Abstract
Context. Planets form in protoplanetary discs. Their masses, distribution, and orbits sensitively depend on the structure of the protoplanetary discs. However, what sets the initial structure of the discs in terms of mass, radius and accretion rate is still unknown. Aims. It is therefore of great importance to understand exactly how protoplanetary discs form and what determines their physical properties. We aim to quantify the role of the initial dense core magnetisation, rotation, turbulence, and misalignment between rotation and magnetic field axis as well as the role of the accretion scheme onto the central object. Methods. We performed non-ideal magnetohydrodynamics numerical simulations using the adaptive mesh refinement code Ramses of a collapsing, one solar mass molecular core to study the disc formation and early, up to 100 kyr, evolution. We paid particular attention to the impact of numerical resolution and accretion scheme. Results. We found that the mass of the central object is almost independent of the numerical parameters such as the resolution and the accretion scheme onto the sink particle. The disc mass and to a lower extent its size, however heavily depend on the accretion scheme, which we found is itself resolution dependent. This implies that the accretion onto the star and through the disc are largely decoupled. For a relatively large domain of initial conditions (except at low magnetisation), we found that the properties of the disc do not change too significantly. In particular both the level of initial rotation and turbulence do not influence the disc properties provide the core is sufficiently magnetised. After a short relaxation phase, the disc settles in a stationary state. It then slowly grows in size but not in mass. The disc itself is weakly magnetised but its immediate surrounding on the contrary is highly magnetised. Conclusions. Our results show that the disc properties directly depend on the inner boundary condition, i.e. the accretion scheme onto the central object. This suggests that the disc mass is eventually controlled by a small-scale accretion process, possibly the star-disc interaction. Because of ambipolar diffusion and its significant resistivity, the disc diversity remains limited and except for low magnetisation, their properties are weakly sensitive to initial conditions such as rotation and turbulence.
Highlights
It is well established that planets form within circumstellar discs, and it is of fundamental importance to know the conditions under which these protoplanetary discs form as well as their physical characteristics such as mass (Testi et al 2014; Dutrey et al 2014)
While the statistics remain hampered by large uncertainties, it seems that there is a clear trend for the discs at this early stage to be limited in size; most discs have a radii below 60 AU and possibly even smaller. Understanding this initial phase is of primary importance to get the complete history of the process, and because the mass of the discs observed around T Tauri stars may not be massive enough to explain the mass of the observed planets (Greaves & Rice 2010; Najita & Kenyon 2014; Manara et al 2018); this suggests that planet formation may start early after protostar formation during the infall of the envelope while the disc is still fed by fresh interstellar medium (ISM) materials
Impact of turbulence The impact of turbulence on disc formation has been studied in the context of ideal MHD and it has been found (Santos-Lima et al 2012; Joos et al 2013) that it reduces the magnetic flux in the core inner part favouring disc formation. It has been proposed (Seifried et al 2013) that the disorganised structure of the field, induced by turbulence, reduces the effect of magnetic braking, while Gray et al (2018) conclude that the most important effect of turbulence is the misalignment it induces. Cases that included both turbulence and ambipolar diffusion are presented in Hennebelle et al (2016) and it has been found that the discs were not different from the cases in which no turbulence was initially present
Summary
It is well established that planets form within circumstellar discs, and it is of fundamental importance to know the conditions under which these protoplanetary discs form as well as their physical characteristics such as mass (Testi et al 2014; Dutrey et al 2014). Further gas is being accreted when the density becomes higher than nacc = nthres/3 within cells located at a distance less than 4dx, where dx is the size of the most refined grid from the sink particle. The reason is that in their calculations, ideal MHD was employed and no sink particle was used Both tend to produce smoother discs, which are easier to define. Ambipolar diffusion dissipates motions and sink particles make the discs much less massive and less prone to gravitational instabilities Another difference comes from the outflow cavities and their boundaries, which are denser in the ideal MHD case and tend to be picked by simple disc criteria. The loop itself does develop in one direction that is not isotropic, and because of gravity Rayleigh-Taylor fingers develop and fall back onto the sink
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