The He-like triplets of C v, N vi, O vii, Ne ix, Mg xi, and Si xiii provide another interest- ing density diagnostic for stellar coronae. Two examples are shown in Fig. 11 (right). The spectra show, in order of increasing wavelength, the resonance, the intercombination, and the forbidden line of the O vii triplet. The ratio between the fluxes in the forbidden line and the intercombination line is sensitive to density (Gabriel and Jordan 1969) for the following reason: if the electron collision rate is sufficiently high, ions in the upper
Fig. 11. Left: Term diagram for transitions in He-like triplets. The resonance, intercombination,
and forbidden transitions are marked. The transition from3S1to3P1re-distributes electrons from the upper level of the forbidden transition to the upper level of the intercombination transition, thus making the f/ i line-flux ratio density sensitive. In the presence of a strong UV field, however, the same transition can be induced by radiation as well. Right: He-like triplet of O vii for Capella (black) and Algol (green). The resonance (r), intercombination (i), and forbidden (f) lines are marked. The f/ i flux ratio of Algol is suppressed probably due to the strong UV radiation field of the primary B star (data from Chandra; both figures courtesy of J.-U. Ness)
level of the forbidden transition, 1s2s3S1, do not return to the ground level, 1s2 1S0,
instead the ions are collisionally excited to the upper levels of the intercombination tran- sitions, 1s2p3P1,2, from where they decay radiatively to the ground state (see Fig. 11
for a term diagram). They thus enhance the flux in the intercombination line and weaken the flux in the forbidden line. The measured ratio R = f/i of the forbidden to the intercombination line flux can be written as
R= R0
1+ ne/Nc =
f
i (19)
where R0 is the limiting flux ratio at low densities and Nc is the critical density at which R drops to R0/2. For C v and N vi, the photospheric radiation field needs to be
considered as well because it enhances the3S1–3P1,2 transitions; the same applies to
higher-Z triplets if a hotter star illuminates the X-ray source (see Ness et al. 2001). The tabulated parameters R0and Ncare slightly dependent on the electron temperature in the emitting source; this average temperature can conveniently be confined by the temperature-sensitive G ratio of the same lines, G= (i + f )/r (here, r is the flux in the resonance line 1s2 1S0–1s2p1P1). A recent comprehensive tabulation is given in
Porquet et al. (2001); Table 2 contains relevant parameters for the case of a plasma that is at the maximum formation temperature of the respective ion. A systematic problem with He-like triplets is that the critical density Ncincreases with the formation temperature of the ion, i.e., higher-Z ions measure only high densities at high T , while the lower-density analysis based on C v, N vi, O vii, and Ne ix is applicable only to cool plasma.
Stellar coronal He-like triplets have become popular with Chandra and XMM-Newt- on. For C v, N vi, and O vii, early reports indicated densities either around or below the low density limit, viz. ne ≈ 109–1010 cm−3for Capella (Brinkman et al. 2000; Canizares et al. 2000; Audard et al. 2001b; Mewe et al. 2001; Ness et al. 2001; Phillips et al. 2001), α Cen (Raassen et al. 2003a), Procyon (Ness et al. 2001; Raassen et al. 2002), HR 1099 (Audard et al. 2001a), and II Peg (Huenemoerder et al. 2001). Note that this sample covers an appreciable range of activity. (A conflicting, higher-density measurement, ne ≈ [2–3] × 1010 cm−3, was given by Ayres et al. 2001b for HR1099 and Capella). A low-density limit (log ne < 10.2) is found for Capella also from the
Table 2. Density-sensitive He-like tripletsa
Ion λ(r, i, f )(Å) R0 Nc log nerangeb T rangec(MK)
C v 40.28/40.71/41.46 11.4 6× 108 7.7–10 0.5–2 N vi 28.79/29.07/29.53 5.3 5.3× 109 8.7–10.7 0.7–3 O vii 21.60/21.80/22.10 3.74 3.5× 1010 9.5–11.5 1.0–4.0 Ne ix 13.45/13.55/13.70 3.08 8.3× 1011 11.0–13.0 2.0–8.0 Mg xi 9.17/9.23/9.31 2.66d 1.0× 1013 12.0–14.0 3.3–13 Si xiii 6.65/6.68/6.74 2.33d 8.6× 1013 13.0–15.0 5.0–20
adata derived from Porquet et al. (2001) at maximum formation temperature of ion brange where R is within approximately [0.1,0.9] times R
0 crange of 0.5–2 times maximum formation temperature of ion dfor measurement with Chandra HETGS-MEG spectral resolution
Ne ix triplet (Ness et al. 2003b). First unequivocal reports on significant, higher densities measured in O vii came for very active main-sequence stars such as AB Dor (Güdel et al. 2001b) and YY Gem (Güdel et al. 2001a), indicating neof several times 1010cm−3. The trend for higher densities in more active main-sequence stars is consistently found across various spectral types (Ness et al. 2002a; Raassen et al. 2003b; van den Besselaar et al. 2003), whereas active binaries may reveal either high or low densities (Ness et al. 2002b; Huenemoerder et al. 2001, 2003), and low-activity stars generally show low densities (Ness et al. 2002a). The most recent, comprehensive compilation of these trends can be found in Ness et al. (2004) who surveyed O vii and Ne ix triplets of a sample of 42 stellar systems across all levels of magnetic activity, and in Testa et al. (2004) who studied a sample of 22 stars with Chandra.
