Reexamination of Cosmic-Ray Ionization Rate in Protoplanetary Disks with Sheared Magnetic Fields

The magnetic fields in protoplanetary disk are stretched to the azimuthal directions due to the velocity shear. Thus, the cosmic rays entering into the disk need to detour while propagating to the midplane. However, most of the previous studies assume that cosmic rays travel to the midplane straightly from the vertical direction.

 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 in the case that magnetic fields threading the protoplanetary disk are connected to its parent molecular cloud, and show that the cosmic-ray density around the disk should be 4 times lower than the isotropic ISM value. Then, we compute the attenuation of cosmic rays in protoplanetary disks. Our results show that the detouring effectively enhances the column density by about two orders of magnitude. 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 the inner to ~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.