EDP Sciences
Free access
Issue A&A
Volume 495, Number 1, February III 2009
Page(s) 359 - 362
Section Atomic, molecular, and nuclear data
DOI http://dx.doi.org/10.1051/0004-6361:200811222
Published online 14 January 2009


Ultraviolet and extreme-ultraviolet line ratio diagnostics for O IV

F. P. Keenan - P. J. Crockett - K. M. Aggarwal - D. B. Jess - M. Mathioudakis

Astrophysics Research Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland, UK

Received 24 October 2008 / Accepted 18 December 2008

Abstract
Aims. We generate theoretical ultraviolet and extreme-ultraviolet emission line ratios for O IV and show their strong versatility as electron temperature and density diagnostics for astrophysical plasmas.
Methods. Recent fully relativistic calculations of radiative rates and electron impact excitation cross sections for O IV, supplemented with earlier data for A-values and proton excitation rates, are used to derive theoretical O IV line intensity ratios for a wide range of electron temperatures and densities.
Results. Diagnostic line ratios involving ultraviolet or extreme-ultraviolet transitions in O IV are presented, that are applicable to a wide variety of astrophysical plasmas ranging from low density gaseous nebulae to the densest solar and stellar flares. Comparisons with observational data, where available, show good agreement between theory and experiment, providing support for the accuracy of the diagnostics. However, diagnostics are also presented involving lines that are blended in existing astronomical spectra, in the hope this might encourage further observational studies at higher spectral resolution.

Key words: atomic processes - Sun: UV radiation - planetary nebulae: general - ultraviolet: general

1 Introduction

Ultraviolet and extreme-ultraviolet emission lines arising from transitions in B-like O IV are detected from a wide variety of astronomical sources, ranging from the Sun (Sandlin et al. 1986) to other stars (Christian et al. 2004), gaseous nebulae (Feibelman 1997) and supernova remnants (Blair et al. 1991). The diagnostic potential of these lines to provide electron temperature ($T_{\rm e}$) and density ($N_{\rm e}$) diagnostics for the emitting plasma was first shown by Flower & Nussbaumer (1975), who also calculated radiative rates plus electron and proton impact excitation cross sections for the ion. Since then, many authors have generated atomic data for O IV that have subsequently been used to derive theoretical diagnostic line ratios (see Tayal 2006, and references therein).

Very recently, Aggarwal & Keenan (2008) have employed the fully relativistic GRASP and Dirac RMATRX codes to calculate radiative rates and electron impact excitation cross sections, respectively, for all transitions among the energetically lowest 75 fine-structure levels of O IV. These results are the most extensive currently available for O IV, and also should be the most reliable, at least for the excitation cross sections, as discussed in detail by Aggarwal & Keenan. In this paper we use these data, supplemented with previous highly accurate calculations for radiative rates and proton excitation cross sections, to derive theoretical O IV ultraviolet and extreme-ultraviolet emission line ratios applicable to a wide range of astrophysical plasmas. We demonstrate the versatility of O IV plasma diagnostics, which can provide temperature and density estimates for a wide variety of astronomical sources ranging from low density gaseous nebulae up to the densest solar and stellar flares.

2 Atomic data and theoretical line ratios

The model ion for O IV consisted of the 75 fine-structure levels arising from the 2s22p, 2s2p2, 2p3, 2s23$\ell$ ($\ell$ = s, p, d), 2s2p3$\ell$ ($\ell$ = s, p, d) and 2s24$\ell$ ($\ell$ = s, p, d, f) configurations. Energies for all these levels were obtained from the compilation of experimental values by the National Institute of Standards and Technology, which may be found at their website http://physics.nist.gov/PhysRefData/. Test calculations including additional levels, such as those arising from the 2s25$\ell$ and 2s2p4$\ell$ configurations, were found to have a negligible effect on the theoretical line ratios considered in the present paper.

