6.98(-05)
	4.04(-03)	2.42(-03)	7.26(-03)	1.21(-02)	7.59(-03)	2.30(-02)
900	1.05(-03)	2.75(-04)	8.31(-04)	1.38(-03)	4.56(-04)	1.06(-03)
	5.05(-04)	2.94(-05)	8.82(-05)	1.48(-04)	2.71(-05)	2.26(-04)
	3.96(-03)	2.33(-03)	7.00(-03)	1.16(-02)	7.75(-03)	2.46(-02)
1350	1.09(-03)	2.74(-04)	8.29(-04)	1.37(-03)	4.38(-04)	9.83(-04)
	1.22(-03)	6.80(-05)	2.04(-04)	3.42(-04)	7.61(-05)	5.12(-04)
	3.80(-03)	2.21(-03)	6.63(-03)	1.10(-02)	7.94(-03)	2.68(-02)
2000	9.86(-04)	2.42(-04)	7.31(-04)	1.20(-03)	3.78(-04)	8.31(-04)
	2.14(-03)	1.15(-04)	3.45(-04)	5.79(-04)	1.63(-04)	8.96(-04)
	3.58(-03)	2.04(-03)	6.12(-03)	1.02(-02)	6.26(-03)	2.97(-02)
3000	8.04(-04)	1.93(-04)	5.86(-04)	9.73(-04)	2.28(-04)	6.47(-04)
	3.04(-03)	1.60(-04)	4.81(-04)	8.06(-04)	3.04(-04)	1.37(-03)
	3.28(-03)	1.83(-03)	5.51(-03)	9.18(-03)	8.51(-03)	3.39(-02)
4500	6.09(-04)	1.45(-04)	4.42(-04)	7.32(-04)	2.23(-04)	4.81(-04)
	3.67(-03)	1.90(-04)	5.72(-04)	9.57(-04)	5.05(-04)	1.88(-03)
	2.94(-03)	1.61(-03)	4.84(-03)	8.06(-03)	8.89(-03)	3.93(-02)
6700	4.51(-04)	1.06(-04)	3.22(-04)	5.33(-04)	1.61(-04)	3.45(-04)
	3.91(-03)	2.01(-04)	6.04(-04)	1.01(-03)	7.70(-04)	2.41(-03)
	2.57(-03)	1.37(-03)	4.12(-03)	6.85(-03)	9.34(-03)	4.65(-02)
10000	3.16(-04)	7.53(-05)	2.28(-04)	3.76(-04)	1.14(-04)	2.42(-04)
	3.81(-03)	1.94(-04)	5.85(-04)	9.77(-04)	1.11(-03)	2.96(-03)

$^{\rm a}$

Direct contribution (from Zhang & Sampson 1987).

$^{\rm b}$

Resonance contribution (from Zhang & Sampson 1987).

$^{\rm c}$

Cascade contribution calculated in this paper.

Note: here a+b+c corresponds to the total collision strength which populates the level considered.

 

 

