6 Conclusions

We have discussed diagnostic methods and atomic data for the determination of densities, the DEM and the chemical composition of the transition regions and coronae of the Sun and active stars. We have described the severe limitations which some of the commonly used methods have. We have illustrated several issues with examples, mainly focusing on the diagnostic methods for the transition region using FUV (900-1700 Å - HST/STIS, FUSE) observations of AU Mic. We have complemented them with FUV observations of the Sun and Capella. We have revised some previous analyses and obtained results that are significantly different from those of other authors.

The problems highlighted are quite general and apply to other stellar transition regions (including the Sun) and to other wavelength ranges. In terms of emission measure analysis, we have indicated what we think is the best approach, which avoids frequently used approximations. We have described the main problems related to the direct determination of the relative elemental abundances, giving warnings about the use of emission measures and line ratio methods.

Figure 8: The emission measures $EM_{\Delta {\rm log}\, T=0.3}$ values, together with the $I\mbox{$\rm _{ob}$ } / (A_{\rm b} \times C(T))$ curves, calculated at constant pressure $P_{\rm e}= 10^{16}$ cm-3 K. From top to bottom: the curves for the allowed lines; the curves for the anomalous allowed lines of the Li- and Na-like sequences; the curves for the forbidden lines.

Figure 9: The DEM of the AU Mic in quiescence (same as Fig. 7), but with the emissivities calculated, from top to bottom: at constant density $N_{\rm e}= 3.5 \times 10^{10}$ cm-3; $N_{\rm e}= 14 \times 10^{10}$ cm-3; at constant pressure $P_{\rm e}= 10^{16}$ cm-3 K. Note the large variations in the forbidden lines Si III], O III], N IV], O IV], O V], and the fact that a constant pressure $P_{\rm e}= 10^{16}$ cm-3 K produces the best agreement in the temperature range shown.

Regarding electron densities, we have discussed the limitations of using single line ratios, and recommended the use of the L-function method, which gives a better overall view of the results. We have presented the limitations in the use of lines that have a small density sensitivity, providing a discussion of the O IV lines at 1400 Å as an example. The use of these lines is further complicated by the presence of an unknown blend.

We have shown the importance of revising earlier results by using more up-to-date atomic calculations. As an example, we have shown that the latest S IV calculations of Tayal (2000) provide density estimates that are significantly different from those reported in the previous literature.

The anomalous behaviour of lines from the Li and Na isoelectronic sequences has been neglected too often in previous solar and stellar publications. We have shown that the use of these lines produces erroneous results in the determination of: a) the DEM; b) the elemental abundances; c) the densities using the emission measure loci method. Note that in most papers these lines have been the primary means of determining the physical characteristics of the solar and stellar transition regions.

In light of the above, we believe that a large body of work in terms of spectroscopic diagnostics of the solar and stellar outer atmospheres (and their application to physical modeling) should be revisited, now that more accurate atomic and observational data are available.

 

 

Table 3: Results of the DEM analysis. The columns consist of: (1) the ion; (2) the theoretical wavelength $\lambda _{\rm th}$; (3) the observed wavelength $\lambda _{\rm ob}$; (4) configuration and term description; (5) observed flux $I_{\rm ob}$ (10^-14 ergs cm^-2 s^-1); (6) ratio between the theoretical $I_{\rm th}$ and the observed flux; (7) the estimated error on the ratio value; (8) the effective temperature (log values); (9) $T_{\rm max}$ (log values); (10) the contribution of each transition to the total calculated intensity of the line. (11) the instrument. The last column indicates: (*) a selection of the observed allowed lines; (a) the anomalous allowed lines of the Li- and Na-like sequences; (d) the forbidden lines. The lines marked in the last column are plotted in Fig. 8.