Einstein A-coefficients for transitions in O IV were obtained from the following sources: (i) Galavís et al. (1998) for the forbidden 2s22p 2P1/2-2s22p 2P3/2 transition; (ii) Corrégé & Hibbert (2002) for the 2s22p 2PJ-2s2p2 4P $_{J^{\prime}}$ intercombination lines; (iii) Corrégé & Hibbert (2004) for allowed and intercombination lines among the 2s22p, 2s2p2, 2p3 and 2s23$\ell$ ($\ell$ = s, p, d) levels; (iv) Aggarwal & Keenan (2008) for all remaining transitions. For electron impact excitation rates, we have adopted the results of Aggarwal & Keenan, which contain several improvements over previous calculations for O IV undertaken with the RMATRX code (Zhang et al. 1994; Tayal 2006), including the greatest number of levels and the largest range of partial waves. They are hence probably the most accurate currently available for this ion, as discussed in detail by Aggarwal & Keenan. However, there is also scope for improvement, mainly due to the fact that the wavefunctions adopted in the calculations of Aggarwal & Keenan are not as accurate as those of some other workers, such as Tachiev & Froese-Fischer (2000) and Corrégé & Hibbert (2002). Indeed, this is why we have adopted the A-values of Corrégé & Hibbert (2002, 2004) where possible, as their results have an estimated uncertainty of only $\pm $5%, compared to $\pm $20% for those of Aggarwal & Keenan. The limitations in the wavefunctions of Aggarwal & Keenan may directly affect the subsequent determination of excitation rates, both for allowed and forbidden transitions. This is because for the weak allowed transitions, the A-values of Aggarwal & Keenan differ by up to 50% with those of Tachiev & Froese-Fischer (2000) and Corrégé & Hibbert (2004), while some of the energy levels show discrepancies of up to 8% with the experimental values (see Tables 1 and 2 of Aggarwal & Keenan). Nevertheless, the estimated accuracy of the Aggarwal & Keenan excitation rate data is $\pm $20% for a majority of transitions, and should be the most reliable currently available for O IV.

As noted by, for example, Seaton (1964), excitation by protons will be important for the 2s22p 2P1/2-2s22p 2P3/2 transition, and in the present analysis we have used the theoretical results of Foster et al. (1996). However, Flower & Nussbaumer (1975) have pointed out that proton excitation should also be included for the 2s2p2 4PJ-2s2p2 4P $_{J^{\prime}}$ transitions in B-like ions, and for these rates we have adopted the calculations of Foster et al. (1997). Both the Foster et al. (1996, 1997) data are estimated to be accurate to $\pm $10%.

Using the above atomic data in conjunction with a recently updated version of the statistical equilibrium code of Dufton (1977), relative O IV level populations and hence emission line strengths were calculated for two grids of electron temperature ($T_{\rm e}$) and density ($N_{\rm e}$) values. The first grid (for $T_{\rm e}$ = 10 000, 15 000, 20 000 and 30 000 K; $N_{\rm e}$ = 102-106 cm-3 in steps of 0.1 dex) is appropriate to nebular plasmas, while the second ($T_{\rm e}$ = 104.8-105.6 K in steps of 0.1 dex; $N_{\rm e}$ = 108-1014 cm-3 in steps of 0.1 dex) is for solar/stellar plasma conditions. In particular, the adopted temperature range for the latter covers that over which O IV has a fractional abundance in ionization equilibrium of N(O IV/N(O) $\geq$ 0.006 (Bryans et al. 2009), and hence should be appropriate to most coronal-type plasmas. Our results are too extensive to reproduce here, as with 75 fine-structure levels in our calculations we have intensities for 2775 transitions at each of the 530 possible ($T_{\rm e}$, $N_{\rm e}$) combinations considered. However, results involving any line pair, in either photon or energy units, are freely available from one of the authors (FPK) by email on request. Given errors in the adopted atomic data of between $\pm $5% and $\pm $20% (see above), we would expect our theoretical ratios to be accurate to better than $\pm $15%.

3 Results and discussion

The O IV intercombination multiplet around 1400 Å provides excellent electron density diagnostics for both nebular and solar plasmas, as shown in Figs. 1-4, where we plot the emission line ratios R1 = I(1407.3 Å)/I(1401.1 Å), R2 = I(1404.7 Å)/I(1401.1 Å) and R3 = I(1407.3 Å)/I(1404.7 Å) as a function of $T_{\rm e}$ and $N_{\rm e}$. The transitions corresponding to these lines are listed in Table 1, as are those for the other O IV features discussed in this paper. We note that the ratios R4 = I(1399.7 Å)/I(1401.1 Å) and R5 = I(1397.2 Å)/I(1401.1 Å) have the same $T_{\rm e}$ and $N_{\rm e}$ dependence as R1 and R2, respectively (due to common upper levels), but with R4 = 1.02 $\times$ R1 and R5 = 0.130 $\times$ R2.

 \begin{figure}
\par\includegraphics[width=9cm,clip]{1222fig1.eps}
\end{figure} Figure 1:

The I(1407.3 Å)/I(1401.1 Å) line intensity ratio in O IV, where I is in energy units, plotted as a function of logarithmic electron density ($N_{\rm e}$ in cm-3) at electron temperatures of $T_{\rm e}$ = 10 000, 15 000, 20 000 and 30 000 K.

