5 Results

It is important to check that the observed lines are optically thin, before performing any density estimate or emission measure modeling.

   
5.1 Optical depth

Fortunately, it is possible in a number of cases to check which lines are optically thick, and to what extent. We can identify two groups of lines in the AU Mic STIS and FUSE observations (see Table 1). The first are the doublets of Si IV, C IV, N V, and O VI. In the optically thin case, the ratios of the two lines of the doublet should be equal to the ratio of the oscillator strengths, i.e. 2. If opacity effects are present, the ratio would decrease, with the brightest component ²S_1/2-²P_3/2 being more affected, having a higher oscillator strength. In this case, the ratio is a direct measure of the ratio of the photon escape probabilities, from which the optical depths of the lines can be obtained (see e.g. Mathioudakis et al. 1999). The observed C IV, N V and O VI ratios indicate that the lines are optically thin. Only Si IV shows an opacity effect, with the ²S_1/2-²P_1/2 line having an optical depth of about 0.3, corresponding to a very small correction factor (a 15% increase).

 

 

Table 1: The line ratios in the STIS and FUSE spectral ranges useful for optical depth estimates. The last two columns indicate the theoretical (optical thin case) and the observed ratio values.

Ion	Terms	Wavelengths (Å)	Th.	Ob.
C II	2P3/2-2S1/2 /
	2P1/2-2S1/2	1037.020/1036.332	2	1.5
Si II	$\prime\prime$	1533.430/1526.706	2	1.2
C III	3P0-3P1 /
	3P2-3P1	1175.265/1176.372	0.8	1.0
Si III	$\prime\prime$	1296.726/1303.323	0.8	0.5
C III	3P2-3P2 /
	3P1-3P2	1175.713/1174.935	3	1.9
Si III	$\prime\prime$	1298.944/1294.543	3	2
Si IV	2S1/2-2P3/2 /
	2S1/2-2P1/2	1393.755/1402.770	2	1.7
C IV	$\prime\prime$	1548.201/1550.772	2	2
N V	$\prime\prime$	1238.821/1242.804	2	2
O VI	$\prime\prime$	1031.914/1037.615	2	2

The other groups of lines that can be used to estimate the opacity are those where there are ratios of lines that originate from a common upper level (a branching ratio). In the optically thin case, the ratios are equal to the ratios of the A-values (see, e.g. Jordan 1967). The STIS and FUSE spectra contain a number of useful ratios, of C II, Si II, Si III, and C III. The C II ratio indicates the presence of opacity effects, although of smaller amplitudes than those reported on the Sun (see, e.g. Brooks et al. 2000). Also Si II appears to be affected by opacity. The Si III is the worst case, since the 1296.726 Å line is very weak in the spectrum, and the 1298.944 Å line is blended with another line of the multiplet. If the blend is accounted for, the observed ratio indicates some opacity in the 1298.944 Å line, similarly to the solar case (cf. Keenan & Kingston 1986).

The first C III ratio is consistent with the theoretical value, while the second one is lower than the predicted one, suggesting some opacity. The latter result is more uncertain, because the measurement of the 1175.713 Å line is difficult, owing to the presence of the 1175.592 Å line. Even with the high spectral resolution of FUSE these two lines are difficult to deblend with a multiple profile fitting. In any case, these C III results are similar to those obtained from solar observations (see, e.g., Doyle & McWhirter 1980; Brooks et al. 2000) and indicate that within the multiplet the 1175.713 Å line has the highest optical thickness, as expected. It is worth noting that the Si III and C III line ratios can be affected by any inhomogeneities of the atmosphere (see, e.g. Doschek & Feldman 1977) because of their density and temperature sensitivity.

In conclusion, we can say that only a small number of lines are somewhat affected by opacity. However, no corrections to the line fluxes have been applied, since they would only slightly affect the lines at the lower temperatures and would not change the main results discussed in the DEM analysis (Sect. 5.3).

   
5.2 Electron density

In what follows, we review the density diagnostics relevant to active stars in the STIS and FUSE spectral regions, by comparing observations with the best atomic data available.

