We examine, parametrically, the interaction between the magnetosphere of a rotating, young stellar object (YSO) and a circumstellar accretion disk using 2.5-D (cylindrically symmetric) numerical magnetoydrodynamic simulations. The interaction drives a collimated outflow, and we find that the jet formation mechanism is robust. For variations in initial disk density of a factor of 16, variations of stellar dipole strength of a factor of 4, and for various initial conditions with respect to the disk truncation radius and the existence of a disk field, outflows with similar morphologies were consistently produced. Secondly, the system is self-regulating, where the outflow properties depend relatively weakly on the parameters above. The large scale magnetic field structure rapidly evolves to a configuration that removes angular momentum from the disk at a rate that depends most strongly on the field and weakly on the rotation rate of the foot-points of the field in the disk and the mass outflow rate. Third, the simulated jets are episodic, with the timescale of jet outbursts identical to the timescale of magnetically induced oscillations of the inner edge of the disk. To better understand the physics controlling these disk oscillations, we present a semi-analytical model and confirm that the oscillation period is set by the spin down rate of the disk inner edge. Finally, our simulations offer strong evidence that it is indeed the interaction of the stellar magnetosphere with the disk, rather than some primordial field in the disk itself, that is responsible for the formation of jets from these systems.
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