Bubble in the Whale: Identifying the Optical Counterparts and Extended Nebula for the Ultraluminous X-ray Sources in NGC 4631

We present a deep optical imaging campaign on the starburst galaxy NGC 4631 with CFHT/MegaCam. By supplementing the HST/ACS and Chandra/ACIS archival data, we search for the optical counterpart candidates of the five brightest X-ray sources in this galaxy, four of which are identified as ultraluminous X-ray sources (ULXs). The stellar environments of the X-ray sources are analyzed using the extinction-corrected color-magnitude diagrams and the isochrone models. We discover a highly asymmetric bubble nebula around X4 which exhibits different morphology in the H$\alpha$ and [O III] images. The [O III]/H$\alpha$ ratio map shows that the H$\alpha$-bright bubble may be formed mainly via the shock ionization by the one-sided jet/outflow, while the more compact [O III] structure is photoionized by the ULX. We constrain the bubble expansion velocity and interstellar medium density with the MAPPINGS V code, and hence estimate the mechanical power injected to the bubble as $P_w\sim 5\times {10}^{40}$ erg s${}^{-1}$ and the corresponding bubble age of $\sim 7\times {10}^5$ yr. Relativistic jets are needed to provide such level of mechanical power with a mass-loss rate of $\sim {10}^{-7}{M}_{\odot }\mathrm{y}{\mathrm{r}}^{-1}$. Besides the accretion, the black hole spin is likely an additional energy source for the super-Eddington jet power.