P. N. Foster

Gravitational collapse of an isothermal sphere

We investigate the spherical gravitational collapse of isothermal spheres using numerical hydrodynamics. The initial configuration is close to hydrostatic equilibrium. In the initial density profile has a finite core radius (i.e., it is not singular), supersonic velocities develop during the initial collapse. At the time of central core formation, when the central density diverges, the central inflow velocity approaches −3.3 times the sound speed and the central density approaches an r −2 profile. These conditions are similar to those found in the self-similar solution of Larson and Penston, but occur only at the center and not at all radii as in the self-similar solution at core formation

INJECTION OF RADIOACTIVE NUCLIDES FROM THE STELLAR SOURCE THAT TRIGGERED THE COLLAPSE OF THE PRESOLAR NEBULA

We examine the gravitational capture of supersonic gas and dust as it impacts and triggers the collapse of a molecular cloud core. We use two techniques to track the triggering material in two dimensions, a set of tracer particles and a color field, much like a dye, computed in the same manner as the hydrodynamic density variable. The two tracking techniques produce very similar results. We find that about 10% to 20% of the supersonic material with an initial impact parameter less than the molecular cloud cores initial radius is captured by the collapsing cloud. This fraction is less than the 100% capture estimate often used to constrain the distance to possible stellar sources of radioactive isotopes, and hence may require these stars to be closer than would otherwise be the case. Rayleigh-Taylor instabilities occur and aid in the mixing of the shock material with the target cloud. The impacting material is injected into the outer layers of the collapsing protostar roughly one free-fall time (2 × 105 yr) after the first contact of the triggering material with the cloud, and injection continues for approximately two more free-fall times. These time intervals are substantially less than the mean life of one of the radioactive nuclides of interest, 1.1 × 106 yr for 26Al, and are comparable to the mean life (1.5 × 105 yr) of another short-lived nuclide,41Ca. Evidence for live 26Al and 41Ca in the early solar system is thus consistent with a scenario involving supersonic triggering and injection of freshly synthesized radioactive nuclides into the presolar cloud. Because injection proceeds at a steady pace, it does not appear to be a significant source of temporal heterogeneity in the distribution of 26Al, though the outer layers of the presolar cloud are preferentially enriched in the injected material.

Injection of short-lived isotopes into the presolar cloud

The evidence for short-lived isotopes such as -->26Al and -->41Ca in meteorites requires their production either by irradiation in the solar nebula or by nucleosynthesis in a supernova or other evolved star. In the latter case, nucleosynthesis must be followed promptly by injection of the isotopes into the presolar cloud, a feat presumably accomplished by the same stellar outflow that transported the isotopes to the presolar cloud and possibly triggered its collapse. If their nucleosynthesis occurs deep within an unmixed star, the short-lived isotopes may lag far behind the leading edge of the stellar outflow, perhaps preventing their injection. However, we show that lagging isotopes can be injected into a collapsing protostar with an efficiency similar to that of material in the leading edge of the outflow, because fast-moving isotopes initially far behind (approximately a few parsecs) the leading edge impact and enter the cloud while the injection process is still underway. Isotope injection proceeds through Rayleigh-Taylor-like clumps in the shock-compressed target cloud.

Triggering presolar cloud collapse and injecting material into the presolar nebula

The evidence for short-lived radioisotopes in chondritic meteorites requires that no more than about a million years elapsed between nucleosynthesis of the isotopes and the formation of cm-sized solids in the solar nebula. We show that this abbreviated time scale can be best accommodated in a scenario where an interstellar shock wave transports the isotopes from the parent star to the presolar cloud, triggers the collapse of the presolar cloud, and injects a significant fraction of its dust grains into the presolar cloud. Shock waves from both distant supernovae and from evolved red giant (AGB) stars appear to have sufficient momentum to trigger collapse of a solar-mass cloud. In addition to momentum-induced collapse, the high temperature regions further behind supernova shock fronts and planetary nebulae shells are also able to crush a presolar cloud into collapsing. Both supernovae and AGB star shock waves are able to inject about 10% to 20% of their incident dust grains into the collapsing presolar cloud.