Protostellar disks subject to infall: a one-dimensional inviscid model
  and comparison with ALMA observations
  A new one-dimensional, inviscid, and vertically integrated disk 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 disk-surface shock. Simulation parameters are chosen to target
the L1527 IRS disk which has been observed using ALMA (Atacama Large Millimeter
Array). The results give an outer envelope of radial infall and $u_\phi \propto
1/r$ which encounters a radial shock at $r_\mathrm{shock} \sim 1.5\ \times$ the
centrifugal radius ($r_\mathrm{c}$) across which the radial velocity is greatly
reduced and the temperature rises from a pre-shock value of $20$ K to $\approx
60$ K. At $r_\mathrm{c}$, the azimuthal velocity $u_\phi$ transitions from
being $\propto 1/r$ 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 $u_\phi \sim 1/r$ region to a
Keplerian inner disk. However, the observed position-velocity map of
cyclic-C$_3$H$_2$, together with a certain ballistic maximum velocity relation,
has suggested that the radial shock coincides with a ballistic centrifugal
barrier, which places the shock at $r_\mathrm{shock} = 0.5 r_\mathrm{c}$, i.e,
inward of $r_\mathrm{c}$, rather than outward as given by our simulations, as
well as previous magnetic rotating-collapse simulations. This discrepancy is
analyzed and discussed, but remains unresolved.
