2010MNRAS.408..436L

We present the theoretical results of a piecewise isothermal shock wind model. This was devised to predict the luminosity and surface brightness profile of diffuse X-ray emissions, primarily from the inner shocked downstream wind zone of a planetary nebula (PN) surrounded by a self-similar shocked dense shell and self-similar outer slow asymptotic giant branch wind envelope, both involving self-gravity. We compare and fit our computational model results with the available observations of a few grossly spherical X-ray emitting PNe. By matching the shocked piecewise isothermal self-similar void solutions with the self-gravity of Lou and Zhai for the outer zone and a stationary isothermal fast tenuous wind with a reverse shock for the inner zone across an expanding contact discontinuity, we can consistently construct dynamic evolution models of PNe with diffuse X-ray emissions. On the basis of such a chosen dynamic wind interaction model, both the X-ray luminosity and the radial X-ray brightness profile are determined by three key parameters: the so-called X-ray parameter, X, and two radii, R_rs and R_c, of the reverse shock and the contact discontinuity. We find that the morphologies of X-ray emissions appear in the forms of either a central luminous sphere or a bright ring embedded within optically bright shells. In contrast to previous adiabatic models, the X-ray brightness peaks around the reverse shock, instead of the contact discontinuity surface just inside the outer shocked dense shell. The diffuse X-ray emissions of a few observed PNe appear to support this piecewise isothermal wind-wind dynamic interaction scenario with shocks.