We report the discovery of active star formation in Digels Cloud 2, which is one of the most distant giant molecular clouds known in the extreme outer Galaxy (EOG). At the probable Galactic radius of ~20 kpc, Cloud 2 has a quite different environment from that in the solar neighborhood, including lower metallicity, much lower gas density, and small or no perturbation from spiral arms. With new wide-field near-infrared (NIR) imaging that covers the entire Cloud 2, we discovered two young embedded star clusters located in the two dense cores of the cloud. Using our NIR and 12CO data as well as HI, radio continuum, and IRAS data in the archives, we discuss the detailed star formation processes in this unique environment. We show clear evidences of a sequential star formation triggered by the nearby huge supernova remnant, GSH 138-01-94. The two embedded clusters show a distinct morphology difference: the one in the northern molecular cloud core is a loose association with isolated-mode star formation, while the other in the southern molecular cloud core is a dense cluster with cluster-mode star formation. We propose that high compression by the combination of the SNR shell and an adjacent shell caused the dense cluster formation in the southern core. Along with the low metallicity range of the EOG, we suggest that EOG could be an excellent laboratory for the study of star formation processes, such as those triggered by supernovae, that occured during an early epoch of the Galaxys formation. In particular, the study of the EOG may shed light on the origin and role of the thick disk, whose metallicity range matches with that of the EOG well.
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