We report the discovery of a new ultraluminous X-ray source (ULX) 2XMM J125048.6+410743 within the spiral galaxy M94. The source has been observed by ROSAT, Chandra, and XMM-Newton on several occasions, exhibiting as a highly variable persistent source or a recurrent transient with a flux variation factor of >100, a high duty cycle (at least ~70%), and a peak luminosity of Lx ~ 2X10^{39} erg/s (0.2-10 keV, absorbed). In the brightest observation, the source is similar to typical low-luminosity ULXs, with the spectrum showing a high-energy cutoff but harder than that from a standard accretion disk. There are also sporadical short dips, accompanied by spectral softening. In a fainter observation with Lx ~ 3.6X10^{38} erg/s, the source appears softer and is probably in the thermal state seen in Galactic black-hole X-ray binaries (BHBs). In an even fainter observation (Lx ~ 9X10^{37} erg/s), the spectrum is harder again, and the source might be in the steep-powerlaw state or the hard state of BHBs. In this observation, the light curve might exhibit ~7 hr (quasi-)periodic large modulations over two cycles. The source also has a possible point-like optical counterpart from HST images. In terms of the colors and the luminosity, the counterpart is probably a G8 supergiant or a compact red globular cluster containing ~2X10^5 K dwarfs, with some possible weak UV excess that might be ascribed to accretion activity. Thus our source is a candidate stellar-mass BHB with a supergiant companion or with a dwarf companion residing in a globular cluster. Our study supports that some low-luminosity ULXs are supercritically accreting stellar-mass BHBs.
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