Complexity of emerging magnetic flux during lifetime of solar ephemeral regions

As a relatively active region, ephemeral region (ER) exhibits highly complex pattern of magnetic flux emergence. We aim to study detailed secondary flux emergences (SFEs) which we define as bipoles that they appear close to ERs and finally coalesce with ERs after a period. We study the SFEs during the whole process from emergence to decay of 5 ERs observed by the Helioseismic and Magnetic Imager (HMI) aboard Solar Dynamics Observatory (SDO) . The maximum unsigned magnetic flux for each ER is around $10^{20}$ Mx. Each ER has tens of SFEs with an average emerging magnetic flux of approximately 5$\times10^{18}$ Mx. The frequency of normalized magnetic flux for all the SFEs follows a power law distribution with an index of -2.08 . The majority of SFEs occur between the positive and negative polarities of ER , and their growth time is concentrated within one hour. The magnetic axis of SFE is found to exhibit a random distribution in the 5 ERs. We suggest that the relationship between SFEs and ERs can be understood by regarding the photospheric magnetic field observations as cross-sections of an emerging magnetic structure. Tracking the ERs' evolution, we propose that these SFEs in ERs may be sequent emergences from the bundle of flux tube of ERs, and that SFEs are partially emerged $\Omega$-loops.