Table 11: Same as Table 10 but for the Ne IX

$T_{\rm e}$/Z3	$^{3} {\rm S}_{1}$	$^{3} {\rm P}_{0}$	$^{3} {\rm P}_{1}$	$^{3} {\rm P}_{2}$	$^{1} {\rm S}_{0}$	$^{1} {\rm P}_{1}$
	2.53(-03)	1.56(-03)	4.67(-03)	7.77(-03)	4.79(-03)	1.45(-02)
400	5.05(-04)	1.41(-04)	4.23(-04)	7.04(-04)	2.44(-04)	5.92(-04)
	3.14(-05)	1.97(-06)	5.91(-06)	9.99(-06)	1.63(-06)	1.64(-05)
	2.53(-03)	1.53(-03)	4.59(-03)	7.65(-03)	4.88(-03)	1.51(-02)
600	6.75(-04)	1.77(-04)	5.35(-04)	8.89(-04)	2.93(-04)	6.76(-04)
	1.64(-04)	9.55(-06)	2.87(-05)	4.84(-05)	8.87(-06)	7.27(-05)
	2.50(-03)	1.49(-03)	4.47(-03)	7.43(-03)	4.96(-03)	1.59(-02)
900	7.34(-04)	1.85(-04)	5.62(-04)	9.29(-04)	2.95(-04)	6.63(-04)
	4.96(-04)	2.77(-05)	8.32(-05)	1.40(-04)	3.02(-05)	2.03(-04)
	2.43(-03)	1.42(-03)	4.27(-03)	7.10(-03)	5.08(-03)	1.71(-02)
1350	6.89(-04)	1.69(-04)	5.11(-04)	8.44(-04)	2.62(-04)	5.78(-04)
	1.03(-03)	5.59(-05)	1.68(-04)	2.83(-04)	7.49(-05)	4.15(-04)
	2.31(-03)	1.33(-03)	4.00(-03)	6.64(-03)	5.21(-03)	1.87(-02)
2000	5.78(-04)	1.40(-04)	4.25(-04)	6.96(-04)	2.14(-04)	4.67(-04)
	1.60(-03)	8.61(-05)	2.59(-04)	4.35(-04)	1.48(-04)	6.83(-04)
	2.15(-03)	1.21(-03)	3.65(-03)	6.06(-03)	5.39(-03)	2.09(-02)
3000	4.49(-04)	1.08(-04)	3.26(-04)	5.37(-04)	1.63(-04)	3.52(-04)
	2.10(-03)	1.11(-04)	3.35(-04)	5.63(-04)	2.61(-04)	9.97(-04)
	1.95(-03)	1.08(-03)	3.24(-03)	5.39(-03)	5.61(-03)	2.40(-02)
4500	3.30(-04)	7.91(-05)	2.39(-04)	3.94(-04)	1.19(-04)	2.56(-04)
	2.39(-03)	1.25(-04)	3.78(-04)	6.33(-04)	4.17(-04)	1.34(-03)
	1.72(-03)	9.32(-04)	2.81(-03)	4.66(-03)	5.86(-03)	2.80(-02)
6700	2.36(-04)	5.65(-05)	1.70(-04)	2.80(-04)	8.50(-05)	1.81(-04)
	2.43(-03)	1.27(-04)	3.85(-04)	6.42(-04)	6.18(-04)	1.68(-03)
	1.49(-03)	7.83(-04)	2.36(-03)	3.91(-03)	6.17(-03)	3.32(-02)
10000	1.64(-04)	3.93(-05)	1.19(-04)	1.97(-04)	5.92(-05)	1.26(-04)
	2.29(-03)	1.19(-04)	3.62(-04)	6.01(-04)	8.73(-04)	2.05(-03)

 

 

Table 12: Same as Table 10 but for the Mg XI

$T_{\rm e}$/Z3	$^{3} {\rm S}_{1}$	$^{3} {\rm P}_{0}$	$^{3} {\rm P}_{1}$	$^{3} {\rm P}_{2}$	$^{1} {\rm S}_{0}$	$^{1} {\rm P}_{1}$
	1.74(-03)	1.05(-03)	3.18(-03)	5.28(-03)	3.39(-03)	1.06(-02)
400	4.41(-04)	1.16(-04)	3.51(-04)	5.86(-04)	1.93(-04)	4.49(-04)
	4.40(-05)	2.59(-06)	7.75(-06)	1.32(-05)	2.40(-06)	2.00(-05)
	1.72(-03)	1.04(-03)	3.11(-03)	5.18(-03)	3.44(-03)	1.10(-02)
600	5.17(-04)	1.32(-04)	3.97(-04)	6.61(-04)	2.10(-04)	4.74(-04)
	1.81(-04)	1.02(-05)	3.06(-05)	5.21(-05)	1.07(-05)	7.46(-05)
	1.69(-03)	1.00(-03)	3.01(-03)	5.00(-03)	3.50(-03)	1.18(-02)
900	5.11(-04)	1.28(-04)	3.84(-04)	6.35(-04)	1.97(-04)	4.39(-04)
	4.65(-04)	2.56(-05)	7.68(-05)	1.30(-04)	3.19(-05)	1.85(-04)
	1.63(-03)	9.50(-04)	2.85(-03)	4.73(-03)	3.58(-03)	1.26(-02)
1350	4.45(-04)	1.10(-04)	3.30(-04)	5.45(-04)	1.67(-04)	3.65(-04)
	8.56(-04)	4.66(-05)	1.40(-04)	2.37(-04)	7.25(-05)	3.50(-04)
	1.53(-03)	8.77(-04)	2.65(-03)	4.38(-03)	3.69(-03)	1.39(-02)
2000	3.60(-04)	8.75(-05)	2.63(-04)	4.35(-04)	1.31(-04)	2.87(-04)
	1.24(-03)	6.66(-05)	2.01(-04)	3.38(-04)	1.35(-04)	5.46(-04)
	1.41(-03)	7.92(-04)	2.40(-03)	3.96(-03)	3.82(-02)	1.57(-02)
3000	2.70(-04)	6.57(-05)	1.85(-04)	3.25(-04)	9.77(-05)	2.12(-04)
	1.52(-03)	8.15(-05)	2.47(-04)	4.14(-04)	2.28(-04)	7.72(-04)
	1.27(-03)	6.96(-04)	2.11(-03)	3.48(-03)	3.99(-03)	1.80(-02)
4500	1.94(-04)	4.72(-05)	1.42(-04)	2.34(-04)	7.04(-05)	1.52(-04)
	1.65(-03)	8.78(-05)	2.68(-04)	4.47(-04)	3.54(-04)	1.01(-03)
	1.11(-03)	5.95(-04)	1.81(-03)	2.98(-03)	4.18(-03)	2.12(-02)
6700	1.37(-04)	3.33(-05)	9.97(-05)	1.65(-04)	4.97(-05)	1.07(-04)
	1.63(-03)	8.60(-05)	2.66(-04)	4.40(-04)	5.13(-04)	1.26(-03)
	9.45(-04)	4.93(-04)	1.51(-03)	2.47(-03)	4.39(-03)	2.51(-02)
10000	9.47(-05)	2.31(-05)	6.91(-05)	1.14(-04)	3.42(-05)	7.37(-05)
	1.49(-03)	7.83(-05)	2.46(-04)	4.02(-04)	7.12(-04)	1.52(-03)