5.2.1 O IV and S IV

The O IV and S IV lines around 1400 Å (see Table 2) are well known density diagnostics in both solar and stellar spectra (cf. Linsky et al. 1995; Cook et al. 1995; Brage et al. 1996; Harper et al. 1999; Teriaca et al. 2001, and references therein). They are considered to be the best diagnostics in the FUV wavelength range because their temperature sensitivity is very small, compared to other cases such as C III, O V and Si III (see below). However, a number of problems and inconsistencies have been reported in the literature, leading to a degree of confusion on the reliability of the O IV and S IV lines. In what follows, we will discuss several issues, complementing the AU Mic observations with those of Cook et al. (1995) and Linsky et al. (1995). Cook et al. (1995) presented a comprehensive list of O IV and S IV solar observations (including active regions, flares), while Linsky et al. (1995) published one of the best spectrum in the FUV, based on HST/GHRS observations of Capella.

 

 

Table 2: The O IV and S IV transitions in the STIS spectral range and some of the density-sensitive ratios commonly used.

Ion	Terms	Wavelength (Å)	Ratio
O IV	2P1/2-4P3/2	1397.217
O IV	2P1/2-4P1/2	1399.779
O IV	2P3/2-4P5/2	1401.171
O IV	2P3/2-4P3/2	1404.793 (bl)
O IV	2P3/2-4P1/2	1407.383
O IV		1401.171/1399.779	R1
O IV		1401.171/1407.383	R2
O IV		1401.171/1404.793	R3
O IV		1404.793/1407.383	R4
O IV		1404.793/1399.779	R5
S IV	2P1/2-4P3/2	1398.040
S IV	2P1/2-4P1/2	1404.808 (bl)
S IV	2P3/2-4P5/2	1406.016
S IV	2P3/2-4P3/2	1416.887
S IV	2P3/2-4P1/2	1423.839
S IV		1416.887/1406.016	R6
S IV		1423.839/1416.887	R7

Let us consider O IV first. The 1397.217 Å is very weak and is rarely observed even in solar spectra. The 1399.779 Å line is also very weak, and usually has a large observational error associated with it. The 1399.779/ 1407.383 Å is a branching ratio, and excellent agreement between theory and observations is normally found (e.g. Cook et al. 1995). The ratios that include the 1401.171 Å line (R₁, R₂, R₃) have often been used to estimate the density, even though they have a very small density sensitivity as already noted by Feldman & Doschek (1979) and as can be judged from Fig. 3. Even with accurate measurements, large errors should be expected, particularly for densities higher than 10¹⁰ cm^-3. On the other hand, ratios including the 1404.793 Å line (R₄, R₅) have a much better density sensitivity, and have therefore often been preferred. Unfortunately, the 1404.793 Å line is a well-known blend with S IV (1404.808 Å) and with another unknown line (as described below), and therefore its use cannot preclude an understanding of the S IV emission.

The S IV 1416.887 Å and 1423.839 Å lines are weak and are often not detected, even in solar spectra. The 1398.040 Å line is even weaker. It is common practice in both solar and stellar physics to use the theoretical ratio of the 1404.808 Å and 1406.016 Å lines to infer the contribution of the 1404.808 Å line to the observed blend with O IV. The first problem with this method is that the 1404.808/1406.016 Å ratio is density sensitive, and therefore, unless there is an independent way of measuring the density, it should not be used. The second problem is in explaining the S IV emission, as discussed below.

In previous publications, the S IV atomic calculations by Dufton et al. (1982) have normally been used. These calculations predict that the intensity of the 1404.808 Å line is about 0.2 the intensity of the 1406.016 Å line, up to densities of $3 \times 10^{11}$ cm^-3. This results in a contribution to the observed blend that is normally only of the order of 5-10%, i.e. it is generally assumed that the observed blend is mostly O IV 1404.793 Å. Now, a further problem is that many authors report inconsistencies between the densities obtained by using different line ratios. For example, Cook et al. (1995) report that densities derived from the R₄ ratio are consistently more than an order of magnitude smaller than those derived from the R₂ ratio, for a wide range of cases (Quiet Sun, Active Regions, Sunspots, Flares). Similarly, many authors found inconsistencies with the densities derived from S IV lines. For example, Cook et al. (1995) pointed out that the densities derived from the R₆, R₇ ratios are beyond the low- or high-density limit, and no comparisons with the densities derived from O IV could be made. These inconsistencies in the O IV and S IV lines therefore suggest various possibilities:

1.

the atomic data for O IV are inaccurate;

2.

the atomic data of Dufton et al. for S IV are inaccurate;

3.

