An interstellar origin for the beryllium 10 in calcium-rich, aluminum-rich inclusions

Beryllium 10 is a short-lived radionuclide (t_1/2 = 1.5 Myr) that was incorporated live into calcium-rich, aluminum-rich inclusions (CAIs) at the birth of our solar system. Beryllium 10 is unique among the short-lived radionuclides in that it is formed only by spallation reactions and not by nucleosynthesis, e.g., in a supernova. Recent work by McKeegan, Gounelle, and others has stated that the high initial abundance of ¹⁰Be in CAIs (¹⁰Be/⁹Be ≈ 1 × 10^-3) cannot be attributed to galactic cosmic rays (GCRs) and therefore concluded that the spallation reactions must have occurred within the solar nebula itself, because of energetic particles emitted by the early Sun. In this paper we reexamine this conclusion. We calculate the contributions of GCRs to the ¹⁰Be abundance in a molecular cloud core as it collapses to form a protostar and protoplanetary disk. We constrain the flux of protons and ¹⁰Be GCRs in the Sun's molecular cloud core 4.5 Gyr ago. We use numerical magneto-hydrodynamic simulations of star formation to model the time evolution of the magnetic field strength and column density of gas in a collapsing cloud core. We account for magnetic focusing and magnetic mirroring and the anisotropic distribution of GCR pitch angles in the cloud core. We calculate the rates at which GCR protons and α-particles induce spallation reactions producing ¹⁰Be atoms, and the rates at which GCR ¹⁰Be nuclei are trapped in the cloud core. Accounting also for the decay of ¹⁰Be over the evolution of the cloud core, we calculate the time-varying ¹⁰Be/⁹Be ratio. We find that at the time of protostar formation ¹⁰Be/⁹Be ≈ 1 × 10 ^-3, with an uncertainty of about a factor of 3. Spallation reactions account for 20% of the ¹⁰Be in CAIs, while trapped GCR ¹⁰Be nuclei account for the other 80%. The initial abundance of ¹⁰Be in CAIs is therefore entirely attributable to cosmic rays. We discuss the implications of this finding for the origin of other short-lived radionuclides and for the use of ¹⁰Be as a chronometer.