 

 

Table 13: Same as Table 10 but for the Si XIII

$T_{\rm e}$/Z3	$^{3} {\rm S}_{1}$	$^{3} {\rm P}_{0}$	$^{3} {\rm P}_{1}$	$^{3} {\rm P}_{2}$	$^{1} {\rm S}_{0}$	$^{1} {\rm P}_{1}$
	1.26(-03)	7.63(-04)	2.31(-03)	3.81(-03)	2.51(-03)	8.07(-03)
400	3.62(-04)	9.39(-05)	2.82(-04)	4.69(-04)	1.50(-04)	3.41(-04)
	5.44(-05)	3.11(-06)	9.32(-06)	1.60(-05)	3.18(-06)	2.31(-05)
	1.24(-03)	7.45(-04)	2.25(-03)	3.71(-03)	2.56(-03)	8.46(-03)
600	3.88(-04)	9.84(-05)	2.95(-04)	4.88(-04)	1.52(-04)	3.39(-04)
	1.87(-04)	1.04(-05)	3.13(-05)	5.34(-05)	1.22(-05)	7.49(-05)
	1.21(-03)	7.13(-04)	2.16(-03)	3.57(-03)	2.60(-03)	9.00(-03)
900	3.59(-04)	9.00(-05)	2.68(-04)	4.45(-04)	1.36(-04)	3.00(-04)
	4.23(-04)	2.34(-05)	7.01(-05)	1.19(-04)	3.28(-05)	1.69(-04)
	1.16(-03)	6.70(-04)	2.04(-03)	3.34(-03)	2.67(-03)	9.79(-03)
1350	3.01(-04)	7.44(-05)	2.22(-04)	3.66(-04)	1.11(-04)	2.44(-04)
	7.14(-04)	3.91(-05)	1.18(-04)	2.00(-04)	6.96(-05)	3.00(-04)
	1.09(-03)	6.16(-04)	1.88(-03)	3.08(-03)	2.75(-03)	1.08(-02)
2000	2.34(-04)	5.78(-05)	1.72(-04)	2.84(-04)	8.54(-05)	1.87(-04)
	9.68(-04)	5.27(-05)	1.60(-04)	2.69(-04)	1.24(-04)	4.51(-04)
	9.88(-04)	5.52(-04)	1.69(-03)	2.75(-03)	2.86(-03)	1.22(-02)
3000	1.72(-04)	4.25(-05)	1.27(-04)	2.09(-04)	6.26(-05)	1.36(-04)
	1.14(-03)	6.17(-05)	1.89(-04)	3.16(-04)	2.02(-04)	6.20(-04)
	8.78(-04)	4.80(-04)	1.48(-03)	2.39(-03)	2.99(-03)	1.41(-02)
4500	1.22(-04)	3.03(-05)	9.01(-05)	1.48(-04)	4.35(-05)	9.61(-05)
	1.19(-03)	6.42(-05)	2.00(-04)	3.30(-04)	3.06(-04)	7.98(-04)
	7.66(-04)	4.06(-04)	1.28(-03)	2.03(-03)	3.13(-03)	1.66(-02)
6700	8.54(-05)	2.12(-05)	6.33(-05)	1.03(-04)	3.10(-05)	6.75(-05)
	1.14(-03)	6.13(-05)	1.95(-04)	3.17(-04)	4.36(-04)	9.81(-04)
	6.47(-04)	3.32(-04)	1.07(-03)	1.66(-03)	3.29(-03)	1.99(-02)
10000	5.88(-05)	1.46(-05)	4.35(-05)	7.15(-05)	2.14(-05)	4.67(-05)
	1.02(-03)	5.46(-05)	1.80(-04)	2.86(-04)	5.97(-04)	1.17(-03)

