Protostellar discs subject to infall: a one-dimensional inviscid model and comparison with ALMA observations

Abstract

A new one-dimensional, inviscid, and vertically integrated disc model with prescribed infall is presented. The flow is computed using a second-order shock-capturing scheme. Included are vertical infall, radial infall at the outer radial boundary, radiative cooling, stellar irradiation, and heat addition at the disc-surface shock. Simulation parameters are chosen to target the L1527 IRS disc which has been observed using Atacama Large Millimeter Array (ALMA). The results give an outer envelope of radial infall and uφ∝ /r which encounters a radial shock at rshock ∼1.5 × the centrifugal radius (rc) across which the radial velocity is greatly reduced and the gas temperature rises from a pre-shock value of ≈25 to ≈180 K over a spatially thin region calculated using a separate shock structure code. At rc, the azimuthal velocity uφ transitions from being ∝1/r to being nearly Keplerian. These results qualitatively agree with recent ALMA observations which indicate a radial shock where SO is sublimated as well as a transition from a uφ ∼1/r region to a Keplerian inner disc. However, in one set of observations, the observed position-velocity map of cyclic-C3H2, together with a certain ballistic maximum velocity relation suggests that the radial shock coincides with a ballistic centrifugal barrier, which places the shock at rshock = 0.5rc, i.e. inward of rc, rather than outward as given by our simulations. It is argued that radial velocity plots from previous magnetic rotating-collapse simulations also indicate that the radial shock is located outward of rc. The discrepancy with observations is analysed and discussed, but remains unresolved.