Abstract
We determine analytically the onset of thin-shell formation time of fast wind bubble with power-law energy injection $E_{in}=E_0t^s$, and power-law ambient density structure, ${\rho}_0(r)={\bar{\rho}}(r/{\bar{r}})^{-{\omega}}$. Thin-shell formation time, $t_{sf}$ can be estimated by minimizing the total time elapsed before the complete cooling of shocked gas. For uniform medium (${\omega}=0$) and constant energy injection (s = 1), the onset of shell formation is found to be at $t_{sf}=5.2{\times}10^3yr$, which agrees Quite well with the results of FCT 1D numerical calculation. We solve the line transfer problem with previous result derived by numerical calculation in order to calculate line profile of [OIII] (${\lambda}=5007{\AA}$) forbidden line. In general, radiative outer shell causes the formation of double peaked line profile. Each peak corresponds to approaching and receeding shells with large velocities. Our line profiles show good agreements with observation of expanding shell structure.