 

 

Table 14: Energy of the three main X-ray lines of C V, N VI, O VII, Ne IX, Mg XI and Si XIII, as well as the corresponding wavelength in Å, in parentheses. w corresponds to the resonance line, x+y corresponds to the intercombination lines (here too close to be separated) and z corresponds to the forbidden line

Multiplet	C V	N VI	O VII	Ne IX	Mg XI	Si XIII
w	307.88	430.65	574.00	921.82	1357.07	1864.44
	(40.27)	(28.79)	(21.60)	(13.45)	(9.17)	(6.65)
x+y	304.41	426.36	568.74	915.02	1343.28	1853.29
	(40.73)	(29.08)	(21.80)	(13.55)	(9.23)	(6.69)
z	298.97	419.86	561.02	905.00	1331.74	1839.54
	(41.47)	(29.53)	(22.10)	(13.70)	(9.31)	(6.74)

We note that for all temperatures (low and high), we have included in the line ratio calculations, RR contribution (direct + upper-level radiative cascade), and collisional excitations inside the n=2 shell. For high temperature plasmas, the CE contribution (direct + resonance + cascade) from the ground level (n=1 shell, 1s²) should be included in the calculations as well as DR (direct + cascade). Figure 5 displays these different contributions which populate a given n=2 level.

As emphasized previously, the cascade contribution from n>2 levels, especially for the ³S₁ level, should be taken into account in line ratio calculations since this level is responsible for the forbidden component (z) line, which appears in both ratios R and G. For a pure photoionized plasma, when no upper level radiative cascade contribution is included in the RR rates, R and G could be underestimated by 6-10% (for O VII). In a hybrid plasma, where collisional processes from the ground level are not negligible, the ratio R is lower by $\sim20$% at $T=3.6\,10^{6}$K, when no cascades from upper levels are taken into account. In a similar way, the value of G would be underestimated.

We also point out the importance of taking into account the branching ratios in the calculations of x and y lines. $B_{{x}}= A_{5\to1}/(A_{5\to1}+A_{5\to2}$), and $B_{{y}}=A_{4\to1}/(A_{4\to1}+A_{4\to2}$) are respectively the branching ratios of the x and y lines ( $A_{{j \to i}}$ being the transition probability from level j to level i, see Fig. 1). Branching ratios are very important in the case of light nuclear charge (Z), as shown in Fig. 6, for C V, $A_{5\to 1}\ll A_{5\to 2}$ as well $A_{4\to 1}<A_{4\to 2}$. When Z increases, most branching ratios become less important but nevertheless some of them should be included in the calculations. Without these branching ratios the intensities of the intercombination lines x and y could be overestimated, resulting in an underestimate of the ratio R. This could lead to huge discrepancies for the value of R as well as for G.

Figure 6: Simplified Gotrian diagrams for C V and Si XIII. Thick curves correspond to the strongest radiative transitions ( $A_{{i} \to { {j}}}$ in s-1), and thin curves correspond to lower values

Figure 7: G (=(x+y+z)/w) is reported as a function of electronic temperature ($T_{\rm e}$) for C V, N VI, O VII, Ne IX, Mg XI, and Si XIII in the density range where G is not dependent on density (see Sect. 3.2). The number (m) associated to each curves means $X_{{\rm ion}}$ = $10^{ {\rm m}}$, where $X_{{\rm ion}}$ is the ratio of H-like ions over He-like ions. As an example for Oxygen (Z=8) it corresponds to ratio of the relative ionic abundance of O VIII/O VII ground state population