the blend observed at 1404.8 Å is mostly due to an unidentified line, and not to either O IV or S IV or a combination of the two;

among with other more subtle explanations, such as fluorescence, suggested by Cook et al. (1995). Regarding option (1), we note that Cook et al. (1995) used the collisional R-matrix calculations of Zhang et al. (1994) for O IV. Brage et al. (1996) presented new O IV atomic structure calculations. They compared their O IV model with a wide range of solar and stellar observations, including the same data presented by Cook et al. (1995), and removing the S IV contribution to the 1404.8 Å blend according to the Dufton et al. (1982) calculations. Brage et al. (1996) claimed that in most cases no inconsistencies were found, in contrast to previous studies such as in Cook et al. (1995). However, it should be noted that Brage et al. considered different line ratios (R₂, R₃, R₅), and their results are therefore not directly comparable with those of Cook et al. (1995). We used the CHIANTI v3.02 atomic model for O IV, which includes the collisional R-matrix calculations of Zhang et al. (1994), together with A-values from Flower & Nussbaumer (1975). The model gives results that are very close to those of Brage et al. (1996), as shown by Teriaca et al. (2001).

Figure 3: The fji curves of the S IV and O IV lines observed by HRTS I during a solar flare - 1973 Sep. 7 12:21 UT (Cook et al. 1995). We have assumed here that 50% of the intensity of the observed blend at 1404.8 Å is due to the S IV 1404.808 Å line, while the other 50% is due to O IV 1404.793 Å.

Regarding option (2), there is now substantial evidence for the inaccuracy of the Dufton et al. calculations. Aside from the studies already mentioned, Harper et al. (1999) used the same S IV ratios and atomic data of Cook et al. and found inconsistencies with the HST/GHRS spectra of the RR Tel nebula. Doschek et al. (1999) reported SOHO/SUMER measurements of S IV over a wide wavelength range (661-1406 Å), and found very large disagreements with the Dufton et al. calculations, of up to a factor of 6. We used the CHIANTI version 3.02 model for S IV, that includes the recent R-matrix calculations of Tayal (2000). We have considered a large number of published solar and stellar observations, and found that the new atomic data for S IV gives very different results, in most cases in good agreement with the observations. A detailed discussion is beyond the scope of this paper. Here, we only mention that in the 661-900 Å range the agreement with the Doschek et al. (1999) data is now excellent, and provide two examples to illustrate this point.

Figure 4: The fji curves of the S IV and O IV lines observed by HST/GHRS on Capella (Linsky et al. 1995).

The first example is presented in Fig. 3, and shows the f_ji curves of the O IV and S IV measurements of Cook et al. (1995) during a solar flare. Contrary to what Cook et al. found, it can be seen that the three unblended S IV lines do indicate a consistent density ( $5 \times 10^{11}$ cm^-3). Agreement with the 1404.808 Å line is also found by assuming that the S IV line contributes to 50% of the observed blend. If one assumes that the other 50% is all O IV 1404.793 Å, agreement is also found with the other O IV lines, although all lines are in the high density limit and therefore no reliable density measurement can be established (contrary to what Cook et al. found). The problem with the O IV and S IV lines appears to have been resolved.

Figure 5: The fji curves of the S IV and O IV lines observed by STIS and FUSE. The intensity of the S IV 1404.808 Å line has been assumed equal to 20% the intensity of the observed blend.

However, we found a number of cases in both solar and stellar spectra where additional blending in the 1404.8 Å line seems to occur. Figure 4 shows the second example: the f_ji curves of the O IV and S IV lines of one of the best stellar spectra (Capella - Linsky et al. 1995). The S IV 1404.808 Å line is in agreement with the other S IV lines only if its intensity is 9% that of the observed line. If one assumes that the rest (91%) is all due to O IV 1404.793 Å, no agreement is found with the other O IV lines. Instead, the contribution of the O IV line should be about 50%. This leaves about 40% of the observed line due to an unknown blend. The measurements have very small errors, indicated in the figure. Figure 4 also shows that no conclusive density measurement based on S IV can be obtained, while the O IV indicates a density of $4 \times 10^{10}$ cm^-3, a value almost an order of magnitude higher than the value indicated by Linsky et al.

