4 Discussion

In this section, we will discuss the results in terms of a FIP-biased abundance pattern. We will also discuss potential problems, such as the relevance of optical depths, and the importance of the choice of solar and stellar photospheric abundances, that could influence the determination of coronal abundances or the abundance pattern.

  
4.1 A pattern for coronal abundances

Figure 4 shows elemental abundance ratios relative to O and to solar photospheric values for our star sample as a function of the first ionization potential. Although the determination of absolute abundances (relative to H) is subject to an accurate description of the underlying continuum, we have found that abundance ratios are robust and similar in the XSPEC and SPEX fits. Highly active stars show an inverse FIP effect, i.e., low-FIP elements are underabundant relative to high-FIP elements, as observed in an early analysis of the XMM-Newton RGS data of HR 1099 (Brinkman et al. 2001). $\lambda$ And however shows no particular FIP bias. For the intermediately active Capella, no clear trend is seen, although a possible overabundance of low-FIP elements compared to high-FIP elements is suggested, which is reminiscent of the solar FIP effect. Figure 4 therefore suggests the presence of a transition from an inverse FIP effect in the most active binaries toward the absence of FIP bias in intermediately active stars. This resembles the transition from an inverse FIP to a normal FIP effect in solar-like stars as a consequence of decreasing activity (Güdel et al. 2002). Similarly, Singh et al. (1999) have observed that the Fe abundance in active late-type dwarfs increases with decreasing activity.

Figure 4: Abundance ratios relative to O and to solar photospheric values (Anders & Grevesse 1989) as a function of FIP. Ratios from XSPEC/APEC are shown as triangles, while ratios from SPEX/MEKAL are shown as squares. Activity/temperature decreases from top to bottom. Note the logarithmic scales.

  
4.2 Optical depths

 

 

Table 5: Photon fluxes ( ${\rm 10^{-4}~photons~cm^{-2}~s^{-1}}$) for two Fe XVII 2p-3d lines and their flux ratio.

Star	Fe XVII		Flux ratio
	$\lambda$ 15.01 Å	$\lambda$ 15.26 Å	F(15.01)/F(15.26)
HR 1099 ...	$5.91 \pm 0.20$	$2.04 \pm 0.21$	$2.90 \pm 0.32$
UX Ari ......	$2.06 \pm 0.13$	$0.66 \pm 0.11$	$3.14 \pm 0.58$
$\lambda$ And ......	$3.71 \pm 0.16$	$1.24 \pm 0.12$	$3.00 \pm 0.33$
VY Ari ......	$1.76 \pm 0.11$	$0.74 \pm 0.10$	$2.37 \pm 0.36$
Capella .....	$46.82 \pm 0.29$	$18.36 \pm 0.39$	$2.55 \pm 0.06$

