Elizabeth A. Myhill

Protostellar hydrodynamics: Constructing and testing a spatially and temporally second-order-accurate method. I - Spherical coordinates

In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.

TRIGGERING COLLAPSE OF THE PRESOLAR DENSE CLOUD CORE AND INJECTING SHORT-LIVED RADIOISOTOPES WITH A SHOCK WAVE. I. VARIED SHOCK SPEEDS

The discovery of decay products of a short-lived radioisotope (SLRI) in the Allende meteorite led to the hypothesis that a supernova shock wave transported freshly synthesized SLRI to the presolar dense cloud core, triggered its self-gravitational collapse, and injected the SLRI into the core. Previous multidimensional numerical calculations of the shock-cloud collision process showed that this hypothesis is plausible when the shock wave and dense cloud core are assumed to remain isothermal at ~10 K, but not when compressional heating to ~1000 K is assumed. Our two-dimensional models with the FLASH2.5 adaptive mesh refinement hydrodynamics code have shown that a 20 km s?1 shock front can simultaneously trigger collapse of a 1 M ? core and inject shock wave material, provided that cooling by molecular species such as H2O, CO, and H2 is included. Here, we present the results for similar calculations with shock speeds ranging from 1?km?s?1 to 100?km?s?1. We find that shock speeds in the range from 5?km?s?1 to 70?km?s?1 are able to trigger the collapse of a 2.2 M ? cloud while simultaneously injecting shock wave material: lower speed shocks do not achieve injection, while higher speed shocks do not trigger sustained collapse. The calculations continue to support the shock-wave trigger hypothesis for the formation of the solar system, though the injection efficiencies in the present models are lower than desired.

Simultaneous Triggered Collapse of the Presolar Dense Cloud Core and Injection of Short-Lived Radioisotopes by a Supernova Shock Wave

Cosmochemical evidence for the existence of short-lived radioisotopes (SLRIs) such as26Al and60Fe at the time of the formation of primitive meteorites requires that these isotopes were synthesized in a massive star and then incorporated into chondrites within ~106 yr. A supernova shock wave has long been hypothesized to have transported the SLRIs to the presolar dense cloud core, triggered cloud collapse, and injected the isotopes. Previous numerical calculations have shown that this scenario is plausible when the shock wave and dense cloud core are assumed to be isothermal at ~10 K, but not when compressional heating to ~1000 K is assumed. We show here for the first time that when calculated with the FLASH2.5 adaptive mesh refinement (AMR) hydrodynamics code, a 20 km s−1 shock wave can indeed trigger the collapse of a 1 M☉ cloud while simultaneously injecting shock wave isotopes into the collapsing cloud, provided that cooling by molecular species such as H2O, CO2, and H2 is included. These calculations imply that the supernova trigger hypothesis is the most likely mechanism for delivering the SLRIs present during the formation of the solar system.

Numerical models for the collapse and fragmentation of centrally condensed molecular cloud cores

A new hydrodynamical code is used to investigate the gravitational collapse and fragmentation of centrally condensed molecular cloud cores. The numerical scheme is second-order accurate and uses explicit finite difference methods to advance the fluid variables on a three-dimensional Cartesian grid. Two initial power-law density profiles are considered, ρ ∞ r -1 and ρ ∞ r -2 , as well as two initial density perturbations in the azimuthal coordinate θ, ρ i = ρ(1 + a cos 2θ) where a = 0.1 and 0.5

Second-order-accurate radiative hydrodynamics and multidimensional protostellar collapse

A second-order-accurate numerical scheme for computing the radiative hydrodynamics of three-dimensional, collapsing protostellar clouds has been developed and implemented in both spherical and cartesian coordinates. The scheme employs spatially second-order-accurate advective fluxes based on van Leer monotonic interpolation and consistent advection. The advective fluxes also contain the terms necessary to make the scheme temporally second-order-accurate in the presence of spatially and temporally varying velocity fields. A predictor-corrector treatment of the source terms completes the requirements for second-order accuracy in time. The Poisson equation for the gravitational potential is solved by either a spherical harmonic expansion or a Greens function method. Radiative transfer in the Eddington approximation is handled through the solution of a mean intensity equation. The numerical scheme has been shown to be second-order-accurate through convergence testing and has been shown to improve the performance on a shock propagation problem compared to schemes that do not contain the spatially and temporally second-order-accurate terms.