Infrared bubbles provide a unique opportunity to study the interactions between massive stars and surrounding material. We conduct a multi-wavelength study on the environment and star formation around an infrared bubble N 13. Three dust clumps and two molecular clumps are identified around N 13, which are all distributed on the layer. Young stellar objects (YSOs) are carefully searched using infrared colors and YSO candidates of WISE and Gaia DR2, and three Class I/II YSOs are found in N 13. In addition, four O-type stars identified in N 13 are probably the exciting stars. The dynamical and fragmentation ages of N 13 are 0.32–0.35 and 1.37–2.80 Myr respectively, which suggest that the radiation-driven implosion model may be dominant in N 13. By comparing the small-size bubble N 13 (R ∼ 1.9 pc) and the larger-size bubble G15.684-0.29 (R ∼ 15.7 pc) we found that star formation activity is more active in the large-size bubble. Brief comparisons of ten bubbles show that small-size bubbles have a small ratio of kinetic age versus the fragmentation time. Triggering star formation may be more active in bubbles with larger ratio between kinetic and fragmentation ages. Furthermore, the collect and collapse mechanism may play the dominant role in the large-size ones.
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