There is a subclass of the X-ray jets from young stellar objects which are heated very close to the footpoint of the jets, particularly DG Tau jets. Previous models attribute the strong heating to shocks in the jets. However, the mechanism that localizes the heating at the footpoint remains puzzling. We presented a different model of such X-ray jets, in which the disk atmosphere is magnetically heated. Our disk corona model is based on the so-called nanoflare model for the solar corona. We show that the magnetic heating near the disks can result in the formation of a hot corona with a temperature of > 10^6 K even if the average field strength in the disk is moderately weak, > 1 G. We determine the density and the temperature at the jet base by considering the energy balance between the heating and cooling. We derive the scaling relations of the mass loss rate and terminal velocity of jets. Our model is applied to the DG Tau jets. The observed temperature and estimated mass loss rate are consistent with the prediction of our model in the case of the disk magnetic field strength of ~20 G and the heating region of < 0.1 au. The derived scaling relation of the temperature of X-ray jets could be a useful tool to estimate the magnetic field strength. We also found that the jet X-ray can have a significant impact on the ionization degree near the disk surface and the dead-zone size.
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