Let us now consider the FUSE and STIS AU Mic observations of S IV and O IV (see Fig. 5). To reach consistency with the other lines, the intensity of the S IV 1404.808 Å line has been assumed equal to 20% the intensity of the observed blend. If we assume that the rest (80%) of the observed blend is due to the O IV 1404.7 Å line, we can see that the O IV f_ji curves are consistent with a density of the order of $5{-}9 \times 10^{10}$ cm^-3. The measurement of the 1399.779 Å line is in obvious disagreement, and might be due to weakness of this line. The same holds for the S IV 1406.016 Å line.

5.2.2 O V

Figure 6: The fji curves of the O V lines observed in the STIS spectrum of AU Mic. Top: values calculated with the Zhang & Sampson (1992 - CHIANTI v. 3.01) and Berrington et al. (1985 - CHIANTI v. 3.02) atomic data at the same temperature. Note the large difference. Bottom: values calculated at two temperatures. Note the large temperature effect.

The Be-like O V is particularly important for the STIS spectral range, since the ratio of the 1218.390 and 1371.292 Å lines is an excellent diagnostic at the densities of active stars. However, many authors in the past reported discrepancies between the densities derived from this ratio with those obtained from other ions. For example, Pagano et al. (2000) used the Zhang & Sampson (1992) collisional data and obtained from this ratio a density of $5 \times 10^{11}$ cm^-3, at odds with what derived from the O IV ratios. If the R-Matrix calculations of Berrington et al. (1985) are used (CHIANTI version 3.02), large differences are found for some transitions, and the densities derived from O V become consistent with those obtained from other ions, as shown in Fig. 6. In fact, at the effective temperature $T_{\rm eff} = 2.7 \times 10^{5}$ K (see Table 3), the observed ratio indicates an electron density of $5 \times 10^{10}$ cm^-3. Note that this $T_{\rm eff}$ is quite different from the temperature of maximum ionisation fraction ( $T = 2.5 \times 10^{5}$ K according to Mazzotta et al. 1998) and that a small difference in temperature has a large effect on the ratio (Fig. 6).

5.2.3 Si III

There are a few Si III lines visible in the FUSE and STIS spectral ranges that could be used for density diagnostics. For example, the resonance 3s^{2 1}S₀-3s 3p ¹P₁ line at 1206.499 Å has a density dependence different compared to the lines of the 3s 3p ³P-3p^2 3P multiplet. All the measurements are consistent with the density derived from O V, with two exceptions, the ³P₁-³P₀ (1301.147 Å) and the ³P₁-³P₂ (1294.543 Å) lines observed by STIS, which are probably blended. However, the Si III results have a large uncertainty, since the density dependence is small, and temperature effects are even greater than in the O V case. This occurs because the DEM of AU Mic presents a a steep gradient at the Si III temperatures (see Sect. 5.3), larger than for O V.

5.2.4 C III

Densities could be obtained using the well-known ratio of the resonance 2s^2 1S₀-2s 2p ¹P₁ line at 977.022 Å with the total intensity of the 2s 2p ³P-2p^2 3P multiplet at 1175 Å. However, this diagnostic is only sensitive up to log $N_{\rm e}=10$ (cm^-3) and is therefore not useful for active stars, that normally have higher densities. Moreover, temperature and opacity effects can be large. The C III 977/1176 Å ratio as measured from FUSE spectra is 1.0, much lower than the high-density limit (1.7), according to the C III CHIANTI model and calculated at $T= 6.3 \times 10^4$ K. This discrepancy can be interpreted in terms of opacity effects in the resonance line. The ratio is therefore not useful for density diagnostic for AU Mic, nor probably for diagnostic of other active stars. Young et al. (2001) and Ake et al. (2000) report FUSE measurements of Capella and AB Dor, a rapidly rotating active star. They report ratios of $2.0 (N_{\rm e} = 2 \times 10^{10}$ cm^-3) and 1.5, close to the high-density limit, but also point out the uncertainties related to opacity effects. Schmitt et al. (1998) report ORFEUS observations of AB Dor, but measured a ratio in the range 1.0-1.3. The authors conclude that the AB Dor TR had densities in excess of 10¹¹ cm^-3. However, these ratio values are much lower than the high-density limit, and we believe that opacity effects are probably significant also in the ORFEUS spectrum, and no conclusions can be drawn.

