In this paper, we try to study the fragmentation conditions of self-gravitational accretion disk in Dead zone. This region is located between 1 and 5 AU from the star. There is a high bump density at the outer boundary of Dead Zone. A bump surface density leads to the production of instability and vortices. Vortices can produce the spiral waves and affect the fragmentation conditions in the system. So, in this paper, we assume a bump density perturbation and obtain the Jeans mass, time scale of fragmentation and critical cooling time for fragmentation. Results show that the critical cooling time has larger values around the density peak. This value is dependent on amplitude and width of bump density (βcrit ∼ 14 for F = 1.3). Therefore, systems with long cooling time can be fragment. Also, the results show that in some areas near the peak, the cooling time can be less than the critical cooling time, which depends on the width and peak of the bump (βc < βcrit). Also the results show that in some disks, the critical cooling time is less than the cooling time of system in thermal equilibrium state. It is found that in the presence of bump density perturbation, the critical value of β is dependent on the radius and it does not have a same value in all radii. Other result obtained from this study is that the Jeans mass decreases near the peak of density and therefore the probability of gravitational instability increases in this area. The Minimum Jeans mass is obtained 0.005Msun ∼ 5MJup for disk with low accretion rate.
