Combined radius of disk and possible spiral structures in dependence of cosmic-ray ionization rates ζ. For reference, the blue bar in the top middle panel indicates the size of a disk with 50 au in diameter. For the shrinking disks, the size of the outer ring denotes size of the initial disk, while the size of the inner bullet denotes the final disk size. For the disk+spiral/frag models, whose spiral structures are growing over time, the symbol size only marks the lower limit of the disk+spiral structures.