Ion	$\lambda _{\rm th}$	$\lambda _{\rm ob}$	Transition	$I_{\rm ob}$	$I_{\rm th}$/	+/-	log	log	frac
	(Å)	(Å)		(10-14)	$I_{\rm ob}$		$T_{\rm eff}$	$T_{\rm max}$
Si II	1533.430	1533.406	3s2 (1S) 3p 2P3/2-3s2 (1S) 4s 2S1/2	0.69	1.09	0.24	4.28	4.43		STIS
Si II	1526.706	1526.687	3s2 (1S) 3p 2P1/2-3s2 (1S) 4s 2S1/2	0.58	0.66	0.15	4.28	4.43		STIS
Si II	1304.369	1304.355	3s2 (1S) 3p 2P1/2-3s 3p2 2S1/2	0.12	1.05	0.23	4.33	4.48		STIS	*
Si II	1309.274	1309.287	3s2 (1S) 3p 2P3/2-3s 3p2 2S1/2	0.32	0.78	0.17	4.33	4.48		STIS
Si II	1264.737	1264.725	3s2 (1S) 3p 2P3/2-3s2 (1S) 3d 2D5/2	0.48	2.01	0.45	4.35	4.49		STIS
Si II	1265.001	1264.986	3s2 (1S) 3p 2P3/2-3s2 (1S) 3d 2D3/2	0.21	0.55	0.12	4.35	4.49		STIS
S II	1253.811	1253.808	3s2 3p3 4S3/2-3s 3p4 4P3/2	0.12	1.65	0.37	4.34	4.45		STIS
S II	1259.519	1259.495	3s2 3p3 4S3/2 -3s 3p4 4P5/2	0.14	0.80	0.18	4.35	4.45		STIS	*
C II	1334.524	1334.535	2s2 (1S) 2p 2P1/2-2s 2p2 2D3/2	6.89	1.00	0.22	4.44	4.58		STIS
C II	1335.709	1335.692	2s2 (1S) 2p 2P3/2-2s 2p2 2D5/2	14.39	0.96	0.21	4.44	4.58		STIS	*
C II	1036.332	1036.302	2s2 (1S) 2p 2P1/2-2s 2p2 2S1/2	0.73	1.06	0.17	4.53	4.63		FUSE
C II	1037.020	1036.982	2s2 (1S) 2p 2P3/2-2s 2p2 2S1/2	1.1	1.39	0.18	4.53	4.63		FUSE
C II	1323.952	1323.929	2s 2p2 2D5/2-2p3 2D5/2	0.14	0.95	0.21	4.63	4.69	0.56	STIS
C II	1323.907		2s 2p2 2D3/2-2p3 2D3/2					4.69	0.36
Si III	1206.499	1206.496	3s2 1S0-3s 3p 1P1	7.9	1.09	0.24	4.64	4.78		STIS	*
Si III	1301.147	1301.139	3s 3p 3P1-3p2 3P0	0.17	0.65	0.14	4.66	4.77		STIS
Si III	1303.323	1303.325	3s 3p 3P2-3p2 3P1	0.15	1.05	0.23	4.66	4.77		STIS
Si III	1298.944	1298.938	3s 3p 3P2-3p2 3P2	0.51	1.11	0.25	4.67	4.77	0.83	STIS	d
Si III	1298.892		3s 3p 3P1-3p2 3P1					4.77	0.17
Si III	1294.543	1294.537	3s 3p 3P1-3p2 3P2	0.21	0.76	0.17	4.67	4.77		STIS
Si III	1296.726	1296.713	3s 3p 3P0-3p2 3P1	0.08	1.60	0.36	4.67	4.77		STIS
Si III	1109.969	1110.006	3s 3p 3P1-3s 3d 3D2	0.25	1.27	0.28	4.69	4.78	0.74	FUSE
Si III	1109.939		3s 3p 3P1-3s 3d 3D1					4.78	0.26
Si III	1108.357	1108.370	3s 3p 3P0-3s 3d 3D1	0.083	1.32	0.68	4.69	4.78		FUSE
Si III	1113.229	1113.270	3s 3p 3P2-3s 3d 3D3	0.31	2.00	0.39	4.69	4.78	0.87	FUSE
Si III	1113.203		3s 3p 3P2-3s 3d 3D2					4.78	0.13
S III	1021.321	1021.357	3s2 3p2 3P2-3s 3p3 3P2	0.083	1.38	0.48	4.71	4.79		FUSE	*