Optical depths in stellar coronae can potentially have an impact on the determination of abundances. Since we interpret our data with optically thin models, we need to verify that the most critical lines seen in our spectra are indeed optically thin. We have therefore measured the fluxes in the Fe XVII $\lambda\lambda$ 15.014 and 15.261 Å lines. The ratio of these 2p⁶-2s²p⁵3d lines is especially sensitive to the optical depth, since the former line has a very large oscillator strength, whereas the latter line does not (e.g., Rugge & McKenzie 1985; Mewe et al. 1995b; Kaastra & Mewe 1995). We used the best-fit models from XSPEC/APEC, then froze the fitting parameters, set the Fe and O abundances to zero, and added 6 emission lines. This procedure conserves the complete model including spectral lines and continuum from all elements except Fe and O, which we re-model separately to obtain explicit, accurately measured fluxes specifically for any one of the selected lines. The line photon fluxes were left free to vary, whereas their widths and their wavelengths were kept fixed. The additional four emission lines correspond to line blends from Fe XVII $\lambda$15.453 Å, Fe XIX $\lambda\lambda$ 15.079 and 15.198 Å, and O VIII Ly$\gamma$ at 15.176 Å. The RGS1 and RGS2 data have been fitted in the wavelength range from 14.8 to 15.5 Å simultaneously to increase the signal-to-noise ratio. Uncertainties for the line photon fluxes were obtained by averaging the 68% upper and lower limits for a single parameter of interest ( $\Delta\chi^2=1$). The observed flux ratios, F(15.01) / F(15.26), range from 2.4 to 3.1 (Table 5). Theoretical ratios range from 3.0-4.7 (e.g., Bhatia & Doschek 1992; also see Table 2 of Brown et al. 1998). Laboratory experiments, e.g., with electron beam ion traps (EBIT) have obtained lower ratios (2.8-3.2, Brown et al. 1998; Laming et al. 2000), suggesting that previous optical depths measurements based on theoretical ratios were overestimated. Using an EBIT ratio of $3.04 \pm 0.12$ measured at an electron energy of 1150 eV (Brown et al. 1998), and on the basis of the "escape-factor'' model (escape probability $P(\tau) \sim [1 + 0.43 \tau ]^{-1}$ for an optical depth $\tau \lesssim 50$) with a homogeneous mixture of emitters and absorbers in a slab geometry (Kaastra & Mewe 1995), we obtain optical depths no larger than $\tau \approx 0.66$, consistent with an optically thin plasma. Using the theoretical ratio of 3.53 from the APEC code, optical depths in $\lambda$ And and possibly Capella approach $\tau = 1$, although the other RS CVns still show $\tau \lesssim 0.5$.

  
4.3 Relation to solar photospheric abundances

Figure 5: Similar to Fig. 4 for XSPEC/APEC, but using C, N, O, Ne, Mg, and Fe abundance of Holweger (2001, filled dots) and the C and O abundances of Allende Prieto et al. (2001, 2002, open squares).

Solar photospheric abundances from Anders & Grevesse (1989) have been chosen except for Fe for which the more recent $A_{\rm Fe} = 7.50$ of Grevesse & Sauval (1999) has been adopted. Recent work has provided new estimates of solar photospheric abundances (e.g., Grevesse & Sauval 1998; Allende Prieto et al. 2001, 2002; Holweger 2001). In this section, we test the impact of choosing different solar photospheric abundances on the abundance pattern in RS CVn binaries; XSPEC/APEC results have been used. However, we emphasize that the SPEX/MEKAL abundance ratios were similar. Using new abundances from Holweger (2001), the observed trend (Fig. 4) is again found (albeit with slightly different ratios). Allende Prieto et al. (2001, 2002) propose new solar photospheric O and C abundances, respectively: $A_{\rm O} = 8.69$ and $A_{\rm C} = 8.39$, thus factors 1.74 and 1.48 smaller than in Anders & Grevesse (1989). The result is that abundance ratios to O in Fig. 4 should be reduced and get closer to the solar photospheric values for high-FIP elements. Although newer values of solar photospheric abundances can be useful for a direct comparison with the solar FIP effect, their adoption does not affect the suggested FIP bias in active stars. Figure 5 is similar to Fig. 4, except that it shows abundance ratios using Holweger (2001) abundances for C, N, O, Ne, Mg, Fe (filled dots), and using the C and O abundances of Allende Prieto et al. (2001, 2002, open squares). We note a possible two-plateau shape, as for the solar FIP effect but reversed: high-FIP abundance ratios are close to solar, whereas low-FIP ratios vary with the activity level. The separation lies around 10 eV, as in the Sun.

  
4.4 Relation to stellar photospheric abundances

Although it is practice to normalize stellar coronal abundances to the solar photospheric abundances, they should better be normalized to the stellar photospheric abundances. Some studies attempted to derive photospheric abundances of active binaries by modeling high-resolution optical spectra. In particular, RS CVn binaries have often been found to display large metallic abundance depletion (e.g., Randich et al. 1994). However, such systems are in general younger than the Sun, and thus nearby stars should show metallicities close to solar (Rocha-Pinto et al. 2000). For example, at an age of a few Gyrs, photospheres have [Fe/H] in the range -0.08 to -0.15 with uncertainties of about 0.12(Rocha-Pinto et al. 2000). The rare measured photospheric abundances are therefore probably biased by the enhanced chromospheric activity, high rotation rate, and the presence of spots. Previous abundance measurements are perhaps also biased by inaccurate determinations of fundamental stellar parameters, such as gravity and effective temperatures (Ottmann et al. 1998).