5.2.5 Summary of density diagnostics

If we restrict to the FUV spectral range and consider the Capella and AU Mic observations as typical for active stars ( $N_{\rm e} = 5{-}10 \times 10^{10}$ cm^-3), we can conclude that: a) the best diagnostic is O V, although with some uncertainties, due to the weakness of the 1371.292 Å line and the temperature effects; b) results based on the O IV diagnostic should be treated with caution given the low density sensitivity and blending; c) the C III diagnostic is only useful at lower densities, and should be treated with caution because of opacity and temperature effects; d) the S IV diagnostic is only useful at higher densities; e) the Si III diagnostic has large temperature effects. Any measurement involving these ions should therefore be treated with caution and complemented with other methods. One possibility (see Sect. 5.3 below) is to use the EM loci method and the O III 1666.142 Å and N IV 1486.496 Å lines, that are density-sensitive (relative to dipole allowed transitions) in the 10¹⁰-10¹¹ cm^-3 regime.

Another method, frequently adopted in the literature, is to use ratios of lines emitted by different elements. This leads to uncertain results unless independent methods for checking the ionisation state and the relative elemental abundances can be used. Temperature effects can also be important. For example, Doschek et al. (1978) and following authors (e.g. Cook & Nicholas 1979) suggest the use of the Si III 1892 Å/C III 1908 Å ratio. As already mentioned, both C III and Si III lines have large temperature effects and therefore can only be used not only when the relative C/Si abundance is known, but also when the DEM is independently estimated. Cook & Nicholas (1979) and following authors (e.g. Byrne et al. 1987) also suggest the use of the Si IV 1402 Å/C III 1908 Å ratio. In this case, aside from the same problems that the Si III/C III ratio has, this ratio is unreliable because the Si IV lines belong to the anomalous class.

   
5.3 The $\mathsfsl{DEM}$ of AU Mic in quiescence

Figure 7: The DEM of AU Mic in quiescence, as derived from FUSE, STIS and EUVE spectra. Note the large deviations of the lines of the Li-like (C IV, N V) and Na-like (Si IV) ions.

We have used the observations detailed in Sect. 4 to derive a DEM. As a first attempt, the photospheric abundances of Grevesse & Sauval (1998) have been used, with a correction for the oxygen abundance to a value of 8.73 (in the usual dex notation, with H fixed at 12), as recently revised by Grevesse (2002). Note that this value is much lower than the value of 8.93 published in Grevesse & Anders (1991), which has been used as a reference in many previous studies. The contribution functions have been calculated at a constant electron pressure $P_{\rm e}=1 \times 10^{16}$ cm^-3 K, for reasons that are explained below. The resulting DEM is plotted in Fig. 7, while Table 3 presents the line list with the details and line identifications. Each experimental data point is over-plotted in Fig. 7 at the effective temperature $T_{\rm eff}$ and at a value equal to the product $DEM(T\mbox{$\rm _{eff}$ }) \times (I_{\rm ob}/I_{\rm th})$. The error bars refer to the combination of observational and theoretical (10%) errors and give an idea of the uncertainties in the derived DEM values.

First, let us examine the DEM at lower temperatures. The DEM is well constrained in the log T =4-6range by all the lines observed by STIS and FUSE. The general agreement between the two sets of lines is very good, considering the lack of simultaneity. The DEM at temperatures as high as 10⁶ K is well constrained by the O VI lines, that have a long tail in their contribution function at high-temperatures. As in the case of the Sun, the DEM has a minimum around $\log\, T = 5.2$, and presents the usual increase toward million-degrees temperatures (see, e.g., Del Zanna & Bromage 1999, for solar DEM distributions). The exact position of the minimum is not well constrained, since there are no observed allowed lines between the temperatures where S IV and O V are emitted. However, further constraints are given by N IV] and O IV], as discussed below. The S III, N III, S IV lines observed by FUSE confirm the anomalous behaviour of the lines of the Li and Na isoelectronic sequences. This anomalous behaviour is quite striking. The Li-like N V and C IV lines are underestimated by factors larger than 3 and 5, respectively. The Na-like Si IV lines are also underestimated by a factor larger than 5. The S VI 933.3 Å (Na-like) is overestimated (only by a 40%), while the O VI lines are the only ones that do not seem to present anomalous behaviour. This confirms the problems with these ions already found in the solar spectra.