S III	1077.171	1077.017	3s2 3p2 1D2-3s2 3p 3d 1D2	0.13	1.10	0.56	4.72	4.80		FUSE	*
C III	977.022	977.015	2s2 1S0-2s 2p 1P1	12	1.49	0.16	4.81	4.92		FUSE
C III	1174.935	1174.939	2s 2p 3P1-2p2 3P2	2	0.70	0.10	4.82	4.92		FUSE
C III	1175.265	1175.281	2s 2p 3P0-2p2 3P1	1.6	0.70	0.10	4.82	4.92		FUSE
C III	1175.592	1175.570	2s 2p 3P1-2p2 3P1	1.1	0.76	0.11	4.82	4.92		FUSE
C III	1175.713	1175.709	2s 2p 3P2-2p2 3P2	3.8	1.10	0.16	4.82	4.92		FUSE	*
C III	1175.989	1175.986	2s 2p 3P1-2p2 3P0	1.8	0.62	0.09	4.82	4.92		FUSE
C III	1176.372	1176.366	2s 2p 3P2-2p2 3P1	1.6	0.87	0.12	4.82	4.92		FUSE
C III	1175.713	1175.694	2s 2p 3P2-2p2 3P2	3.98	1.05	0.24	4.82	4.92		STIS
Si IV	1402.770	1402.747	3s 2S1/2-3p 2P1/2	2.92	0.18	0.04	4.88	4.87		STIS	a
Si IV	1393.755	1393.744	3s 2S1/2-3p 2P3/2	4.93	0.21	0.05	4.88	4.88		STIS	a
Si IV	1128.325	1128.350	3p 2P3/2-3d 2D5/2	0.2	0.12	0.04	4.95	4.90	0.90	FUSE	a
Si IV	1128.340		3p 2P3/2-3d 2D3/2					4.90	0.10
Si IV	1122.500	1122.578	3p 2P1/2-3d 2D3/2	0.11	0.12	0.05	5.20	4.90		FUSE	a
N III	989.787	989.752	2s2 2p 2P1/2-2s 2p2 2D3/2	0.46	1.16	0.40	4.88	4.94		FUSE	*
N III	991.564	991.538	2s2 2p 2P3/2-2s 2p2 2D5/2	1.2	0.87	0.16	4.88	4.94	0.90	FUSE	*
N III	991.495		2s2 2p 2P3/2-2s 2p2 2D3/2					4.94	0.10
O III	1666.142	1666.109	2s2 2p2 3P2-2s 2p3 5S2	0.13	1.02	0.23	4.94	4.98		STIS	d
S IV	1406.016	1406.031	3s2 3p 2P3/2-3s 3p2 4P5/2	0.04	2.76	0.62	4.95	5.00		STIS	d
S IV	1072.974	1072.930	3s2 3p 2P3/2-3s 3p2 2D5/2	0.23	1.18	0.32	4.98	5.03		FUSE	*
S IV	1062.664	1062.572	3s2 3p 2P1/2-3s 3p2 2D3/2	0.19	0.93	0.23	4.99	5.03		FUSE	*
N IV	1486.496	1486.510	2s2 1S0-2s 2p 3P1	0.09	0.72	0.16	5.15	5.16		STIS	d
C IV	1550.772	1550.746	1s2 2s 2S1/2-1s2 2p 2P1/2	11.34	0.20	0.04	5.19	5.03		STIS	a
C IV	1548.201	1548.181	1s2 2s 2S1/2-1s2 2p 2P3/2	21.36	0.21	0.05	5.19	5.03		STIS	a
O IV	1404.793	1404.811	2s2 2p 2P3/2-2s 2p2 4P3/2	0.11	1.15	0.26	5.22	5.21	0.79	STIS
S IV	1404.808		3s2 3p 2P1/2-3s 3p2 4P1/2					4.99	0.21
O IV	1399.779	1399.765	2s2 2p 2P1/2-2s 2p2 4P1/2	0.07	1.72	0.39	5.24	5.18		STIS
O IV	1407.383	1407.361	2s2 2p 2P3/2-2s 2p2 4P1/2	0.12	0.93	0.21	5.24	5.18		STIS	d
O IV	1401.171	1401.140	2s2 2p 2P3/2-2s 2p2 4P5/2	0.4	1.14	0.25	5.26	5.20		STIS	d
O V	1218.390	1218.322	2s2 1S0-2s 2p 3P1	1.83	1.01	0.23	5.42	5.37		STIS	d
O V	1371.292	1371.285	2s 2p 1P1-2p2 1D2	0.35	0.90	0.20	5.44	5.38		STIS	*

