cases with different input stellar XUV fluxes, showing outflow velocity (*upper-panel*), temperature (*middle-panel*), and ionization fraction (*lower-panel*) as functions of altitude throughout the simulation domain. In all panels, the crosses on each line show where the atmospheres become supersonic. []{data-label="fig:hydrogrid"}](TgasGrid.pdf "fig:"){width="45.00000%"} ![ Vertical structures of the hydrodynamically outflowing atmospheres for several cases with different input stellar XUV fluxes, showing outflow velocity (*upper-panel*), temperature (*middle-panel*), and ionization fraction (*lower-panel*) as functions of altitude throughout the simulation domain. In all panels, the crosses on each line show where the atmospheres become supersonic. []{data-label="fig:hydrogrid"}](VelGrid.pdf "fig:"){width="45.00000%"} ![ Vertical structures of the hydrodynamically outflowing atmospheres for several cases with different input stellar XUV fluxes, showing outflow velocity (*upper-panel*), temperature (*middle-panel*), and ionization fraction (*lower-panel*) as functions of altitude throughout the simulation domain. In all panels, the crosses on each line show where the atmospheres become supersonic. []{data-label="fig:hydrogrid"}](XionGrid.pdf "fig:"){width="45.00000%"}

![ Several properties of the outflowing atmospheres as functions of the input stellar X-ray flux. []{data-label="fig:hydrogridFx"}](TgasFxGrid.pdf "fig:"){width="45.00000%"} ![ Several properties of the outflowing atmospheres as functions of the input stellar X-ray flux. []{data-label="fig:hydrogridFx"}](altSonicFxGrid.pdf "fig:"){width="45.00000%"} ![ Several properties of the outflowing atmospheres as functions of the input stellar X-ray flux. []{data-label="fig:hydrogridFx"}](XionFxGrid.pdf "fig:"){width="45.00000%"}

![ *Upper-panel:* outward hydrodynamic mass flux 