Open with DEXTER

 \begin{figure}
\par\includegraphics[width=9cm,clip]{1222fig2.eps}
\end{figure} Figure 2:

Same as Fig. 1, but for the I(1404.7 Å)/I(1401.1 Å) ratio.

Open with DEXTER

The above theoretical ratios are in good agreement with observations for gaseous nebulae, such as those by Keenan et al. (1993). For example, for the planetary nebula NGC 7662, Keenan et al. measured R1 = 0.30, R2 = 0.69 and R4 = 0.29, implying electron densities of log $N_{\rm e}$ = 3.5, 4.0 and 3.5, respectively, from Figs. 1 and 2. These values are consistent, and also in agreement with the electron densities derived for NGC 7662 from line ratios in species with similar ionization potentials and hence spatial distributions to O IV, such as I(4711 Å)/I(4740 Å) in Ar IV and I(2424 Å)/I(2422 Å) in Ne IV, both of which indicate log $N_{\rm e}$ = 3.5 (Keenan et al. 1997, 1998). In addition, we note that Keenan et al. (2002) have measured O IV line ratios for the symbiotic star RR Tel. The diagnostic ratios for other species in the RR Tel spectrum, ranging from Al II to O V, indicate log $N_{\rm e}$ $\simeq$ 5-8 (see Keenan et al. 2002, and references therein), over which density interval the theoretical values of R1 through R5 are predicted to be effectively constant (see Figs. 1 and 2). Once again, there is excellent agreement between theory and observation, with measured and predicted values of (theory in brackets) R1 = 0.16 $\pm $ 0.02 (0.18), R2 = 0.54 $\pm $ 0.05 (0.60), R4 = 0.17 $\pm $ 0.02 (0.18) and R5 = 0.077 $\pm $ 0.008 (0.077).

In existing solar spectra, such as those from the HRTS and SOHO/SUMER instruments, the O IV 1404.7 Å line is significantly blended with S IV (Brage et al. 1996; Keenan et al. 2002), although we note that the blending is negligible under nebular plasma conditions (Keenan et al. 2002). Additionally, the 1397.2 Å feature is very weak in solar spectra, and possibly blended, and hence its intensity should usually be considered an upper limit (Brage et al. 1996). However, the remaining useable density diagnostic line ratios R1 and R4 do provide consistent derivations of $N_{\rm e}$. For example, for Active Region B at +2 $^{\prime\prime}$ relative to the limb, Feldman & Doschek (1978) measured R1 = 0.20 and R4 = 0.19 from Skylab/S082A spectra, which both imply log $N_{\rm e}$ = 10.1 from Fig. 3, in good agreement with the value of log $N_{\rm e}$ = 10.2 found from line ratios in N IV, which is formed at the same temperature as O IV (Keenan et al. 1994).

 \begin{figure}
\par\includegraphics[width=9cm,clip]{1222fig3.eps}
\end{figure} Figure 3:

The I(1407.3 Å)/I(1401.1 Å) line intensity ratio in O IV, where I is in energy units, plotted as a function of logarithmic electron density ($N_{\rm e}$ in cm-3) at the electron temperature of maximum O IV fractional abundance in ionization equilibrium, $T_{\rm e}$ = 105.2 K (Bryans et al. 2009), plus $\pm $0.2 dex about this value.

Open with DEXTER

 \begin{figure}
\par\includegraphics[width=9cm,clip]{1222fig4.eps}
\end{figure} Figure 4:

Same as Fig. 3, but for the I(1407.3 Å)/I(1404.7 Å) ratio.

Open with DEXTER

Table 1:   Summary of O IV transitions.

 \begin{figure}
\par\includegraphics[width=9cm,clip]{1222fig5.eps}
\end{figure} Figure 5:

Same as Fig. 3, but for the I(1343.5 Å)/I(1407.3 Å) ratio.

