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.

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Context. Cosmic rays (CRs) are transported out of the galaxy by diffusion and advection due to streaming along magnetic field lines and resonant scattering off self-excited magnetohydrodynamic (MHD) waves. Thus momentum is transferred to the plasma via the frozen-in waves as a mediator assisting the thermal pressure in driving a galactic wind. Aims. Galactic CRs (GCRs) are accelerated by shock waves generated in supernova remnants (SNRs), and they propagate from the disc into the halo. Therefore CR acceleration in the halo strongly depends on the inner disc boundary conditions. Methods. We performed hydrodynamical simulations of galactic winds in flux tube geometry appropriate for disc galaxies, describing the CR diffusive-advective transport in a hydrodynamical fashion (by taking appropriate moments of the Fokker-Planck equation) along with the energy exchange with self-generated MHD waves. Results. Our time-dependent CR hydrodynamic simulations confirm that the evolution of galactic winds with feedback depends on the structure of the galactic halo. In case of a wind-structured halo, the wind breaks down after the last super nova (SN) has exploded. Conclusions. The mechanism described here offers a natural and elegant solution to explain the power-law distribution of CRs between the “knee” and the “ankle”. The transition will be naturally smooth, because the Galactic CRs accelerated at SN shocks will be “post-accelerated” by shocks generated at the inner boundary and travelling through the halo.

Context. The spin evolution of young protostars, surrounded by an accretion disk, still poses problems for observations and theoretical models. In recent studies, the importance of the magnetic star-disk interaction for stellar spin evolution has been elaborated. The accretion disk in these studies, however, is only represented by a simplified model and important features are not considered. Aims. A more realistic representation of the accretion disk is indispensable for a better understanding of the star-disk interaction and the stellar spin evolution. The aim of this study is to investigate the influence of a hydrodynamic disk evolution on the stellar rotational period and vice versa during the accretion phase. Methods. We combined the implicit hydrodynamic TAPIR disk code with a stellar spin evolution model. The influence of stellar magnetic fields on the disk dynamics, the radial position of the inner disk radius, as well as the influence of stellar rotation on the disk were calculated self-consistently. Results. Within a defined parameter space, we can reproduce the majority of fast and slow rotating stars observed in young stellar clusters. Additionally, the back reaction of different stellar spin evolutionary tracks on the disk can be analyzed. Disks around fast rotating stars are located closer to the star. Consequently, the disk midplane temperature in the innermost disk region increases significantly compared to slow rotating stars. We can show the effects of stellar rotation on episodic accretion outbursts. The higher temperatures of disks around fast rotating stars result in more outbursts and a longer outbursting period over the disk lifetime. Conclusions. The combination of a long-term hydrodynamic disk and a stellar spin evolution model allows the inclusion of previously unconsidered effects such as the back-reaction of stellar rotation on the long-term disk evolution and the occurrence of accretion outbursts. However, a wider parameter range has to be studied to further investigate these effects. Additionally, a possible interaction between our model and a more realistic stellar evolution code (e.g., the MESA code) can improve our understanding of the stellar spin evolution and its effects on the pre-main sequence star.

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