Time-dependent, long-term hydrodynamic simulations of the inner protoplanetary disk

Abstract

Aims. We conduct simulations of the inner regions of protoplanetary disks (PPDs) to investigate the effects of protostellar magnetic fields on their long-term evolution. We use an inner boundary model that incorporates the influence of a stellar magnetic field. The position of the inner disk is dependent on the mass accretion rate as well as the magnetic field strength. We use this model to study the response of a magnetically truncated inner disk to an episodic accretion event. Additionally, we vary the protostellar magnetic field strength and investigate the consequences of the magnetic field on the long-term behavior of PPDs. Methods. We use the fully implicit 1+1D TAPIR code which solves the axisymmetric hydrodynamic equations self-consistently. Our model allows us to investigate disk dynamics close to the star and to conduct long-term evolution simulations simultaneously. We assume a hydrostatic vertical configuration described via an energy equation which accounts for the radiative transport in the vertical direction in the optically thick limit and the equation of state. Moreover, our model includes the radial radiation transport in the stationary diffusion limit and takes protostellar irradiation into account. Results. We include stellar magnetic torques, the influence of a pressure gradient, and a variable inner disk radius in the TAPIR code to describe the innermost disk region in a more self-consistent manner. We can show that this approach alters the disk dynamics considerably compared to a simplified diffusive evolution equation, especially during outbursts. During a single outburst, the angular velocity deviates significantly from the Keplerian velocity because of the influence of stellar magnetic torques. The disk pressure gradient switches sign several times and the inner disk radius is pushed towards the star, approaching < 1.2 R⋆. Additionally, by varying the stellar magnetic field strength, we can demonstrate several previously unseen effects. The number, duration, and the accreted disk mass of an outburst as well as the disk mass at the end of the disk phase (after several million years) depend on the stellar field strength. Furthermore, we can define a range of stellar magnetic field strengths, in which outbursts are completely suppressed. The robustness of this result is confirmed by varying different disk parameters. Conclusions. The influences of a prescribed stellar magnetic field, local pressure gradients, and a variable inner disk radius result in a more consistent description of the gas dynamics in the innermost regions of PPDs. Combining magnetic torques acting on the innermost disk regions with the long-term evolution of PPDs yields previously unseen results, whereby the whole disk structure is affected over its entire lifetime. Additionally, we want to emphasize that a combination of our 1+1D model with more sophisticated multi-dimensional codes could improve the understanding of PPDs even further.