5 Concluding remarks

We performed detailed non-equilibrium calculations of the thermal and ionization structure of atomic, self-similar magnetically-driven jets from keplerian accretion disks. Current dissipation in ion-neutral collisions - ambipolar diffusion -, was assumed as the major heating source. Improvements over the original work of (Safier 1993a,b) include: a) detailed dynamical models by Ferreira (1997) where the disk is self-consistently taken into account but each magnetic surface assumed isothermal; b) ionization evolution for all relevant "heavy atoms'' using Mappings Ic code; c) radiation cooling by hydrogen lines, recombination and photoionization heating using Mappings Ic code; d) H-H⁺ momentum exchange rates including thermal contributions; and e) more detailed dust description.

We obtain, as Safier, warm jets with a hot temperature plateau at $T \simeq 10^4$ K. Such a plateau is a robust property of the atomic disk winds considered here for accretion rates less than a few times $10^{-5}~M_{\odot}$ yr ^-1. It is a direct consequence of the characteristic behavior of the wind function $G(\chi )$ defined in Eq. (26): (i) $G(\chi )$ increases first and becomes larger than a certain value fixed by the minimum ionization fraction (see Fig. 5); (ii) $G(\chi )$ is flat whenever ionization freezing occurs (collimated jet region). More generally, we formulate three analytical criteria that must be met by any MHD wind dominated by ambipolar diffusion heating and adiabatic cooling in order to converge to a hot temperature plateau.

The scalings of ionization fractions and temperatures in the plateau with $\dot{M}_{\rm acc}$ and $\varpi _0$ found by Safier are recovered. However the ionizations fractions are 10 to 100 times smaller, due to larger H-H⁺ momentum exchange rates (which include the dominant thermal velocity contribution ignored by Safier) and to different MHD wind dynamics.

We performed detailed consistency checks for our solutions and found that local charge neutrality, gas thermalization, single fluid description and ideal MHD approximation are always verified by our solutions. However at low accretion rates, for the base of outer wind regions ( $\varpi_0\sim 1$ AU) and increasingly for higher $\xi$, single fluid calculations become questionable. For the kind of jets under study, a multi-component description is necessary for field lines anchored after $\varpi_0 > 1$ AU. So far, all jet calculations assumed either isothermal or adiabatic magnetic surfaces. But our thermal computations showed such an increase in jet temperature that thermal pressure gradients might become relevant in jet dynamics. We therefore checked the "cold'' fluid approximation by computing the ratio of the thermal pressure gradient to the Lorentz force, along ( $\beta _\parallel$) and perpendicular ( $\beta _\perp$) to a magnetic surface. Both ratios increase for lower accretion rates and outer wind regions. We found that for some solutions, thermal pressure gradients play indeed a role, however only at the wind base (possible acceleration) and in the recollimation zone (possible support against recollimation). Fortunately, (as will be seen in a companion paper, Paper II), the dynamical solutions which are found inconsistent are also those rejected on an observational ground. Therefore, it turns out that the models that best fit observations are indeed consistent.

Acknowledgements

P. J. V. G. acknowledges financial support from Fundação para a Ciência e Tecnologia by the PRAXIS XXI/BD/5780/95, PRAXIS XXI/BPD/20179/99 grants. The work of LB was supported by the CONACyT grant 32139-E. We thank the referee, Pedro N. Safier, for his helpful comments. We acknowledge fruitful discussions with Alex Raga, Eliana Pinho, Pierre Ferruit and Eric Thiébaut. We are grateful to Bruce Draine for communicating his grain opacity data, and to Pierre Ferruit for providing his C interface to the Mappings Ic routine. P. J. V. G. warmly thanks the Airi team and his adviser, Renaud Foy, for their constant support.