On the sizes of stellar X-ray coronae

Spatial information from stellar X-ray coronae cannot be assessed directly, but scaling laws from the solar corona make it possible to estimate sizes of stellar coronae from the physical parameters temperature and density. While coronal plasma temperatures have long been available, we concentrate on the newly available density measurements from line fluxes of X-ray lines measured for a large sample of stellar coronae with the Chandra and XMM-Newton gratings. We compiled a set of 64 grating spectra of 42 stellar coronae. Line counts of strong H-like and He-like ions and Fe XXI lines were measured with the CORA single-purpose line fitting tool by Ness & Wichmann ( 2002). Densities are estimated from He-like f/i flux ratios of O VII and Ne IX representing the cooler (1-6 MK) plasma components. The densities scatter between log n(e) approximate to 9.5-11 from the O VII triplet and between log n(e) approximate to 10.5-12 from the Ne IX triplet, but we caution that the latter triplet may be biased by contamination from Fe XIX and Fe XXI lines. We find that low-activity stars (as parameterized by the characteristic temperature derived from H- and He-like line flux ratios) tend to show densities derived from O VII of no more than a few times 10(10) cm(-3), whereas no definitive trend is found for the more active stars. Investigating the densities of the hotter plasma with various Fe XXI line ratios, we found that none of the spectra consistently indicates the presence of very high densities. We argue that our measurements are compatible with the low-density limit for the respective ratios (approximate to5 x 10(12) cm(-3)). These upper limits are in line with constant pressure in the emitting active regions. We focus on the commonly used Rosner et al. (1978) scaling law to derive loop lengths from temperatures and densities assuming loop-like structures as identical building blocks. We derive the emitting volumes from direct measurements of ion-specific emission measures and densities. Available volumes are calculated from the loop-lengths and stellar radii, and are compared with the emitting volumes to infer filling factors. For all stages of activity we find similar filling factors up to 0.1.