In order to estimate the importance of density effects in the ion balance calculations for this case, we have performed a DEM analysis using ionisation fractions calculated at a density $N_{\rm e}=10^{10}$ cm^-3 (J. Raymond 2001, priv. comm.). As already shown by Vernazza & Raymond (1978), density effects can be quite large. Indeed, we have found significant changes, not only to the calculated fluxes, but also to the effective temperatures. The fluxes of the Li- and Na-like lines increase (e.g. by factors of 2 for C IV and 3 for Si IV), suggesting that these density effects are in fact very important, although still not sufficient to completely remove the discrepancy in this particular case.

Our DEM distribution is in stark contrast with those obtained by Quin et al. (1993) and Pagano et al. (2000). The latter found a minimum in the DEM at $\log\, T = 4.7$, with a nearly flat DEM until $\log\, T = 5.4$, and concluded that the energy balance in the transition region of AU Mic is very different from that of the Sun. The large discrepancy in the results obtained by Pagano et al. (2000) is due to the fact that they used the Si III, Si IV, C IV, N V lines observed by STIS to constrain the log T = 4.5-5.5 region. Pagano et al. presented the results in terms of the $I\mbox{$\rm _{ob}$ } / (A_{\rm b} \times C(N_{\rm e}, T))$ curves. For comparison, we show in Fig. 8 (top) these curves, together with the $EM_{\Delta {\rm log}\, T=0.3}$ values, i.e. the emission measures calculated with a $\Delta {\rm log}\, T=0.3$, for all the allowed lines, excluding those of the Li and Na isoelectronic sequences, that are plotted in Fig. 8 (middle). The erroneous DEM derived by Pagano et al. (2000) resulted in the particularly high densities required to explain the fluxes of the density-sensitive lines of O III, N IV, O IV, O V (log $N_{\rm e} = 11.5{-}12$) by using the emission measure loci. Figure 8 (bottom) clearly shows that the much lower densities found here are perfectly consistent with the emission measure values. We note that the use of the emission measure loci method can provide misleading results, since the $I\mbox{$\rm _{ob}$ } / (A_{\rm b} \times C(T))$ curves only provide upper limits to the emission measure. Instead it is important to calculate the line fluxes, i.e. the emissivities integrated over the DEM distribution. In this respect, it is interesting to examine the behaviour of the line fluxes when the emissivities are calculated at different densities (or pressures). Figure 9 shows the results obtained when the emissivities are calculated at two constant densities ( $N_{\rm e}= 3.5$ and $14 \times 10^{10}$ cm^-3) and at constant pressure ( $P_{\rm e}= 10^{16}$ cm^-3 K). Figure 9 shows that:

a) the O III] and N IV] lines are very sensitive to small density variations;

b) the Si III] lines are very sensitive to both density and temperature effects;

c) it is impossible to reproduce all the intensities of the density sensitive lines if the emissivities are calculated at constant density;

d) a constant pressure $P_{\rm e}= 10^{16}$ cm^-3 K produces good agreement for all the transition region lines in the $\log\, T = 4.5{-}5.5$ range (Si III], O III], N IV], O IV], O V], with the exception of S IV] 1406.016 Å, that probably has an erroneous observed flux, see Sect. 4.2.1) and confirms the densities derived from the L-function method;

e) with this constant pressure, the N IV and O IV lines confirm the presence of a minimum at $\log\, T = 5.2$ in the DEM.

At higher temperatures, the DEM is not well constrained between log T = 6-6.7. The EUVE measurements suggest a peak at log $T \simeq 6.1$ and a decrease at log T = 6.5. It is interesting to note that the Chandra and XMM gratings observe only few lines that cover this important temperature range, where the bulk of the quiet Sun emission is. The DEM has a peak at log T = 6.9, well constrained by the FUSE and STIS data, together with the EUVE ones. This peak is typical of the coronae of active stars and of solar flares.

Regarding elemental abundances, no significant departures from the adopted solar photospheric abundances are found. This includes low-FIP elements (Si), medium-FIP elements (S), and high-FIP ones (C, N, O, Ne). This is in stark contrast to the result obtained by Quin et al. (1993), where solar coronal abundances were found to be satisfactory. Again, this erroneous result was due to the use of the Si IV, C IV, N V lines in the DEM analysis.

Finally, it should be noted that erroneous DEM distributions and chemical abundances such as those found for the AU Mic transition region by Quin et al. (1993) and Pagano et al. (2000) lead to inaccurate calculations of the radiative losses, and to misconceptions about physical processes that are derived from them.