Open with DEXTER

 \begin{figure}
\par\includegraphics[width=8.9cm,clip]{1222fig6.eps}
\end{figure} Figure 6:

The I(790.20 Å)/I(554.51 Å) line intensity ratio in O IV, where I is in energy units, plotted as a function of logarithmic electron temperature ($T_{\rm e}$in K) at logarithmic electron densities ($N_{\rm e}$ in cm-3) of log $N_{\rm e}$ = 8-13.

Open with DEXTER

The intercombination line ratios in O IV only provide useful electron density diagnostics for values of $N_{\rm e}$ up to about 1012 cm-3 (see Figs. 3 and 4). However, Kastner & Bhatia (1984) have pointed out that the allowed lines of O IV arising from 2s2p2 2P-2p3 2D transitions lie only $\sim$60 Å from the intercombination multiplet, and their intensity ratios are very sensitive to the electron density for $N_{\rm e}$ > 1011 cm-3. They hence should provide good $N_{\rm e}$-diagnostics for very high density astronomical plasmas such as solar and stellar flares. In Fig. 5 we plot the ratio R6 = I(1343.5 Å)/I(1407.3 Å) as a function of both $T_{\rm e}$ and $N_{\rm e}$, as the 1343.5 Å transition is the only line in the 2s2p2 2P-2p3 2D multiplet which is unblended in existing solar spectra (Cook et al. 1994). The measured values of R6 = 0.89 and 0.90 for the flares of 1973 August 9 and 1973 September 7, from Skylab/S082B spectra (Cook et al. 1994), both indicate log $N_{\rm e}$ = 12.5 at the temperature of maximum fractional abundance for O IV in ionization equilibrium, $T_{\rm e}$ = 105.2 K (Bryans et al. 2009). These are consistent with the values of log $N_{\rm e}$ $\simeq$ 12.3 determined for high density flares using extreme-ultraviolet lines of O V, formed at a similar temperature to O IV (Keenan et al. 1991).

For temperature diagnostics, Flower & Nussbaumer (1975) have shown that the intensity ratio of lines within the 2s22p 2P-2s2p2 2D multiplet at $\sim$790 Å to those in 2s22p 2P-2s2p2 2P at $\sim$554 Å allows $T_{\rm e}$ to be estimated for the O IV emitting region of a plasma. This is shown in Fig. 6, where we plot the R7 = I(790.20 Å)/I(554.51 Å) ratio as a function of $T_{\rm e}$ and $N_{\rm e}$. Similarly, Curdt et al. (1997) have noted that the R8 = I(779.91 Å)/I(787.71 Å) ratio is a $T_{\rm e}$-diagnostic, and this is plotted in Fig. 7. An inspection of the two figures reveals that R7 is in principle a better temperature diagnostic than R8, as it is less sensitive to the adopted value of $N_{\rm e}$. However, the emission lines in R8 are much closer in wavelength and hence the ratio is more likely to be reliably measured. Indeed, Curdt et al. have determined R8 = 0.033 from a SOHO/SUMER spectrum of the solar disk, which indicates $T_{\rm e}$ $\simeq$ 105.1-105.3 K from Fig. 7 (the exact value depending on the adopted density), in good agreement with the temperature of maximum fractional abundance in ionization equilibrium for O IV, $T_{\rm e}$ = 105.2 K (Bryans et al. 2009). Unfortunately, to our knowledge, the R7 ratio has not been measured due to the low spectral resolution of existing solar observations spanning the 554-790 Å wavelength range. However, O'Shea et al. (1996) have determined values of the multiplet intensity ratio I(790 Å)/I(554 Å) for several solar features from spectra obtained with the S-055 spectrometer on Skylab. These measurements lie in the range 0.47-0.56, and imply temperatures within $\sim$0.2 dex of that of maximum fractional abundance for O IV.

 \begin{figure}
\par\includegraphics[width=8.8cm,clip]{1222fig7.eps}
\end{figure} Figure 7:

Same as Fig. 6, but for the I(779.91 Å)/I(787.71 Å) ratio.

