Exclusion of Cosmic Rays in Protoplanetary Disks: Stellar and Magnetic Effects

Cosmic rays (CRs) are thought to provide an important source of ionization in the outermost and densest regions of protoplanetary disks; however, it is unknown to what degree they are physically present. As is observed in the solar system, stellar winds can inhibit the propagation of CRs within the circumstellar environment and subsequently into the disk. In this work, we explore the hitherto neglected effects of CR modulation by both stellar winds and magnetic field structures and study how these processes act to reduce disk ionization rates. We construct a two-dimensional protoplanetary disk model of a T-Tauri star system, focusing on ionization from stellar and interstellar FUV, stellar X-ray photons, and CRs. We show that stellar winds can power a heliosphere-like analog, i.e., a "T-Tauriosphere," diminishing CR ionization rates by several orders of magnitude at low to moderate CR energies (E _CR <= 1 GeV). We explore models of both the observed solar wind CR modulation and a highly simplified estimate for "elevated" CR modulation as would be expected from a young T-Tauri star. In the former (solar analog) case, we estimate the ionization rate from galactic CRs to be ζ_CR ~ (0.23-1.4) × 10^-18 s^-1. This range of values, which we consider to be the maximum CR ionization rate for the disk, is more than an order of magnitude lower than what is generally assumed in current models for disk chemistry and physics. In the latter elevated case, i.e., for a "T-Tauriosphere," the ionization rate by CRs is ζ_CR <~ 10^-20 s^-1, which is 1000 times smaller than the interstellar value. We discuss the implications of a diminished CR ionization rate on the gas physics by estimating the size of the resulting magnetorotational instability dead zones. Indeed, if winds are as efficient at CR modulation as predicted here, short-lived radionuclides (now extinct) would have provided the major source of ionization (ζ_RN ~ 7.3 × 10^-19 s^-1) in the planet-forming zone of the young solar nebula.