show the results of individual simulations []{data-label="fig:MdotgridFx"}](NfluxGrid.pdf "fig:"){width="43.00000%"} ![ *Upper-panel:* outward hydrodynamic mass flux at $10^5$ km altitude as a function of input stellar X-ray flux. *Middle-panel:* outward hydrodynamic particle fluxes of oxygen and hydrogen atoms (including those contained in molecules and ions), with the solid lines and circles showing the simulation results and the dotted red line showing half the hydrogen flux, indicating the oxygen loss rate expected if the dissociation products of H$_2$O were lost with the same efficiency. *Lower-panel:* fractionation factors for H and D, $f_\mathrm{H,D}$, and for H and O, $f_\mathrm{H,O}$, as a function of the mass flux. In all panels, the circles show the results of individual simulations []{data-label="fig:MdotgridFx"}](fractionationMfluxGrid.pdf "fig:"){width="43.00000%"}

To understand the hydrodynamic outflow of water vapor atmosphere, I calculate fourteen models for an Earth-mass planet with a fully H$_2$O atmosphere orbiting a solar mass star at 1 AU. The cases considered differ in the input stellar XUV spectrum calculated using the method and codes presented by @Claire12. Specifically, I use the their solar spectra corresponding to solar ages of 4.25, 4.30, 4.35, 4.40, 4.45, 4.46, 4.47, 4.48, 4.49, 4.50, 4.51, 4.52, 4.53, and 4.54 Gyr ago. Note however that the correspondence between age 