  Using the homogeneous X-ray catalog from ROSAT observations, we conducted a
comprehensive investigation into stellar X-ray activity-rotation relations for
both single and binary stars. Generally, the relation for single stars consists
of two distinct regions: a weak decay region, indicating a continued dependence
of the magnetic dynamo on stellar rotation rather than a saturation regime with
constant activity, and a rapid decay region, where X-ray activity is strongly
correlated with the Rossby number. Detailed analysis reveals more fine
structures within the relation: in the extremely fast rotating regime, a
decrease in X-ray activity was observed with increasing rotation rate, referred
to as super-saturation, while in the extremely slow rotating region, the
relation flattens, mainly due to the scattering of F stars. This scattering may
result from intrinsic variability in stellar activities over one stellar cycle
or the presence of different dynamo mechanisms. Binaries exhibit a similar
relation to that of single stars while the limited sample size prevented the
identification of fine structures in the relation for binaries. We calculated
the mass loss rates of planetary atmosphere triggered by X-ray emissions from
host stars. Our findings indicate that for an Earth-like planet within the
stellar habitable zone, it would easily lose its entire primordial H/He
envelope (equating to about 1% of the planetary mass).
