2 Previous abundance determinations and the role of X-ray spectroscopy

These predictions of stellar evolution theory have of course been tested by optical spectroscopists. The principal source of information on the photospheric abundances of carbon and nitrogen in cool stars comes from CH and CN molecules which have absorption bands in the blue part of the spectrum (cf. Luck 1978; Parthasarathy et al. 1983). The measurements of carbon and nitrogen abundances are made even more difficult if the star is in rapid rotation; further, in Algol systems the much brighter primary star contaminates the spectrum, and useful data can only be obtained during a primary eclipse - if at all. Quantitative abundance determinations require the use of model atmospheres, which predict only relatively small effects in the blue part of the spectrum on varying the carbon and nitrogen abundances so that an accurate model of the atmospheric temperature stratification is required. Finally, a value for the oxygen abundance must be chosen or somehow determined from the data; this is particularly difficult if NLTE-effects are important as maybe the case for supergiants. Despite these difficulties, the secondaries of the Algol systems U Cep and U Sge have been studied by Parthasarathy et al. (1983), who find - relative to iron - a carbon deficiency and nitrogen enhancement as expected from theory. In the atmospheres of giants and supergiants anomalously large N/C-ratios were also reported (Luck 1978; Luck & Lambert 1981, 1985; Sneden et al. 1986). A summary of carbon/nitrogen abundance determinations is given by McCluskey & Kondo (1992).

Ultraviolet emission lines provide another means to obtain information on elemental abundances. Böhm-Vitense & Mena-Werth (1992) use the emission lines from C  II, C  IV, and N  V measured with the IUE satellite, to determine elemental abundances. Their approach heavily relies on the underlying form of the differential emission measure distribution function, which is assumed to have the form $EM = B\ T^{-\gamma}$, with T denoting temperature. The two constants B and $\gamma$ are found from the C  II and C  IV emission lines at 1330 Å and 1550 Å respectively, and the abundances of other elements (i.e., nitrogen and silicon) are then computed from a comparison of the observed line flux with those expected from the above power law emission measure distribution. With this method Böhm-Vitense & Mena-Werth (1992) find N/C-abundances in general agreement with photospherically derived abundances, but an inspection of their Table 4 reveals differences of up to $\Delta~\log{\rm (N/C)} = 0.79$ for individual stars.

X-ray spectroscopy opens up a new window to determine elemental abundances and to independently test the above described evolutionary scenarios. The specific advantage of X-ray lines is that they come directly from the atomic species, not from molecules with their sometimes rather complicated chemistry. Further, no assumptions on the abundance of oxygen have to be made. Here we will pursue an approach even independent of the coronal temperature stratification and only relying on hydrogen-like lines, the atomic physics of which appears to be well understood. We stress that the results derived in this paper do not assume a power-law emission measure distribution, and thus the only assumptions entering our abundance studies are the ionization equilibrium for carbon and nitrogen and the excitation rates for those lines.

The secondaries of Algol systems are - almost per definitionem - rapidly rotating and hence active late type stars. Most single giants in a volume-limited sample around the Sun are found to be X-ray sources (cf. Schröder et al. 1998), and only for a few stars really sensitive low upper limits to the absence of any X-ray emission have been established (cf. Ayres et al. 1991). Therefore for the secondaries of Algol systems as well as single giants X-ray emission is the rule rather than the exception. This X-ray emission is produced by plasma in collisional equilibrium at temperatures where carbon, nitrogen, and oxygen are predominantly found as helium-like and hydrogen-like ions. The strongest line from hydrogen-like ions is the Ly$_{\alpha }$-line, from helium-like ions it is the resonance line $^1{\rm S}_0{-}^1{\rm P}_1$ in the triplet transition array. The Ly$_{\alpha }$ lines of carbon, nitrogen, and oxygen are located at 34.74 Å, 24.74 Å, and 18.97 Å, and the helium-like resonance lines at 40.3 Å, 28.7 Å, and 21.6 Å respectively. They can therefore be perfectly observed with the LETGS onboard Chandra.

Figure 1: LETGS spectra (background subtracted) of Algol, $\beta$ Cet, UX Ari, and Procyon in the spectral regions 21-25 Å covering the O  VII triplet and the N  VII Ly$_{\alpha }$-line as well as 29-39 Å covering the C  VI Ly$_{\alpha }$-line; note the different relative strengths of the N and C Ly$_{\alpha }$-lines in the sample stars.

 

 

Table 1: Measured line fluxes and 1$\sigma$ errors for the N and C Ly$_{\alpha }$-lines and their flux ratio $R_{\rm NC}$, where effective areas by (Pease et al. 2000) were used.

	N  VII	C  VI	$R_{\rm NC}$
$\lambda$/Å	24.74	33.74	$\left(\frac{{\rm N}~\mathsc{vii}}{C~\mathsc{vi}}\right)\times$
$A_{\rm eff}$/cm2	15.26	11.59	$\frac{(A_{\rm eff}\lambda)_{{\rm C}_\mathsc{vi}}}{(A_{\rm eff}\lambda)_{{\rm N}_\mathsc{vii}}}$
Procyon	206.9 $\pm$ 16.95	697.5 $\pm$ 28.1	0.31 $\pm$ 0.03
$\pi^1$ UMa	17.9 $\pm$ 80	14.78 $\pm$ 80	1.25 $\pm$ 0.90
$\alpha$ Cen A	17.67 $\pm$ 11.44	117.65 $\pm$ 4.96	0.16 $\pm$ 0.10
$\alpha$ Cen B	32.07 $\pm$ 6.89	102.86 $\pm$ 11.26	0.32 $\pm$ 0.08
$\epsilon$ Eri	178.85 $\pm$ 15.85	289.88 $\pm$ 18.66	0.64 $\pm$ 0.07
YY Gem	91.8 $\pm$ 11.5	138.4 $\pm$ 13.3	0.69 $\pm$ 0.11
AD Leo	146.35 $\pm$ 14.41	203.38 $\pm$ 15.54	0.74 $\pm$ 0.12
HR 1099	501.93 $\pm$ 29.32	627.51 $\pm$ 29.62	0.83 $\pm$ 0.06
Capella	2280.3 $\pm$ 53.6	2151.1 $\pm$ 51.3	1.10 $\pm$ 0.04
UX Ari	602.85 $\pm$ 27.97	309.36 $\pm$ 20.95	2.02 $\pm$ 0.17
$\beta$ Cet	200.53 $\pm$ 16.5	24.48 $\pm$ 6.72	8.48 $\pm$ 2.44
Algol	1119.05 $\pm$ 38.38	<50	>23.3