Escape and evolution of Titans N$_2$ atmosphere constrained by $^{14}$N/$^{15}$N isotope ratios

We apply a 1D upper atmosphere model to study thermal escape of nitrogen over Titans history. Significant thermal escape should have occurred very early for solar EUV fluxes 100 to 400 times higher than today with escape rates as high as $approx 1.5times 10^{28}$ s$^{-1}$ and $approx 4.5times 10^{29}$ s$^{-1}$, respectively, while today it is $approx 7.5times 10^{17}$ s$^{-1}$. Depending on whether the Sun originated as a slow, moderate or fast rotator, thermal escape was the dominant escape process for the first 100 to 1000 Myr after the formation of the solar system. If Titans atmosphere originated that early, it could have lost between $approx 0.5 - 16$ times its present atmospheric mass depending on the Suns rotational evolution. We also investigated the mass-balance parameter space for an outgassing of Titans nitrogen through decomposition of NH$_3$-ices in its deep interior. Our study indicates that, if Titans atmosphere originated at the beginning, it could have only survived until today if the Sun was a slow rotator. In other cases, the escape would have been too strong for the degassed nitrogen to survive until present-day, implying later outgassing or an additional nitrogen source. An endogenic origin of Titans nitrogen partially through NH$_3$-ices is consistent with its initial fractionation of $^{14}$N/$^{15}$N $approx$ 166 - 172, or lower if photochemical removal was relevant for longer than the last $approx$ 1,000 Myr. Since this ratio is slightly above the ratio of cometary ammonia, some of Titans nitrogen might have originated from refractory organics.