Evolution of the solar nebula. VI. Mixing and transport of isotopic heterogeneity

Meteoritical studies have shown that the solar nebula was basically well mixed, as shown by the homogeneity of many isotopes of refractory elements. However, isotopic anomalies in certain elements, such as the short-lived isotope Al-26, imply the presence of either spatial or temporal heterogeneity. Spatial heterogeneity could result from the injection of short-lived isotopes into the solar nebula following their production in a supernova or from spraying these isotopes across the nebula's surface following their production by solar flares and transport outward by an X-wind. If the nebula was thoroughly mixed soon after the introduction of spatially heterogeneous Al-26, producing a homogeneous spatial distribution of Al-26, then the measured abundances of Al-26 would provide a chronometer for early solar system processes. For these reasons and others it is important to understand the efficiency of mixing and transport processes in the solar nebula. Here we study mixing and transport in fully three-dimensional models of gravitationally unstable disks that are likely to occur during the phase when planetesimal growth is beginning. The three-dimensional models show that isotopes that are sprayed onto an annular region of the surface of a disk around 9 AU remain remarkably concentrated after similar to 10(3) yr, in spite of mixing by convection, which transports material between the surface and midplane on timescales of similar to 30 yr, and radially inward and outward as well. Mixing caused by a generic turbulent viscosity dominates only when alpha greater than or equal to 0.01, implying that the effective alpha of the convective motions and gravitational torques is alpha similar to 10(-3). The three-dimensional models show that spatial heterogeneity can persist in a disk evolving by gravitational torques for significant periods, even in the most dynamically active region. This period, similar to10(3) yr, is similar to the timescale for presolar dust grains to coagulate while settling to the midplane and growing to centimeter size. If such solids can be preserved and incorporated into chondrites, then it is conceivable that some observed isotopic anomalies could have been derived from a spatially heterogeneous nebula.