Figure 8: In case of pure photoionized plasmas (i.e. RR dominant at low temperature and DR dominant at high temperature), ratio R (=z/(x+y)) is reported as a function of $n_{\rm e}$ for C V, N VI, O VII, Ne IX, Mg XI, and Si XIII at different electronic temperatures ($T_{\rm e}$ in Kelvin). For low temperatures (the two first reported here: solid curves and dot-dashed curves), the value of R is independent of the value of $X_{{\rm ion}}$. As the temperature increases, $X_{{\rm ion}}$ is high enough to maintain recombination dominant compared to collisional excitation from the ground level: $\sim$ 102 and 103-4 (for increasing temperature: respectively for long-dashed curves and short-dashed curves)

Figure 9: In case of hybrid plasmas (partially photoionized: recombination plus collisional excitation from the ground level), the ratio R (=z/(x+y)) is reported as a function of $n_{\rm e}$ for C V, N VI, O VII, Ne IX, Mg XI, and Si XIII at different values of $X_{{\rm ion}}$ (=H-like/He-like ionic fraction). R is calculated at the temperature corresponding to the maximum of the He-like ion abundance for a collisional plasma (see Arnaud & Rothenflug [1985]). Solid curves: the lowest values of $X_{{\rm ion}}$ corresponds to hybrid plasmas, and the highest value of $X_{{\rm ion}}$ to pure photoionized plasmas. Long-dashed curves: $X_{{\rm ion}}$ is equal to the ratio H-like/He-like in a case of collisional plasma (from Arnaud & Rothenflug [1985]). Note: for C V, N VI and O VII at these temperatures, the curves for $X_{{\rm ion}}=100$ and 10000 are indistinguishable

Figure 10: At left: This figure reports for each ion treated in this paper the two decades (approximatively) where the ratio R is strongly sensitive to the density. At right: the approximative range of temperatures for each ion where the plasma can be considered purely photoionized, independent of the $X_{{\rm ion}}$ value

Figure 11: O VII theoretical spectra constructed using the RGS (XMM) resolving power ( $E/\Delta E$) for three values of density (in cm-3). This corresponds (approximatively) to the range where the ratio R is very sensitive to density. z: forbidden lines, x+y: intercombination lines and w: resonance line. At left: "hybrid plasma'' at $T_{\rm e}=1.5\,10^{6}$K and $X_{{\rm ion}}=1$; At right: "pure'' photoionized plasma at $T_{\rm e}=10^{5}$K (at this temperature this part of the spectra are independent of the value of $X_{{\rm ion}}$, see Fig. 7). Note: the intensities are normalized so as the sum of the lines to be equal to unity

  
3.2 Ionizing process diagnostics

First of all, the ionization processes that occur should be determined. High resolution spectra enable us to measure the intensities of the forbidden (z), intercombination ( x+y) and resonance (w) lines of a He-like ion. They give an indication of the ionization processes which occur in the gas using the relative intensity of the resonance line w compared to those of the forbidden z and the intercombination x+y lines. This corresponds to the G ratio (see Eq. (2)). RR to the ³S and ³P (triplet) levels is more than a factor 4 greater than the ¹P (singlet) level, due to the higher statistical weights of the triplet levels. When RR dominates compared to CE from the ground level (1s²), this results in a very intense forbidden z (³S₁ level) or (x+y) (³P_1,2 levels) lines, compared to the resonance w line (¹P₁ level). On the contrary, when CE from the ground level dominates compared to RR, the ¹P₁ level is preferentially populated (high value of $\Upsilon$(1s²¹S$_{0}\to$1s2p¹P₁)), thus implying an intense resonance w line. We also introduce the parameter $X_{{\rm ion}}$ which is the relative ionic abundance of the H-like and He-like ions. As an example for oxygen, it corresponds to the ratio of O VIII/O VII ground state population. A low value of $X_{{\rm ion}}$ means that the H-like ion relative abundance is small compared to the He-like one and thus CE from the 1s² ground level is dominant compared to RR (H-like$\to$He-like), when the temperature is high enough to permit excitation from the ground level. Figure 7 displays the ratios G as a function of electronic temperature ($T_{\rm e}$) for different values of $X_{{\rm ion}}$. The range of temperatures (low values) where the ratio (>4 see Sect. 3.2) is almost independent of $T_{\rm e}$ and $X_{{\rm ion}}$ occurs for a plasma dominated by RR (pure photoionized plasmas).