Figure 6: Abundance ratios to oxygen vs. FIP for $\lambda$ And using the XSPEC/APEC results. Stellar photospheric abundances from Donati et al. (1995, red open diamonds) and from Savanov & Berdyugina (1994, blue open squares) have been used. For comparison, we plot the ratios to solar photospheric values (Anders & Grevesse 1989; Grevesse & Sauval 1999, filled circles).

On the other hand, photospheric abundances of $\lambda$ And, a slowly rotating giant, can be found in the literature. We have used abundances from Donati et al. (1995) and Savanov & Berdyugina (1994) since these authors provide estimates for several elements. Note that Ottmann et al. (1998) give values for Fe, Mg, and Si only, all of which are low-FIP elements with very similar FIP values. Figure 6 shows FIP-ordered abundance ratios to oxygen relative to stellar photospheric abundances (red open diamonds for Donati et al. 1995 and blue open squares for Savanov & Berdyugina 1994) in comparison with ratios relative to solar photospheric. Abundance ratios are slightly different, the overall shape of the coronal abundance pattern in $\lambda$ And stays similar, however: there is no apparent bias related to the first ionization potential. The Ca/O ratio using stellar abundances of Donati et al. (1995) is similar to the ratio relative to solar photospheric, but it is larger when abundances from Savanov & Berdyugina (1994) are used, although with larger uncertainties, thus formally compatible. Unfortunately, abundances of noble gases in stellar photospheres cannot be measured, preventing us from obtaining abundance ratios at ${\rm FIP} > 15$ eV.

$\lambda$ And may be regarded as an exceptional case where stellar photospheric abundances have been measured with some confidence. It would be interesting to obtain measurements for highly active stars, such as UX Ari and HR 1099, for which a clear inverse FIP effect is observed. However, abundance determinations are rare or often unclear (e.g., for the X-ray bright K star in HR 1099, ${\rm [Fe/H]} = 0$ from Savanov & Tuominen 1991 but ${\rm [Fe/H]} \approx -0.6$ for Randich et al. 1994; these authors used solar abundances from Anders & Grevesse 1989, thus a correction of +0.17 dex must be introduced for the Fe abundance).

  
4.5 Coronal abundances in stars

RS CVn binaries show enhanced magnetic activity thought to arise from the tidal interaction with their companions. Intermediately active binaries often correspond to loosely bound stars. Our sample thus investigates the upper range of coronal activity. In contrast, the solar-like stars sampled by Güdel et al. (2002) span all activity levels. Assuming that abundance ratios relative to solar photospheric in our sample approximately correspond to ratios relative to stellar photospheric abundances, we have compared the correlation between the FIP bias and the coronal activity, here characterized by the average coronal temperature, in RS CVn binaries and in solar analogs (Fig. 7). The average coronal temperature for the solar analogs were obtained with the same procedure as in Sect. 3.3. They are similar to those derived in previous studies, e.g., Güdel et al. (1997). Low-FIP abundance ratios (here exemplified by Fe) vary dramatically with the coronal temperature, whereas high-FIP abundance ratios (exemplified by Ne) show no variation. Note that ratios relative to Fe naturally show the inverse trend (low-FIP ratios constant, high-FIP ratios increasing with temperature). Together with the apparent increase of the absolute Fe abundance with decreasing activity level in RS CVn binaries, this suggests that abundances of elements with low first ionization potential vary with magnetic activity, whereas those of elements with high FIP stay constant.

Figure 7: Fe/O and Ne/O abundance ratios relative to solar photospheric values (Anders & Grevesse 1989; Grevesse & Sauval 1999) for RS CVn and solar analogs using the XSPEC/APEC results (the SPEX/MEKAL results give similar relations) as a function of the average coronal temperature. Low-FIP abundance ratios follow an anticorrelation with $k\overline {T}$, whereas high-FIP elements show no correlation.