The formation of binary star cluster in our galaxy from fractal stellar distribution

Observations showed that there are star clusters in paired condition, called as binary star cluster. Some statistical studies attempted to identify the existence of binary and multiple clusters in our Galaxy and Magellanic Clouds. MIStiX survey also found that most of embedded younger star clusters (a few Myr) have clumpy structures, indicating star distribution in young clusters cannot be simply described as spherical shape. This structure can be the key-factor of the formation of primordial binary cluster in our Galaxy. In this work, we simulate the formation of binary star cluster from fractal distribution in isolated condition and under Galactic tidal field for 50 Myr. This aims to investigate the most probable condition to let the highly formation of binary star cluster in our Galaxy and the role of Galactic tidal field in that formation. We find that the clumpier structure of star cluster, the number of binary/multiple cluster will increase, and the same condition also occurs for the warmer condition or higher α_vir (the kinetic to potential energy ratio). But this number will decrease at larger time due to the merger processes between the star clusters. By these arguments, we conclude that the most probable condition of star cluster to let the highly formation of binary star cluster is the one with highly sub structured and warm condition. For such condition of star cluster, the fraction of binary/multiple in our Galaxy is 0.87 ± 0.06 at time 20 Myr and decreases to be 0.63 ± 0.09 at time 50 Myr, with reduction 0.24 ± 0.08. As comparison, this reduction is only 0.07 ± 0.05 for the same condition in isolated. The higher deflation shows that the Galactic tidal field has important role in the formation of binary star cluster, as well as the initial mass of star cluster. And we suggest the discovery of multiple clusters in this work is interesting to learn more deeply in the future work.