As for higher-Z He-like triplets, reports become quite ambiguous, echoing both the results and the problems encountered in the analysis of Fe lines. Mewe et al. (2001) found ne = 3 × 1012 cm−3 – 3× 1013 cm−3 in Capella from Mg xi and Si xiii as measured by the Chandra LETGS. These high values agree with EUVE measurements (e.g., Dupree et al. 1993), but they contradict simultaneous Chandra measurements obtained from Fe xx-xxii (Mewe et al. 2001). Osten et al. (2003) derived densities from He-like triplets, Fe xxi and Fe xxii line ratios over a temperature range of≈ 1 − 15 MK. They found a sharply increasing trend: densities from lines formed below 6 MK point at a modest electron density of a few times 1010 cm−3, while those formed above indicate densities exceeding 1011cm−3, possibly reaching up to a few times 1012cm−3. Somewhat perplexingly, though, the Si xiii triplet that is formed at similar temperatures as Mg xi suggests ne <1011cm−3, and discrepancies of up to an order of magnitude become evident depending on the adopted formation temperature of the respective ion. The trend for an excessively high density implied by Mg can also be seen in the analysis of Capella by Audard et al. (2001b) and Argiroffi et al. (2003).
Clearly, a careful reconsideration of line blends is in order. Testa et al. (2004) have measured densities from Mg xi in a large stellar sample after modeling blends from Ne and Fe, still finding densities up to a few times 1012 cm−3but not reaching beyond 1013cm−3. All measurements from Si xiii imply an upper limit≈ 1013cm−3, casting some doubt on such densities derived from EUV Fe lines (see above). A trend similar to results from O vii is found again, namely that more active stars tend to reveal higher overall densities.
In the case of Ne, the problematic situation with regard to line blends is illustrated in Fig. 12. If the density trend described above is real, however, then coronal loop pressures should vary by 3–4 orders of magnitude. This obviously requires different magnetic loop systems for the different pressure regimes, with a tendency that hotter plasma occupies progressively smaller volumes (Osten et al. 2003; Argiroffi et al. 2003).
Contrasting results have been reported, however. Canizares et al. (2000), Ayres et al. (2001b), and Phillips et al. (2001) found, from the Chandra HETG spectrum of Capella, densities at, or below the low-density limit for Ne, Mg, and Si. A similar result applies to II Peg (Huenemoerder et al. 2001).
A summary of the present status of coronal density measurements necessarily re- mains tentative. Densities measured from Mg xi and Si xiii may differ greatly: despite their similar formation temperatures, Mg often results in very high densities, possibly induced by blends (see Testa et al. 2004); there are also discrepancies between densities
Fig. 12. The spectral region around the Ne ix triplet, showing a large number of Fe lines, some of
which will blend with the Ne lines of interest if the resolving power is smaller than shown here (data from Chandra HETGS; the smooth red line shows a fit based on Gaussian line components; figure courtesy of J.-U. Ness)
derived from lines of He-like ions and from Fe xxi and Fe xxii line ratios, again for sim- ilar temperature ranges; and there is, lastly, disagreement between various authors who have used data from different instruments. The agreement is better for the cooler plasma components measured with C v, N vi, and O vii. There, inactive stars generally show ne<1010cm−3, whereas densities of active stars may reach several times 1010cm−3, values that are in fact in good agreement with measurements based on eclipses or rota- tional modulation (Sect. 11).