Cosmic-ray ionization rate in protoplanetary disks with sheared magnetic fields

Abstract: We investigate the effects of magnetic field configurations on the ionization rate by cosmic rays in protoplanetary disks. First, we consider cosmic-ray propagation from the interstellar medium (ISM) to the protoplanetary disks and showed that the cosmic-ray density around the disk should be 2 times lower than the ISM value. Then, we compute the attenuation of cosmic rays in protoplanetary disks. The magnetic fields in the disk are stretched to the azimuthal directions, and cosmic rays need to detour while propagating to the midplane. Our results show that the detouring effectively enhances the column density by about two orders of magnitudes. We employ a typical ionization rate by cosmic rays in diffuse ISM, which is considered too high to be consistent with observations of protoplanetary disks, and find that the cosmic rays are significantly shielded at the midplane. In the case of the disk around IM Lup, the midplane ionization rate is very low for $r\lesssim\,100$ au, while the value is as large as a diffuse ISM in the outer radii. Our results are consistent with the recent ALMA observation that indicates the radial gradient in the cosmic-ray ionization rate. The high ionization rate in the outer radii of disks may activate the magnetorotational instability that was thought to be suppressed due to ambipolar diffusion. These results will have a strong influence on the dynamical and chemical evolutions of protoplanetary disks.