We have analyzed high-resolution X-ray spectra of a sample of 22 active stars observed with the High Energy Transmission Grating Spectrometer on 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 .
Si XIII lines in all stars of the sample are compatible with the low-density limit ( i.e. n _ { \mathrm { e } } \lesssim 10 ^ { 13 }  cm ^ { -3 } ) , casting some doubt on results based on lower resolution EUVE spectra finding densities n _ { \mathrm { e } } > 10 ^ { 13 }  cm ^ { -3 } .
Mg XI lines betray the presence of high plasma densities up to a few 10 ^ { 12 }  cm ^ { -3 } for most of the sources with higher X-ray luminosity ( \gtrsim 10 ^ { 30 }  erg/s ) ; stars with higher L _ { \mathrm { X } } and L _ { \mathrm { X } } / L _ { \mathrm { bol } } 
tend to have higher densities at high temperatures .
Ratios of OÂ VII lines yield much lower densities of a few 10 ^ { 10 } Â cm ^ { -3 } , indicating that the “ hot ” and “ cool ” plasma resides in physically different structures .
In the cases of EV Lac , HD 223460 , Canopus , \mu  Vel , TY Pyx , and IM Peg , our results represent the first spectroscopic estimates of coronal density .
No trends in density-sensitive line ratios with stellar parameters effective temperature and surface gravity were found , indicating that plasma densities are remarkably similar for stars with pressure scale heights differing by up to 3 orders of magnitude .
Our findings imply remarkably compact coronal structures , especially for the hotter ( \sim 7  MK ) plasma emitting the Mg XI lines characterized by coronal surface filling factor , f _ { \mathrm { MgXI } } , ranging from 10 ^ { -4 } to 10 ^ { -1 } , while we find f _ { \mathrm { OVII } } values from a few 10 ^ { -3 } up to \sim 1 
for the cooler ( \sim 2 Â MK ) plasma emitting the OÂ VII lines .
We find that f _ { \mathrm { 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 _ { \mathrm { MgXI } } is seen to increase more sharply with increasing surface flux .
These results appear to support earlier suggestions that hot 10 ^ { 7 } Â 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 .
Comparison of our measured line fluxes with theoretical models suggests that significant residual model inaccuracies might be present , and in particular that cascade contributions to forbidden and intercombination lines resulting from dielectronic recombination might be to blame .