The fragmentation of protoplanetary disks by the self-gravitational
instability is a candidate mechanism for the formation of the distant
gas giants that have been observed. Since the formation of such a
planet by dust growth would take too long, self-gravitational
fragmentation, which takes less time than dust growth, is considered as
the most likely mechanism. While the self-gravitational instability has
been investigated as a formation mechanism for the observed planets, the
fragmentation condition is still under debate. Takahashi et al.
(2016) found that after the formation of spiral arms in a
self-gravitating disk, the condition for the self-gravitational
fragmentation is given by "the condition that the spiral arm structure
becomes self-gravitationally unstable." This result indicates that in
order to predict whether the disk fragmentation occurs or not, it is
necessary to clarify the conditions under which gravitationally
unstable spiral arms are formed. In particular, a protoplanetary disk
is expected to be gravitationally unstable at the disk formation
stage. In this study, we investigate the conditions for the disk
fragmentation during the disk formation stage by performing
two-dimensional hydrodynamic simulations. The spiral arms formed in
the disk are closely related to the mass accretion rate of the disk
through the angular momentum transport by the gravitational torque. We
show the relationship between the self-gravitational fragmentation of
the disk, the mass accretion rate and the angular momentum transfer in
the disk, and discuss the condition of the disk fragmentation.