Open with DEXTER

Under solar plasma conditions, O IV extreme-ultraviolet line ratios containing a component of the 2s2p2 4P-2p3 4S multiplet at $\sim$625 Å are strongly density sensitive (O'Shea et al. 1996). Unfortunately, in existing solar spectra the transitions - which lie at wavelengths of 624.62, 625.13 and 625.85 Å - are all blended with the strong Mg X resonance line at 624.94 Å. However, if the O IV features could be resolved, then in conjunction with other relatively nearby O IV lines they would allow the temperature and density of the O IV emitting region of a plasma to be simultaneously determined via ratio - ratio diagrams, as illustrated in Fig. 8.

 \begin{figure}
\par\includegraphics[width=8.8cm,clip]{1222fig8.eps}
\end{figure} Figure 8:

Plot of the O IV line intensity ratio I(779.91 Å)/I(787.71 Å) against I(625.85 Å)/I(790.20 Å), where I is in energy units, for logarithmic electron temperatures ($T_{\rm e}$ in K) of log $T_{\rm e}$ = 4.8-5.6, and logarithmic electron densities ($N_{\rm e}$ in cm-3) of log $N_{\rm e}$ = 8-13.

Open with DEXTER

In summary, we see that ultraviolet and extreme-ultraviolet emission lines of O IV provide a diverse portfolio of $T_{\rm e}$ and $N_{\rm e}$ diagnostics, applicable to a wide variety of astronomical sources ranging from gaseous nebulae to high electron density stellar flares. The present line ratio calculations, which include the most up-to-date atomic physics data, show good agreement with observations where available, hence providing support for their accuracy. However, higher spectral resolution observations of several O IV lines, such as the components of the 2s2p2 4P-2p3 4S multiplet at $\sim$625 Å, would be very useful to allow their intensities to be reliably measured and employed as diagnostics.

Acknowledgements
This work has been financed by the Science and Technology Facilities Council and Engineering and Physical Sciences Research Council of the United Kingdom, while P.J.C. and D.B.J. are grateful to the Department of Education and Learning (Northern Ireland) for the award of studentships. F.P.K. is grateful to AWE Aldermaston for the award of a William Penney Fellowship.

References


All Tables

Table 1:   Summary of O IV transitions.

All Figures

  \begin{figure}
\par\includegraphics[width=9cm,clip]{1222fig1.eps}
\end{figure} Figure 1:

The I(1407.3 Å)/I(1401.1 Å) line intensity ratio in O IV, where I is in energy units, plotted as a function of logarithmic electron density ($N_{\rm e}$ in cm-3) at electron temperatures of $T_{\rm e}$ = 10 000, 15 000, 20 000 and 30 000 K.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=9cm,clip]{1222fig2.eps}
\end{figure} Figure 2:

Same as Fig. 1, but for the I(1404.7 Å)/I(1401.1 Å) ratio.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=9cm,clip]{1222fig3.eps}
\end{figure} Figure 3:

The I(1407.3 Å)/I(1401.1 Å) line intensity ratio in O IV, where I is in energy units, plotted as a function of logarithmic electron density ($N_{\rm e}$ in cm-3) at the electron temperature of maximum O IV fractional abundance in ionization equilibrium, $T_{\rm e}$ = 105.2 K (Bryans et al. 2009), plus $\pm $0.2 dex about this value.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=9cm,clip]{1222fig4.eps}
\end{figure} Figure 4:

Same as Fig. 3, but for the I(1407.3 Å)/I(1404.7 Å) ratio.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=9cm,clip]{1222fig5.eps}
\end{figure} Figure 5:

Same as Fig. 3, but for the I(1343.5 Å)/I(1407.3 Å) ratio.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.9cm,clip]{1222fig6.eps}
\end{figure} Figure 6:

The I(790.20 Å)/I(554.51 Å) line intensity ratio in O IV, where I is in energy units, plotted as a function of logarithmic electron temperature ($T_{\rm e}$in K) at logarithmic electron densities ($N_{\rm e}$ in cm-3) of log $N_{\rm e}$ = 8-13.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{1222fig7.eps}
\end{figure} Figure 7:

Same as Fig. 6, but for the I(779.91 Å)/I(787.71 Å) ratio.

Open with DEXTER
In the text

  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{1222fig8.eps}
\end{figure} Figure 8:

Plot of the O IV line intensity ratio I(779.91 Å)/I(787.71 Å) against I(625.85 Å)/I(790.20 Å), where I is in energy units, for logarithmic electron temperatures ($T_{\rm e}$ in K) of log $T_{\rm e}$ = 4.8-5.6, and logarithmic electron densities ($N_{\rm e}$ in cm-3) of log $N_{\rm e}$ = 8-13.

Open with DEXTER
In the text


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