The Density of Coronal Plasma in Active Stellar Coronae

We have analyzed high-resolution X-ray spectra of a sample of 22 active stars observed with the High Energy Transmission Grating Spectrometer on {\em Chandra} in order to investigate their coronal plasma density. Densities where investigated using the lines of the He-like ions O VII, Mg XI, and Si XIII. While Si XIII lines in all stars of the sample are compatible with the low-density limit, Mg XI lines betray the presence of high plasma densities ($> 10^{12}$ cm$^{-3}$) for most of the sources with higher X-ray luminosity ($> 10^{30}$ erg/s); stars with higher $L_X$ and $L_X/L_{bol}$ tend to have higher densities at high temperatures. Ratios of O VII lines yield much lower densities of a few $10^{10}$ cm$^{-3}$, indicating that the ``hot'' and ``cool'' plasma resides in physically different structures. Our findings imply remarkably compact coronal structures, especially for the hotter plasma emitting the Mg XI lines characterized by coronal surface filling factor, $f_{MgXI}$, ranging from $10^{-4}$ to $10^{-1}$, while we find $f_{OVII}$ values from a few $10^{-3}$ up to $\sim 1$ for the cooler plasma emitting the O VII lines. We find that $f_{OVII}$ approaches unity at the same stellar surface X-ray flux level as solar active regions, suggesting that these stars become completely covered by active regions. At the same surface flux level, $f_{MgXI}$ is seen to increase more sharply with increasing surface flux. These results appear to support earlier suggestions that hot $10^7$ K plasma in active coronae arises from flaring activity, and that this flaring activity increases markedly once the stellar surface becomes covered with active regions.