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

(Abridged) 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 cosmic rays within the circumstellar environment and subsequently into the disk. In this work, we explore the hitherto neglected effects of cosmic ray 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 cosmic rays. We show that stellar winds can power a Heliosphere-like analogue, i.e., a "T-Tauriosphere," diminishing cosmic ray 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 cosmic ray modulation and a highly simplified estimate for "elevated" cosmic ray modulation as would be expected from a young T-Tauri star. In the former (solar analogue) case, we estimate the ionization rate from galactic cosmic rays to be zeta_CR~(0.23-1.4) x 1e-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 case, i.e., for a "T-Tauriosphere," the ionization rate by cosmic rays is zeta_CR<1e-20 s^-1, which is 1000 times smaller than the interstellar value. Indeed, if winds are as efficient at cosmic ray modulation as predicted here, short-lived radionuclides (now extinct) would have provided the major source of ionization (zeta_RN~7.3e-19 s^-1) in the planet-forming zone of the young Solar Nebula.