At higher temperatures, i.e. large enough to permit excitation from the ground level to upper levels, G becomes sensitive to both parameters ($T_{\rm e}$, $X_{{\rm ion}}$). High values of $X_{{\rm ion}}$ favour mainly DR (H-like ions towards He-like ions), but for photoionized plasma such high temperatures (where G<4) are probably extreme cases (i.e. not realistic) for WA plasmas. On the contrary, for lower values of $X_{{\rm ion}}$ the lines are produced mainly by collisional excitation ("hybrid'' plasma in our nomenclature). A value of G<4 will be the signature of a plasma where collisional processes are no longer negligible and even be dominant compared to recombination. We should notice that this is no more the case when G is sensitive to $n_{\rm e}$, i.e. when the resonance w line becomes sensitive to density due to the depopulation of the 1s2s¹S₀ level to the 1s2p¹P₁ level (see also Figs. 4-6-9 in Gabriel & Jordan [1972]). In conclusion, the relative intensity of the resonance w line, compared to the forbidden z and the intercombination (x+y) lines, contains informations about the ionization processes that occur: a weak w line compared to the z or the (x+y) lines corresponds to a pure photoionized plasma. It leads to a ratio of G=(z+x+y)/w>4. On the contrary a strong w line corresponds to a hybrid plasma (or even a collisional plasma), where collisional processes are not negligible and may even dominate (see Sect. 3.3.2). In this case, w is at least as intense as the z or x+y lines.

  
3.3 Density diagnostic

In the low density limit, all n=2 states are populated by electron impact directly or via upper-level radiative cascade from He-like ground state and by H-like recombination (see Figs. 1 and 5). These states decay radiatively directly or by cascade to the ground level. The relative intensities of the three intense lines are then independent of density. As $n_{\rm e}$ increases from the low density limit, some of these states (1s2s³S₁ and ¹S) are depleted by collision to the nearby states where $n_{{\rm crit}}$C$\sim$A, with C being the collisional coefficient rate, A being the radiative transition probabilities from n=2 to n=1 (ground state), and $n_{{\rm crit}}$ being the critical density. Collisional excitation depopulates first the 1s2s ³S₁ level (metastable) to the 1s2p ³P_0,1,2 levels. The intensity of z decreases and those of x and y increase, hence implying a reduction of the ratio R (according to Eq. (1)). For much higher densities, 1s2s¹S₀ is also depopulated to 1s2p¹P₁.

3.3.1 Pure photoionized plasmas

As explained previously, pure photoionized plasmas are characterized by a weak resonance w line compared to the forbidden z or the intercombination (x+y) lines. The ratio R as a function of electronic density $n_{\rm e}$ is reported in Fig. 8 for C V, N VI, O VII, Ne IX, Mg XI, Si XIII at different values of $T_{\rm e}$.

For low values of $T_{\rm e}$ corresponding to the density range where G is independent of $X_{{\rm ion}}$ (Fig. 8), R is almost insensitive to temperature. But in the case of high temperature (with a high $X_{{\rm ion}}$ value so that the medium is dominated by recombination), the value of R is larger. Thus in the density range where R takes a constant value (i.e. low density values), a high value of R corresponds to a high temperature. This also imply a very intense H-like line (K$_{\alpha}$) since the ratio $X_{{\rm ion}}$ = H-like/He-like need to be large enough so that the gas is dominated by recombinations (see caption of the Fig. 7).

  
3.3.2 Hybrid plasmas

Hybrid plasmas, where both recombination and collisional processes occur, are characterized by G < 4, i.e. an intense resonance w line. For high temperature, the ratio R as a function of electronic density $n_{\rm e}$ is reported in Fig. 9 for C V, N VI, O VII, Ne IX, Mg XI, Si XIII for different values of $X_{{\rm ion}}$. R is calculated at the temperature corresponding to the maximum abundance of the He-like ion for a collisional plasma (see Arnaud & Rothenflug [1985]). In the low density limit, in the range where R is independent of density, its value is correlated with $X_{{\rm ion}}$. However for intermediate values of $X_{{\rm ion}}$, R is similar to the R calculated for photoionized plasmas (see also Fig. 8), especially for low charge ions (C V, N VI and O VII). Thus discriminating between ionization processes is difficult using this R ratio. As one can also see, at higher densities this ratio is almost insensitive to the $X_{{\rm ion}}$ value.