1 Introduction

The hot plasma in the corona of the Sun and of other stars is thought to be in "coronal equilibrium''. Atomic excitations occur through collisions with electrons. The excited atoms decay radiatively and the emitted radiation escapes without any further interaction with the emitting plasma. As a consequence, the emission is optically thin, and the total flux emitted in some spectral band or in a given emission line is proportional to the emission measure EM, defined as the integral of the square of the plasma density n over the emitting volume elements dV through $EM = \int n^2 {\rm d}V$ . Thus, observationally, the contributions of density and volume to a given observed value of EM cannot be disentangled.

Stellar X-ray surveys carried out with the Einstein and ROSAT satellites have shown an enormous range of X-ray luminosity ( $L_{\rm X}$ ) for stars of given spectral type (cf., Vaiana et al. 1981; Schmitt 1997). Typically, one observes star to star variations in $L_{\rm X}$ of up to four orders of magnitude, with the largest X-ray luminosities found among the stars with the largest rotation rates. While one definitely finds a correlation between mean coronal temperature and X-ray luminosity (Schmitt et al. 1985; Schmitt 1997), it is also clear that the single-most important factor contributing to the large variations in $L_{\rm X}$ is the variation in emission measure. The conclusion therefore is that active stars (can) have a couple of orders of magnitude higher coronal emission measure, while maintaining the same optical output as low-activity stars like our Sun.

The emission measure is directly linked to the structure of stellar coronae, if we assume, going along with the solar analogy, that the X-ray emitting plasma of a stellar corona is confined in magnetic loops. The observed values of EM and $L_{\rm X}$ for a given star could be accounted for either by the existence of more loops than typically visible on the solar surface, by higher density loops or by longer, more voluminous loops. Thus the question is reduced to the following: if $EM_{\star} \gg EM_{\odot}$ for an active star, one wants to know whether this is due to $n_{\star} > n_{\odot}$ or $V_{\star} > V_{\odot}$ or both.

Spatially resolved solar observations allow to disentangle density and volume contributions to the overall emission measure. One finds the total X-ray output of the Sun dominated - at least under maximum conditions - by the emission from rather small, dense loops. Stellar coronae always appear as point sources. The only way to infer structural information in these unresolved point sources has been via eclipse studies in suitably chosen systems where one tries to constrain the emitting plasma volume from the observed light curve. Another method to infer structure in spatially unresolved data are spectroscopic measurements of density. The emissivity of plasma in coronal equilibrium in carefully selected lines does depend on density. Some lines may be present in low-density plasmas and disappear in high-density plasmas such as the forbidden lines in He-like triplets, while other lines may appear in high-density plasmas and be absent in low-density plasmas (such as lines formed following excitations from excited levels). With the high-resolution spectroscopic facilities onboard Chandra it is possible to carry out such studies for a wide range of X-ray sources. The purpose of this paper is to present and discuss some key density diagnostics available in the high-resolution grating spectra obtained with Chandra. We will specifically discuss the spectra obtained with the Low Energy Transmission Grating Spectrometer (LETGS) for the stars Capella and Procyon.

**Table 1:** Properties of Procyon and Capella: mass M, radius R, effective temperature $T_{\rm eff}$ , log g and the limb darkening coefficient $\epsilon$
	Procyon	Capella
d/pc	3.5	13
$M/M_\odot$	$1.7\pm0.1^4$	$2.56\pm0.04^3$
$R/R_\odot$	$2.06\pm0.03^4$	$9.2\pm0.4^3$
$T_{\rm eff}$ /K	$6530\pm 90^2$	$5700\pm 100^3$
log g	$4.05\pm0.04^2$	$2.6\pm0.2^5$
Spectr. type	F5 IV-V	Ab: G1 III
		(Aa: G8/K0 III)
$\epsilon$	0.724¹	0.83¹

Both Capella and Procyon are known to be relative steady and strong X-ray sources; no signatures of flares from these stars have ever been reported in the literature. Both Capella and Procyon are rather close to the Sun at distances of 13 pc and 3.5 pc (Table 1), so that effects of interstellar absorption are very small. Both of them have been observed with virtually all X-ray satellites flown so far. Capella was first detected as an X-ray source by Catura et al. (1975), and confirmed by Mewe et al. (1975), Procyon by Schmitt et al. (1985). The best coronal spectra of Capella were obtained with the Einstein Observatory FPCS and OGS (Vedder et al. 1983; Mewe et al. 1982), the EXOSAT transmission grating (Mewe et al. 1986; Lemen et al. 1989) and EUVE (Dupree et al. 1993; Schrijver et al. 1995), while high-spectral resolution spectral data for Procyon have been presented by Mewe et al. (1986) and Lemen et al. (1989) using EXOSAT transmission grating data and Drake et al. (1995) and Schrijver et al. (1995) using EUVE data. Note that Schmitt et al. (1996b) and Schrijver et al. (1995) investigated the coronal density of Procyon using a variety of density sensitive lines from Fe X to Fe XIV in the EUV range and found Procyon's coronal density consistent with that of solar active region densities.

The plan of our paper is as follows: We first briefly review the atomic physics of He-like ions as applicable to solar (and our stellar) X-ray spectra. We briefly describe the spectrometer used to obtain our data, and discuss in quite some detail the specific procedures used in the data analysis, since we plan to use these methods in all our subsequent work on Chandra and XMM-Newton spectra. We then proceed to analyze the extracted spectra and describe in detail how we dealt with the special problem of line blending with higher dispersion orders. Before presenting our results we estimate the formation temperatures of the lines, the influence of the stellar radiation field and the influence of optical depth effects followed by detailed interpretation. The results will then be compared to measurements of the Sun and we close with our conclusions.

References:
¹Díaz-Cordovés et al. (1995).
²Fughrman et al. (1997).
³Hummel et al. (1994).
⁴Irwin et al. (1992).
⁵Kelch et al. (1978).