 

Table 3: continued.

Ion	$\lambda _{\rm th}$	$\lambda _{\rm ob}$	Transition	$I_{\rm ob}$	$I_{\rm th}$/	+/-	log	log	frac
	(Å)	(Å)		(10-14)	$I_{\rm ob}$		$T_{\rm eff}$	$T_{\rm max}$
Ne V	1145.596	1145.624	2s2 2p2 3P2-2s 2p3 5S2	0.15	1.05	0.36	5.52	5.46		FUSE	*
S VI	933.378	933.397	3s 2S1/2-3p 2P3/2	0.48	1.38	0.48	5.55	5.30		FUSE	a
N V	1242.804	1242.794	1s2 2s 2S1/2-1s2 2p 2P1/2	2.11	0.31	0.07	5.57	5.27		STIS	a
N V	1238.821	1238.799	1s2 2s 2S1/2-1s2 2p 2P3/2	4.52	0.29	0.07	5.57	5.27		STIS	a
Ne VI	999.182	999.181	2s2 2p 2P3/2-2s 2p2 4P5/2	0.45	0.75	0.38	5.64	5.60		FUSE	*
O VI	1037.615	1037.583	1s2 2s 2S1/2-1s2 2p 2P1/2	9.6	1.07	0.11	5.72	5.47		FUSE	*
O VI	1031.914	1031.920	1s2 2s 2S1/2-1s2 2p 2P3/2	19	1.09	0.11	5.72	5.47		FUSE	*
Fe IX	171.073	171.000	3p6 1S0-3p5.3d 1P1	22.9	1.08	0.48	5.92	5.85		EUVE	*
Fe XV	284.160	284.200	3s2 1S0-3s3p 1P1	40.8	0.76	0.33	6.42	6.32		EUVE	*
Fe XVI	335.410	335.300	3s 2S1/2-3p 2P3/2	27.9	1.02	0.70	6.61	6.41		EUVE	*
Fe XVIII	93.923	94.100	2s2 2p5 2P3/2-2s 2p6 2S1/2	8.7	1.03	0.58	6.85	6.83		EUVE	*
Fe XVIII	974.860	974.810	2s2 2p5 2P3/2-2s2 2p5 2P1/2	0.48	0.94	0.48	6.85	6.83		EUVE	*
Fe XIX	1118.057	1118.013	2s2 2p4 3P2-2s2 2p4 3P1	0.22	1.28	0.29	6.90	6.90		FUSE	*
Fe XIX	108.355	108.500	2s2 2p4 3P2-2s 2p5 3P2	7.96	0.69	0.25	6.92	6.90		EUVE	*
Fe XX	121.845	121.700	2s2 2p3 4S3/2-2s 2p4 4P3/2	6.2	0.98	0.41	6.97	6.97		EUVE	*
Fe XXI	1354.080	1354.045	2p2 3P0-2p2 3P1	0.77	0.93	0.21	7.02	7.02		STIS	*
Fe XXI	128.752	128.600	2p2 3P0-2s 2p3 3D1	8.7	1.05	0.57	7.02	7.02		EUVE	*
Fe XXII	135.755	135.800	2s2 2p 2P1/2-1s2 2s 2p2 2D3/2	7.8	0.70	0.28	7.09	7.08		EUVE	*
Fe XXI	117.499	117.600	2p2 3P1-2s 2p3 3P1	3.2	0.89	0.56	7.11	7.02	0.50	EUVE
Ni XXV	117.911		2s2 1S0-2s 2p 1P1					7.24	0.28
Ni XXII	117.918		2s2 2p3 4S3/2-2s 2p4 4S5/2					7.05	0.11
Fe XXIII	132.906	132.800	2s2 1S0-2s 2p 1P1	22.6	1.09	0.29	7.13	7.14	0.67	EUVE	*
Fe XX	132.840		2s2 2p3 4S3/2-2s 2p4 4P5/2					6.97	0.31
Fe XXIV	192.029	191.700	1s2 2s 2S1/2-1s2 2p 2P3/2	10.4	0.90	0.61	7.24	7.23	0.84	EUVE	*
S XI	191.266		2s22p2 3P2-2s2p3 3S1					6.28	0.14

Acknowledgements

G. Del Zanna and H. E. Mason acknowledge support from PPARC (UK). M. Landini and G. Del Zanna acknowledge support from ASI and MIUR (Italy). We thank R. Mewe for his helpful suggestions.